BSM-SG Atlas of Atomic nuclear Structures - viXravixra.org/pdf/1107.0031v1.pdf · The Atlas of...

Atlas of Atomic Nuclear Structures

Copyright © 2001, by S. Sarg A-1

ATLAS OF ATOMIC NUCLEAR STRUCTURESStoyan Sarg

The Atlas of Atomic Nuclear Structures (ANS) is one of the major output results of the Basic Structuresof Matter – Supergravitation Unified Theory (BSM-SG), based on an alternative concept of the physicalvacuum. The atlas of ANS illustrates the material structure of the elementary particles and atomic nucleias they are revealed in BSM-SG. While they exhibit the same interaction energies as the QuantumMechanical models, they are not point-like structures. The atlas also provides information about the spa-tial arrangement of the protons and neutrons in the atomic nuclei, atoms and molecules. The Z-numbertrend of the nuclear build-up follows a shell structure that complies strictly with the row-column patternof the Periodic table, while obeying the Hund’s rules and Pauli exclusion principle. The nuclear structuresof the stable isotopes exhibit a higher degree of symmetry. The trend of faster increase of the number ofneutrons in comparison to the protons in heavier elements and their spatial positions play a role in redis-tribution of the repulsive Coulomb forces between protons. The proposed physical models could findapplications in different fields, such as the chemistry, nanotechnology, biomolecules and deeper under-standing of the nuclear stability and reactions.

1. S. Sarg © 2001, “Atlas of Atomic Nuclear Structures”, monograph

Archived in the National Library of Canada (April 2002)http://www.nlc-bnc.ca/amicus/index-e.html(AMICUS No. 27106037)

Canadiana: 2002007655XISBN: 0973051515

Classification:LC Class no.: QC794.6*Dewey: 530.14/2 21

2. S. Sarg, “Atlas of Atomic Nuclear Structures According to the Basic Structures of Matter Theory, Jour-nal of Theoretics, Extensive papers, 2003.http: www.journaloftheoretics.com



Tables of contents

Page1. Introduction....................................................................................................................A-12. Part I: Structure of the elementary particles...................................................................I-13. Part II: Atomic nuclear structure of the elements...................................................(see Table 1)4. View of the nuclei of some elected elements................................................................II-21

Note: BSM-SG Periodic Table of Atomic Nuclei is included at the end (300dpi resolution). Higher reso-lution Periodic Table is available upon request.

References:

[1]. S. Sarg, Basic Structures of Matter Supergravitation Unified Theory, monograph, ISBN 9781412083874, Amazon.com, also in http://collection.nlc-bnc.ca/amicus/index-e.html (AMICUS No. 27105955) LC Class no.: QC794.6*; Dewey: 530.14/2 21, (first edition, 2002); second edition, 2005)[2]. S. Sarg, New approach for building of unified theory about the Universe and some results, http://lanl.arxiv.org/abs/physics/0205052 (2002)[3]. S. Sarg, Brief introduction to BSM theory and derived atomic models, Journal of Theoretics, (2003). http://www.journaloftheoretics.com/Links/Papers/Sarg.pdf[4]. S. Sarg, A Physical Model of the Electron According to the Basic Structures of Matter Hypothesis, Physics Essays (An international journal dedicated to fundamental questions in Physics), v. 16, No. 2, 180-195, (2003), viXra:1104.0051 [5] Basic Structures of Matter - Supergravitation Unified Theory Based on an Alternative Concept of the Physical Vacuum, viXra:1104.0046

Table 1: Page location of the elements

Z Page Z Page

1 - 2 II-1 53 - 56 II-11

3 - 7 II-2 57 - 61 II-12

8 - 13 II-3 62 - 67 II-13

14 - 18 II-4 68 - 72 II-14

19 - 24 II-5 73 -78 II-15

24 - 29 II-6 79 - 84 II-16

30 - 35 II-7 85 - 89 II-17

36 - 40 II-8 90 - 95 II-18

41 - 46 II-9 96 - 101 II-19

47 - 52 II-10 102-103 II-20

Notes: The symbols used for notation of the pro-tons and neutrons and their connections in the atomic nucleus are given in Page II-).

