Journal of Theoretics

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Brief Introduction to the Basic Structures of Matter Theory

and Derived Atomic Models

S. Sarg

sarg@helical-structures.org

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Note: For easy reference to the theoretical source,the numbering of equations and figures in squarebrackets matches the numbering in BSM thesis(first digit indicates the Chapter’s number). Thenumbering of new equations and figures appears ina normal way.

1. The concept of the vacuum space as a key issue for building of unified field theoryOne of the long standing problems in theoreticalphysics is how the gravitational field is related tothe electrical and magnetic field. This is part of theproblems related to development of successful uni-fied field theory in order to understand better thereal world. The building of such theory is depend-able of the correctness of the adopted fundamentalconcepts and postulates in physics. One of them isthe concept of the vacuum. Is the currently adoptedconcept about the vacuum space completely cor-rect? Until the 17th century the Aristotel’s view hasbeen accepted, according to which the vacuum is aphysically impossible. It has been overthrown afterthe invention of the barometer by Evangelista Tor-richelli in 1644. The vacuum has been accepted asa pure empty space. This concept has been changedagain in 19th century after the physicists discoverthe electromagnetic radiation.

In the last decades of 19 century the concept of thevacuum has been dominated by the aether theories.In the beginning of 20 century the aether theory hasbeen ovethrown and replaced by the Einstein visionabout the vacuum. In the article "Can Quantum-mechanical Description of Physical Reality BeConsidered Complete?", A. Einstein, B. Podolskyand N. Rosen (1935) write: "Every element of thephysical reality must have a counterpart in thephysical theory." In one of its articles H. E. Puthoff,(1997) writes about the Einstein’s view about histheory of General Relativity” "With the rise of special relativity which did not re-quire reference to such an underlying substrate,Einstein in 1905 effectively banished the ether infavour of the concept that empty space constitutesa true void. Ten years later, however, Einstein'sown development of the general theory of relativitywith its concept of curved space and distorted ge-ometry forced him to reverse his stand and opt fora richly-endowed plenum under the new labelspacetime metric".

In another article H. E. Puthoff (1997) pro-vides a citation from A. Sakharov (the developer ofrussian hydrogen bomb) "Searching to derive Ein-stein's phenomenological equations for general rel-ativity from a more fundamental set ofassumptions, Sakharov came to the conclusion that

Brief introduction to Basic Structures of Matter theory and derived atomic modelsS. Sarg

Abstract. Our vision about the physical reality might be distorted if the currently adopted concept about vac-uum is not correct. This may refer to processes in the micro world - beyond the limit of detection, and in themacro world - events of cosmological time scale. The thesis titled Basic Structures of Matter (BSM) presentsa theory based on one alternative concept about the vacuum space that has not been studied in history of phys-ics. The suggested concept provides a reference point allowing separation of space from time parameters inthe analysis. This gives a possibility for theoretical study of complex physical phenomena in three dimension-al space and unidirectional time scale with strongly observed principles of objective reality, causality and log-ical understanding. Analysing physical phenomena from a new point of view allows shedding a light on therelations between different physical fields and forces. An interdisciplinary study based on suggested conceptleads to unveiling of hidden structural features of the elementary particles and atomic nuclei. The obtainedphysical models of the atoms exhibit the same energetic levels as the Quantum Mechanical models; however,the parameters and positions of the quantum orbits are strictly defined by the nuclear configuration. The de-rived models open a new possibility for analysis of sub-molecular and sub-atomic processes. The new conceptallows finding logic behind quantum mechanical and relativistic phenomena. It logically leads also to a dif-ferent hypothesis about the Universe, challenging the theory of Big Bang.

Keywords: Zero point energy, vacuum, spacetime, unified field theories, physical structures of atoms,quantum orbits, embedded fine structure constant, molecular structures

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the entire panoply of general relativistic phenome-na could be seen as induced effects brought aboutby changes in the quantum-fluctuation energy ofthe vacuum due to the presence of matter".

The “dark matter” is an extensively hot topicin cosmology today. Currently it is already accept-ed that the “dark matter” predominates the visiblematter in the Universe. In recent years it has beenfound that in the centre of most of the galaxies thereis a supermassive black hole in order of billion so-lar masses (keyword for search “supermassiveblack holes”). A surprising strong relation has beenfound between the mass of the supermassive blackhole and the mass of the whole galaxy (L. Ferrar-ese, D. Merrit, 2000) It seams that this black holeknow how much mass exists in the host galaxy orthere is some kind of mass-energy balance. Addi-tionally to this, one of the largest rotation curvedata base of spiral galaxies clearly shows that the“dark matter” is rather a rule, than exception. (Ananalysis of 900 optical rotation curves: Dark matterin a corner?, by D. F. Roscoe, (1999)). Then itstands to reason raising a question: Isn’t the “dark”matter around us and even “within us” and if soisn’t the “hidden matter” more appropriate name?Then the concept of the vacuum should be insepa-rable from the concept of “dark” or “hidden” mat-ter.

Large number of not solved problems andeven mysteries in the range from particle physics tocosmology indicates that our current vision aboutthe Nature and Universe may not present the realpicture. This may lead to a serious gap between thefields of the theoretical physics from one side andapplied sciences from the other. This is not an iso-lated opinion among the applied field scientists. Ina recently published article “Physics in crisis” inPhysics Today and FermiNews, Sidney Nagel(2002) points out the gap that now exists betweenthe fields of fast advancing applied science and theparticle physics. He writes; “So, in order to studygeology, condensed matter physics, or biology,does one really need to know the standard model?Does it even help? Of course not.”

In the same perspective, we may take one ex-ample about the complex molecules, such as the or-ganic and biomolecules. Despite the huge numberof possible configurations of the atoms in suchmolecules they preserve their shape in proper envi-

ronments. This is especially valid for the long chainbiomolecules. If considering only the QuantumMechanical considerations a protein moleculefrom 2,000 atoms, for example should possess anastronomical number of degrees of freedom. It isknown, however, that this number is drastically re-duced by some strong structural restrictions, suchas bond lengths, relative bond angles and rotations.All this restrictions could not get satisfactory ex-planation by the Quantum Mechanical models ofthe atoms. This problem is known as a Levinthal’sparadox.

The above considerations and citations arepresented only to show that the presently acceptedconcept about vacuum space could not be consid-ered as a final truth. This may deform our knowl-edge about a large number of phenomena.

Inspired by the above considerations exten-sive search has been done about possible differentconcepts about vacuum that have not been studiedso far. Apart of this a broad interdisciplinary studyfrom different fields of physics and chemistry wasdone. It led to a conclusion that the Quantum Me-chanical models may not show some structural fea-tures of the atoms. The search of alternativevacuum concept and the results of the interdiscipli-nary study led to development of original unifiedfield theory called Basic Structures of Matter(BSM). In order to build such theory, however, thevacuum concept and some of the initially adoptedpostulates in modern physics had to be reconsid-ered. This led to derivation of quite different mod-els of the atoms, possessing rich physicalstructures. The structural features are able to ex-plain the observed length and angular restrictionsof the chemical bonds. Such features are not appar-ent by the Quantum Mechanical models. In thesame time, the physical models of the atoms exhibitthe same energy levels and interaction properties asthe Quantum Mechanical models. The valuablefeatures of the derived models allows explanationof number of not solved problems in the fields ofstructural chemistry, biomolecules and the fastgrowing fields of nanotechnology.

The purpose of this article is to provide briefintroduction into the concept and models of BSMtheory. Without such introduction the potential ofthe these models for applications in different fieldsof applied science could not be understood.

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2. The new point of view of the BSM theoryA new theoretical study, provided by BSM theory,indicates that the vacuum is not a void space, butpossessing a underlying grid structure of super-dense particles. Extensive analysis of phenomenafrom different fields of physics allowed to formu-late the search criteria for the possible physicalmodel of this structure. Its properties must explainthe basic physical effects in the complex “matter -energy - space - time - gravitation - fields”. Thesearch for the correct model took also into accountnumber of recently published theoretical articlesabout the vacuum properties. They are related withsome features, such as the Zero Point Energy, thequantum fluctuations and the polarizability of thevacuum. Number of theoretical works in this fieldare provided by T. H. Boyer, H. E. Puthoff, A. Rue-da, M. Ibison, B. Haisch and others.

The defined criteria allowed to narrow therange of search, so one of the most promising mod-el is suggested. According to this model, the vacu-um space possesses a underlying grid structureof sub-elementary particles arranged in nodes.These particles called twisted prisms are formed oftwo types super dens intrinsic matter substances.Prisms of the same type are attracted in a pure voidspace by Intrinsic Gravitational (IG) forces, FIG,that are inverse proportional to a cube of thedistance.

[(2.1)]

where: mo1 and mo2 are intrinsic masses (of this su-perdense particles), Go is the Intrinsic Gravitation-al constant (there is an indication that it could beequal to the Newton’s gravitational constant if thedifference between the two type of intrinsic matteris taken into account), r - distance.

It is assumed that the IG force is related tothe theoretically known physical parameter calledPlanck’s frequency,

(1)

In the article “Gravity as a zero-point fluc-tuation force”, H. E. Puthoff (1989) begins fromthe equation of the Planck’s frequency and usingone hypothesis of Sakharov successfully derives

the Newton’s law of gravitation. This result is usedas a valuable initial point in BSM concept. Relyingon the Planck’s frequency as a real physical param-eter is a step in a right direction in the process ofbuilding the BSM concept. The confidence aboutthis is increased by the results obtained latter fromthe analysis of the derived models and their consis-tency with known physical parameters and experi-mental results.

Let focussing on the prisms and the singlenode of the introduced grid structure. The prismsare hexagonal sub-elementary particles with alength a few time larger than the diameter. Theypossess axial IG anisotropy with a twisting compo-nent, due to a lower level structure, so they arecalled twisted prisms. The dimensions ratio be-tween the two types of prisms is 2:3. Every node iscomprised of four prisms of same substance, nor-mally at angle 109.5o between them. The two typesof nodes are alternatively arranged forming a gridsimilar as the atoms in a diamond. Governed onlyby the IG forces, the node geometry has some flex-ibility, while their mutual positions - some limitedfreedom. In some conditions part of the nodescould be displaced and folded, so they could passthrough a normal grid structure. The IG field is atype of energy interaction between intrinsic matterat lower level of matter organization involved in anintrinsic energy balance. The gaps between the al-ternatively arranged nodes of different types arealso results of an intrinsic energy balance. The es-timated distance between neighbouring nodes ofthe grid is in order of (1 ~ 2)E-20 (m), while thematter density of the prisms is about 1E13 timeshigher than the density of the average atomic mat-ter. This structure fills all the visible volume of theUniverse. It is called a Cosmic Lattice (CL), so thevacuum space in which we live and observe is ref-erenced in BSM theory as a CL space.

The new concept about the vacuum broad-ens our vision about the space-time and matter-en-ergy relations. Using the vacuum grid as a frame ofreference, the BSM theory allows to separate thespace from time parameters at low level of matterorganization and to perform physical analysis in areal three dimensional space. In such approach theQuantum Mechanical rules and the relativistic phe-nomena are completely understandable and ex-

FIG G0mo1mo2

r3-------------------=

ωPL

ωPL2πc5

G------------=

4

plainable by the human logic without need of theuncertainty principle.

