CEM03 and LAQGSM03: Extension of the CEM2k+GEM2 and … · cade (INC) Photonuclear Reaction Model...

Journal of Nuclear and Radiochemical Sciences, Vol. 6, No.2, pp. A1-A19, 2005

© 2005 The Japan Society of Nuclear and Radiochemical SciencesPublished on Web 11/07/2005

Accounts

1. Introduction

The 2003 version1−3 of the improved4 Cascade-Exciton Model(CEM)5 as realized in the code CEM2k merged6−8 with the Generalized Evaporation Model code GEM2 by Furihata9 and ofthe Los Alamos version of the Quark-Gluon String Model codeLAQGSM10 merged6−8 with GEM2 have been recently incor-porated into the transport codes MARS1511 and LAHET312 andare planned to be incorporated in the future into the transportcodes MCNPX13 and MCNP6.14 Initially, neither CEM2k+GEM2 nor LAQGSM+GEM2 considered photonuclear reac-tions and were not able to describe such reactions, either asstand-alone codes or as event generators in transport codes. Toaddress this problem, here we extend CEM03 (the 2003 ver-sion of CEM2k+GEM2) and LAQGSM03 (the 2003 version ofLAQGSM+GEM2) codes to describe photonuclear reactions atintermediate energies (from ~ 30 MeV to ~ 1.5 GeV). Wedevelop a model that is based on the Dubna IntraNuclear Cas-cade (INC) Photonuclear Reaction Model (PRM),15−17 usesexperimental data now available in the literature, and a revi-sion of recent systematics for the total photoabsorption crosssections by Kossov.18 Our photonuclear reaction model stillhas some problems and is under further development, but eventhe current version allows us to describe reasonably well inter-mediate energy photonuclear reactions. In the following, wepresent a description of our model together with several illus-trative results.

2. Dubna Photonuclear Reaction Model

The Dubna intranuclear cascade photonuclear reactionmodel (Dubna INC) was initially developed 35 years ago byone of us (KKG) in collaboration with Iljinov and Toneev15 todescribe photonuclear reactions at energies above the GiantDipole Resonance (GDR) region. [At photon energies Tγ =10 – 40 MeV, the de Broglie wavelength D is of the order of20 – 5 fm, greater than the average inter-nucleonic distance in

the nucleus; the photons interact with the nuclear dipole reso-nance as a whole, thus the INC is not applicable.] Below thepion production threshold, the Dubna INC considers absorp-tion of photons on only “quasi-deuteron” pairs according to theLevinger model:19

σγA = L σγ d , (1)

where A and Z are the mass and charge numbers of thenucleus, L ≈ 10, and σγ d is the total photoabsorption crosssection on deuterons as defined from experimental data.

At photon energies above the pion-production threshold, theDubna INC considers production of one or two pions; theconcrete mode of the reaction is chosen by the Monte Carlomethod according to the partial cross sections (defined fromavailable experimental data):

γ + p → p + π0 , (2)

→ n + π+ , (3)

→ p + π+ + π− , (4)

→ p + π0 + π0 , (5)

→ n + π+ + π0 . (6)

The cross sections of γ + n interactions are derived fromconsideration of isotopic invariance, i.e. it is assumed that σ(γ+ n) = σ(γ + p). The Compton effect on intranuclear nucleonsis neglected, as its cross section is less than ≈ 2% of other reac-tion modes (see, e.g. Figure 6.13 in Reference 20). The DubnaINC does not consider processes involving production of threeand more pions; this limits the model applicability to photonenergies Tγ ~< 1.5 GeV [for Tγ higher than the threshold forthree-pion production, the sum of the cross sections (4) – (6) isassumed to be equal to the difference between the total inelasticγ + p cross section and the sum of the cross sections of the two-body reactions (2)– (3)].

The kinematics of two-body reactions (2) – (3) and absorp-tion of photons by a pair of nucleons is completely defined bya given direction of emission of one of the secondary particles.Similarly to the procedure followed for N + N and π + N inter-

S. G. Mashnik,*,a M. I. Baznat,b K. K. Gudima,b A. J. Sierk,a and R. E. Prael aaLos Alamos National Laboratory, Los Alamos, New Mexico 87545, USA bInstitute of Applied Physics, Academy of Science of Moldova, Chisinau, Moldova

Received: April 30, 2005; In Final Form: July 26, 2005

The improved Cascade-Exciton Model (CEM) code CEM2k+GEM2 and the Los Alamos version of the Quark-Gluon String Model code LAQGSM are extended to describe photonuclear reactions. First, we incorporate newevaluations of elementary cross sections based on the latest experimental data into CEM2k+GEM2 and also makeseveral improvements in the description of the de-excitation of nuclei remaining after the cascade stage of reac-tions induced by arbitrary projectiles. Next, for photonuclear reactions we include a normalization to evaluatedexperimental absorption cross sections based on the recent systematics by Kossov in CEM2k+GEM2. Then, weextend our high-energy code LAQGSM by adding the photonuclear mode which was ignored in all its previousversions, and add to it the photonuclear part from our improved CEM2k+GEM2. Presently, these codes do notinclude a calculation for GDR and describe properly photonuclear reactions only at intermediate energies from ~ 30 MeV to ~ 1.5 GeV. In this work we present a short description of the photonuclear mode as incorporatedinto our codes, show several illustrative results, and point out some unresolved problems.

CEM03 and LAQGSM03: Extension of the CEM2k+GEM2 and LAQGSM Codes toDescribe Photo-Nuclear Reactions at Intermediate Energies (30 MeV to 1.5 GeV)

*Corresponding author. E-mail: [email protected]. FAX: +1-505-667-1931.

Z(A – Z)A

MashnikA2 J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005

actions,21, 22 the cosine of the angle of emission of secondaryparticles can be represented in the center of mass (c.m.) systemas a function of a random number ξ, distributed uniformly inthe interval [0,1]

cos θ = 2ξ1/2 ∑anξn + (1–∑an)ξN+1 –1, (7)

where N = M = 3,

an = ∑ankTγk , (8)

where the coefficients ank were fitted to describe the availableexperimental data and are published in Tables 1 and 2 ofReference 17 (the corresponding coefficients for N + N and π +N interactions are published in Table 3 of Reference 22 and inTable 72 of the monograph by Barashenkov and Toneev16).The distribution of the secondary particles over the azimuthalangle ϕ is assumed to be isotropic. After simulating the angleΘ1, using eqs 7 and 8, and ϕ1 isotropically for the first particleof any reaction with two particles in the final state, the anglesΘ2 and ϕ2 of the second particle, as well as the energies of bothparticles T1 and T2 are uniquely determined from four-momentum conservation.

The analysis of experimental data has shown that thechannel (4) of two-pion photoproduction proceeds mainlythrough the decay of the ∆++ isobar listed in the last Review ofParticle Physics by the Particle Data Group23 as having themass M = 1232 MeV

γ + p → ∆++ + π− ,

∆++ → p + π+ ,(9)

whereas the production cross section of other isobar compo-nents ( , ) are small and can be neglected. The Dubna INCuses the Lindenbaum-Sternheimer resonance model24 to simu-late the reaction (9). In accordance with this model, the massof the isobar M is determined from the distribution

~F(E, M)σ (M) , (10)

where E is the total energy of the system, F is the two-bodyphase space of the isobar and π− meson, and σ is the isobarproduction cross section which is assumed to be equal to thecross section for elastic π+p scattering.

The c.m. emission angle of the isobar is approximated usingeqs 7 and 8 with the coefficients ank listed in Table 3 of Reference17; isotropy of the decay of the isobar in its c.m. system isassumed.

In order to calculate the kinematics of the non-resonant partof the reaction (4) and two remaining three-body channels (5)and (6), the Dubna INC uses the statistical model. The totalenergies of the two particles (pions) in the c.m. system aredetermined from the distribution

~(E– Eπ1– Eπ2)Eπ1 Eπ2 / E , (11)

and that of the third particle (nucleon, N) from conservation ofenergy. The actual simulation of such reactions is done asfollows: Using a random number ξ, we simulate in the begin-ning the energy of the first pion using

Eπ1 = mπ1 + ξ (E π1max – mπ1),

where

E π1max = [E 2 + m2π1 – (mπ2 + mN)

2]/2E .

Then, we simulate the energy of the second pion Eπ2 accordingto eq 11 using the Monte Carlo rejection method. The energyof the nucleon is then calculated as EN = E– Eπ1 – Eπ2, checking

that the “triangle law” for momenta

pπ1 – pπ2≤ pN ≤ pπ1 + pπ2

is fulfilled, otherwise this sampling is rejected and the procedureis repeated. The angles Θ and ϕ of the pions are sampledassuming an isotropic distribution of particles in the c.m. system,

cos Θπ1 = 2ξ1 – 1, cos Θπ2 = 2ξ2 – 1,

ϕ π1 = 2πξ3, ϕ π2 = 2πξ4,

and the angles of the nucleon are defined from momentumconservation,

rpN = – (

rpπ1 +

rpπ2).