Notations: Z- number of protons in the nucleusN - number of neutrons in the nucleus



Introduction

The Atlas of Atomic Nuclear Structures (ANS) is one of the major output results of the BasicStructures of Matter - Supergravitation Unified Theory (BSM-SG), based on an alternative concept of thephysical vacuum. While the physical structures of the elementary particles obtained by analysis accord-ing to the BSM-SG theory exhibit the same interaction energies as the Quantum Mechanical models, theyallow unveiling the spatial configurations of the atomic nuclei, atoms and molecules. The unveiled struc-tural features of the atomic nuclei provide explanation about the particular angular positions of the chem-ical bonds. Such features are in good agreement with the VSEPR model used in the chemistry. Otherintrinsic features defined by the structural composition of the nuclei provide strong evidence that the pro-posed models are real physical atomic structures. The arguments for this claim are presented in the BSM-SG theory and more particularly in Chapter 8. The proposed physical models allows understanding thestability of the isotopes and the radioactivity. The nuclear models could be useful in different fields, suchas chemistry, nanotechnology, biomolecules and deeper understanding of the nuclear reactions.

The atlas of ANS contains two parts. Part I illustrates the geometry and the internal structure ofthe basic atomic particles, built of helical structures. (The helical structures are building blocks of all ele-mentary particles. Their type and classification are shown in §2.7, Chapter 2 of BSM). Part II illustratesthe three dimensional atomic nuclear structures of the elements in a range of 1 < Z < 103, where Z is thenumber of protons in the nucleus. Only the stable isotopes given in the Periodic table are shown. In orderto simplify the complex views of the nuclei they are shown as plane projections of symbols. For this pur-pose two types of symbols are used: symbols for hadron (nucleon) particles (proton, neutron and Henucleus) and symbols for the type of the nuclear bonding of the nucleons. The symbolic views contain thenecessary information for presenting the real three-dimensional structures of the atomic nuclei by differ-ent sectional views. This is demonstrated in page 21 of the atlas, where nuclear sectional views of someselected elements are shown.

The rules according to which the protons and neutrons are arranged in shells in the nuclei are dis-cussed in Chapter 8 of BSM-SG. The trend of consecutive nuclear building by Z-number follows a shellstructure that complies strictly with the row-column pattern of the Periodic table. The periodic law ofMendeleev appears to reflect not only the Z-number, but also the shell structure of the atomic nuclei. Thelatter becomes apparent in the BSM-SG analysis. The protons (also deuterons) shells get stable comple-tion at column 18 (noble gases). The separate rows of the Lanthanides and the Actinides are characterisedby a consecutive grow and completion of different shells. The nuclear structures of all stable elements(isotopes) possess a clearly identifiable polar axis of rotational symmetry. One or more He nuclear struc-tures are always positioned along this axis. The most abundant sub-nuclear compositions are deuterons,tritium and protons. The strong SG forces hold them together, while the proximity E-fields play a role fortheir orientations. The identified different types of bonds are shown in the atlas by symbolic notations.For more details, see Chapter 8 of BSM-SG. In the same Chapter, the conditions for instability of theshort-lived isotopes are also discussed. They are partly apparent from the Atlas drawings - especially forthe alpha decay. The stability limit for elements with a high Z-number is apparent from the nuclear shelfcompletion overal shape. The strong SG forces falls fast with the distance.

The electronic orbits are not shown in the nuclear drawings, but their positions are defined by thespatial positions of the nucleons. The Hund's rules and the Pauli exclusion principle are both identifiablefeatures related to the available positions and mutual orientations of the quantum orbits. The quantumvelocity of the orbiting and oscillating electron, defines the length trace of any quantum orbit (see §3.12,Chapter 3; §7.7, Chapter 7 of BSM-SG)

BSM Atlas of Atomic Nuclear Structures Part I Page I-1

Copyright 2001, by S. Sarg November 12, 2001 Page I-1

109.5

109.5

lef t handed pr ism 60 o

pr ism

Fig. 2.6

r ight handed60 o

d 109.5

A - A

abcd

109.5

A

o

o

A

Electron structure geometrical parameters

Rc

se

re

rp

RL(T)+ structureRL(T)- structure

Core node from prisms of same type(building element of the helical structure)Note: The twisted prisms model is used

Fig. 2.8.B

Oscil lating electron

Shape and envelope structure of proton and neutron

2(Rc+rp)

protoneutron

proton

Lpc/2π

Lpc

Wp

Lpc

π

neutron

2Rc

rp

Lp

e+



Fig. 2.15.B. Axial sectional view of proton (neutron) show-ing the external positive shell (envelope) and the internal ele-mentary particles - pions and kaon. All of them are formed byhelical structures possessing internal RL structures (notshown).