The self-sustainable CL structure of thevacuum space is supported by super strong interac-tions between the highly dens prisms arranged innodes. In the same time, the node distance is veryweakly influenced by the atomic matter of massiveastronomical objects. This effect is very weak be-cause for the length scale range of CL node dis-tance the Newtonian gravitation is negligible incomparison to the Intrinsic Gravitation. While thenode distance is about 10E9 times smaller than theaverage internuclear distance of the atoms in a sol-id body, the matter density in the prisms is about1E13 times higher than the average atomic matter.Therefore, the massive astronomical objects areable to influence the parameters of the surroundingCL space. This defines the local conditions of thelight velocity, while the gradient of slightly affect-ed node distance defines the General relativisticconditions.

Another specific feature of the CL space isthe ability of the CL nodes to fold and pass throughthe grid structure of a normal CL space when a lessmassive object moves in a CL space of a more mas-sive one. Such unique feature does not have coun-terpart in any concept of aether or ideal fluid.

The folding properties of the CL nodes isalso closely related to the inertial properties of theatomic matter in CL space and plays a role in theequivalence between gravitational and inertialmass.

Analysing the dynamics and mutual inter-actions of the CL nodes (§2.9 of BSM), it is possi-ble to understand some of the fundamental physicalparameters, such as: unit charge, magnetic field,Planck constant, Zero Point Energy, photonwavetrain structure, light velocity, permeabilityand permittivity of vacuum.

Fig. 2.20 illustrates a geometry of a singlenode in position of geometrical equilibrium withtwo sets of axes, denoted as abcd and xyz.

The CL node has two sets of axes: one setof 4 axes along anyone of the prisms called abcdaxes, and another set of 3 orthogonal axes calledxyz axes. In geometrical equilibrium the angles be-tween anyone of abcd axes is 109.5o. The abcdaxes define a tetrahedron. The xyz axes passthrough the middle of every two opposite edges of

the tetrahedron. In the same time, the orthogonalxyz axes of the neighbouring CL nodes are aligned.

Fig. 2.20 CL node in geometrical equilibrium posi-tion The two sets of axes are: abcd and xyz

Such arrangement gives conditions forcomplex node oscillations under the inverse cubiclaw of intrinsic gravitation. The return forces (ofinverse cubic law) acting on deviated from the cen-tral position CL node exhibits set of minimums.These minimums can be associated with energywells. Two symmetrical minimums appearalong anyone of xyz axes and one minimumalong the positive direction of anyone of abcdaxes. These set of minimums provide conditionsfor complex oscillations of the CL node. From apoint of view of CL node dynamics they are re-sponsible for the total energy well of the CL node(Zero Point Energy of vacuum). Fig. [2.24] illus-trates the return forces along the two sets of axesand the associated with them energy wells.

The right vertical axis indicates specific en-ergy points. The energy level EC2 corresponds tothe filled energy wells or the Zero Point Energy ofthe vacuum. The complex CL node oscillations arecharacterised by two types of cycles: a resonancecycle and a SPM cycle (the latter is described by aSpatial Precession Momentum vector). The trace of

Fig. [2.24]

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the resonance cycle is approximately flat but opencurve with four bumps, as shown in Fig. [2.26] Thebumps are caused by the different stiffness betweendeviations along abcd and xyz axis (within finiteangle). Therefore, the resonance cycle is character-ized by a vector with for momentum maximums attwo orthogonal axes. The points A and B from theresonance cycle are pretty close but not coinciding,so the segment AB points almost at 90 deg in re-spect to the drawing plane. The lack of coincidencebetween any initial (A) and final (B) point from oneresonance cycle is a result of the asymmetrical spa-tial positions of the energy wells in respect to thecentral node point (node point for zero deviation).

The average plane of the resonance trace isslightly rotated with every cycle, so after a largenumber of such cycles the node trace passesthrough the same (arbitrary selected) initial pointA. This is a SPM cycle. The vector describing thiscycle is called SPM vector (Spatial Precessionmomentum). The number of the resonance cyclein one SPM cycle, estimated in BSM, is

. The tip of SPM vector for one full cycle cir-

cumscribes a closed surface with central point sym-metry and six bumps aligned along the axes xyz.Such type of surface is referenced in BSM as aSPM quasisphere. It is found that the resonancecycle is related to the velocity of the energy wavepropagation (light velocity), while the SPM cycleis related to quantum features of the CL space. Insuch conditions, the SPM cycle is responsible forthe constant light velocity, due to the quantumproperties of the SPM quasispheres and their mutu-al interactions. The frequency of SPM cycle isequal to the known Compton frequency. In absenceof any electrical charge, the SPM quasisphere pos-sesses a central point of symmetry and it is calleda Magnetic Quasisphere (MQ). This is a normal

state of the oscillating CL node that appears to berelated to the magnetic permeability of the vacuum.

In presence of electrical charge, the SPMquasisphere obtains a deformation as an elongationalong its diameter connecting two opposite bumps,so it is called an Electrical Quasisphere (EQ).The shapes of MQ and EQ are shown in Fig. 1.

Fig. 1 MQ and EQ of SPM vector

By studying the dynamics of CL nodes it isfound that the EQ type node possesses larger ener-gy than MQ type. The electrical field is composedof spatially oriented and synchronized EQ CLnodes, so a domain of EQ type CL nodes possessesa larger energy than a domain of MQ type CLnodes.

From the other hand, the magnetic field isa closed loop in CL space involving only MQtype of nodes whose SPM frequencies are syn-chronized. Such arrangement, however, has somespecific spatial and temporally features:

- The CL nodes of right handed prisms arecommonly synchronized

- The CL nodes of the left-handed prismsare commonly synchronized

- The phase difference between the in-volved left and right handed nodes determines thedirection of the magnetic field, for example, +90deg phase difference for N-S direction and -90 degphase difference for S-N direction.

- The involved MQ nodes may additionallyhave a helical arrangement along the closed loop

The above considerations are for perma-nent magnetic field. In case of alternative magneticfield, the commonly spatially dependable synchro-nizations of the left and right-handed stationarynodes vary with the time.

Fig. [2.26]

AB

NRQ 0.88431155 9×10=

MQ SPM EQ SPM

a. b.

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Physically the EQ type node is a stationaryand defined by a local gravitational field of a mas-sive object (in our case - the Earth). When studyingthe conditions of energy propagation as a wave,however, it is convenient to use imaginary run-ning CL nodes. In such case the temporal variationof a common synchronization of the CL nodes areeasily studied. The analysis in such approach led tounveiling the structure of the photon wavetrain as acomplex but well defined spatial arrangement ofEQ and MQ running nodes.

The photon wavetrain is a complex ar-rangement of running EQs with decreasing de-formation gradient from the central axis of thewavetrain to its boundary radius, where run-ning MQs are formed. Thus, it is found that thephoton wavetrain has boundary conditions (a solu-tion of one long standing problem).

The analysis of the CL node dynamics asEQ and MQ type and the unveiled photonwavetrain structure in a normal CL space (possess-ing a normal Zero Point Energy) are presented inChapter 2 of BSM thesis. CL space with subnormalZero Point Energy is related to superconductivityeffects. The CL node dynamics and the charge par-ticles behaviour in this state of the matter-spacecomplex is analysed in Chapter 4 of BSM.

The applied new approach allows also un-veiling the real physical structures of the atomicand subatomic particles. The Bohr atomic modelappears to be only a mathematical model providingcorrect energy levels, but it is not identical to thephysical one. When taking into account the vacu-um structure and the structure of elementary parti-cles, the physical models of the Hydrogen and allstable elements appear quite different.

From a BSM point of view, the interpreta-tion of the scattering experiments does not providecorrect real dimensions, because the structures ofthe vacuum and elementary particles are not takeninto account. BSM analysis found that the stableparticles, such as proton, neutron and electron (andpositron) posses structures with well defined spa-tial geometry and denser internal lattices. They arecomprised of complex but understandable three-di-mensional helical structures whose elementarybuilding blocks are the same as those involved inthe vacuum grid - the two types of prisms. Analys-ing the interactions between the vacuum space and

elementary particles, but from a new point of view,the BSM theory allowed a derivation of number ofuseful equations, such as a light velocity equation -expressed by the CL space parameters, a massequation (the mass we are familiar with), an equa-tion about the vacuum energy (zero point energy),and some relations between CL space parametersand the known physical constants. The BSM pro-vides also an understandable physical explanationof what is an elementary electrical charge and whyit is constant.

The motion analysis of the smallest chargeparticle - the electron from a new point of view(Chapter 3 and 4 of BSM) allows to unveil its phys-ical structure and intrinsic properties. The electronis a system comprised of three helical structures asillustrated by Fig. 2. Two of its helical structurespossess denser lattices located in the internal spac-es of the helix envelopes (this lattice is not shownin Fig. 2).

The physical dimensions of this structuresare: RC - Compton radius of electron (known), re -a small electron radius, rp a small positron radius,se - helix step.

External helical structure with internaldenser lattice (from right handed prisms, for exam-ple) is referenced in BSM as external electron shell.It is responsible for the modulation of the CL spacearound the electron and creation of a negativecharge. The internal helical structure with internaldenser lattice (from a left-handed prisms, respec-tively) with a central core (from right handedprisms) is an internal positron. Regarded as a 3body oscillating system the electron has two properfrequencies:

- a first proper frequency: between the ex-ternal electron shell and the internal positron

- a second proper frequency: between theinternal positive shell and the central negative core.

Fig. 2

Oscillatingelectron

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It is found that the first proper frequency ofthe electron is equal to the SPM frequency of theCL node. This is well known Compton frequency.

It is found that in conditions of screw-likemotion of the electron with tangential velocityequal to the light velocity, the phase of the firstproper frequency of the rotating electron matchesthe phase of the SPM vector. They both oscillatewith a Compton frequency. In the same time, theinternal core oscillation (with a proper frequency ofthree times the Compton frequency) provides athird harmonic feature for this motion. As a resultthe rotating and oscillating electron exhibit a max-imum interaction with the CL space - a kind ofquantum interaction. The electron axial velocity forthis case is , corresponding to kinetic ener-gy of 13.6 eV. In such type of motion the helicalstep, se, is given by the following expression:

(m) [(3.9)]

[(3.12.a)]where: Rc - is the Compton radius, - is the finestructure constant, ge - is the gyromagnetic factor,

- is the Compton wavelength (CL space param-eter).

From the analysis of the Fractional QuantumHall experiments in Chapter 4 of BSM, it is foundthat: . Then all the of geometrical param-eters of the electron are determined.

Electron confined motion with suboptimalvelocities corresponding to where n is asmall integer is also possible but with decreasingstrength of quantum interactions. They corre-sponds to kinetic energies of 13.6 eV. 3.41 eV,1.51. eV, 0.85 and so on. The quantum conditionsproviding stabilizing effect for these velocities arediscussed later.

The configuration of one of the internal lattic-es of the helical structures of the electron called aRectangular Lattice (RL) is shown in Fig. [2.16].Every RL node is comprised of six prisms of thesame type. The axial section contains number ofconcentric layers. Starting from the cylindricalboundary defined by the helix envelope, the mostexternal layer is connected to the helix by IG forc-es, while every internal layer is connected to theneighbouring external one. The thickness of everyinternal layer is half of the thickness of the neigh-

bouring external layer. These are pure geometricalconsiderations for a stable internal lattice. The ra-dially alined prisms of the neighbouring nodes arewithout gaps, while the gap between the tangential-ly aligned prisms varies when moving from exter-nal to the internal radius of the layer.