So an interaction of a photon with a nucleon inside a nucleusleads to two or three fast cascade particles. Depending on theirmomenta and coordinates, these particles can leave the nucleus,be absorbed, or initiate a further intranuclear cascade. All theremaining details of the Dubna INC (followed by the evapora-tion/fission of excited nuclei produced after the cascade stageof reactions) calculation are the same as for N+A and π+Areactions and are described in detail in the monograph.16

The Dubna INC PRM was used successfully for many yearsas a stand-alone model to study different aspects of photonu-clear reactions and was also incorporated without modificationsinto the transport codes CASCADE25 and GEANT4,26 and withsome improvements, via CEM95,27 CEM97,28 and CEM2k,4 intothe transport codes MARS1429 and MCNPX,13, 30, 31 respectively.In the middle of the 1970s, one of the authors of the initialversion of the Dubna INC PRM, Iljinov, moved from JINR,Dubna to INR, Moscow and continued to develop further theDubna INC with his Moscow Group, which evolved into whatis now known in the literature as the Moscow INC model (see,e.g. Reference 32 and references therein). The Moscow INCmodel was recently extended to describe photonuclear reactionsat energies up to 10 GeV.33

3. From CEM95 to CEM03

Photonuclear reactions were not considered in the initialversion of the CEM.5 The Dubna PRM was incorporated34 firstinto the CEM9527 version of the CEM and used thereafter toanalyze a large number of photonuclear reactions.35 Later on,CEM95 was incorporated as an event generator into theMARS1429 transport code and used in some applications.

By early 1997, one of the authors of the CEM (SGM) movedfrom JINR, Dubna to LANL, Los Alamos, and continued todevelop further with his collaborators the cascade-exciton modelfor LANL needs, e.g. as an event generator for the Los Alamostransport code MCNPX13 and for other applications.

3.1. New Approximations for p Cross Sections. The firstimprovements in the CEM of the photonuclear mode of theDubna INC was done in the CEM97 version28 of the CEM.The improved cascade-exciton model in the code CEM97differs from the older CEM95 version by incorporating newapproximations for the elementary NN, πN, and γp cross sectionsused in the cascade, using more precise values for nuclearmasses and pairing energies, employing a corrected system-atics for the level-density parameters, adjusting the crosssections for pion absorption on quasi-deuteron pairs inside anucleus, including the Pauli principle in the preequilibriumcalculation, and improving the calculation of fission widths.Implementation of significant refinements and improvementsin the algorithms of many subroutines led to a decrease of thecomputing time by up to a factor of 6 for heavy nuclei, whichis very important when performing simulations with transportcodes.

Concerning specifically the photonuclear reactions, in CEM97we developed improved approximations for the elementary γ pcross sections compared with the Dubna INC PRM.15

γγ

n=0

N

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32

32

dWdM

dWdEπ1 dEπ2

In the Dubna INC PRM15 used in CEM95, the cross sectionsfor the free γ p (and for NN and πN) interactions are approxi-mated using a special algorithm of interpolation/extrapolationthrough a number of picked points, mapping the experimentaldata as possible. This was done very accurately by the authorsof the Dubna INC PRM15 using all experimental data availableat that time, about 35 years ago. Currently there are manymore experimental data on cross section; therefore we revisedthe approximations of all elementary cross sections used inCEM97.28 We collected all published experimental data fromavailable sources, then developed an improved algorithm forapproximating cross sections and developed simple and fastapproximations for elementary cross sections which fit verywell presently available experimental data not only up to ~ 1.5GeV, where the Dubna INC PRM is assumed to be used, or upto about 5 GeV, the upper recommended energy for the presentversion of the CEM for nucleon- and pion-induced reactions,but up to 50 – 100 GeV and higher, depending on availabilityof data. So far we have such approximations for 8 different

types of γ + p elementary cross sections and for 24 types ofreactions induced by nucleons and pions. Cross sections forother types of interactions taken into account by CEM arecalculated from isospin considerations using the former as theinput. These cross sections are used in CEM97,28 CEM2k,4

and CEM03,1 and were incorporated recently into the latestversion of our LAQGSM10 code, LAQGSM03.1, 2

We consider this part of the CEM improvement as an inde-pendently useful development, as our approximations are reli-able, fast, and easy to incorporate into any transport, INC,BUU, or Glauber-type model codes. For example, our newapproximations recently have been successfully incorporatedby Mokhov into the MARS1429 and MARS1511 versions of theMARS code system at Fermilab.

An example of 8 compiled γ + p experimental cross sectionstogether with our new CEM03 approximations and the oldapproximations from the Dubna INC PRM used in CEM95 isshown in Figure 1. We see that these approximations describeall data very well. Although presently we have much more

CEM03 and LAQGSM03 A3J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005

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Figure 1. Comparison of eight experimental total γ + p(d) cross sections with the old approximations from the Dubna INC PRM and with our newapproximations incorporated into the CEM03 and LAQGSM03 codes. Experimental data (circles and squares) are compiled from: γ + p → p + π0:Refs. 36−45; γ + p → n + π+: Refs. 36−39 and 46−51; γ + d → n + p: Refs. 23, 37, and 52−72; γ + p → p + π+ + π−: Refs. 37, 42, and 73−76; γ + p→ p + 2π0: Refs. 73 and 77−79; γ + p → n + π+ + π0: Refs. 73, 80, and 81; γ + p → ∆++ + π−: Ref. 37; γ + p total cross sections: Refs. 23, 37, 51, and52, respectively. The squares show recent experimental data that became available to us after we completed our fit; although these recent data agreereasonably well with our approximations, a re-fitting would slightly improve the agreement.

data than 35 years ago when the Dubna group produced theirapproximations used in the Dubna INC PRM,15 for a numberof interaction modes like the total γp cross sections at energiesbelow 1.2 GeV (where the initial Dubna INC PRM wasassumed to be used), and for such modes as γ + p → p + π0, γ+ p → n + π+, γ + p → p + π+ + π−, and γ + d → n + p, at ener-gies not too close to their thresholds, the original approxima-tions also agree very well with presently available data, in theenergy region where the Dubna INC PRM was developed towork. This is a partial explanation of why the old DubnaINC16 and the younger CEM9527 describe so well many char-acteristics of different nuclear reactions. On the other hand,for some elementary cross sections like γ + p → p + 2π0 and γ+ p → n + π+ + π0, the old approximations differ significantlyfrom the present data, demonstrating the need for a betterdescription of all modes of photonuclear reactions. (Similarresults were obtained in CEM9728 for hadron-hadron crosssection approximations.)

The CEM97 code with these cross sections and the othermentioned improvements was incorporated by Gallmeier30 intothe MCNPX transport code,13 allowing MCNPX to consider forthe first time interaction of intermediate-energy photons withthick targets of practically arbitrary geometry.

3.2. New Approximations for Differential + p CrossSections. The CEM2k4 version of CEM is a “new generation”of the CEM following CEM97.28 Its development was partially

motivated by the availability of some new, very precise anduseful experimental data obtained recently at GSI in Darmstadt,Germany, where a large number of measurements have beenperformed using inverse kinematics for interactions of 56Fe,197Au, 208Pb, and 238U at 1500, 1000, 800, 750, 500, and 300MeV/nucleon with liquid 1H. These measurements provide alarge set of cross sections for production of practically allpossible isotopes from such reactions in a “pure” form, i.e.individual cross sections from a specific given bombardingisotope (or target isotope, when considering reactions in theusual kinematics, p + A). Such cross sections are much easierto compare to models than the “camouflaged” data from γ -spectrometry measurements. In addition, many reactionswhere a beam of light, medium, or heavy ions with energy nearto or below 1 GeV/nucleon interact with different nuclei, fromthe lightest, d, to the heaviest, 208Pb, were measured recently atGSI. References on these measurements and many tabulatedexperimental cross sections may be found on the Web page ofSchmidt.82

(We have analyzed with CEM2k and LAQGSM all measure-ments done at GSI of which we are aware, both for proton-nucleus and nucleus-nucleus interactions; some examples ofour results compared with the GSI data and calculations byother available models may be found in Reference 3 and refer-ences therein.)