Fig. 2.15.A. Radial sectional view of a proton (neutron) corewith internal elementary particles and their internal RL struc-tures. The RL structures are not twisted for the kaon, partlytwisted for the pions and fully twisted for the external shell.

Fig. 2.29.E. Radial section of positive FOHS with twisted in-ternal RL(T)+ structure generating E-field in CL space. Theradial section of the FOHS envelope core and the central coreis formed of 7 prisms. rp - is a radius of the FOHS envelope.

shell(+ ) ex ternal

K0L

π+

π−rp

re

re

rp

K0L

π−

π+

shell(+) external

RL+ RL-

2Rc

b.

a.

Fig. 2.16 Axial (a) and radial (b) section geometry of the internal RL structure of FOHS (not twisted). The real number of radial layers is large since the prism’s length is

much smaller than the boundary radius r.

CL space

RL(T)+

E-field lines Central (-) core

rp



The equation of the quantum orbit trace length, isderived in §3.12.3 (Chapter 3 of BSM).

(3.43.i)

where: n is the subharmonic number of the quantumorbit; - is the Compton wavelength; - is the fine struc-ture constant; - is the length of the boundary orbit ( -is the Bohr model radius)

The shape of the orbit is defined by the proximity E-field of the proton. The most abundant quantum orbit has ashape of Hippoped curve with a parameter . Orbits ofsuch shapes serve also as electronic bonds connecting the at-oms in molecules (see Chapter 9 of BSM).

The trace length and the long axis length ofthe possible simple quantum orbits (formed by singlequantum loops) are given in Table 1.

The estimated distance between the CL nodes inabcd axis is: (m).

The calculated geometrical parameters of the stableatomic particles: proton, neutron, electron and positron aregiven in Table 2. The last reference column points to theBSM chapters, related to the calculations and cross valida-tions of these parameters.

Deuteron with Balmer series orbital He nucleusp - proton; n - neutron; e- - electron

Lqo(n)

Lq(n)

Simple quantum orbit (n - is the subharmonicnumber)

Idealized shape of stable (quantum) orbit defined by the quan-tum magnetic line conditions. The peripheral and axial magne-tic li nes are generated by the screw-like confined motion of the electron in CL space (see §7.7 in Chapter 7 of BSM)

Lqo

Lqo n( )2πao

n------------

λc

αn-------= =

λc α2πao ao

a 3=

Lqo Lq

dabcd 0.54920–×10≈

Table 1:

n [A] [A] e- energy [eV]

1 3.3249 1.3626 13.6

2 1.6625 0.6813 3.4

3 1.1083 0.4542 1.51

4 0.8312 0.3406 0.85

5 0.665 0.2725 0.544

6 0.5541 0.2271 0.3779

Lqo Lq



Notes: (1) (m) - is the Compton radius of the electron.(2) (m) - is the Amstrong unit for length

Table 2:

Parame-ter

Value DescriptionCalculations and

cross validations in:

1.6277 (A) proton (neutron) core length Chapters 5 and 6

0.667 (A) proton length Chapters 6, 7, 8, 9

0.19253 (A) proton (neutron) width Chapters 6, 7 ,8 ,9

8.8428E-15 (m) small radius of electron Chapters 3, 4, 6

1.7706E-14 (m) electron( positron) step Chapter 3

5.8952E-15 (m) small radius of positron Chapters 3, 4, 6

7.8411E-13 (m) thickness of proton (neutron) Chapters 6, 7, 8, 9

LPC

LP

WP

re

se

rp

2 Rc rp+( )

Rc 3.8615913–×10=

1A 1010–×10=

C I Page II-0

tes of H2 are normal to the proton's quasiplanes

mple B

s share a common orbit)

ected by EB bondscted by GBclp bonds

(1)

) fourth subharmonic QO (0.85 eV)

) second subharmonic QO (3.4 eV)

) sixth subharmonic QO (0.377 eV)

) first harmonic QO (13.6 eV)

) third subharmonic QO (1.51 eV)

) fifth subharmonic QO (0.544 eV)

H2 ortho molecule

PC(1)

BSM-SG

opyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures Part I

Polar section of Ar nucleus

embedded in a heavier nucleusPolar section of Ar nucleus

fron

t vie

w

scale for structures and quantum orbi ts

D - deuteronp - proton

Ar - ArgonHe - HeliumT - Tritii

n - neutron

Notations:

1 A

botto

m v

iew

GB - (intrinsic) gravitational bond (strong)

PC - polar connection or clamp for Ar polar GB

GBclp - (proton) club proximity GBGBpc - polar clamped GB

EB - electronic bond (weak)

Sketch symbols of nuclear atomic structures

Shape symbols of nuclear atomic structures

n p D

n p D

T He

T He

view

fron

t

Note: QOs for para and ortho sta

Exa

H2 para molecule (two electron

Example A: Two pairs of Ds connExample B: Two pairs of Ds conn

(1)

Example A

bott

omvi

ew

(4

(2

(6

(1

(3

(5

EB GBclp GBpc

Connection symbols

(1)

Simple quantum orbits (QOs)

(3)(2) (4) (5) (6)

t II Page II-1

BSM-SG

Copyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures Par

I Page II-2

C

Z=7 N=7N

142

N=6

BSM-SG

Copyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures Part I

Z=5 N=6Z=3 N=4Z=3 N=3Li

6Li

7

Z=4 N=6

9Be B

11 1

Z=6

I Page II-3

4

2 N=12Mg

27

Z=13 N=14Al

BSM-SG


16

Z=8 N=8O

19

Z=9 N=10F

20Ne

Z=10 N=10

23Na

Z=11 N=12

2

Z=1

rt II Page II-4

(Ar)

N=22 N=22Ar

Z=18 N=22

40Ar

BSM-SG

Copyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures Pa

Z=17 N=18 Z=15 N=16P

Z=14 N=16

28Si

31

Z=16 N=16

32S

Z=18 Z=18Cl

35 40

t II Page II-5

(Ar)

Z=23 N=28V

=26

51

BSM-SG


(Ar)

Z=21 N=24

(Ar) (Ar)

Z=19 N=20K

39Ca Sc

Z=20 N=20

40 45

(Ar)

Ti Z=22 N

48

rt II Page II-6

(Ar) (Ar)

Z=28 N=31Ni

59

Z=29 N=34

63Cu

BSM-SG


(Ar)(Ar) (Ar)

Z=25 N=30Mn

Z=24 N=28

52Cr

55

Z=26 N=30

56Fe

(Ar)

Z=27 N=32Co

59

Part II Page II-7

Z=34 N=45

79Se Br

(Ar) (Ar)

Z=35 N=45

79.9

BSM-SG

Copyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures

Z=31 N=39

(Ar) (Ar)

Z=30 N=36

65.4Zn

69.7Ga

(Ar) (Ar)

Z=32 N=41

72.6Ge

Z=33 N=42

74.9As

rt II Page II-8

(Ar) (Ar)

(Ar) (Ar)

89Y

Z=39

91Zr

Z=40

BSM-SG


Z=36 N=48 Z=38 N=50

(Ar)(Ar)

Z=36 N=48

84Kr

(Ar)

84Kr

(Ar) (Ar)

Z=37 N=48

(Ar)

85Rb

(Ar)

88Sr

I Page II-9

(Ar) (Ar)

(Ar) (Ar)

Z=46 N=60

106.4

N=58

h Pd

BSM-SG


(Ar)

(Ar)

Ru

Z=44 N=57

(Ar) (Ar)(Ar)

(Ar) (Ar) (Ar)

Z=42 N=54

92.9

Z=41 N=52

Nb95.9

Mo

Z=43 N=55

98.9Tc

101.1

Z=45

102.9R

Page II-10

Ar)

Ar)

(Ar)

(Ar)

Z=52 N=76

b

N=71

Te127.6

BSM-SG

Copyright 2001, by S. Sarg Atlas of Atomic Nuclear Structures Part II

(Ar)

(Ar)

(Ar)

(Ar)

(Ar)

(Ar)

Z=48 N=64 Z=47 N=61

Ag In114.8

Z=49 N=66

Sn118.7

Z=50 N=69

(

(

S121.7

Z=51

107.9

(Ar)

(Ar)

112.4Cd

Page II-11

(Ar)

(Ar)

(Ar)

Z=56 N=81

Ba137.3

BSM-SG


(Ar)

(Ar)

(Ar)

(Ar)

Z=53 N=74

I126.9

Z=54 N=77

Xe131.3

(Ar)

(Ar)

(Ar)

(Ar)

(Ar)

Z=54 N=77

131.3Xe

(Ar)

Z=55 N=78

132.9Cs

rt II Page II-12

r)

r)