Fig. [2.16] Configuration of internal lattice of typeRL (Rectangular Lattice) inside the cylindricalspace enveloped by the first order helical structure

The electron structure, shown in Fig. 2 hastwo internal RL lattices. They are built of sametype prisms like their envelope. The RL structureshown in Fig. 2 is the internal one and it possessesa central hole where the central core of the electronoscillates. The other RL lattice has a larger wholewhere the internal first order helical structure oscil-lates.

The stiffness of RL defined by the prism den-sity is about 1000 times larger than the stiffness ofCL structure of the vacuum. Consequently, the vol-ume of RL structure is not penetrative even forfolded CL nodes. Then it displaces the CL struc-ture, or in other words, it feels a CL pressure. Thisis a Static CL pressure discussed later. For openhelical structures like those in the electron (the bothends are not connected) the internal RL structure isstabilised by twisting. In such way, it becomes atwisted type of RL structure, denoted as RL(T).The twisted radial stripes of RL(T) modulate theCL nodes converting them to EQ type nodes ar-ranged in a proper spatial configuration. It is evi-dent that the modulated EQ nodes are arranged aslines extensions from the twisted radial stripe ofRL(T). This is illustrated by Fig. [2.17]. Theselines form the electrical field of the charge particle.It is evident that in a proximity range these linesmight be slightly curved but in a far range they ap-pear as emerging from a point. The line shape and

Vax αc=

se2πRcα

1 α2–-------------------

λcα

1 α2–------------------- 1.7706 14–×10= = =

se gere 2.002319re= =α

λc

rp/re 2/3=

Vax αc/n=

8

their connection to the twisted radial stripes ofRL(T) is very important feature of the electronstructure. It allows to explain magnetic type inter-actions of the electron moving in CL space.

Fig. [2.17] Proximity E-field lines from RL(T) structure

It is apparent that one type of prisms (for in-stance the right handed) is associated with one signof charge while other type with - another. There-fore we may address the two types of prisms as pos-itive and negative, while keeping in mind that thephysical charge appears only in CL space.

All elementary particles are built of helicalstructures that from their hand possess internal RLlattices. The RL and RL(T) parameters of the heli-cal structures are determined in Chapter 6 of BSM,where physical meanings for number of experi-mentally obtained parameters from the particlephysics are unveiled. This includes: the ratio be-tween pion-muon mass, the tau particle (Regge res-onance at 1.7778 MeV), the resonance at 1.44MeV, the Fermi coupling constant , the effectivemixing parameter , the energy equivalenceof the “masses” of the W+- and Z bosons.

By using the unveiled structure of the elec-tron as a reference etalon, the basic parameters ofthe CL space are obtained and expressed by theknown physical constants. The basic parametersare: the Static CL pressure - related to the Newto-nian mass, the Dynamic CL pressure - related to theZero point Energy of vacuum, the Partial CL pres-sure - related to the inertial properties of the atomicmatter in CL space, the Compton frequency as acharacteristic parameter of CL node and electronoscillating properties, the light velocity and the

Compton wavelength. The obtained expression ofStatic CL pressure is:

[(3.53)]

The static CL pressure allows defining theNewtonian mass (the mass we are familiar with)for any particle in a stable phase of its existence.

[(3.48)]

where: Ve is the envelope volume of the electronand VH - is the total volume of similar structures fora particle under consideration.

The energy from displaced CL nodes can bedirectly estimated by the Einstein’s equation

.When the electron or any stable helical struc-

ture is in motion, it displays CL nodes. The dis-placement process for the stationary nodes involvethe following phases: a node folding and displace-ment, a returning to the initial position and unfold-ing. There is not boundary between these twophases and the folding in partial. The displacednode preserves it energy momentum by convertingthe oscillation energy into rotational energy. Insuch conditions it may interact with the oscillatingnormal nodes. This is an inertial interaction thatany moving helical structure exhibits in CL space.

A deeper study of this process leads to under-standing the effects of Special relativity. It alsoleads to a conclusion (in Chapter 10 of BSM) thatdisplaced nodes exist permanently around theatomic particles but only in motion in respect to thestationary CL space. The amount of the displacednodes could be expressed by a CL space parameterPartial CL pressure. In Chapter 10 of BSM, wherethe inertial properties of the matter are discussed, itis found that the ratio between Partial and Static CLpressure is related to the fine structure constant bythe relation:

[(10.18)]

The capability of the CL nodes to fold andpenetrate in the normal CL space is one of the veryspecific feature related to the inertia of any particlein CL space. Therefore, it is involved in the defini-tion of the inertial mass of the atoms and the matter

GFsin2θeff

lept

PSmec2

Ve------------

hνc4ge

2 1 α2–( )

πα2c3-----------------------------------= = N

m2------

mPS

c2------VH=

E mc2=

PP/PS α2/ 1 α2–=

9

build of atoms. (On the other hand, the intrinsicmatter possesses intrinsically small inertia in pureempty space, so it is possible to handle much largerenergy. This is valid also for the CL structure).

The confined screw like motion of the oscil-lating electron in CL space is characterized bystrong quantum interactions with the oscillating CLnodes. This effect is contributed by two conditions:a phase match between the involved cycles (dis-cussed above) and conditions of integer number ofCompton wavelengths for boundary conditions ofthe induced magnetic field from the rotating elec-tron. These two conditions allow strong quantumeffects to appear at particular velocities of screw-like motion of the electron, corresponding to theenergy levels of 13.6 eV, 3.4 eV, 1.51 eV, 0.85 eVand so on.

The magnetic radius rmb in a plane normalto Vax is defined from the conditions that the ro-tating IG field of the internal lattice of the elec-tron helical structure (that modulates the CLspace) could not exceed the light velocity.

The magnetic radius for 13.6 eV is verifiedfrom the analysis of the quantum magnetic field(see §3.11 in Chapter 3 of BSM thesis): The accurate value of rmb for 13.6 eV is almostequal to Rc, but slightly larger due to a finite thick-ness of the electron helical structure.

If relating the above energy levels with thenumber of full rotations of the electron one obtains:

13. 6 eV - 1 rotation per SPM cycle3.4 eV - 1/2 rotations per SPM cycle1.51 eV - 1/3 rotations per SPM cycle 0.85 eV = 1/4 rotations per SPM cycle1 SPM cycle = Compton time BSM uses a parameter called subharmonic

number, n, in order to notify the quantum motionconditions of the electron. This number is related tothe electron axial velocity by the expression

. In the same time the subharmonicnumber matches the quantum number of the elec-tron orbit in Bohr atomic model. A quantum mo-tion with a first harmonic velocity corresponds to13.6 eV, with a second subharmonic - 3.4 eV, witha third subharmonic - 1.51 eV and so on. The termsubharmonic number is chosen because it anno-tates the spin rotation of the electron in its confinedmotion.

Analysing the efficiency of the quantum in-teractions between the confined moving electronand CL space at relativistic velocities the relativis-tic gamma factor is derived in §3.11.A. The analy-sis provides a physical explanation of therelativistic effect of mass increase. It is a result ofthe finite rate at which the CL node could be foldedand displaced. A limiting factor of this rate is theresonance frequency of CL node, estimated in§2.11.3, Chapter 2 of BSM, as:

(Hz) [(2.55)]

3. Quantum loops and possible orbits for elec-tron with optimal confined velocity. Embedded signature of the fine structure constant.

3.1 Quantum motion of the electron in closed loop trajectories.

The motion of the electron is always a resultof external forces. Such forces exists even withoutacceleration fields. The driving mechanism in suchcase is supported by the condition of accuratelykept relation between the Static and Partial pres-sure of CL space, expressed by Eq. [(10.18)]. Thepartial pressure is contributed by the velocity andspin momentum of the folded nodes. They can existonly in motion. Therefore they are behind the driv-ing mechanism that keeps the oscillating and orbit-al motion of the electrons in the atom. The orbitalmotion could be regarded as a motion in closedloop, whose trajectory follows equipotential sur-face of electrical field defined by one or more pos-itive charges. All this conditions are ideal for aquantum motion of the electron in a closed loop.

Let considering a repetitive motion in aclosed loop. Obviously, the length of such loop willdepend of the conditions of phase matching be-tween the SPM frequency of the CL node, fromone side and the first and second proper frequen-cies of the electron, from the other. All of them canbe expressed by the Compton frequency.

Let us find the path length at which the quan-tum loop condition for the electron moving with afirst harmonic velocity (13.6 eV) is fulfilled. Ini-tially we will ignore the relativistic effect forsimplicity. It is reasonable to look for path lengthdefined by some CL space parameter. One of thisparameter is the Compton wavelength

Φ0 h/qo=

Vax αc/n=

νR 1.092646 29×10=

λc λSPM=

10

For one orbital cycle in a closed loop with length, the number of turns NT is:

[ (3.43.d)] The value of NT could be regarded as a con-

dition of screw-like motion of the electron at whichthe initial phase in any one point of the closed loopis repeated. We see that it appears slightly differentfrom the reciprocal value of the fine structure con-stant.

Therefore, the round number of turns is: [(3.43.e)]The obtained number of turns as , howev-

er, is not a whole number. In the same time, thetrace length of this loop is quite small, when com-paring to the Bohr orbit length of (also withthe proton dimensions determined in Chapter 6 asa result of the accepted concept of the vacuumspace). Therefore, we may look for the phase con-ditions at larger loop length. The close value of NTto is not occasional. Then, one may substitutethe NT with and multiply the result by thatis associated with the circumference length of theelectron coil. In such case we obtain:

(m) [(3.43.f)]

We see that the obtained value with dimen-sion of length is equal to the Bohr orbit length:

(m) [(3.43.g)]

where: (m) - is the radius ofthe Bohr atomic model of hydrogen.

The expression {(3.43.f)] is not somethingnew. The important, fact, however, is the way of itsderivation related with the suggested physicalmodel of the electron. The obtained loop length ap-pears equal to the orbit length of the Bohr atom. Itis defined by Bohr atomic radius which is one ofthe very basic parameters used in the Quantum me-chanics. From a point of view of BSM, however,the physical meaning of this parameter appears dif-ferent.

According to BSM concept, the wellknown parameter a0 used as a radius in theBohr model, appears defined only by the quan-tum motion conditions of the electron moving ina closed loop with an optimal confined velocitycorresponding to electron energy of 13.6 eV.

Then the main characteristic parameter of thequantum loop is not its shape, but its length.

For a motion with optimal confined velocitythe number of electron turns in the quantum orbit isequal to the orbital length divided by the helixstep (se).

turns [(3.43.h)]

The analysis of the confined motion of theelectron in Chapter 3 and 4 of BSM indicates thatits second proper frequency is three times higherthan the first one (the first one is equal to theCompton frequency)

Let find at what number of complete orbitalcycles (for orbit length of ) the phase repetitionof the first and second proper frequencies of theelectron is satisfied (in other words the smallestnumber of orbital cycles containing whole numberof two frequency cycles). Eq. [(3.43.h)] shows thatthe number of first proper frequency cycle is closeto 1/3. If assuming that it is exactly 1/3 (due to notvery accurate determination of the participating pa-rameters), then the condition for phase repetition ofboth frequency cycles will be met for three orbitalcycles. The whole number of turns then should be

. Substituting in this with expression giv-en by Eq. [(3.9)] we must get a whole number ofturns

(2) We have ignored so far the relativistic correc-

tion, but for accurate estimation it should be takeninto account. The relativistic gamma factor for theelectron velocity of is . Multi-plying the above expression by the gamma factorwe get.