During the development of the CEM2k version of CEM and

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Figure 2. Example of eight angular distributions of π0 from γ p → π0p as functions of Θπc.m.s at photon energies from 260 MeV to 1.4 GeV. Thedashed lines show the old approximations of the Dubna INC PRM while the solid lines are our new approximations incorporated into the CEM03and LAQGSM03 codes. Experimental data are shown by symbols and are from: CL75,83 GE74,84 FI70,85 MC57,86 AL78,87 WA55,88 YO77,89

BE73,90 AL76,91 DE65,92 FE74,93 WO68,94 WE78,95 DE69,96 WO60,97 HU77,98 BA75,99 JA60,100 AL79,101 and LO70;102 tabulated values are avail-able at: http://wwwspires. dur.ac.uk/ hepdata/reac2.html.

of LAQGSM, we concentrated mainly on proton-nucleus andnucleus-nucleus reactions and tried to improve the generaldescription of different types of nuclear reactions by our models,without focusing specifically on photonuclear reactions. Themain difference of CEM2k from its precursor CEM97 is in thecriterion for when to move from the intranuclear-cascade stageof a reaction to its preequilibrium stage, and when to move fromthe latter to the evaporation/fission slow stage of the reaction. Inshort, CEM2k has a longer cascade stage, less preequilibriumemission, and a longer evaporation stage with a higher excitationenergy, as compared to CEM97 and CEM95. Besides thesechanges to CEM97, we also made in CEM2k a number of otherimprovements and refinements, such as imposing momentum-energy conservation for each simulated event (the Monte Carloalgorithm previously used in CEM provides momentum-energyconservation only statistically, on the average, but not exactlyfor each simulated event); using real binding energies fornucleons at the cascade stage of a reaction instead of the approx-imation of a constant separation energy of 7 MeV used in theprevious versions of the CEM; using reduced masses of particlesin the calculation of their emission widths instead of using theapproximation of no recoil used in the previous versions; andcoalescence of complex particles from fast cascade nucleonsalready outside the nucleus. On the whole, CEM2k describesmany nuclear reactions, including the ones induced by photonsbetter than CEM97 and CEM95 do. CEM2k was incorporated

by Gallmeier into MCNPX to replace CEM97, and this versionof MCNPX was extended by him to describe photonuclearreactions also in the GDR region31 (as a stand-alone code,CEM2k was developed to describe photonuclear reactions onlyat energies above the GDR region).

We have focused on the improved description of specificallythe photonuclear reactions when developing our latest versionof CEM, CEM03.1 Although CEM97 contained new approxi-mations and algorithms to better describe the integrated ele-mentary NN, πN, and γN cross sections as mentioned above,the double differential distributions of secondary particles fromsuch interactions were simulated by CEM2k and all its precur-sors using the old Dubna INC approximations (7)– (11) for γ preactions (and similar relations, for NN and πN collisions).These were obtained by Gudima et al.15, 21, 22 36 years ago, usingthe measurements available at that time. In CEM03, for NNand πN collisions, we addressed this problem by developing newapproximations similar to (7) – (11) and by using recent sys-tematics by other authors, based on the experimental data avail-able today (see details on NN and πN reactions in Reference 1).In the case of γ p reactions (2) and (3), we chose another way:Instead of fitting the parameters an from eq 7 at different Eγ wefound data (see, e.g. Figures 2 and 3) and finding the energydependence of parameters ank in eq 8 using the values obtainedfor an as was done in the old Dubna INC, we took advantage ofthe event generator for γ p and γ n reactions from the Moscow


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Figure 3. Example of eight angular distributions of π+ from γp → π+n as functions of Θπc.m.s at photon energies from 200 MeV to 1.52 GeV. Thedashed lines show the old approximations of the Dubna INC PRM while the solid lines are our new approximations incorporated into the CEM03and LAQGSM03 codes. Experimental data are shown by symbols and are from: AD67,103 AD60,104 AL63,105 FR65,106 BE56,107 WA55,108 FU77,109

FI72,110 BE68,111 CL75,83 BE63,112 DI60,113 DA73,114 FI71,115 AL83,116 EC67,117 AL70,118 BU67,119 ZH03,120 and EK72;121 tabulated values are avail-able at: http://wwwspires.dur.ac.uk/ hepdata/reac2.html.

INC33 kindly sent us by Pshenichnov. That event generatorincludes a data file with smooth approximations through presentlyavailable experimental data at 50 different gamma energiesfrom 117.65 to 6054 MeV (in the system where the p or ninteracting with γ is at rest) for the c.m. angular distributionsdσ /dΩ of secondary particles as functions of Θ tabulated forvalues of Θ from 0 to 180˚ with the step ∆Θ = 10˚ for 60 dif-ferent channels of γ p and γ n reactions considered by theMoscow INC (see details in Reference 33). We use part ofthat data file with data for reactions (2) and (3), and have writ-ten an algorithm to simulate unambiguously dσ /dΩ and tochoose the corresponding value of Θ for any Eγ , using a singlerandom number ξ uniformly distributed in the interval [0,1].This is straightforward due to the fact that the function ξ(cos Θ)

ξ(cos Θ) = dσ /dΩ dcos Θ / dσ /dΩ dcos Θis a smooth monotonic function increasing from 0 to 1 as cosΘ varies from –1 to 1. Naturally, when Eγ differs from thevalues tabulated in the data file, we perform first the neededinterpolation in energy. We use this procedure to describeangular distributions of secondary particles from reactions (2)and (3), as well as for isotopically symmetric reactions γ + n→ n + π0 and γ + n → p + π− in CEM03.

Examples of eight angular distributions of π0 from γ p → π0pand of π+ from γ p → π+n as functions of Θπc.m.s are presented inFigures 2 and 3. We see that the approximations developed inCEM03 (solid histograms) agree much better with the avail-able experimental data than the old Dubna INC approxima-tions (7) – (8) used in all precursors of CEM03 (dashedhistograms).

4. New Approximations for + A Absorption Cross Sections

CEM03 (and its predecessors) does not consider absorptionof low energy photons in the GDR region and takes intoaccount photoproduction on free nucleons of only two pions.This restricts its applicability to the range 30 MeV ~< Eγ ~< 1.5GeV, which is not convenient when it is used as an eventgenerator in a transport code.

To extend the applicability of CEM03 (and LAQGSM03)into the GDR region, it is necessary to omit the intranuclearcascade (INC) and to consider such reactions as starting withthe preequilibrium model. The INC used by CEM03 as thefirst stage of arbitrary reactions is a semiclassical model thatdoes not consider any collective degrees of freedom of a nucleus,including the GDR; in addition, the photon-energy in the GDRregion is too low to justify the use of any INC. In our approach,it is possible to deal with this limitation as was done 30 yearsago,122 using the Modified Exciton Model (MEM)123, 124 used in the initial version of CEM5 and 25 years later,125 using animproved version of the MEM contained in the CEM9527 code.We plan to extend CEM03 to describe photonuclear reactionsin the GDR region in the near future, but this requires a largeamount of tedious work: 1) to make sure that we use the mostreliable parameters of the GDR for all nuclei, 2) to define anoptimal transition from the current three-stage (INC, preequi-librium, and evaporation/fission) description of reactions to atwo-stage approach needed in the GDR region, and 3) to testthe extended model against the available experimental data.

To describe properly with CEM03 and LAQGSM03 pho-tonuclear reactions above Eγ ~ 1.5 GeV, it is necessary to takeinto account production of more than two pions in γN colli-sions, as well as to consider production of resonances heavierthan ∆(1232), as has been done, i.e. in the Moscow INC.33 Weplan to extend CEM03 and LAQGSM03 to higher Eγ in subse-quent versions.

In the meantime, it is possible to get quite reasonable resultsfor spectra of emitted nucleons and complex particles and for

the nuclide production cross sections with our present CEM03model for photonuclear reactions both in the GDR region andat Eγ ~> 1.5 GeV, by employing a correct total photoabsorptioncross section. Indeed, CEM03 starts a reaction in the GDRregion with a cascade and since the γ energy is below the pion-production threshold, the only available reaction channel is toabsorb such photons on a quasi-deuteron pair of nucleons,generating two “cascade” nucleons inside the nucleus. As theenergy of these nucleons is low, ~ 10 MeV, these nucleons are“absorbed” by the nucleus generating two excited nucleons(excitons) and two holes, then CEM03 would proceed with thisprocess as a preequilibrium reaction followed by evapora-tion/fission. All the real calculation of such reactions would bedone with only the preequilibrium and evaporation models andthe INC would serve only to provide the number of excitons,as an input to the MEM. At the end of the calculation, the totalphotoabsorption (reaction) cross section is needed to normalizethe results. CEM03 (and most other INC models) calculatesthe total reaction cross section, σin, by the Monte Carlo methodusing the geometrical cross section, σgeom, and the number ofinelastic, Nin, and elastic, Nel, simulated events, namely: σin =σgeomNin/(Nin + Nel). This approach provides a good agreementwith available data for reactions induced by nucleons, pions,and photons at incident energies above about 100 MeV, but isnot reliable at energies below 100 MeV (see, e.g. Figures 3 and4 and Reference 7).

