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

Accounts
CEM03 and LAQGSM03: Extension of the CEM2k+GEM2 and LAQGSM Codes to
Describe Photo-Nuclear Reactions at Intermediate Energies (30 MeV to 1.5 GeV)
S. G. Mashnik,*, a M. I. Baznat,b K. K. Gudima,b A. J. Sierk,a and R. E. Prael aa

Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Institute of Applied Physics, Academy of Science of Moldova, Chisinau, Moldovab

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 QuarkGluon String Model code LAQGSM are extended to describe photonuclear reactions. First, we incorporate new
evaluations 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 reactions 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, we
extend our high-energy code LAQGSM by adding the photonuclear mode which was ignored in all its previous
versions, 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 incorporated
into our codes, show several illustrative results, and point out some unresolved problems.

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 of
the Los Alamos version of the Quark-Gluon String Model code
LAQGSM10 merged6−8 with GEM2 have been recently incorporated into the transport codes MARS1511 and LAHET312 andare planned to be incorporated in the future into the transport
codes MCNPX13 and MCNP6.14 Initially, neither CEM2k+
GEM2 nor LAQGSM+GEM2 considered photonuclear reactions and were not able to describe such reactions, either asstand-alone codes or as event generators in transport codes. To
address this problem, here we extend CEM03 (the 2003 version of CEM2k+GEM2) and LAQGSM03 (the 2003 version of
LAQGSM+GEM2) codes to describe photonuclear reactions atintermediate energies (from ~ 30 MeV to ~ 1.5 GeV). We
develop a model that is based on the Dubna IntraNuclear Cascade (INC) Photonuclear Reaction Model (PRM), 15−17 uses
experimental data now available in the literature, and a revision of recent systematics for the total photoabsorption crosssections by Kossov.18 Our photonuclear reaction model still
has some problems and is under further development, but eventhe current version allows us to describe reasonably well intermediate energy photonuclear reactions. In the following, we
present a description of our model together with several illustrative results.
2. Dubna Photonuclear Reaction Model
The Dubna intranuclear cascade photonuclear reaction
model (Dubna INC) was initially developed 35 years ago by
one of us (KKG) in collaboration with Iljinov and Toneev15 todescribe photonuclear reactions at energies above the Giant
Dipole Resonance (GDR) region. [At photon energies Tγ =10 – 40 MeV, the de Broglie wavelength D is of the order of
20 – 5 fm, greater than the average inter-nucleonic distance in*Corresponding author. E-mail: mashnik@lanl.gov. FAX: +1505-667-1931.

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

σγ A = L

Z(A – Z)σγ d ,
A(1)

where A and Z are the mass and charge numbers of thenucleus, L ≈ 10, and σ γ 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 Carlo
method according to the partial cross sections (defined fromavailable experimental data):

γ + p → p + π0 ,

(2)

+

(3)

→n+π ,→ p + π+ + π− ,

(4)

0

0

(5)

+

0

(6)

→p+π +π ,→n+π +π .

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 reaction modes (see, e.g. Figure 6.13 in Reference 20). The Dubna
INC does not consider processes involving production of threeand more pions; this limits the model applicability to photon
energies 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 inelastic
γ + p cross section and the sum of the cross sections of the twobody reactions (2) – (3)].
The kinematics of two-body reactions (2) – (3) and absorption 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-© 2005 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 11/07/2005

A2

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

Mashnik21, 22

actions,
the cosine of the angle of emission of secondary
particles can be represented in the center of mass (c.m.) system
as a function of a random number ξ, distributed uniformly in
the interval [0,1]
N

N

n=0

n=0

cos θ = 2ξ1/2 ∑ anξ n + (1– ∑ an)ξ N+1 –1,(7)

where N = M = 3,
Man = ∑ ankTγk ,where the coefficients ank were fitted to describe the available
experimental 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 in
Table 72 of the monograph by Barashenkov and Toneev 16).
The distribution of the secondary particles over the azimuthal
angle ϕ is assumed to be isotropic. After simulating the angle
Θ1, using eqs 7 and 8, and ϕ1 isotropically for the first particleof any reaction with two particles in the final state, the angles
Θ2 and ϕ2 of the second particle, as well as the energies of bothparticles T 1 and T 2 are uniquely determined from fourmomentum conservation.
The analysis of experimental data has shown that thechannel (4) of two-pion photoproduction proceeds mainly
through the decay of the ∆++ isobar listed in the last Review ofParticle Physics by the Particle Data Group23 as having themass M = 1232 MeV∆++ → p + π+ ,(9)whereas the production cross section of other isobar components ( 32 , 32 ) are small and can be neglected. The Dubna INC
uses the Lindenbaum-Sternheimer resonance model24 to simulate the reaction (9). In accordance with this model, the massof the isobar M is determined from the distributiondW~F(E, M) σ (M) ,
dM