(3) Eqs. (2) and (3) provide a possibility for ver-

ification of the phase repetition condition if the ac-curacy of the experimentally estimated finestructure constant exceeds some threshold level.The procedure is simple: calculation the expressionby the recommended value of , rounding the re-sult to the closer integer and recalculating the cor-responding value for . The whole number of turnscondition could be correct only if the recalculatedvalue is in the range of the accuracy of the experi-

λcNT λc/se 137.03234= =

1/α 137.03598949=

NT 1/α≈1/α

2πao

1/α1/α λc

NTλc1α---λc≈ 3.249187 10–×10=

2πao 3.3249187 10–×10=

ao 0.52917725 10–×10=

2πao

2πaose

------------λc

αse-------- 18778.362= =

2πao

3λc/αse se

3 1 α2–α2

---------------------- integer=

V αc= γ 1 α2–( )-1/2

=

3/α2 integer=

α

α

11

mentally determined . The recommended valueof according CODATA 98 is

(CODATA 98) (4)where the digits in bracket is the uncertainty error.

The calculated values of from Eq. (2) and(3) exceed quite a lot the uncertainty value of ex-perimentally determined given by Eq. (4). Con-sequently, the condition of phase repetitions of thetwo proper frequencies is not fulfilled for three or-bital cycles with total trace length of .Therefore, we may search for the smallest numberof orbital cycles in which the phase repetition con-ditions are satisfied. It stands to reason that the ap-proximate value of the orbital cycles could beabout 137 ( ). Then if not considering relativisticcorrection, the number of electron turns is

When applying relativistic correction (multi-plying by relativistic gamma factor) the number ofelectron turns is . The phase repetition condi-tions will be satisfied if this number is integer.

[(3.43.i)]Substituting with its value from CODATA

98 (Eq. (4)) we get

For plus and minus deviation in a range of un-certainty error (value in brackets in Eq. 4)) we getrespectively 2573380.55 and 2573380.6.

Consequently, we may accept that the fullnumber of turn is 2573380.

It is evident that theoretical expression[(3.43.i)] can be used only if the experimental ac-curacy exceeds some threshold. Then the more ac-curate theoretical value is:

(5)The small difference of the theoretically ob-

tained value of from the experimental one is like-ly caused by the method of its determination byexperiments. One of the most useful expression forexperimental estimation is based on the measure-ment of the Josephson constant, KJ. Its connectionto is given by the expression, where all otherphysical parameters are known with high accuracy.

(6)

where: - is the permeability of vacuum, me - isthe electron mass, c - is a light velocity, - is theCompton wavelength.

The accuracy of according to this methoddepends of the accuracy of the Josephson constantmeasurement. The recommended value for thisconstant according to CODATA 98 is

(hz/V)If substituting in Eq. (6) the recommended by

CODATA 98 value of alpha with the calculatedone by Eq. (5), the value of the Josephson coeffi-cient is still in the uncertainty range (shown inbrackets).

From the following later analysis we will seethat it is more appropriate to use the number of fullcycles of the first and proper frequencies. They arecompletely defined by the quantum velocity of theelectron and the orbit trace length. In such way wearrive to the conclusion:

(A) The number of cycles of the first andsecond proper frequency of the electron in theorbital trace is defined only by the fine structureconstant.

The conclusion (A) is reasonable from aphysical point of view when having in mind the dy-namical interactions between the oscillating elec-tron and the oscillating CL nodes from one side andthe embedded fine structure constant in the electronstructure from the other.

The integer value 2573380 is proposed alsoby Michael Wales, based on quite different methodfor analysis of the electron behaviour (See MichaelWales book “Quantum theory; Alternative per-spectives”)

The introduced subharmonic number (n) cor-responds to the principal quantum number of Bohrmodel. The magnetic radius of electron motionwith different number n is analysed in §3.1 (Chap-ter 3 of BSM). Its value for matches to the es-timated magnetic radius corresponding to themagnetic moment of the electron. For larger num-bers, however, the magnetic radius shows and in-crease. The physical explanation by BSM is that atdecreased electron rotation its IG field of the twist-ed internal RL structure is able to modulate the sur-rounding CL space up to a radius until the rotatingmodulation of the circumference reaches the speedof light. At this moment the circumference lengthof the modulation boundary is equal to a whole

αα

α 7.2973525 27( ) 10 3–×=

α

α

3 2πao×

1/α

1 α2–α3

-------------------

1/α3

1/α3 integer=α

1/α3 2573380.57=

α 2573380( )-1/3 7.2973531 3–×10= =

α

α

KJ2c--- 2α

µomeλc------------------=

µoλc

α

KJ 483597.898 19( ) 109×=

n 1=

12

number of Compton wavelengths. These condi-tions in fact define the stable velocity at any onevalue of subharmonic number n.

Table 1 shows the quantum motion parame-ters of the electron in a quantum loop for velocitiescorresponding to different subharmonic numbers.

Table 1------------------------------------------------------------------------No E (eV) Vax Vt rmb lql Lq (A)------------------------------------------------------------------------- -------------------------------------------------------------------------

where: E - is the electron energy, Vax - is theaxial velocity, Vt - is the tangential velocity of therotating electron structure, rmb - is the value of theboundary electron magnetic radius in a plane nor-mal to Vax vector, c - is a light velocity, Rc - is theCompton radius, ao - is the Bohr radius, lql - is thetrace length for a motion in closed loop (singlequantum loop), Lq - is the length size of the quan-tum loop as Hippoped curve with parameter

The introduced parameter subharmonicnumber shows the rotational rate of the wholeelectron structure. The rotational rate decreaseswith the consecutive increase of this number, butthe number of the first and second proper frequen-cy cycles is not changed. This is very importantfeature formulated by the conclusion (B).

(B) The number of first and second properfrequency cycles of the electron in closed loopwith any subharmonic number is a constant.

From the provided analysis we find that theelectron makes 18778.362 rotations for one quan-tum loop. One quantum orbit may contain one oremore quantum loops. From Table 1 we see that fora confined moving electron the circumferencelength of the boundary of the electron’s magneticradius in a plane normal to Vax is equal to a wholenumber of

While the Compton frequency, , expressesthe frequency of the SPM vector and the first prop-er frequency of the oscillating electron, the Comp-ton wavelength, , is a characteristic parameter ofCL space related with the light velocity by the sim-ple relation . The frequency of SPM vector

from its side is directly related to the known phys-ical parameter permeability of vacuum.

3.2. Quantum orbits. Emission and absorption of photon.

It is apparent from the provided analysis thata stable quantum loop is defined by the repeatablemotion of oscillating electron. The shape of suchloop is defined by external conditions. Such condi-tions may exist in the following two options:

- a quantum loop obtained between particlewith equal but opposite charges and same mass, asin the case of positronium (see Chapter 3 of BSM)

- a quantum loop obtained between oppositecharges but different masses (a hydrogen atom as amost simple case and other atoms and ions as morecomplex cases).

In both options the quantum loops are repeat-able and we may call them quantum orbits. Thequantum orbit may contain one or few serially con-nected quantum loops. It is obvious that the shapeof the quantum orbit is defined by the proximityfield configuration of the proton (or protons). Thevacuum space concept of BSM allows unveilingnot only the electron structure but also the physicalshape of the proton with its proximity electricalfield. The shape of any possible quantum orbit isstrictly defined by these proton’s parameters.

The conditions defining the quantum orbit al-low unveiling the parameters of the possible quan-tum orbits in atoms and molecules. The mostsimplest examples are the possible quantum orbitsof hydrogen atom. In Chapter 7 of BSM a model ofBalmer series is suggested. Its analysis confirmsthe concept of confined motion of the electron. Thetrace length of the quantum orbit of Balmer seriesmatches the quantum loop No 2 from Table 1. Thesame quantum loop exists also in Deuteron. TheBSM model of Hydrogen is different from the Bohrmodel, but all quantum numbers and their energylevels are identifiable. The principle quantum num-bers are obtainable by considering a whole numberof Compton wavelengths but in specific environ-ments defined by the proximity distributed E-fieldof the proton and the proton’s Intrinsic Gravitation-al field.

It appears that the limiting orbit has a lengthof and all other quantum orbits are inferior.

1 13.6 αc c ~Rc 2πa0 1.36262 3.4 αc/2 c/2 2Rc 2πa0/2 0.68133 1.51 αc/3 c/3 3Rc 2πa0/3 0.45424 0.85 αc/4 c/4 4Rc 2πa0/4 0.34065 0.544 αc/5 c/5 5Rc 2πa0/5 0.2725

a 3=

λcνc

λc

λc c/νc=2πa0

13

This is valid not only for Balmer series in Hydro-gen but also for all possible quantum orbits in dif-ferent atoms, if they are able to provide linespectra. Therefore, the obtained physical model ofHydrogen provides a solution of the boundaryconditions problem of the electron orbits. Simi-lar solution exists for all atoms.

The analysis of interactions between the os-cillating electron in confined motion and oscillat-ing CL nodes allows unveiling the process of thephoton generation. According to the BSM concept,the emission of photon contributing to a particularspectral line is a result of pumping of CL nodesfrom the orbiting and simultaneously rotating andoscillating electron. In this process usually morethan one orbital cycles are involved. The emissionof a photon occurs from the surrounding CLspace in the moment when the electron dropsfrom higher to lower energy orbit.

This explains why the Quantum Mechanicalmodel needs the Heizenberg’s uncertainty princi-ple, while the BSM model does not need such one.In Quantum Mechanical models the CL substanceis missing and the process of the photon generationhas to be directly connected to the orbiting elec-tron. In such case, it seems that the electron posi-tion could not be located, so a concept of “electroncloud” is used. In BSM modes of the atoms everyelectron is moving in orbit with well defined spatialparameters, so its motion could be theoretically an-alysed in any point of this orbit.

Fig. [7.19] illustrates the close match be-tween the energy levels calculated by BSM modelof Balmer series in Hydrogen and those providedby the Quantum mechanics.

Fig. [7.19] Comparison between calculated and experi-mental energy levels for Balmer series

The electron with unveiled structural param-eters is used also as a probe for estimation of theCL space parameters and formulation of massequation valid for Newtonian gravitation and mass(the gravitation and mass we are familiar with).The Newtonian gravitation (known also as univer-sal gravitational law) appears as a field of the In-trinsic Gravitation in CL space, where IG forces arepropagated through the CL structure.

3.3 Lifetime of the orbital motion of the elec-tronIn section 3.1 it was found that the condition forphase repetition of the two proper frequencies ofthe electron with velocity (13.6 eV) are ac-curately met for 2573380 electron turns (about 137orbital cycles ) and approximately met for three or-bital cycles. The full travel of the rotating electronin both cases can be expressed by the product of thenumber of turns and helical step. Taking into ac-count the relativistic gamma correction the fulltravel is . In the same time the quantumvelocity of the electron is known. Then dividing thefull travel by the velocity one obtains the orbitallifetime.