To address this problem for photonuclear reactions, we havewritten a FORTRAN routine called GABS.FOR based on therecent approximation by Kossov,18 that provides reliable pho-toabsorption cross sections on arbitrary targets at all energiesfrom the hadron production threshold to about 40 TeV. Wehave added GABS.FOR to CEM03 to normalize our photonu-clear results to this systematics rather than to σin calculated bythe Monte Carlo method, as we have done previously. (As arule, we use LAQGSM03 only at energies above several GeV,where CEM03 becomes already not reliable; at such high ener-gies, LAQGSM03 describes quite well σin and does not requirerenormalization of its results to any systematics; therefore wedo not incorporate GABS.FOR into LAQGSM03.)

The Kossov approximation18 of the energy dependence ofphotonuclear cross sections is subdivided into three mainregions: the GDR region, the nucleon resonance region, andthe high-energy region. Its functional form is also subdividedinto three groups depending on the mass number of the target:the σγ p cross section, the cross section for γ d reactions, and theσγA cross section for A > 2.

We note that eq 41 in Reference 18 was misprinted in theoriginal publication by Kossov, where a “+” sign occursinstead of a “–” sign. The misprinted formula does not repro-duce the cross sections presented in Reference 18, whereas thecorrected version does.

Figures 4 and 5 show examples of twelve photoabsorptioncross sections on several light, medium, and heavy nuclei. Inthese figures, we compare predictions of the Kossov system-atics as implemented in the routine GABS.FOR with availableexperimental data and with the Los Alamos National Labora-tory (LANL), Korean Atomic Energy Institute (KAERI), andthe Institute of Physics and Power Engineering (IPPE),Obninsk, Russia and the Center for Photonuclear ExperimentalData [Centr Dannykh Fotoyasdernykh Eksprtimentov (CDFE),in Russian], Moscow, Russia, Modified (MOD) Library ofPhotonuclear Data [Biblioteka Fotoyadernykh Dannykh(BOFOD), in Russian], BOFOD(MOD), evaluations from theIAEA Photonuclear Data Library,126 as well as with calcula-tions by two older versions of CEM, namely, the CEM95 pho-tonuclear code version34 and CEM2k as modified by Gallmeier31

for MCNPX. The Kossov systematics describe well the experimental

photoabsorption cross sections and agree with the LANL,

γγ


–1

cosΘ 1

∫∫ –1∫∫

KAERI, and the BOFOD evaluations, especially for heavytargets. For 12C, 27Al, and 63Cu (and several other nuclei wetested but did not include in Figures 4 and 5) the agreement inthe GDR region is not so good. This is because we use herethe “global” approximation given by the Kossov systematics tocalculate the photoabsorption cross section in the GDR regionfor all nuclei. It is known from the literature that the GDR oflight nuclei differ significantly from the ones of heavy nuclei,and should be addressed carefully for each light nucleus sepa-rately. In fact, Kossov18 had fitted the parameters of the lightnuclei separately and his results shown in Figures 2 to 7 ofReference 18 for the light nuclei agree better with the data thanthe “global” systematics shown here does. Unfortunately, Kossovdid not publish the parameterization of the GDR he found forevery light nucleus in Reference 18 (some details of this arelisted in the recent GEANT4 Physics Reference Manual156 andin Reference 157, but only for some light nuclei, and thosedetails differ from what is published in Reference 18). To fillthis gap, we hope to determine ourselves a parameterization ofthe GDR photoabsorption on light nuclei using all available

experimental data.

5. Illustrative Results

In this Section, we present several illustrative results fromCEM03 and LAQGSM03 extended to describe photonuclearreactions. Let us start with photofission cross sections. Wehave compiled from the literature all reliable experimental dataon photofission cross sections that we could identify and haveanalyzed them with both CEM03 and LAQGSM03. Figure 6shows a comparison of such data for 197Au, 208Pb, 209Bi, 232Th,233U, 235U, 238U, and 237Np with the results of CEM03, as well asto several earlier versions, namely, the photonuclear versions ofCEM95,34 CEM98,158 CEM2k+GEM2,8 and by the modifiedversion of CEM2k incorporated into MCNPX by Gallmeier.31

The CEM03 results agree well with the experimental fissioncross sections, and better than the results of the earlier models.The Kossov approximation for the total photoabsorption crosssections in CEM03 (and CEM2k+GEM2) allows us to describethe fission cross section, not only for photon energies from ~ 30


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Figure 4. Examples of total photoabsorption cross sections for 12C, 16O, 27Al, 40Ca, 63Cu, and 109Ag as functions of photon energy. The thick solid linesmarked as “GABS.FOR” are from our subroutine written to reproduce Kossov’s18 systematics, as described in the text. The thin solid line markedas “LANL” (or “KAERI”, for 109Ag) show the evaluations by LANL (or KAERI, for 109Ag) from the IAEA Photonuclear Data Library.126 Resultsfrom the photonuclear version of CEM9534 and from CEM2k as modified for MCNPX by Gallmeier31 are shown by the long-dashed and dashedlines, respectively. Experimental data (symbols) are from: AHR85,127 BRU73,128 BIA96,129 BUR63,130 ARA83,131 ARA85,132 MUC99,133

WYC65,134 AHR75,135 ARE81,136 MIC77,137 ARA78,138 and CAL73.139

MeV to ~ 1.5 GeV, where the model is expected to be reliable,but also outside this region, i.e. in the whole range from 10 MeVto 5 GeV.

This is an example of getting reasonably good resultsoutside the region where the model is justified, as discussed inthe previous section. Results of LAQGSM03 for these fissioncross sections practically coincide with the ones by CEM03above the GDR region, as the calculation of fission crosssections in CEM03 and LAQGSM03 were developed to be(see details in Reference 8), but are significantly lower than thedata in the GDR region, as LAQGSM03 does not use theKossov approximation and so should not be applied in theGDR region. Results of CEM95, CEM98, and CEM2k arealso below the data in the GDR region, for the same reason.

We note that all the CEM03 and LAQGSM03 results shownin Figure 6 and in the following figures are obtained using defaultand fixed values of all parameters, without fitting anything. Weonly specify the energy of the incident photons and A and Z ofthe target in the inputs to CEM03 (and CEM2k+GEM2) andLAQGSM03, and then calculate. CEM95, CEM98, and CEM2k

use a parameter whose value affects drastically the calculatedfission cross sections, just as in many similar statistical models:This is the ratio of the level density parameters used in the fissionand evaporation channels, af /an (or, Bs, in the case of CEM98,see details in Reference 158). The fission cross sections calcu-lated by any code employing the statistical evaporation andfission models depend so much on af /an that by fitting this ratioto available data it is possible to get a good agreement with themeasured data (but not to predict unmeasured fission crosssections) with any reasonable values for the fission barriers,nuclide masses, pairing energies, and deformations, for anyparticular measured reaction. This is why some publishedpapers that analyze fission cross sections or even pretend toobtain “experimental fission barriers” without addressing thequestion of af /an are of low significance. In our CEM95,CEM98, and CEM2k calculations, we use the default optionsfor nuclear masses, pairing energies, and fission barriers (the“recommended” options, in the case of CEM95, where severaloptions are available in its input; see details in Reference 27),but we still need to define (more exactly, to fit) the values of


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Figure 5. Examples of total photoabsorption cross sections for 118Sn, 181Ta, 197Au, 208Pb, 232Th, and 238U as functions of photon energy. The thicksolid lines marked as “GABS.FOR” are results by our subroutine written to reproduce Kossov’s18 systematics, as described in the text. The thinsolid line marked as “LANL”, “KAERI”, or “BOFODM” show the evaluations by LANL, KAERI, or by a collaboration between IPPE/ Obninsk andCDFE/Moscow (the BOFOD(MOD) Library) from the IAEA Photonuclear Data Library.126 Results from the photonuclear version of CEM9534 andfrom CEM2k as modified for MCNPX by Gallmeier31 are shown by the long-dashed and dashed lines, respectively. Experimental data (symbols) arefrom: BIA96,129 BRU73,128 LEP81,140 MUC99,133 FUL69,141 GUR81,142 TAV93,143 TER96,144 TER98,145 MAR89,146 MAR91,147 MIC77,137

ARA78,138 CHO83,148 CAL73,139 AHR85,127 GUR76,149 BIR76,150 GUR74,151 SHE85,152 TAV91,153 ARA90,154 and BIA93.155

af /an (or, Bs, in the case of CEM98): These values are listed onour plots in Figure 6. Naturally, CEM2k+GEM2, CEM03, andLAQGSM03 also had the problem of af /an in the beginning, butthis problem was solved in Reference 8 by fitting these parame-ters for proton-induced measured fission cross sections for alltargets for which we found data, at all incident energies, and bytheir extrapolation/interpolation for unmeasured targets. Thefitted values are fixed and are used in all our further CEM03 andLAQGSM03 calculations without subsequent variation; thisallows us not only to describe well most of the measured databut also to predict reasonably well unmeasured fission crosssections. The fitting procedure8 was done so that both CEM03(and CEM2k+GEM2) and LAQGSM03 describe as well aspossible all available proton-induced measured fission crosssections; this is why the fission cross sections calculated by CEM03practically coincide with the ones obtained by LAQGSM03 andwith the experimental data.