Z=61

r)

d Pm145

N=84

BSM-SG


(A

(A

(A

N144.2

Z=58 N=82 Z=60

(Ar)

(Ar)

Z=57 N=82

138.9

(Ar)

La

(Ar)

(Ar)

(Ar)

(Ar)

(Ar)

Ce140.1

(Ar)

Pr

Z=59 N=82

140.9

rt II Page II-13

Z=67Dy Ho5 164.9

BSM-SG


Z=66

162.157.2

Z=64Gd

Z=65

158.9 Tb Z=62

Sm150.4 152

Z=63Eu

t II Page II-14

Z=72Z=72Hf Hf

178.5 178.5

BSM-SG


Z=68Er

167.3

Z=69Tm

168.9

Z=70

173Yb

175

Z=71Lu

rt II Page II-15

Z=78=77Ir Pt2.2 195.1

BSM-SG


Z

19

Z=73Ta180.9

Z=74

183.5 W Z=75

186.2 Re Z=76

190.2 Os

rt II Page II-16

Bi=83

Po Z=84

209 209

BSM-SG


Z Z=79Au197

Z=80

200.6 Hg Z=81

204.4 Tl 207.2

Z=82Pb

Part II Page II-17

Ra Z=88

226Ac

Z=89

(227)

BSM-SG


Fr Z=87

(223)At

(210)

Z=85 Z=86

(222)Rn Rn

Z=86

(222)

Part II Page II-18

Pu Z=94

244 Am Z=95

243

BSM-SG


Z=90Th232

Z=91Pa231 238

Z=92U

Z=93

237 Np

rt II Page II-19

Fm=100

Md Z=101

257) (258)

BSM-SG


Z=97Es

Z=99 Z

(247) (252) (

Z=96

(247)Cm Bk Cf

Z=98

(251)

I Page II-20

BSM-SG


Z=103

(262)No

Z=102

(259)Lr Lr

Z=103

(262)

Page II-21

8 se

ctio

ns4

sect

ion

Z=47

80 Z=86Rn

g Z=54Xe

8 se

ctio

ns8

sect

ions

8 se

ctio

ns

8 se

ctio

ns

(a)

them is 22.5 deg

BSM-SG


Z=36

Z=64 Z=74 Z=79 Z=AuG d W Hg

Ar Ca Kr AZ=10 Z=18 Z=20

BSM Atlas of Atomic Nuclear Structures Pojection views of selected elements

(a)

(b)

Note: (a) and (b) are polar sections of the nucleus with two selected planes. The angle between

Ce Z=58

OHe Z=2 Z=8 Ne

Z=9 N=10

17

( 2 6 0 ) Z=103

Z=711 7 5

Hg

( 2 1 0 )

Z=85

Z=53 N=74

Z=35 N=45

7 9 . 9

1 2 6 . 9

Z=17 N=18

3 5

��

��

��

��

��

2 3 2

9

Z=90

8

Z=581 4 0 . 1

��2 3 1 � ��2 3 72 3 8 �( 2 4 2 ) Z=91 Z=92 Z=93 Z=94

��

��

��

� Z=59

1 4 0 . 9

��

��

��

�� Z=61 Z=60

1 4 4 . 91 4 4 . 2 � Z=62

1 5 0 . 4

��

7

( 2 2 7 )

Z=89��( 2 2 6 )

Z=88 Z=87

( 2 2 3 )� ��

6

1 3 8 . 9

Z=71��1 3 7 . 31 3 2 . 9��

��

��

��

��

��

��

Z=56 Z=55�� 1 7 8 . 5

��

��

��

Z=72

Gd

��1 8 0 . 9

Z=73��1 8 6 . 2�1 8 3 . 9

Z=75 Z=74

1 9 0 . 2�� Z=76

��( 2 4 3 ) �� ( 2 4 7 ) ( 2 4 7 ) ( 2 5 1 )�� Z=95 Z=98 Z=97 Z=96

�1 5 2 Z=63 Z=66

1 6 2 . 5�� Z=64

�� Z=65

1 5 8 . 91 5 7 . 2 ��

��( 2 5 7 )��( 2 5 2 ) �� ( 2 5 8 ) ( 2 5 9 ) Z=100 Z=99 Z=102 Z=101

�1 6 7 . 3�� Z=67

1 6 4 . 9 Z=68

�� Z=69

!� Z=70

1 7 31 6 8 . 9

W

"1 9 2 . 2

Z=77 Z=80�1 9 7�#1 9 5 . 1

Z=79 Z=78�$2 0 0 . 6 ��2 0 7 . 2

Z=82�%2 0 4 . 4

Z=81��( 2 0 9 )�&2 0 9

Z=84 Z=83

Note: QOs for para and ortho states of H2 are normal to the proton's quasiplanes

Example B: Two pairs of Ds conncted by GBclp bondsExample A: Two pairs of Ds connected by EB bonds