(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 isobar
production 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 Reference
17; 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 distributiondW~(E – Eπ 1– Eπ 2 )Eπ 1 Eπ 2 / E ,dEπ1 dEπ 2

pπ1 – pπ 2≤ pN ≤ pπ1 + pπ 2
is fulfilled, otherwise this sampling is rejected and the procedure
is 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 Θπ 2 = 2ξ2 – 1,

(8)

k=0

γ + p → ∆++ + π− ,that the “triangle law” for momenta(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 beginning the energy of the first pion using
E π1 = m π 1 + ξ (E max
π1 – mπ1),
where
E πmax= [E 2 + m 2π1 – (m π 2 + m N)2]/2E.
1Then, we simulate the energy of the second pion E π 2 according
to eq 11 using the Monte Carlo rejection method. The energyof the nucleon is then calculated as EN = E – E π 1 – E π 2, checking

ϕ π1 = 2π ξ 3,

ϕ π 2 = 2π ξ 4,

and the angles of the nucleon are defined from momentumr
r r
conservation, pN = – ( pπ 1 + pπ 2).
So an interaction of a photon with a nucleon inside a nucleus
leads to two or three fast cascade particles. Depending on their
momenta 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 evaporation/fission of excited nuclei produced after the cascade stageof reactions) calculation are the same as for N + A and π + A
reactions and are described in detail in the monograph.16
The Dubna INC PRM was used successfully for many years
as a stand-alone model to study different aspects of photonuclear reactions and was also incorporated without modifications
into the transport codes CASCADE25 and GEANT4,26 and withsome improvements, via CEM95,27 CEM97,28 and CEM2k,4 into
the transport codes MARS1429 and MCNPX,13, 30, 31 respectively.
In the middle of the 1970s, one of the authors of the initial
version of the Dubna INC PRM, Iljinov, moved from JINR,
Dubna to INR, Moscow and continued to develop further the
Dubna INC with his Moscow Group, which evolved into what
is now known in the literature as the Moscow INC model (see,e.g. Reference 32 and references therein). The Moscow INC
model was recently extended to describe photonuclear reactions
at energies up to 10 GeV.33
3. From CEM95 to CEM03
Photonuclear reactions were not considered in the initial
version of the CEM.5 The Dubna PRM was incorporated34 first
into 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 the
MARS1429 transport code and used in some applications.
By early 1997, one of the authors of the CEM (SGM) moved
from 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 Alamos
transport code MCNPX13 and for other applications.
3.1. New Approximations for γ p Cross Sections. The first
improvements in the CEM of the photonuclear mode of the
Dubna INC was done in the CEM97 version28 of the CEM.
The improved cascade-exciton model in the code CEM97
differs from the older CEM95 version by incorporating new
approximations for the elementary NN, πN, and γ p cross sections
used in the cascade, using more precise values for nuclear
masses and pairing energies, employing a corrected systematics for the level-density parameters, adjusting the crosssections for pion absorption on quasi-deuteron pairs inside a
nucleus, including the Pauli principle in the preequilibrium
calculation, 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, which
is very important when performing simulations with transport
codes.
Concerning specifically the photonuclear reactions, in CEM97
we developed improved approximations for the elementary γ pcross sections compared with the Dubna INC PRM.15

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

CEM03 and LAQGSM03
15

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 the
input. These cross sections are used in CEM97, 28 CEM2k,4and CEM03,1 and were incorporated recently into the latest
version of our LAQGSM10 code, LAQGSM03.1, 2
We consider this part of the CEM improvement as an independently useful development, as our approximations are reliable, fast, and easy to incorporate into any transport, INC,
BUU, or Glauber-type model codes. For example, our new
approximations recently have been successfully incorporated
by Mokhov into the MARS1429 and MARS1511 versions of the
MARS code system at Fermilab.
An example of 8 compiled γ + p experimental cross sections
together 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 describe
all data very well. Although presently we have much moreIn the Dubna INC PRM used in CEM95, the cross sections
for the free γ p (and for NN and πN) interactions are approximated using a special algorithm of interpolation/extrapolation
through a number of picked points, mapping the experimental
data as possible. This was done very accurately by the authorsof the Dubna INC PRM15 using all experimental data available
at that time, about 35 years ago. Currently there are many
more experimental data on cross section; therefore we revised
the approximations of all elementary cross sections used in
CEM97.28 We collected all published experimental data fromavailable sources, then developed an improved algorithm forapproximating cross sections and developed simple and fast
approximations for elementary cross sections which fit very
well presently available experimental data not only up to ~ 1.5
GeV, where the Dubna INC PRM is assumed to be used, or up
to about 5 GeV, the upper recommended energy for the present
version 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
10