We note that both CEM03 and LAQGSM03 assume that thereactions occur generally in three stages (see e.g. Reference 185).The first stage is the IntraNuclear Cascade (INC), in whichprimary particles can be re-scattered and produce secondaryparticles several times prior to absorption by, or escape from thenucleus. When the cascade stage of a reaction is completed, both

our codes use the coalescence model described in Reference 186to “create” high-energy d, t, 3He, and 4He by final-state interac-tions among emitted cascade nucleons, already outside of thetarget. The emission of the cascade particles determines theparticle-hole configuration, Z, A, and the excitation energy that isthe starting point for the second, pre-equilibrium stage of thereaction. The subsequent relaxation of the nuclear excitation istreated in terms of the modified exciton model of pre-equilibriumdecay followed by the equilibrium evaporation/fission stage ofthe reaction. Generally, all four components may contribute toexperimentally measured particle spectra and other distribu-tions. But if the residual nuclei after the INC have atomicnumbers with A ≤ 12, both CEM03 and LAQGSM03 use theFermi break-up model described in Reference 10 to calculatetheir further disintegration instead of using the preequilibriumand evaporation models. The Fermi break-up is much fasterthan, and gives results very similar to, the continuation of themore detailed models to much lighter nuclei.

Figures 7 and 8 show two examples of proton spectra calcu-lated by CEM03 and LAQGSM03 compared with the experi-mental data for the reactions 300 MeV γ + Cu187 and 198 MeVγ + C,188 respectively. Both codes describe quite well theproton spectra in the case of copper, but less well for carbon.


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Figure 6. Comparison of the calculated photofission cross sections on 197Au, 208Pb, 209Bi, 232Th, 233U, 235U, 238U, and 237Np with the experimental data(symbols), results by the previous versions of CEM (see details and references in the text), and the statistical evaluation by Varlamov et al. fromindependent measurements,159 as indicated. Experimental data are from: TER98,145 TER96,144 MAR89,146 MAR91,147 LU89,160 AND72,161 TER92,162

CET02,163 LEM80,164 BEL83,165 MOR69,166 MIN57,167 TER96a,168 RAN67,169 GUA87,170 JUN57,171 CAL80,172 KAP69,173 LEP87,174 VEY73,175

ZHA86,176 BER86,177 DEM93,178 HUI62,179 OST78,180 VAR87,159 REI84,181 FRO94,182 CES83,183 OST78,180 and SOL97.184

Figure 9 shows examples of π+ angular distributions from213 MeV γ ’s interacting with Pb, Sn, Ca, and C targets. Onecan see that the π+ angular distributions calculated by CEM03agree reasonably well with the experimental data189 for C, Ca,and Sn targets, but underestimate by a factor of 2 to 3 the Pbdata. We do not have a good understanding of this disagree-ment. One possible explanation of this would be if CEM03absorbs too strongly the low-energy pions produced in γ pcollisions inside the target. The heavier the target the biggerwould be this effect, therefore we may see it with Pb but notobserve it for C, Ca, and Sn targets. There also could be prob-lems with the experimental data for Pb. As noted in Reference189, there is a systematic error in these data associated withthe correction for the electron contamination in the yield forthe forward detectors with Z ≥ 20 targets. For instance,because of the magnitude of this background, no experimentalcross sections are reported for the Pb target at 51˚.189

We now consider another type of photonuclear reaction,induced by bremsstrahlung photons. In contrast to reactionsinduced by monoenergetic photons of a given energy E, thebremsstrahlung beam is produced by monoenergetic electronsand has a spectrum of photon energies E of the form N(E, E0) ~1/E,190 from 0 to E0, where the end-point energy E0 is the

maximum energy of photons produced by the given electronbeam. In addition, all the experimental characteristics for reac-tions induced by bremsstrahlung photons are normalized per“equivalent quanta”, Q, defined as:

Q = E ·N(E, E0)dE / N(E, E0)dE. (12)As discussed above, CEM03 and LAQGSM03 do not describeproperly photonuclear reactions in the GDR region, we cancalculate bremsstrahlung reactions with our codes while limitingourselves to photon energies only above the GDR region.

This means that we need to simulate the energies of thebremsstrahlung photons according to their spectrum N(E, E0)~ 1/E up to E0 not from 0, but from a value Emin, above theGDR region in our calculations, and we need to use Emin for thelower limits of the integrals in eq 12 instead of 0 in calculatingthe number of equivalent quanta Q. This is easy to do in ourMonte Carlo calculations. After simulation of Nin numbers ofinteractions of bremsstrahlung gammas of energy Ei with anucleus, the number of equivalent quanta Q will be:

Q = ∑Ei = , (13)

where the mean energy of the bremsstrahlung photons isequal to

= = , (14)

and Emin ≤ Ei ≤ E0. In the present paper, we use Emin = 30 MeVfor all the reactions we discuss. The total inelastic (photoab-sorption) cross section σ in in the case of bremsstrahlungphotons is calculated as following:

σin = = , (15)

where σγin(Ei) is the photoabsorption cross section by a nucleusof a photon with Eγ = Ei, simulated in a particular Monte Carloevent i.

By using here a value of 30 MeV instead of 0 for Emin, wewill miss the products from interaction of γ with energies


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below 30 MeV, like the cross sections for (γ, n), (γ, 2n), and, toa certain degree, (γ, np) in our results, but this limitation doesnot affect at all the description of products in the deep spalla-tion, fission (for preactinides), and fragmentation regions, aswell as the pion photoproduction and spectra of nucleons andcomplex particles at energies above the evaporation region.

Figures 10 and 11 present examples of proton and π+ spectrafrom bremsstrahlung interaction with carbon at E0 = 1050 and305 MeV, respectively. One can see that CEM03 describeswell both the measured proton and pion spectra and agreeswith the data better than the direct knockout model192 and thequasi-deuteron calculations193 do.

Since the 1980s, a large number of radiochemical measurementsof bremsstrahlung-induced reactions have been performed inJapan by the group of Sakamoto (see the recent reviews195, 196

and references therein). Thousands of useful product crosssections were measured by this group on target nuclei from 7Lito 209Bi at bremsstrahlung end-point energies E0 from 30 MeVto 1.2 GeV, including photopion reactions, fragmentation andfission of preactinides, deep spallation reactions, and recoilstudies (mean kinetic energy and the forward/backward (F/B)ratios of products). The authors of these measurements haveanalyzed most of their data with the PICA code by Gabriel etal.197, 198 with its improved version PICA95,199, 200 as well as withits latest version, PICA3, merged201 with the GEM evaporation-fission code by Furihata9 mentioned above, i.e. PICA3/GEM.

Recently, this group provided us with numerical values ofsome of their measured reactions and we have calculated themwith CEM03. Figure 12 shows an example of the comparisonof CEM03 results with data for bremsstrahlung-induced fissioncross sections of 197Au202 and 209Bi,203 compared as well withother available experimental data for Au169, 171, 204−209 and forBi,166, 169, 171, 207, 208, 210−212 and with results by PICA3/GEM201

from Reference 203. There is a reasonable agreement of theCEM03 results with the experimental data in the whole intervalof E0 measured, from the threshold to the highest measuredenergy.

Figure 13 presents the experimental data202, 203, 213−216 and thecalculations by PICA3/GEM201 and by CEM03 for the massyields of products produced by bremsstrahlung reactions on197Au and 209Bi at E0 = 1 GeV. For convenience, all theisotopes produced in these reactions were divided into fourgroups, namely: 1) spallation products produced by sequentialemission of several nucleons, positive pions, and complex


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γ(Emax =305 MeV) + 12C → π+ + ...

Tπ /MeV

d2σ

/dT

/dΩ

/Q (

µb/M

eV/s

r/Q

)

Figure 11. Comparison of measured194 differential cross section for π+

photoproduction on carbon at 90˚ by bremsstrahlung photons withEmax(≡ E0) = 305 MeV (circles) with CEM03 calculations (histogram).