(s) (7)

For a second harmonic quantum loops thenumber of electron turns is twice smaller, so its ve-locity and travel length are also twice smaller andthe lifetime appears the same. Consequently theobtained equation (7) appears valid for a quan-tum orbit with any subharmonic number, n, andcomprised of single quantum loop (as shown inTable 2). It is quite reasonable to consider this to bethe lifetime for spontaneous emission. For quan-tum orbit comprised of m number of quantum loopsthe lifetime will be m times larger. Such conditionsappear for the higher order series of Hydrogen inrespect to the Balmer series.

In case of simulated emission, the lifetime ofthe orbiting electron could be shortened. It is inter-esting to find what could be the shortest lifetime inwhich a photon generation is still possible. FromEq. [(3.43.h)] we see that this could be the lifetimecorresponding to three orbital cycles. Proceeding ina similar way as for the spontaneous emission wearrive to the result

V αc=

1/α3( ) se×

τsp3λc

α3c 1 α2–----------------------------- 6.248 14–×10= =

14

(s) (8)

Note: The simplified equations (7) and (8) donot take into account the relativistic considerations.

Summary:• The orbital lifetime for spontaneous emission is

the time for which the first electron frequency makes 2573380 cycles

• The shorter lifetime for simulated emission is the time for which the first electron frequency make 18778.3 cycles (the secondary electron frequency makes 56335 cycles)

4. External shape and geometry of the proton and neutron

It is known from the particle physics experi-ments that the electron (positron) is an end productin the most frequent reactions of the type: pion -muon - electron (positron) or charged kaon - pion -muon - electron (positron). This feature allows us-ing the unveiled structural and interaction parame-ters of the electron in order to solve the inversetask: to restore and find the physical structures ofmuon, pion, kaon and finally the structure of thestable particles proton and neutron. For this pur-pose, the derived mass equation Eq. [(3.48)] and itsmodification are used in the analysis provided inChapter 6 of BSM. When applied for the proton,the parameter VH takes into account the total vol-ume of all helical structures defined by the volumeof their internal Rectangular Lattice. The unknownparameters of mass budget are obtained by usingaccurately measured experimental data from parti-cle physics but applied according to their corre-spondence to the unveiled physical models,according to BSM. One still missing parameter forsolution of the necessary set of equations is thelength of the proton central core (LPC). It, however,participates in the proton envelope that is found outto be involved in a permanent interaction processwith a Zero Point Waves of CL space. It is foundthat these waves, permanently persistent in CLspace, are directly related to the background tem-perature of CL space. A theoretical expression ofthis temperature is derived in Chapter 5 of BSM byusing the concept of Zero Point Waves (ZPW)bouncing on the envelope surface of the proton. In

conditions of dynamical equilibrium, the energy ofthe bouncing ZPW is equal to the energy radiatedfrom the atoms and molecules, dispersed in theinterstellar space. The signature of this process ac-cording to BSM concept is the measured CosmicMicrowave Background (CMB) corresponding totemperature of 2.72 K. In the derivation of the the-oretical equation of this temperature the followingphysical laws and parameters are involved: the ide-al gas law, the Avogadro number, the proton geo-metrical parameters, the relation between themagnetic moments of electron and neutron (neu-tron is used more accurately instead of proton in or-der to reflect the neutrality of the involved atomsand molecules contributing to the CMB).

[(5.8)]

where: SW = 1 m2 participates as a reference sur-face in SI system, - are the magnetic mo-ments of electron and neutron, respectively.

The approximate determination of the LPCfrom Eq. [(5.8)] allows to solve a set of mass budg-et equations in Chapter 6 of BSM. In these equa-tions, some additional data are used from theparticle physics, such as: the mass of eta particle,the antiproton/proton ratio of stopping power, andthe energy-mass equivalence of W bosons and tauparticle. The calculations allow accurate determi-nation of the proton (neutron) geometrical parame-ters and its internal structure. The proton is atwisted loop hardware structure with a curledshaped external helical structure of positive prisms.Inside this envelope there are two pions (positiveand negative) also with shapes of curled twistedloops but with larger secondary helical step. Onecentral kaon structure has a similar shape as the en-velope of the twisted proton. When the proton isbroken in one place (means the hardware loop iscut) its positive external helical structure envelopeis usually firstly destroyed (releasing a huge IG en-ergy from the dens internal RL structure). The in-ternal so far pions and kaons are released and theyare also broken in one place but in this configura-tion they are not stable. More often, the kaon decayinto pions, and the pions decay into muon, whoseshape is like a multiturn electron (or positron)structure. Then the decay of muon is accompaniedby destruction of its internal Rectangular Lattice

τmin3λc

α2c 1 α2–----------------------------- 4.5596 16–×10= =

TNA

2

SW-------

hνc Rc rp+( )3Lpc2

2cRcreRig------------------------------------------

µeµn------

2.6758 K= =

µe and µn

15

(also twisted) that is much denser than the CosmicLattice. During this process an enormous energy isreleased. This energy gives the infinities in the Fey-nman diagrams. Some signatures of released ener-gies from RL destruction of helical structures, forexample, are the following: the experimentally es-timated energies corresponding to the “mass” ofW- and W+ bosons (from the kaon structures, ac-cording to BSM); the experimentally measured en-ergies corresponding to the “mass” of the tauparticle and the Regge resonance at 1.44 GeV (bothfrom the helical structures of the normal electron,according to BSM). All high order helical struc-tures are built of same lower order helical struc-tures similar as the single turn structure of electron(with internal lattice) but they are multiturn, in-stead. The parameters re and rp of all type helicalstructures, however, are the same (slightly differentonly for the internal pions and kaon because oftheir different degree of twisting).

The briefly described process of proton de-struction occurs in experiments provided by parti-cle colliders. One important feature that has beeninitially understood in BSM analysis is the strongand narrow Regge resonances (term in particlephysics experiments) providing a logical indicationthat a hardware loop is broken in one place andinternal hardware loops also broken in oneplace are released.

The proton core length (LPC) participating inEq. [(5.8)] is cross-validated by the Balmer seriesmodel (Chapter 7 of BSM) and by vibrational mod-els of some simple molecules (Chapter 9 of BSM).

The proton is a loop of finite thickness twist-ed in a shape of figure 8, while the neutron is asame structure but with a shape of double foldedloop. More accurately the plane projection of theproton envelope is quite close to a Hippoped curvewith parameter . The twisting (and folding)direction is strongly defined by the underlinedstructures of pions and kaon inside the proton (neu-tron) envelope. Consequently all protons (and neu-trons) involved in atomic nuclei have one and asame handedness (direction of twisting) but differ-ent degree of twisting). The shapes of the protonand neutron are shown in Fig. 3.

Fig. 3. Geometrical parameters of the proton and neu-tron. The magnified view shows only the external helicalshell without the internal structures of pions and kaon (extrac-tion from Atlas of ANS)

The estimated geometrical parameters of theproton (neutron) and electron are given in Table 2.

Physical dimensions of stable elementary particles Table 2===========================================Parameter Value Description Reference BSM (m) Chapter No.------------------------------------------------------------------------- 1.6277E-10 p and n core length 5, 6 0.667E-10 p length 6, 7, 8, 9 0.19253E-10 p width 6, 7, 8, 9 8.8428E-15 small radius of e- 3, 4, 6 5.8952E-15 small radius of e+ 3, 4, 6 1.7706E-14 e- (e+) helix step 3 3.86159E-13 e- Compton radius Known

7.8411E-13 p and n thickness 6, 7, 8, 9------------------------------------------------------------------------- Notations: p - proton, n - neutron, e- - electron, e+ - positron

The calculated physical dimensions of protonand neutron appear quite different from those ob-tained by the scattering experiment. However, im-portant factors such as the vacuum grid and theparticle structures are both not taken into accountin the interpretation of these experiments so far.The proton and neutron both have exactly the sameinternal structure, so they are distinguishable onlyby their overall shape (and a slight difference intheir internal structural twisting that provides aslight mass difference). Then a question may arise:why the proton possesses a charge while, the neu-tron - not. The answer is: The electrical charge is a

a 3=

LPCLPWPrerpseRc

2 Rc rp+( )

16

result of the modulation of the surrounding CLnodes by the RL(T) lattice of the helical structures(external shells). In case of neutron, all helicalstructures get overall symmetry in respect to its ax-is. For such shape, the modulation of CL space inthe far field is compensated and the electrical fieldis a zero. In case of proton, the overall torus istwisted and the axial symmetry of RL(T) is de-stroyed. Therefore, it is able to modulate the CLnode in the near and far field.

Fig 4 shows the spatial geometry of the Deu-teron, where: p - is the proton and n - is the neu-tron. The neutron is centred over the proton saddleand kept by the Intrinsic Gravitation (IG) field andthe proximity electrical fields of the neutron andproton. In such conditions the neutron is kept stable(it is not able to unfold and convert to proton).

Fig. 5 illustrates the protons and neutronsarrangement in the nucleus of He. In such close dis-tance, the internal lattices of the proton’s helicalstructures are kept by IG forces that are inverseproportional to the cube of the distance. The nucle-us of helium is the most compact atomic structure.Therefore, its influence on the CL space parame-ters in comparison to other atomic structures is thestrongest one. As a result, the helium nucleus pos-sesses the largest binding energy between the in-volved protons and neutrons. .

When taking into account the two features ofthe proton: a finite geometrical size and the distrib-uted proximity electrical field it is evident that theCoulomb law is valid down to some limit, definedby the finite size of the proton structure. This is ver-ified by the model of Balmer series in Hydrogenpresented in Chapter 7. The idealized shape ofBalmer series orbit is shown in Fig. [7.7].

Fig. [7.7]. Idealized shape of Balmer series orbit. Rc- is the Compton radius, rqm - is a magnetic radius of electronat sub optimal quantum velocity. The Compton wavelength

shown as standing waves is is not in scale

5. Atlas of Atomic Nuclear Structures

5.1. Physical atomic models according to BSM concept.

One of the most useful results of BSM theorywith practical importance is the Atlas of AtomicNuclear Structures (ANS). The analysis leading tounveiling the spatial arrangement of the protonsand neutrons in atomic nuclei is provided in Chap-ter 8 of BSM. It is found that the protons and neu-trons follow a strict spatial order. This order isconnected to well defined building nuclear tenden-cy related to the Z number of the elements. Thesignature of this tendency matches quite well therow-column pattern of the Periodic table, theHund’s rules and the Pauli exclusion principle. TheAtlas of ANS provides nuclear configurations ofthe elements from Hydrogen to Lawrencium (Z =103). For drawing simplification of the nuclearstructures, the protons and neutrons are presentedby simplified patterns reminding their shape. Theleft part of Fig. 6 shows the patterns used for theproton, deuteron, tritii and helium, while the rightpart shows the most common shapes and possibledimension of the quantum orbits. The dimensionsof the quantum orbits and the proton and neutronare given in one and a same scale.

Fig. 4. Deuteron withelectron in Balmer seriesaccording to BSM physi-cal model

Fig. 5. Helium nucleusaccording to BSM phy-sical model

λc

17

For any atomic nucleus, a polar axis is identi-fiable. It is defined by the long symmetrical axis ofone or more He nuclei that are always in the middleof atomic nucleus. The atomic nuclei posses alsotwisting features due to the proton twisting, but it isnot shown in the drawings. In the Atlas of ANS, thepattern of proton is symbolized by arrow in orderto simplify the drawings. Additional symbolic no-tations are used for the the different types of bondsand pairing in which IG and EM fields are in-volved.