Simple quantum orbits (QOs)

EB GBclp GBpc

Connection symbols

H2 para molecule (two electrons share a common orbit)

Per iodic Table of atomic nuclear st ructures (according to BSM-SG)

Z=44 N=57

Z=26 N=30

Z=12 N=12 Z=12 N=12scale for structures and quantum orbits

��

��

Z=40 N=51

Z=22 N=26

n - neutronp - proton

Ar - ArgonHe - Helium

D - deuteron

Notations:

T - Trit i i

��

5

�� ! ' Z=39 N=50

��

��

Z=38 N=50

��

��

Z=37 N=48

��

��

8 7 . 68 5 . 5 8 8 . 9 9 1 . 2 2

4

3

Z=21 N=24

4 4 . 9 6��

4 0

Z=20 N=20 Z=19 N=20(

3 9 . 1 � �&

4 7 . 8 8

��

��

��

��9 2 . 9 1

Z=41 N=52��

Z=43 N=55

��

��

Z=42 N=54

��

��

9 8 . 99 5 . 9 4

��

1 0 1 . 1

��

Z=23 N=28)

5 0 . 9

1 A

Z=25 N=30 *

Z=24 N=28

5 2 5 4 . 9�

GB - (intrinsic) gravitational bond (strong)

PC - polar connection or clamp for Ar polar GBGBpc - polar clamped GBGBclp - (proton) club proximity GB

EB - electronic bond (weak)

��5 5 . 8

n

Sketch symbols of nuclear atomic structures

n

Shape symbols of nuclear atomic structures

2

��&

Z=4 N=6 Z=3 N=4

6 . 9 4 9 . 0 1

botto

m v

iew

front

vie

w

$��2 3 2 4 . 3

2

1

1

�

Z=1 N=0

1 . 0 0 8

3 4

p D T He

p D T He

Example A

botto

mvie

wvie

wfro

nt

(1)

embedded in heavier nuclei

Polar section of Ar nucleus

(2) (4)

5 6 7 8

(3)Polar section of Ar nucleus

Z=14 N=16 Z=13 N=14 Z=16 N=16 Z=15 N=16

��

��

��

Z=45 N=58

1 0 2 . 9

��

�$��

��

��

��

��

Z=47 N=61 Z=46 N=60 Z=48 N=64

��

��

1 0 7 . 91 0 6 . 4

��

1 1 2 . 4

Z=27 N=32��

5 8 . 9

(1)

�& Z=28 N=31

5 8 . 7�

Z=29 N=34

6 3 . 5'*

Z=30 N=36

6 5 . 4

��

��

��

* Z=50 N=69

1 1 8 . 7"*

Z=49 N=66

��

��

��

1 1 4 . 8��

Z=52 N=76

��

��

��

��

Z=51 N=71

��

1 2 7 . 61 2 1 . 7

�� Z=32 N=41

7 2 . 6

Z=31 N=39��

6 9 . 7

Z=34 N=45

(2) (2)

�� Z=33 N=42

7 8 . 9 67 4 . 9

(4) fourth subharmonic QO (0.85 eV)

(2) second subharmonic QO (3.4 eV)

(6) sixth subharmonic QO (0.377 eV)

(1) first harmonic QO (13.6 eV)

(3) third subharmonic QO (1.51 eV)

(5) fifth subharmonic QO (0.544 eV)

(1)

(1)

Example B

PC

H2 ortho molecule

(5) (6)

9 10 11 12

Z=5 N=6

�1 0 . 8 1 2 �1 6�1 4�

Z=6 N=6 Z=8 N=8 Z=7 N=7

&2 8�%2 7 3 2�3 1

13 14 15 16

�

�

�# �*( 2 2 2 )

Z=86

Z=18 N=22

" +� Z=54 N=77

��

��

��

��

( A r )��

1 3 1 . 3

Z=36 N=48� (

8 3 . 8

Z=10 N=10

�1 9 ��2 0 . 1 8

�% �4 0

18

Z=2 N=2

4 . 0 0 3��

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