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Direct knockout

Quasideuteron

Tp /MeV

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/(dT

·dΩ

)/µb

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Figure 10. Comparison of measured191 differential cross section for pro-ton photoproduction on carbon at 43˚, 90˚, and 154˚ by bremsstrahlungphotons with Emax(≡ E0) = 1.05 GeV (symbols) with CEM03 calcula-tions (histograms), and predictions by the direct knockout model192

(dashed lines) and a quasideuteron calculation193 (dotted lines), respec-tively. The experimental data and the results by the direct knockoutand quasi-deuteron models were taken from Figure 5 of Ref. 192.

0 500 1000 1500 2000

This workJungerman and SteinerRanyuk and SorokinMethasiri and JohanssonKroon and ForkmanAndersson et al.David et al.Vartapetyan et al.Emma et al.Kiely et al.PICA3/GEMCEM03

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E0 / MeV

(b)

Figure 12. Bremsstrahlung-induced fission cross sections of 197Au (a)and 209Bi (b) as functions of the end-point energy E0. The experi-mental data for Au indicated in the insert of the figure as “This work”are from Ref. 202; other experimental data on Au are from Refs. 169,171, and 204–209, as indicated. The data for Bi indicated as “Thiswork” are from Ref. 203 and other data for Bi are from Refs. 166,169, 171, 207, 208, and 210–212, as indicated. The PICA3/GEM201

results shown with filled circles are from Ref. 203; our presentCEM03 results are shown with crossed squares. We thank Haba formaking this figure for us by adding our CEM03 results to Figure 19 ofthe review.195

particles during the INC, followed by preequilibrium and evap-oration processes; 2) intermediate-mass nuclides produced viafission of excited compound nuclei; 3) light fragments emittedeither via evaporation or by “fragmentation” (Fermi break-upmodel, in the case of our present results), and 4) “photopion”products produced in (γ, π− xn) and (γ, 2π− xn) reactions, wherethe charge of the products is higher than that of the initialtarget. One can see that CEM03 describes quite well the yieldsof products in all these groups and agrees with the experi-mental data and results by PICA3/GEM. CEM03 does notdescribe well the spallation products very near the target, thatare produced via (γ, xn) reactions, because it does not considerphotons with energies in the GDR region (Emin = 30 MeV), asdiscussed above.

Some of the experimental data points in the spallation region(in the case of 197Au) are overestimated by calculations up to afactor of two or three, while some of the experimental yields inthe fission region are underestimated up to a factor of five ormore. We do not have yet a clear understanding of this dis-agreement and we plan to address it in the future. Comparingour calculation results with experimental data isotope-by-iso-tope, as we did earlier for proton-induced reactions (see, e.g.Reference 3 and 217 and references therein), rather than themass distributions, may help us understand better and solvethis problem. We plan to perform such an analysis of isotopicyields from photonuclear reactions in the future.

Our preliminary analysis shows that CEM03 also allows us

to describe the recoil properties (forward and backward productyields, their F/B ratio, and mean kinetic energies) of nuclidesproduced in bremsstrahlung-induced reactions on medium andheavy targets at intermediate energies (see Reference 196 andreference therein). We plan to publish our analysis in a futurepaper. Below, we present only several predictions by CEM03for the bremsstrahlung-induced reaction on Au at E0 = 1 GeV,as we find such results informative and useful to better under-stand the mechanisms of nuclear reactions.

Due to the momentum transferred by the bombardinggammas to the nuclear target, one may expect that most of thespallation products would fly in the forward direction in thelaboratory system. The lower-right plot in Figure 14 shows themean laboratory angle Θ of all products as a function of A.We see that the mean angle of the spallation products ispredicted by CEM03 to be between 72 and 80 degrees. (It isnot equal to 0 degrees, as the probability of projectiles to havean impact parameter exactly equal to zero is equal to zero, andphotons hit more often the periphery of the nucleus rather thanits center.) The thick solid curve in the upper-left plot ofFigure 14 shows the yield of all products as a function of A,the same results compared in Figure 13 with the experimentaldata and the calculations by PICA3/GEM. Besides the totalyield, this plot shows also its components from nuclidesproduced in the forward (thick long-dashed line) and backward(thin dotted line) directions. One can see that for all the spalla-tion isotopes, the cross sections for the forward products areabout a factor of two higher than those for backward products,


0 40 80 120 160 200

Product mass number, A0 40 80 120 160 200

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Figure 14. Results by CEM03 for 1 GeV bremsstrahlung-inducedreactions on Au. Upper left plot: mass yield of all products (thicksolid line), isotopes produced in the forward laboratory direction(thick long-dashed line), and backward products (thin dotted line);Upper right plot: mean laboratory kinetic energy of all products (solidline) and of only forward (long-dashed line) and backward products(dotted line); Lower left plot: mean laboratory velocity vz of all prod-ucts in the beam direction; Lower right plot: mean laboratory angle Θof all products as a function of A. The big fluctuations in the values ofvz and Θ for masses around A = 20 and 130 do not provide real phys-ical information, as they are related to the limited statistics of ourMonte Carlo simulation caused by the very low yield of isotopes at theborder between spallation and fission, and at that between fission andfragmentation. Our calculation provides only a few (or even one)isotopes of a given A in these mass regions, and mean values for suchevents do not have any significance.

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mb/

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.Y

ield

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b/eq

.q.

fissionspallation

fragmentation

photopion

Product mass number

7Be

10Be

22Na

24Na28Mg

ExperimentalPICA3/GEMCEM03

197Au target

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ExperimentalPICA3/GEMCEM03

209Bi target

Figure 13. Comparison of CEM03 results for the mass yields of prod-ucts produced by bremsstrahlung reactions on 197Au and 209Bi at E0 = 1GeV with the experimental data202, 203, 213−216 and the calculations byPICA3/GEM.201 The experimental yields from fission of 197Au and209Bi are from Ref. 213; those by spallation on 197Au are from Refs.214 and 216; those by fragmentation of 197Au are from Ref. 215; thePICA3/GEM results are from several publications of Sakamoto’s groupand are presented in Figure 18 of the review195 with the correspondingcitations. The mass yields for the fission products shown by blackcurves represent approximations based on the experimental data obtainedin Refs. 202 and 203. We thank Matsumura for making this figure for usby adding our CEM03 results to Figure 18 of the review.195

in complete accordance with the available experimental data(see the review196 and references therein). But the situationchanges completely for fission products: The momenta of thefissioning nuclei is small, their mean kinetic energy in thelaboratory system is a few MeV (see the upper-right plot inFigure 14), that is much less than the kinetic energy from severaltens to about a hundred MeV that fission fragments receive dueto the Coulomb repulsion of the fragments. If we neglect theeffects of angular momentum, the fission fragments would bedistributed isotropically in the system of the fissioning nucleus,and the small momentum of the fissioning nuclei makes thisdistribution almost isotropic also in the laboratory system. Theupper left plot of Figure 14 shows that the predicted yields forthe fission fragments in the forward and backward directionsare almost the same, i.e. the F/B ratio for the fission fragmentsis almost equal to one, again in complete agreement with theavailable experimental data (see Reference 196 and referencestherein).

The mean kinetic energy of the forward products shown inthe upper-right plot of Figure 14 is only very slightly higherthan that of the backward products (the momenta of fissioningnuclei are low, as discussed above), with a little higher effectfor the spallation products than for fission fragments, as is tobe expected. Due to this fact and to the near isotropy of thefission fragments, some fission fragments may have their meanvelocity in the direction opposite the beam, as can be seenfrom in the lower-left plot of this figure.

It is much more informative to study the F/B problemconsidering the forward and backward cross sections for everyproduct separately, as shown in Figures 15 and 16, rather thanaddressing only the A-distribution of their yields. Whereas theZ-averaged A-dependence of the F/B ratio is about a factor oftwo for all the spallation region (see also Figure 17), the situa-tion changes for individual isotopes. The cross sections of theforward-emitted isotopes are still about a factor of two higherthan the backward cross sections for most of the spallationproducts, but their ratio is much higher for Hg and Tl, anddepends strongly on the mass numbers of the products. Hgand Tl are “photopion” products produced via (γ, π−xn) and (γ,2π−xn), respectively, with emission of only a few neutrons in


80400 120 160 200Product mass number, A

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rat

io fo

r H

g

CEM03 prediction

γ (E0 = 1 GeV) + 79Au → 80Hg + ...