5.2. Three-dimensional structure of atomic nuclei and limited angular freedom of the valence protons.

The Atlas of Atomic Nuclear Structures pro-vides the nuclear configurations of the stable iso-topes. One or more He nuclei are in the nuclearcentre, aligned with the polar axis of symmetry.The peripheral building blocks of the lighter ele-ments are usually deuterons, while the elementtritii appears more frequently in the nuclei of heav-ier elements. The positions of the protons are de-fined by the consecutive number of proton’s shelland by the type of the bonds between the protons.Fig [8.2] illustrates the backbone structure of nu-cleus allowing the most dens pack of the protonsand neutrons, having in mind the opposite forceskeeping their positions: the attractive IG forces andthe repulsive electrical forces between the proxim-ity fields of the protons and the neutrons. Thechain structure appears for the atoms with Z > 18(after Argon).

The structural restrictions of the positions ofthe atoms in the molecules comes from two factors:

- stable structural arrangements of the bondedprotons of the nucleus

- angular restrictions of the valence protons

Fig. [8.2]a. - polar structure; b. - polar-chain structure

The unveiled type of bonds between protonsand neutrons in the atomic nucleus are given by Ta-ble 3. The gravitational bonds are held by the IGfield of the intrinsic matter (more explicitly the IGfield of the internal lattices of the helical structuresfrom which the proton and neutron are built). TheIG field controls also the proximity E-field of theproton (and proximity locked E-field of neutron)and its unity charge appearance. For this reason, allGB types of bonds are very stable.

Bonds in the atomic nuclear structure Table 3

===========================================Bond notation Description------------------------------------------------------------------------- GB Gravitational bond by IG forces GBpa polar attached GB GBpc polar clamped GB GBclp (proton) club proximity GB GBnp neutron to proton GB EB electronic bond (weak bond)-------------------------------------------------------------------------

The four different types of the gravitationalbonds and one type of electronic bond are illustrat-ed in Fig. [8.4], where the positions of some quan-tum orbits are also shown. The GBpa bonds forvalence protons have an angular restricted freedomof motion in a plane close to the polar section. Pro-tons (deuterons) held by GBpa and GBclp bondsdo not have any freedom of motion. The EB typeof bonds are valid only for the valence protons butthey are provided by electron orbit pairing, corre-sponding to the Hund rules. There are few types ofsuch pairings. The two of them are more important:

Fig. 6

Patterns forsimple ele-ments and quantum orbits

18

a first type - two orbits in separated parallel orbitalplanes; a second type - a single orbit with two elec-trons with different QM spins, according to a Pauliexclusion principle (they are orbiting in oppositedirections). The second type of Hund rule appearsvalid for EB bonds.

Fig. [8.4] The left-side structure is 7Li nucleus,. Theright-side structure is only a portion of nucleus showing thedifferent type of bonds, according to Table 3. The planes ofthe shown quantum orbits are normal to the drawing plane.

The GB type bonds could not be broken inany type of chemical reaction, but only in nuclearreactions where quite large energies are involved.The EB type of bond however is weak. Bonds ofsuch type begin from the raw 13 of the Periodic ta-ble while in raw 18 (noble gazes) they are convert-ed to GBclp bonds. The EB bonds normallyexclude the external shell protons from chemicalvalence, so they play a role for the principal va-lence of the elements from group 13 to 17. This isvalid for rows 1, 2, 3 of the Periodical table. Insome conditions, however, the EB bonds could bebroken, so the element may exhibit multiple oxida-tion numbers.

For some chemical compounds between ele-ments with large number of valence protons, not allof them can be connected by electronic bonds. Thisis a result of the finite nuclear size of the atoms andthe angular restriction of the valence protons.

It is evident from the nuclear structure thatthe positions of the electron orbits are strictlydetermined by the positions of the protons withtheir proximity electrical fields and the condi-tions of quantum orbits provided by Table 1.Therefore, the electron orbits are not shown in theAtlas of ANS but their positions are easily identifi-

able. Having in mind the above consideration thewell defined orbital positions are characterized bythe same first ionization potential embedded in theQuantum Mechanical models and obtained experi-mentally.

6. Electronic bonds between atoms in moleculesIt is evident that the BSM model of the atom

allows identification of the orbital planes andchemical bond orientation of the atoms when con-nected in molecules. Additionally the QuantumMechanical spin of the orbiting electron in respectto the proton twisting is also identifiable. The pro-ton envelope is twisted torus, so it possesses a well-defined handedness along any one of its axes ofsymmetry. Then, the electron in the quantum orbitshown in Fig. 4 has an option to move in two dif-ferent direction in respect to the proton direction oftwisting. This will correspond to two slightly dif-ferent energy levels for one and a same quantumnumber. Its signature is a fine structure splittingof the spectral line.

The intrinsic conditions of the quantum orbitsdefined by the two proper frequencies of the elec-tron and the CL space properties are valid also forthe bonding electrons in molecules. Let consider-ing the most simple case of H2 molecule identifiedas an ortho-I state. Its shape is illustrated in Fig.[(19.2)].

Fig. [9.12] Structure of H2 - ortho-I state molecule Lp - is a proton length

Lq(1) is a long side of a first harmonic quantum orbitrn - is the distance between the Hydrogen atomsr - distance between the electron and the proton’s core in the circular section (for the most external orbit

Note: The quantum orbit quasiplane is perpendicular to thequasiplane of the protons. However, they both are shown inone plane for simplification of the drawing

In this figure, the three-dimensional shape ofthe proton is replaced, for simplicity, by a 2-dimen-

protonr

rn

0.65Lp 0.65Lp

Lp

Lq(1)

quantum orbit

19

sional Hippoped curve with parameter . Themolecular vibration in such simple system is of lin-ear type. The long axes of the protons and quantumorbit are aligned with the molecular vibrational ax-is. The both electrons move in a common quantumloop (orbit) but in opposite directions (oppositeQM spins). The quantum orbit crosses the Hip-poped curves of the protons in the locus points. Wemay assume that every orbiting electron is able toneutralize one charge, by interconnecting its E-filed lines to the proton E-field. Let considering themoment, when both electron are in the locus pointsof the Hippoped curves, representing the protons.Their velocity vectors in this case are perpendicularto the direction of the molecular vibration and donot contribute to the momentum energy of the sys-tem. Then, their moment interaction can be esti-mated by considering only two unit charges atdistance rn. Now, let assume that the left proton andthe right electron are both missing. The system en-ergy in this case is [eV]. The same consid-erations and results are valid also for the othersymmetrical case. Adding the energies from thetwo symmetrical cases we get the full system ener-gy.

[(9.40)]

where: the factor 0.6455 defines the distance of thelocus from the central symmetrical point of theHippoped curve with factor .

7. Vibrational motion of atoms connected in molecule by electronic bonds.

One of the features of the Intrinsic Gravita-tional (IG) field of the helical structures fromwhich particles are built is the ability to create elec-trical charge. BSM analysis unveils the physicalmeaning of the electrical charge as modulation ofCL nodes by internal RL structures of the helicalstructures from which the elementary particles arebuilt. In such aspect the energy of the electricalcharge could be regarded as a part of IG energy ofthe particle in CL space environment. In a nearfiled range the proximity field of the charge parti-cle possesses a spatial configuration, while in a farfield range it appears as a point charge. The analy-sis of the vibrational motion of two atoms connect-ed in molecule by electronic bonds allows to

identify some quantum mechanical features. Thevibration causes spatial modulation of the nearelectrical field created by the protons participatingin the electronic bond. The mechanism responsiblefor this modulation is a quantum quasishrink effectdiscussed in Chapter 2. This effect is a result ofslight change of the resonance frequency of EQ CLnode in comparison to MQ CL node. The modula-tion features of CL space are analysed by using atotal energy of the system that involves:

- the IG energy- the energy of the electrical charge- the kinetic energy of the involved particles- the energy of the emitted or absorbed photon- the vibrational energy

In analysis the IG field energy is presented asintegration of IG forces from some initial value toinfinity. Practically the integration does not go toinfinity because in case of inverse cubic law thefield strength falls vary fast with the distance.

[(9.13)]

where: mpo is the Intrinsic mass of the proton,Go is the intrinsic gravitational constant

- IG factorNote: The factor 2 in front of the integral

comes from the two arm branches (along abcd ax-es) of the CL space cell unit. They both are includ-ed in the xyz cell unit to which all the CL spaceparameters are referenced. All equations using CIGfactor in the following analysis confirms the needof factor 2.

The vibrational motion of the simple H2 mol-ecule is analysed based on the total energy balancein which the energy of IG field is a major compo-nent. The total momentum energy balance at theequilibrium point is given by

(eV) [(9.18)]

where: - is the energy of the twoelectrical charges (for two protons);

- is the kinetic energy of the twoelectrons.

The analysis unveils the vibrational statesand one metastable state of H2 ortho-I molecule.The obtained expression for the vibrational levels

a 3=

q/4πεorn

E 2q4πε0 Lq 1 ) 0.6455Lp+( )[ ]--------------------------------------------------------------- 16.06 eV= =

a 3=

EIG CP( ) 2–Gompo

2

r3---------------- rd

rne

∞

∫CIG

Lq 1( ) 0.6455Lp+( )2--------------------------------------------------= =

CIG Gompo2=

CIG

q Lq 1( ) 06455Lp+( )2----------------------------------------------------

2Eqq

---------2EK

q----------+=

2Eq/q = 511 KeV

2EK/q = 2 x 13.6 eV

20

of this molecule with good for accuracy for theiridentification is:

(9.23)

(9.23.a)

The photoelectron and optical spectrum areanalysed and the corresponding transitions and vi-brational levels are identified. The calculated vi-brational levels are compared to those identifiedfrom the optical spectrum. The calculated vibra-tional curve fits quite well to these levels after ad-justing a small offset level corresponding to EX,whose value is 6.26 (eV). It is likely a constantfrom the integration in Eq. [(9.13)] that influencesslightly only the vertical position of the vibrationalcurve. The influence of this parameter on CIG,however, is intrinsically small (beyond 5 signifi-cant digit), so for the number of tasks it could beomitted. Therefore, Eq. [(9.18)] allows determina-tion one very useful parameter of IG field - the fac-tor CIG

[(9.17)]

Fig. [9.24] shows simultaneously the vibra-tional energy levels Ev, calculated by Eq. [(9.23)]and those estimated from the optical transitionsE(0-ν’’) and E(1-ν’’) in UV spectrum (Lyman sys-tem) provided by I. Dabrowsky (1984). More de-tails about identification of the transitions are givenin §9.6 in Chapter 9 of BSM. The fractional errorbetween calculated levels and experimental data isin a range of +/- 0.035%. While the vibrationalcurve is usually drawn as energy level towards in-ternuclear distance, the step-like curve is an energylevel towards a vibrational quantum number. Theobtained value of energy difference between thesmallest and largest vibrational number is 4.4834eV, pretty close to the experimentally obtained val-ue of 4.478 eV.

The analysis indicates that the total energybalance according to Eq. [(9.18)] is kept very accu-rate, despite the large IG energy. Therefore:

The emission or absorption of a photon isa result of comparatively small disturbance ofthe total energy balance.