0

10

1

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γ+p→p+πCross Section/mb

Cross Section/mb

0

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old
new
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γ+p→n+ π

1

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+

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Cross Section/mb

Cross Section/mb

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old
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−

γ+p →p+π +π

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Lab. Energy / MeV

10Lab. Energy / MeV

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Cross Section/mb

γ + p → p + 2π

Cross Section/mb

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+

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++

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Lab. Energy / MeV
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γ + p total cross section

γ+p→ ∆ +π

Cross Section/mb

100

γ+p →n+π +π1Lab. Energy / MeV

Cross Section/mb

4

10

Lab. Energy / MeV

γ+d →n+p10+

2Lab. Energy / MeV
10

A3

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old
new

old
new
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Lab. Energy / MeV

4

10

10

2
2

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3

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5

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Lab. Energy / MeV

Figure 1. Comparison of eight experimental total γ + p(d) cross sections with the old approximations from the Dubna INC PRM and with our new
approximations 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 agree
reasonably well with our approximations, a re-fitting would slightly improve the agreement.

A4

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

Mashnik

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 γ p cross sections at energies
below 1.2 GeV (where the initial Dubna INC PRM wasassumed to be used), and for such modes as γ + p → p + π 0, γ
+ p → n + π +, γ + p → p + π + + π −, and γ + d → n + p, at energies not too close to their thresholds, the original approximations 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 Dubna
INC16 and the younger CEM9527 describe so well many characteristics of different nuclear reactions. On the other hand,for some elementary cross sections like γ + p → p + 2π 0 and γ+ p → n + π + + π 0, the old approximations differ significantly
from the present data, demonstrating the need for a better
description of all modes of photonuclear reactions. (Similar
results were obtained in CEM9728 for hadron-hadron crosssection approximations.)
The CEM97 code with these cross sections and the othermentioned improvements was incorporated by Gallmeier30 into
the MCNPX transport code,13 allowing MCNPX to consider for
the first time interaction of intermediate-energy photons withthick targets of practically arbitrary geometry.
3.2. New Approximations for Differential γ + p Cross
Sections. The CEM2k4 version of CEM is a “new generation”
of the CEM following CEM97.28 Its development was partiallymotivated 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 been
performed using inverse kinematics for interactions of 56Fe,
197
Au, 208Pb, and 238U at 1500, 1000, 800, 750, 500, and 300
MeV/nucleon with liquid 1H. These measurements provide alarge set of cross sections for production of practically all
possible isotopes from such reactions in a “pure” form, i.e.
individual cross sections from a specific given bombarding
isotope (or target isotope, when considering reactions in theusual kinematics, p + A). Such cross sections are much easier
to compare to models than the “camouflaged” data from γ spectrometry measurements. In addition, many reactions
where 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 at
GSI. References on these measurements and many tabulated
experimental cross sections may be found on the Web page ofSchmidt.82(We have analyzed with CEM2k and LAQGSM all measurements done at GSI of which we are aware, both for protonnucleus 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 references therein.)
During the development of the CEM2k version of CEM and
10

0

2

0

260 MeV γ + p → π + p

300 MeV γ + p → π + pdσ/dΩ/µb sr -1

dσ/dΩ/µb sr -1

101

CL75
GE74
FI70
MC57
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BE73: 500 MeV
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dσ/dΩ/µb sr -1

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WO68: 1070 MeV
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HU77: 880 900 MeV
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WO68: 911 MeV
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YO77
AL76
DE65: 660 MeV
DE65: 680 MeV
FE74: 675 MeV
WO68: 669 MeV
newoldΘ c.m.s. /deg

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900 MeV γ + p → π + pdσ/dΩ/µb sr -1

dσ/dΩ/µb sr -1

0160

Θ c.m.s. /deg
0

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0

800 MeV γ + p → π + p

1120670 MeV γ + p → π + pΘ c.m.s. /deg
10100

Θ c.m.s. /deg

490 MeV γ + p → π + p

10

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BA75
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Θ c.m.s. /degπFigure 2. Example of eight angular distributions of π0 from γ p → π0p as functions of Θc.m.s
at photon energies from 260 MeV to 1.4 GeV. The
dashed lines show the old approximations of the Dubna INC PRM while the solid lines are our new approximations incorporated into the CEM03
and 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 available at: http://wwwspires. dur.ac.uk/ hepdata/reac2.html.