Figure 17. Upper plot: Z-averaged A-dependence of the F/B ratio ofthe forward product cross sections to the backward ones, as predictedby CEM03 for the reaction of E0 = 1 GeV bremsstrahlung photons onAu. Lower plot: The F/B ratio of the Hg isotopes produced in thesame reaction as a function of the mass number of the Hg nuclei.

17Cl 23V 29Cu 35Br 41Nb 47Ag

18Ar 24Cr 30Zn 36Kr 42Mo 48Cd

19K 25Mn 31Ga 37Rb 43Tc 49In

20Ca 26Fe 32Ge 38Sr 44Ru 50Sn

21Sc 27Co 33As 39Y 45Rh 51Sb

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Figure 16. The same as Figure 15, but for fission and fragmentationproducts.

53I 59Pr 65Tb 71Lu 77Ir

54Xe 60Nd 66Dy 72Hf 78Pt

55Cs 61Pm 67Ho 73Ta

79Au

56Ba 62Sm 68Er 74W

80Hg

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forwardbackward

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ectio

n/µ

b/Q

Mass Number, A

γ (E0 = 1000 MeV) + 197Au

Figure 15. Predicted cross sections of the spallation products from theE0 = 1 GeV bremsstrahlung photon-induced reaction on Au: Opencircles show the yield of the products produced in the forward direc-tion in the laboratory system, while the black circles show results forthe backward products.

addition to the pions. When the number of emitted neutrons issmall, the product “remembers” the momentum transfered tothe target by the projectile, and such neutron-rich products gomainly forward, with a ratio F/B up to ten or higher. On thecontrary, in reactions where many neutrons are emittedapproximately isotropically, the residual nucleus has lost mostof its “memory” of the initial momentum. Therefore theneutron-deficient products from such reactions have a smallerF/B ratio, usually around a factor of two. The farther awayfrom the target are the products, the smaller is this effect; forproducts with Z ~< 70, it practically disappears. Approachingthe border around A = 130 of the transition between spallationand fission products, the F/B ratio decreases and for Ce, La,Ba, Cs, Xe, and I nuclei shown in the left column of Figure 15,the F/B ratio becomes almost equal to one and remains so forall the fission products shown in Figure 16.

The Z-averaged F/B ratio for all nuclides of a given A as afunction of A is presented in the upper plot of Figure 17. Thelower plot of this figure show the F/B ratio for isotopes of Hg:One can see that it decreases from about thirty-seven forneutron-rich 195Hg produced by the 197Au(γ, π−2n) reaction toabout three for neutron-deficient 181Hg produced by the197Au(γ, π−16n) reaction.

We think that an analysis of such recoil characteristics isquite informative not only for photonuclear reactions, but alsofor proton-induced and other types of reactions. Analyses ofthe experimental data for such characteristics would allow us tounderstand better the mechanisms of nuclear reactions and mayhelp us to distinguish the fission processes from the fragmenta-tion (or evaporation) ones in the production of heavy fragmentsfrom reactions on medium-mass targets, like Fe (see discussionof this problem in References 1 and 2). New measurements onthe recoil properties from reactions with any type of projectiles,including bremsstrahlung photons, would be very useful.

6. Conclusions

The 2003 versions of the codes CEM2k+GEM2 andLAQGSM, CEM03 and LAQGSM03, are extended to describephotonuclear reactions. Both our models consider photopro-duction of at most two pions, which limits their reliable appli-cation to photon energies up to only about 1.5 GeV. Thepresent version of our models do not consider photoabsorptionin the GDR region, which defines the lower limit of the photonenergy to about 30 MeV. Nevertheless, developing and incor-porating of a routine based on the phenomenological system-atics for the total photoabsorption cross section by Kossov intoCEM03 allow us to enlarge the region of applicability ofCEM03 and to get quite reasonable results for applicationsboth in the GDR region and above 1.5 GeV.

As shown by several examples, CEM03 and LAQGSM03allow us to describe reasonably well, and better than theirprecursors, many photonuclear reactions needed for applica-tions, as well as to analyze mechanisms of photonuclear reac-tions for fundamental studies. But our models still have severalproblems. Figure 18 shows examples of such problems onproton and deuteron spectra from reactions induced by 60MeV monoenergetic photons on Ca: One can see that bothCEM03 and LAQGSM03 describe reasonably well the shapeof the proton spectrum, but their absolute values differ by morethan a factor of two. This is because the CEM03 results arenormalized to the total photoabsorption cross section predicted

by the Kossov systematics, which gives 3.49 mb for this reac-tion, while the LAQGSM03 results are normalized to the Monte-Carlo-calculated total photoabsorption cross section of 8.5 mb.If we refer to Figure 4, we see that the Kossov systematics forthe reaction γ + Ca predicts values that are a factor of twobelow the available experimental data at energies around 60MeV. This explains the difference between the CEM03 andLAQGSM03 results shown in Figure 18, and suggest that theKossov systematics should be further improved. Even allowingfor this normalization problem, both codes appear to underesti-mate the cross sections for the higher-energy protons.

A further problem shown in Figure 18 is for the spectra ofdeuterons. The predicted spectra of deuterons differ both intheir shapes and absolute values for the two codes. CEM03and LAQGSM03 have different intranuclear-cascade models,leading after the INC stage of any reactions to differentaverage values for A, Z, and E of the excited nuclei, as astarting point for the preequilibrium and evaporation stages ofreactions, where most of the deuterons are produced. Thisexplains the difference in the deuteron spectra predicted by thetwo codes and suggests that further work to improve thedescription of complex-particle emission is necessary.

The overestimation of the high-energy tail of the deuteronspectrum by CEM03 is partially related with an imperfectdescription of the preequilibrium emission of d from this reac-tion, due to an excessively simplified estimation of the proba-bility of several excited nucleons (excitons) coalescing into acomplex particle that can be emitted during the decay of theexcited nuclei produced after the cascade.

We plan to address these problems in the future. In addition,we plan to extend our models to describe photoabsorption inthe GDR region, as discussed previously, and to extend ourmodels to describe photonuclear reactions at energies of 10GeV or more.†

Our present study suggests that analysis of characteristics of


†Actually, after completing the manuscript of the present paper, we have extended already LAQGSM03 to describe photonuclear reactions onnuclei to higher energies, up to 10 GeV and higher. This version of LAQGSM is called LAQGSM03.01. It considers 56 different channels forelementary γ p interactions and 56 channels for similar γn interactions and it is described briefly in our recent LANL paper: S. G. Mashnik, K. K.Gudima, M. I. Baznat, A. J. Sierk, R. E. Prael, and N. V. Mokhov, “CEM03.01 and LAQGSM03.01 Versions of the Improved Cascade-ExcitonModel (CEM) and Los Alamos Quark-Gluon String Model (LAQGSM) Codes,” Los Alamos National Laboratory Research Note X-5-RN (U) 05-11, LANL Report LA-UR-05-2686 (2005). LAQGSM03.01 will be described in details in a separate future paper.

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60 MeV γ + 40Ca → p/d (90 deg) + ...

T / MeV

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/(dT

·dΩ

)/µb

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-1

Figure 18. Examples of two problems with the current versions of ourcodes: proton and deuteron spectra at 90˚ from the reaction 60 MeV γ+ Ca. Symbols are experimental data from Ref. 218, solid lines anddashed histograms are results from LAQGSM03 and CEM03, respec-tively. The CEM03 spectra are normalized to the total absorptioncross section as predicted by Kossov’s systematics, equal to 3.49 mbfor this reaction, while the LAQGSM03 spectra are normalized to theMonte-Carlo total absorption cross section calculated by that code tobe equal to 8.5 mb.

recoil nuclei produced by photonuclear and other types of reac-tions is a powerful tool to understand mechanisms of nuclearreactions. We encourage future measurements of such charac-teristics both for photonuclear and proton-or/and nucleus-induced reactions.

Acknowledgments. We thank Dr. Kumataro Ukai for pro-viding us with numerical values of single pion photoproductioncross sections from their compilation.36 We are grateful to Dr.Igor Pshenichnov for sending us the γ p and γ n event generatorsused in their Moscow photonuclear reaction INC.33 We thankProf. Koh Sakamoto and Drs. Hiroshi Matsumura, HiromitsuHaba, and Yasuji Oura for providing us with their publicationsand numerical tables of their measured data, as well as for usefuldiscussions, help in drawing several figures for us, and theirinterest in our modeling.

This work was partially supported by the Advanced SimulationComputing (ASC) Program at the Los Alamos National Laboratoryoperated by the University of California for the US Departmentof Energy, the Moldovan-US Bilateral Grants Program, CRDFProject MP2-3045-CH-02, and the NASA ATP01 Grant NRA-01-01-ATP-066.