Fig. [9.24]. Energy levels Ev, (eV) calculated by Eq.(9.23) towards the vibrational levels for H2 - ortho. The cal-culated levels are shown by step line, while the optical transi-tions corresponding to two different QM spins are shown bydiamonds.

Similar analysis is provided also for D2 mol-

ecule since it is a more typical building element inthe atomic nuclei.

Note: The BSM model of vibrational motionworks in highly nonlinear IG field, so it is quite dif-ferent than the Quantum mechanical models. Theobtained results are only for identification of the in-volved quantum effects and verification of thestructure and spatial parameters of the particles:proton, neutron, electron. Therefore, despite thegood match shown in Fig. [9.24] the calculated byEq. [(9.23)] energy levels may differ from QM lev-els and especially for higher vibrational numbers.

Applying a total energy balance analysis fordiatomic molecules an approximate expression forvibrational levels, of homonuclear molecules isobtained (BSM, Chapter 9, §9.15.2) It is approxi-mate because the participated IG mass of the atom-ic nucleus is considered located in a point. Innumber of cases, however, the accuracy is enoughfor determination of the possible quantum orbitfrom the set of available quantum orbits. For thispurpose a direct expression of internuclear distanceof diatomic homonuclear molecule is derived froma conditions of total energy balance.

(9.56)

EυCIG

qr2---------

2Eqq

---------–2EK

q----------– EX+=

r Lq 1( )[ ] 1 πα4 υm υ–( )2–( )[ ] 0.6455Lp+=

CIG 2hνc hνcα2+( ) Lq 1( ) 0.6455+ Lp( )=

CIG G0mn02 5.2651 33–×10= =

∆E

rn n A p, ,( ) A p–( )2αCIGpEB n( )------------------=

21

(9.56.a)

where: - is a total energy involved in thebond connection of pair valence protons (deuter-ons), A - is the atomic mass for one atom in daltons(atomic mass units), p - is the number of protons in-volved in the bonding system (also per one atom),n - is the subharmonic quantum number of thequantum orbit, rn - is the internuclear distance atthe equilibrium vibrational point.

The quantum orbit could contained not onlyone but more quantum loops (see §7.4, Chapter 7 ofBSM). In such case Eq. (9.56) and (9.56.a) obtainsmodifications, discussed in §9.15.3 of Chapter 9 ofBSM.

The conditions defining the interatomicquantum orbits in molecules are different fromthose of atomic quantum orbits. In a latter case, theconditions determined the possible quantum orbitare determined by the proton dimensions, so theyare stable. For interatomic quantum orbits in mole-cules, however, the defining conditions are influ-enced by the nuclear motion of involved atoms, inwhich the IG field interactions are involved. TheIG forces are able to modulate the spatial configu-ration of the proximity E-field of the protons in-volved in the electronic bond. As a result, thevibrational quantum conditions occur at intrinsical-ly small deviations from the internuclear distance.The actual vibrational range for H2 ortho-I mole-cule is given by the expression

(9.26)For the identified maximum vibrational

number , the range of vibrations is only (m) while the estimated internucle-

ar distance is 2.23E-10 (m).

8. Method for determination the possible con-figurations of diatomic molecules

The possible configuration of diatomic mole-cules could be unveiled by simultaneous applica-tion of the following methods:

(a) a drawing method: using the spatial con-figuration of the nucleus and selected possible orbitfrom the quantum orbit set

(b) a theoretical calculation of the internucle-ar distance by Eq. (9).

(c) calculation of low number energy levelsand comparing the results with transitions of iden-tified spectral bands from the optical and photo-electron spectra (Note: The expression [(9.34)] isbased on point IG masses and may not be accuratefor diatomic molecules with a large Z number of at-oms).

The intrinsically small change of the internu-clear distance of vibrating within one band mole-cule, mentioned in the previous paragraph,facilitates the task for identification of the possibleconfiguration of a simple molecule. Applying Eq.[(9.34)] for diatomic molecules in which Z>4, it isfound that a quantum orbit of Lq(1) is not possibledue to the restrictions imposed by the finite size ofthe atomic nuclei. This additionally facilitates thetask for identification of the possible states.

Fig. [9.42] shows the photoelectron spectraof O2 molecule. They likely correspond to differentinternuclear distances.

Fig. [9.42]. PE spectrum of O2 molecule excited by He I ra-diation (Turner et all., courtesy of K. Kimura et al., (1981)).The capital letters in brackets is a notation used by BSM.

Table 9.6 shows the calculated internucleardistances for different quantum orbits Lq, using Eq.[(9.55)] (first raw) and the estimated distances bythe drawing method (second raw).

Calculated by Eq. (9.55) values for rn for Table 9.6O2 states. The values are given in Angstroms (A). =========================================== rn Lq(2) Lq(2) Lq(2x) Lq(3) (A) (1 bond) (2 bonds) (2 bonds) (2 bonds)-------------------------------------------------------------------------by Eq. (9) 2.57 A 1.698 A 1.219 A by drawing 2 A 1.7 A 1.74 A 1.25 A -------------------------------------------------------------------------possible state {B}or {C} {D} {E} {A}-------------------------------------------------------------------------

EB n( )CIG

Lq n( ) 0.6455Lp+[ ]2-------------------------------------------------- hνc 2 α2

n------–

–=

EB n( )

δr 2πα4υm2 Lq 1( )=

υm 18=δr 7.866 16–×10=

22

The bottom raw of Table 9.6 provides thepossible states of O2 molecule obtained by the twomethods and their probable correspondence to thestates of the photoionization spectrum shown inFig. [9.42].

Some of the possible configurations the O2molecule, corresponding to different states areshown in Figures [9.43], [9.44] and [9.45].

9. Examples of possible configurations of some moleculesNote: In most of the following drawings the pro-tons and neutrons in the central polar section of theatomic nucleus are only shown.

Fig. [9.43] Possible configurations of O2(D) and O2(A). {D} and {A} are states of O2 according BSM model. The or-bital planes of electrons do not lie in the drawing plane, butthey are shown in this way for drawing simplification. Thenumber in a bracket indicates the subharmonic number of thequantum orbit.

Fig. [9.45] A possible configuration of O2 molecule in {E}state

Fig. [9.53] Two views of the probable configuration of ox-ygen atom in Airglow state responsible for line emissionsat 5577 A and 6300 A..

Fig. [9.53.A] Ozone molecule with second subharmonic bonding orbits Every one of the three bonding orbits contains two electrons with opposite Quantum Mechanical spins

Fig. [9.54] Configuration of (OH)- ion. Every elec-tronic bond orbit contains two electrons with opposite QMspins, so the molecule is symmetrical (the planes of bondingorbits are at 90 deg, in respect to the protons equivalentplanes)

Fig. 9.56 One view of CO2 molecule. The CO2 mol-ecule possesses rotational symmetry about the polar axis dueto the 90 deg rotational symmetry of C atom. If rotating 90deg around zz axis the view of the left side will change withthe view of the right side.

23

.

Fig. [9.59] Water molecule .

Fig. 9.7 Cl2 molecule. The dashed oval is the envelope of Ne nucleus. A set of the possible quantum orbits is shown in thesquare box, where the number in bracket indicates the subhar-monic number of electron quantum velocity. The experimen-tal value of internuclear distance between Cl atoms is 1.98 A.

10. Rotational component in vibrational rota-tional spectra of molecules

The electronic type of chemical bonds allowsa vibrational type of motion of the involved nuclei.The vibrational levels obtained by Eq. [(9.23)] forH2 and [(9.34] for diatomic molecules correspondsto the most energetic transitions of the optical spec-trum for zero rotational states. The BSM analysisleads to a conclusion that the rotational compo-nents in the vibrational rotational spectra, ac-cording to BSM, are likely result of shapedistortion of the quantum electronic orbits.

The possible types of the shape distortion are:- a symmetrical distortion- an asymmetrical distortionThe both types of distortion are shown re-

spectively in Fig. [9.16], a. and b.

Fig. [9.16] a. - symmetrical and b. - asymmetrical distortion of

the bonding orbitThe vibrational motion of linear diatomic

molecules involves symmetrical distortions of thebonding orbits. The effect of the distortion of thebonding orbit and its signature in the vibrational-rotational spectrum is illustrated by Fig. [9.17].

Fig. [9.17] Section of three consecutive levels of thevibrational ladder with fine structure levels from the bondingsystem frequency set. In the right side the corresponding op-tical spectrum from transition between these levels and thelowest level is shown.

For molecules with two binding orbits one ofthe bonds is a point of rotation at any moment (con-tributing to Q branch), while the other undergoes asymmetrical distortion (contributing to P and Rbranches) and they change alternatively.

The vibrational motion in bent molecules in-volves additional asymmetrical distortion of thebinding quantum orbits. This effect contributes tofolded P or R branches in some molecules withbent shape.

24

11. Structural and angular restrictions of the chemical bonds of electronic type

11.1. Restrictions from atomic nuclear configu-ration

The provided considerations in §5, §6 and §7demonstrate that the structural and angular restric-tions reduce significantly the degree of freedom ofthe atoms connected by electronic bonds. The samerestrictions are also responsible for the molecularbending. These features are not apparent from theQuantum Mechanical models of the atoms.

The mentioned considerations are not validfor ionic bonds where the atoms are not connectedby electronic bonds but by attractive forces be-tween oppositely charged ions. The internucleardistances in ionic bonds are also larger and suchmolecules exhibit different physical properties.Consequently they are not able to possess vibra-tional motion in which the quantum orbits play im-portant roles. For this reasons the ionic compoundsdon’t have vibrational rotational spectra. Only sep-arated ions are able to provide ionic line spectra.

The following conclusion is valid only forchemical compounds with electronic bonds, butnot for compounds with ionic bonds.• The degrees of freedom of connected atoms

in molecules by electronic bonds are reduced by structural restrictions and limited angu-lar freedom of the valence protons. This restrictions are defined by the nuclear con-figurations of the involved atoms.

11.2. Restrictions imposed by the nuclear con-figurations of the involved atoms

If not taking into account the existing one ormore He nuclei (with their polar electrons) in thenucleus of anyone of the atoms, every single pro-ton in the atom has own electron, connected to thefree proton club (the club that is not polar at-tached). Some of these proton clubs, however, areGBclp or EB bonded in pairs. For EB bonded pro-tons the two electrons with opposite QM spin cir-culate in a common orbit whose plane is almostparallel to the polar atomic axis. For GBclp bondedprotons the two electrons with opposite spin circu-late in a common orbit whose plane is almost per-pendicular to the polar axis. In both cases, the

common quantum orbit passes through the clubs ofthe protons. The orbital trajectory is well definedby the proximity E-field of the involved protons.The positions of GBclp protons are strongly fixed,while the EB protons are weakly fixed by the quan-tum orbits. Any fixed orbit may not lye in a planebut it is quite close to a fixed equivalent orbitalplane that gets a proper symmetrical position in re-spect to the polar nuclear axis. From above men-tioned consideration it is evident that the quantumorbits connected to BGps, GBclp and EB type ofbonds have fixed orientation of their equivalentplanes. These fixed positions are much strongerheld in comparison to the orbital plane positions ofthe chemical bonds.