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

CEM03 and LAQGSM03

A5

by Gallmeier into MCNPX to replace CEM97, and this versionof MCNPX was extended by him to describe photonuclear
reactions also in the GDR region31 (as a stand-alone code,
CEM2k was developed to describe photonuclear reactions only
at 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 approximations and algorithms to better describe the integrated elementary NN, πN, and γ N cross sections as mentioned above,the double differential distributions of secondary particles fromsuch interactions were simulated by CEM2k and all its precursors using the old Dubna INC approximations (7) – (11) for γ preactions (and similar relations, for NN and π N collisions).
These were obtained by Gudima et al.15, 21, 22 36 years ago, using
the measurements available at that time. In CEM03, for NN
and πN collisions, we addressed this problem by developing new
approximations similar to (7) – (11) and by using recent systematics by other authors, based on the experimental data available 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 energy
dependence of parameters ank in eq 8 using the values obtained
for 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

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. The
main 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. In
short, CEM2k has a longer cascade stage, less preequilibrium
emission, 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 momentumenergy conservation for each simulated event (the Monte Carloalgorithm previously used in CEM provides momentum-energy
conservation only statistically, on the average, but not exactly
for each simulated event); using real binding energies fornucleons at the cascade stage of a reaction instead of the approximation of a constant separation energy of 7 MeV used in theprevious versions of the CEM; using reduced masses of particles
in 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 nucleons
already outside the nucleus. On the whole, CEM2k describes
many nuclear reactions, including the ones induced by photons
better than CEM97 and CEM95 do. CEM2k was incorporated++

200 MeV γ + p → π + n

250 MeV γ + p → π + n1

dσ/dΩ/µb sr -1

dσ/dΩ/µb sr -1

10

AD67
AD60
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WA55
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400 MeV γ + p → π + n1

dσ/dΩ/µb sr -1

dσ/dΩ/µb sr -1

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dσ/dΩ/µb sr -1

0

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Θ c.m.s. /deg
3+

1 GeV γ + p → π + n

10

AL70
BU67
AL83: 1390 MeV
ZH03: 1659 MeV
DA73: 1397 MeV
EK72: 1450 MeV
EC67: 1269 MeV
new
old

+

1.52 GeV γ + p → π + n

2

1

10

dσ/dΩ/µb sr -1

10dσ/dΩ/µb sr -1

120+

600 MeV γ + p → π + n
1

10

10

100

Θ c.m.s. /deg

AL83
FI71
DI60
EC67: 1002 MeV
new
old

0

10

1

10

0

10

-1

10

-2

10

-1

10

-3

0

20

40

60

80

100

Θ c.m.s. /deg

120

140

160

180

10

0

20

40

60

80

100

120

140

160

180

Θ c.m.s. /degπFigure 3. Example of eight angular distributions of π+ from γ p → π+n as functions of Θc.m.s
at photon energies from 200 MeV to 1.52 GeV. The
dashed lines show the old approximations of the Dubna INC PRM while the solid lines are our new approximations incorporated into the CEM03
and 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 available at: http://wwwspires.dur.ac.uk/ hepdata/reac2.html.

A6

J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005
33

INC kindly sent us by Pshenichnov. That event generator
includes a data file with smooth approximations through presently
available experimental data at 50 different gamma energies
from 117.65 to 6054 MeV (in the system where the p or ninteracting with γ is at rest) for the c.m. angular distributions
dσ /dΩ of secondary particles as functions of Θ tabulated forvalues of Θ from 0 to 180˚ with the step ∆Θ = 10˚ for 60 different channels of γ p and γ n reactions considered by the
Moscow INC (see details in Reference 33). We use part ofthat data file with data for reactions (2) and (3), and have written an algorithm to simulate unambiguously d σ /d Ω and tochoose the corresponding value of Θ for any Eγ , using a single
random 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) = ∫