References

(1) S. G. Mashnik, K. K. Gudima, A. J. Sierk, and R. E.Prael, Los Alamos National Laboratory Report LA-UR-04-0039 (2004); Proc. ND2004, Santa Fe, USA, 2004, ed.R. C. Haight, M. B. Chadwick, T. Kawano, and P. Talou,(AIP Conf. Proc. 769, Melville, New York, 2005), p. 1188;E-print: nucl-th/0502019.

(2) S. G. Mashnik, K. K. Gudima, R. E. Prael, and A. J.Sierk, Los Alamos National Laboratory Report LA-UR-03-7277 (2003).

(3) S. G. Mashnik, K. K. Gudima, R. E. Prael, and A. J. Sierk,Proc. Workshop on Nuclear Data for the Transmutation ofNuclear Waste, GSI-Darmstadt, Germany, 2003, ISBN 3-00-012276-1, ed. A. Kelic and K.-H.Schmidt, http://www-wnt. gsi.de/tramu/; E-print: nucl-th/0404018.

(4) S. G. Mashnik and A. J. Sierk, Proc. AccApp2000, WashingtonDC, USA, 2000, (ANS, La Grange Park, USA, 2001), p.328; E-print: nucl-th/0011064.

(5) K. K. Gudima, S. G. Mashnik, and V. D. Toneev, Nucl.Phys. A 401, 329 (1983).

(6) S. G. Mashnik, K. K. Gudima, and A. J. Sierk, Proc. SATIF-6, SLAC, USA, 2002, (NEA/OECD, Paris, France, 2004),p. 337; E-print: nucl-th/0304012.

(7) S. G. Mashnik, A. J. Sierk, and K. K. Gudima, Los AlamosNational Laboratory Report LA-UR-02-5185 (2002); E-print: nucl-th/0208048.

(8) M. Baznat, K. Gudima, and S. Mashnik, Los AlamosNational Laboratory Report LA-UR-03-3750 (2003); Proc.AccApp’03, San Diego, USA, 2003, (ANS, La Grange Park,USA, 2004), p. 976; E-print: nucl-th/0307014.

(9) S. Furihata, Nucl. Instr. Meth. B 171, 252 (2000); Ph.D.thesis, Tohoku University (2003).

(10) K. K. Gudima, S. G. Mashnik, and A. J. Sierk, Los AlamosNational Laboratory Report LA-UR-01-6804 (2001).

(11) N. V. Mokhov, K. K. Gudima, C. C. James, M. A. Kostin,S. G. Mashnik, E. Ng, J.-F. Ostiguy, I. L. Rakhno, A. J.Sierk, and S. I. Striganov, Los Alamos National LaboratoryReport LA-UR-04-3047 (2004); E-print: nucl-th/0404084;Proc. ICRS-10/RPS2004 Int. Conf., Funchal, Madeira,Portugal, 2004, in press.

(12) R. E. Prael, Los Alamos National Laboratory Report LA-UR-01-1655 (2001).

(13) J. S. Hendricks, G. W. McKinney, L. S. Waters, T. L.Roberts, H. W. Egdorf, J. P. Finch, H. R. Trellue, E. J.Pitcher, D. R. Mayo, M. T. Swinhoe, S. J. Tobin, J. W.

Durkee, F. X. Gallmeier, J.-C. David, W. B. Hamilton,and J. Lebenhaft, Los Alamos National LaboratoryReport LA-UR-04-0570 (2004) and references therein;http://mcnpx.lanl.gov/.

(14) F. B. Brown, Los Alamos National Laboratory Report LA-UR-04-2648 (2004), Proc. PHYSOR-2004, 4-29-2004; R.A. Forster, L. J. Cox, R. F. Barrett, T. E. Booth, J. F.Breismeister, F. B. Brown, J. S. Bull, G. C. Geisler, J. T.Goorley, R. D. Mesteller, S. E. Post, R. E. Prael, E. C.Selcow, and A. Sood, Nucl. Instrum. Methods B 213, 82(2004); J. F. Briesmeister, Ed., Los Alamos NationalLaboratory Report LA-13709-M (2000); www-xdiv.lanl.gov/x5/MCNP/.

(15) K. K. Gudima, A. S. Iljinov, and V. D. Toneev, Communi-cation JINR P2-4661, Dubna (1969).

(16) V. S. Barashenkov and V. D. Toneev, Interaction of HighEnergy Particles and Nuclei with Atomic Nuclei, Atomizdat,Moscow (1972).

(17) V. S. Barashenkov, F. G. Geregi, A. S. Iljinov, G. G.Jonsson, and V. D. Toneev, Nucl. Phys. A 231, 462 (1974).

(18) M. V. Kossov, Eur. Phys. J. A 14, 377 (2002). (19) J. S. Levinger, Phys. Rev. 84, 43 (1951); Nuclear Photo-

Disintegration (Oxford University Press, 1960); Phys.Lett. B 82, 181 (1979).

(20) W. O. Lock and D. F. Measday, Intermediate EnergyNuclear Physics (London, Methuen, Distributed in theU.S.A. by Barnes and Noble, 1970).

(21) V. S. Barashenkov, K. K. Gudima, and V. D. Toneev,JINR Communication P2-4065, Dubna (1968).

(22) V. S. Barashenkov, K. K. Gudima, and V. D. Toneev,JINR Communication P2-4066, Dubna (1968); ActaPhysica Polinica 36, 415 (1969).

(23) S. Eidelman et al. (Particle Data Group), Phys. Lett. B592, 1 (2004); http://pdg.lbl.gov.

(24) S. J. Lindenbaum and R. M. Sternheimer, Phys. Rev. 105,1874 (1957).

(25) V. S. Barashenkov, Le Van Ngok, L. G. Levchuk, Zh. Zh.Musul’manbekov, A. N. Sosnin, V. D. Toneev, and S.Yu. Shmakov, JINR Communication R2-85-173, Dubna(1985); V. S. Barashenkov, Comp. Phys. Commun. 126,28 (2000).

(26) N. Amelin, Preprint CERN/IT/99/6, CERN, Geneva(1999); http://atlas.web.cern.ch/Atlas/ GROUPS/SOFT-WARE/OO/domains/simulation/G4PhysicsStudies/docu-mentation/ameline/ makebookphysics.html#tex2html1.

(27) S. G. Mashnik, User Manual for the Code CEM95 (JINR,Dubna, USSR, 1995); OECD NEA Data Bank, Paris,France; http://www.nea.fr/abs/html/iaea1247.html; RSIC-PSR-357 (Oak Ridge, USA, 1995).

(28) S. G. Mashnik and A.J. Sierk, Proc. SARE-4, Knoxville,TN, 1998, ed. T. A. Gabriel, (ORNL, 1999), p. 29; E-print: nucl-th/9812069.

(29) N. V. Mokhov, S. I. Striganov, A. Van Ginneken, S. G.Mashnik, A. J. Sierk, and J. Ranft, Proc. SARE-4,Knoxville, TN, 1998, ed. T. A. Gabriel, (ORNL, 1999), p.87; E-print: nucl-th/9812038.

(30) F. X. Gallmeier and S. G. Mashnik, Proc. AccApp00, 2000,Washington DC, USA, (ANS, La Grange Park, 2001), p. 342.

(31) F. X. Gallmeier, Proc. ICRS-10/RPS 2004, 2004, Funchal,Madeira, Portugal, http://www.itn.mces.pt/ICRS-RPS/presentations.html, in press.

(32) A. S. Iljinov, M. V. Kazarnovsky, and E. Ya. Paryev,Intermediate-Energy Nuclear Physics, (CRC Press, BocaRaton, 1994).

(33) A. S. Iljinov, I. A. Pshenichnov, N. Bianchi, E. De Sanctis,V. Muccifora, M. Mirazita, and P. Rossi, Nucl. Phys. A616, 575 (1997).

(34) T. Gabriel, G. Maino, and S. G. Mashnik, JINR PreprintE2-94-424, Dubna, 1994; Proc. XII Int. Sem. on High


Energy Phys. Problems, Dubna, Russia, 1994, ed. A. M.Baldin and V. V. Burov (JINR E1,2-97-79, Dubna, 1997),p. 309.

(35) F. G. Gereghi, V. A. Zolotarevsky, K. K. Gudima, S. G.Mashnik, and L. V. Bordianu, Calculation of CrossSections for Photoneutron Reactions, Kishinev StateUniversity (1990).

(36) K. Ukai and T. Nakamura, INS-T-550 (1997), Inst. forNucl. Study, University of Tokyo, and private communi-cation from K. Ukai to SGM (1997).

(37) S. I. Alekhin, A. Baldini, P. Capiluppi, M.

CEM03 and LAQGSM03: Extension of the CEM2k+GEM2 and … · cade (INC) Photonuclear Reaction Model...

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