Table 4 provides the number of different typeproton bonds in the nuclei of some elements andthe total electrons with commonly aligned equiva-lent orbital planes (where: Ne - is the number ofelectrons with aligned equivalent orbital planes)

Table 4.===========================================

Atom GBclp EB Ne-------------------------------------------------------------------------

C 0 0 2N 0 1 2O 2 0 6P 4 1 10S 4 2 10Cl 4 3 10Ca 8 0 18Fe 8 0 18Cu 8 4 18

-------------------------------------------------------------------------In the analysis provided in Chapter 8 and 9 of

BSM it is found that two of the external shell pro-tons of the oxygen atom are GBclp bonded. Thesignature indicating such type of bonding appearsin the first ionization potential trend as a functionof Z-number and also in the photoionization poten-tial of the oxygen (known as autoionization fea-ture). The nuclear structure of Oxygen is illustratedin Fig. 7.

In the right part of the drawing, the commonpositions of the fixed electron orbits are shown asviewed from the polar axis. The projections pat-terns of the two polar orbit electrons (1s electronsaccording to QM model) are shown by differentcolours. Their similar patterns exhibit angular ro-

25

tation around the polar axis due to the nucleartwisting of the atomic nucleus. This feature, validfor all atoms, is a result of the proton twisting. TheGBclp bonded protons (deuterons) are shown in theplane of drawing while the valence protons (deuter-ons) are closely aligned to a perpendicular plane,but shown at oblique angles for a drawing simplifi-cation purpose.

Fig. 7 Nuclear structure of the Oxygen atom. The twovalence type protons in the left side of the nucleus are in factin a plane perpendicular to the drawing

The stability of such nuclear configurationwith two GBclp pairs is a result of the nuclear sym-metry in which the two polar electrons (from 1sshell) have strong influence. This configurationprovides much larger angular freedom of the twovalence protons that may explain the large chemi-cal activity of the Oxygen atom.

12. Validation of the structural features of BSM atomic models by the organic and biomolecules with known structure and atomic composition.

12.1. General considerationsThe 3D structures and atomic compositions

of many biomolecules now are well known. In suchstructures, the individual atoms are identified asnodes with known coordinates. The angular coordi-nates of their chemical bonds are also known. Thisinformation is sufficient in order to replace thenodes in the 3D structure of any large moleculewith the physical models of the atoms according toBSM concept. If the BSM models are correct, theirspatial configuration and angular bond restrictionsshould match the 3D structure of the biomolecules.Once the BSM models are validated and corrected

if necessary, the complex biomolecules and anymacromolecule with known shape could be studiedfrom a new point of view. The application of theBSM models, for example, allows identification ofthe positions of all orbits. This includes the nuclearand the chemical bonds electronic orbits. Then theconditions for possible interactions, modificationsand energy transfer could be analysed at atomiclevel. The carbon atom is one of the most abundantelements in the organic and biomolecules. The leftpart of Fig 8. shows the 3D structures of the carbon,while the right part shows the possible quantum or-bits in the same scale. They are denoted by theirsubharmonic number (defined by the quantum ve-locity of the electron)

Fig. 8. Nuclear structure of carbon atom

12.2. Ring atomic structures in organic mole-cules.

Most of the organic molecules contain ringatomic structures. The molecule of benzene couldbe considered as a simple example of a ring struc-ture. The biomolecules usually possess a largenumber of ring atomic structures. Fig. 9. shows the3D molecular structure of aspirin where the ringstructure of 6 carbon atoms is similar as in benzene.Fig. 10 shows the same structure of aspirin at atom-ic level by application of BSM atomic models.

26

.

Fig. 9 Three dimensional structure of the molecule ofaspirin (PDB file visualized by Chime software)

Fig. 10 Three dimensional structure of aspirin byBSM atomic models

The single atoms Deuteron, Oxygen and Car-bon and the size of quantum orbit of second subhar-monic are shown in the left upper corner. Thevalence protons (deuterons) of the oxygen atom arein fact in a plane perpendicular to the plane of EB

bonded protons (deuterons) but they are shownwith reduced dimensions in order to imitate an ob-lique angle in 3D view. The same is valid also forthe valence protons of the carbon atom. In Fig. 9the electronic orbits providing chemical bonds areonly shown. For molecule with known 3D structureand composition the common positions of all elec-tronic orbits with their equivalent orbital planes areidentifiable. It is clearly apparent that the 3D struc-ture of the molecule is defined by the followingconditions:

(a) a finite size of the involved atomic nuclei(b) an angular restricted freedom of valence

protons(c) a finite orbital trace length defined by the

quantum conditions of the circulating electron(d) orbital interactions(e) a QM spin of the electron (the motion di-

rection of the electron in respect to the proton twist-ing)

The QM mechanical models of atoms aremathematical models in which the features (c), (d),and (e) are directly involved, while the features (a)and (b) are indirectly involved by the selection ofproper wavefunctions. In this process howeversome of the spatial and almost all angular restric-tions are lost. Let emphasize now the difference be-tween the suggested BSM models of atoms andmolecules and the QM models:

- QM model: the electrons participating inchemical bonds are orbiting around both point-likenuclei, i. e. they are not localised

- BSM model: the electrons involved in thechemical bonds are localised

-QM model: the chemical bond lengths areestimated from the electron microscopy assumingthe planetary atomic model in which the largerelectron concentrations are centred around thepoinlike nucleus

- BSM model: the chemical bond length mayneed re-estimation, because the orbits of the chem-ical bond electrons do not encircle the bound atom-ic nuclei.

- BSM model: the length of single C-C bondmay vary only by the subharmonic number ofquantum orbit, while the length in a double C=Cbond is additionally dependent of the angular posi-tions of the valence protons.

27

12.3 Some abundant atomic structures in bio-molecules.

Ring structures are very abundant in many bi-omolecules and they are very often arranged inparticular order along their chain. DNA and pro-teins contain large number of ring structures.

Fig.11 shows the spatial arrangement of ringatomic structures in a portion of β−type DNA. Thepositions of some (O+4C) rings from the deoxyri-bose molecule that is involved in the helical back-bone strands of DNA are pointed by arrows.

Fig. 11 Part of DNA structure with indicated positionsof some of (O+5C) atomic rings

Fig. 12 shows the ring atomic structure

(O+4C) from the DNA strand. The valence deuter-ons involved in the ring structure practically havesome small twisting, but the quantum orbit of sin-gle valence bond also could be twisted. This featuregives some freedom for formation of ring struc-tures of different atoms. The rotational freedom ofthe single valence bonds, however, may be accom-panied by some stiffness that increases with the de-gree of the orbital twisting. Some of the atoms ofthe ring structure are also connected to other exter-nal atoms. All this considerations provide explana-tion why the ring structure (O+5C) connected tothe DNA strand is not flat but curved.

The BSM atomic models unveil one impor-tant feature of the ring structure. The quantum or-bits are localised in a ring. Therefore, it is likelypossible the ring structure to be able to hold energyas a rotating excited state. This is reasonable if tak-ing into account the spin-orbital interaction exist-ing in atoms (discussed in Chapter 8). Then thiscould be a kind of energy storage mechanism. Thisissue is discussed in BSM_Application_3.

Fig. 12 Ring atomic structure from the deoxyribose molecule involved in DNA strand

12.4 Weak hydrogen bondsIt is known that a weak hydrogen bond is pos-

sible between two atoms, one of which does notpossess a free valence. The bond connection is a re-sult of orbital interactions. In such aspects the hy-drogen bonds connecting the purines topyramidines in DNA molecule are of two types: <N-H...O> and <N-H...N>, where the single va-lence electronic bond is denoted by “-” and the H-bond is denoted by “...”. The BSM concept allowsfinding of the possible orbital orientation for suchtype of bond. This is illustrated by Fig. 13.

In a hydrogen bond of type N-H...O the planeof electronic orbit of hydrogen appears almost par-allel to the commonly oriented nuclear orbits of ox-ygen atom in which six electrons are involved (seeTable 4 and Fig. 7). In a hydrogen bond of type N-H...N the plane of electronic orbit of hydrogen isalmost parallel to the equivalent planes of the twopolar orbits of N in which two electrons are in-volved. It is evident that the hydrogen bond is char-acterized by the following features:

- the connection is a result of common orbitalorientation

- the H-bond requires critical range of distance - the H-bond allows a large rotational freedom

This three features allows the DNA moleculeto possess excellent folding properties.

28

Fig. 13. Two types of hydrogen bonds

13. BSM atomic models and nanotechnology.Fig. 14 shows a sheet of the unfolded cylindricalwall with identified valence of the chemical bonds,so that the four valences of all carbon atoms (ex-cluding the edge atoms) are connected.

Let considering the hexagonal ring as a unitstructure of the sheet. Then the sheet is comprisedof two types of ring structures: - ring structure of I-st type (containing only sin-gle valence bonds) - ring structures of II-nd type (containing tree sin-gle valence bonds and three second valence bonds).

Fig. 15 provides an axonometric view of asheet, corresponding to unfolded cylindrical part ofsingle walled carbon nanotube. The rings of I-sttype are clearly distinguishable from the rings of II-nd type. The protons, involved in the second va-lence bonds lie in a plane perpendicular to the sheetplane. In the same figure all quantum orbits provid-ing chemical bonding are also shown.

Fig. 15 Axonometric view of model of single wallsheet of carbon nanotube

Conclusions. BSM theory is developed using a new ap-

proach and methodology with resurrected principleof objectivity, causality and logical understanding[18]. The reconsideration of space-time formula-tion gives a possibility for analysis of wide range ofphysical phenomena from a different point of viewwithout need of the Heisenberg uncertainty princi-ple. This allows unveiling deterministic relations intough problems where the human logic was consid-ered as failed. In such aspect the mysteries of theQuantum Mechanics, the General and the SpecialRelativity obtain logical explanations.

Between the major output results of theBSM theory are the unveiled structures of atomicnuclei and the physical models of the atoms. Theycan be reliably validated by existed data base aboutthe atomic structure and compositions of organicand biomolecules. The physical models and under-standable quantum interactions could be used fortheoretical analysis of the energy processes in thebiomolecules (see BSM _Application_3). Anotherpotentially useful application is a “New visionabout a controllable fusion reaction D+D->He withefficient energy yield” (BSM_Application_1).

The suggested BSM atomic models do notintend to undermine the Quantum Mechanicalmodels of the atoms. The new vision is that theyprovide accurate calculations of QM interactionsfrom energetic point of view, but they are not ableto unveil the physical structures of the involvedparticles. Therefore they are mathematical models

Fig. 14

only. From a point of view of BSM concept the ability of these models to provide accurate calculations of interaction energies is a result of intrinsic linearization feature in the unique conditions of self-sustainable CL grid, valid only for the energy scale. The linearization process appears slightly disturbed only in boundary conditions of the ground state orbits (apparent in BSM model of Hydrogen, for example, presented in Chapter 7 of BSM). Its signature is the Lamb shift.

Applied in the field of cosmology the BSM analysis leads to a different concept about the evolution processes in the Universe, challenging the Big Bang model. A hypothesis of stationary universe with recycling galaxies is presented in Chapter 12 of BSM.

Finally the BSM theory may serve for building of successful unified field theory. The interdisciplinary analysis indicates that the relation matter-energy-gravitation is a fundamental one from which all known physical laws and postulates could be derived. The understanding of this relation may allow us to adopt the cold fusion energy and to control the gravitation.

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