cosΘ

–1

/

1

dσ /dΩ dcos Θ ∫ dσ /dΩ dcos Θ–1is a smooth monotonic function increasing from 0 to 1 as cos
Θ 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 describe
angular 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 → π0p
πare presented inand of π+ from γ p → π+n as functions of Θc.m.s
Figures 2 and 3. We see that the approximations developed in
CEM03 (solid histograms) agree much better with the available experimental data than the old Dubna INC approximations (7) – (8) used in all precursors of CEM03 (dashedhistograms).
4. New Approximations for γ + A Absorption Cross Sections
CEM03 (and its predecessors) does not consider absorptionof low energy photons in the GDR region and takes into
account photoproduction on free nucleons of only two pions.
This restricts its applicability to the range 30 MeV <~ Eγ <~ 1.5
GeV, which is not convenient when it is used as an event
generator in a transport code.
To extend the applicability of CEM03 (and LAQGSM03)
into the GDR region, it is necessary to omit the intranuclear
cascade (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 that
does not consider any collective degrees of freedom of a nucleus,
including the GDR; in addition, the photon-energy in the GDR
region 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 years
ago,122 using the Modified Exciton Model (MEM)123, 124 usedin the initial version of CEM5 and 25 years later,125 using an
improved 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 large
amount of tedious work: 1) to make sure that we use the mostreliable parameters of the GDR for all nuclei, 2) to define an
optimal transition from the current three-stage (INC, preequilibrium, and evaporation/fission) description of reactions to a
two-stage approach needed in the GDR region, and 3) to test
the extended model against the available experimental data.
To describe properly with CEM03 and LAQGSM03 photonuclear reactions above Eγ ~ 1.5 GeV, it is necessary to take
into account production of more than two pions in γ N collisions, as well as to consider production of resonances heavier
than ∆(1232), as has been done, i.e. in the Moscow INC.33 We
plan to extend CEM03 and LAQGSM03 to higher Eγ in subsequent versions.
In the meantime, it is possible to get quite reasonable results
for spectra of emitted nucleons and complex particles and for

Mashnik
the nuclide production cross sections with our present CEM03
model for photonuclear reactions both in the GDR region and> 1.5 GeV, by employing a correct total photoabsorption
at Eγ ~
cross section. Indeed, CEM03 starts a reaction in the GDR
region with a cascade and since the γ energy is below the pionproduction 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 evaporation/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 total
photoabsorption (reaction) cross section is needed to normalize
the results. CEM03 (and most other INC models) calculates
the total reaction cross section, σin, by the Monte Carlo method
using the geometrical cross section, σgeom, and the number of
inelastic, 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 is
not reliable at energies below 100 MeV (see, e.g. Figures 3 and
4 and Reference 7).
To address this problem for photonuclear reactions, we havewritten a FORTRAN routine called GABS.FOR based on the
recent approximation by Kossov,18 that provides reliable photoabsorption cross sections on arbitrary targets at all energies
from the hadron production threshold to about 40 TeV. We
have added GABS.FOR to CEM03 to normalize our photonuclear results to this systematics rather than to σin calculated by
the 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 energies, LAQGSM03 describes quite well σin and does not require
renormalization of its results to any systematics; therefore we
do not incorporate GABS.FOR into LAQGSM03.)
The Kossov approximation18 of the energy dependence ofphotonuclear cross sections is subdivided into three main
regions: the GDR region, the nucleon resonance region, andthe high-energy region. Its functional form is also subdivided
into three groups depending on the mass number of the target:the σγ p cross section, the cross section for γ d reactions, and theσγ A cross section for A > 2.
We note that eq 41 in Reference 18 was misprinted in theoriginal publication by Kossov, where a “+” sign occurs
instead of a “–” sign. The misprinted formula does not reproduce the cross sections presented in Reference 18, whereas thecorrected version does.
Figures 4 and 5 show examples of twelve photoabsorption
cross sections on several light, medium, and heavy nuclei. In
these figures, we compare predictions of the Kossov systematics as implemented in the routine GABS.FOR with available
experimental data and with the Los Alamos National Laboratory (LANL), Korean Atomic Energy Institute (KAERI), andthe Institute of Physics and Power Engineering (IPPE),
Obninsk, Russia and the Center for Photonuclear Experimental
Data [Centr Dannykh Fotoyasdernykh Eksprtimentov (CDFE),in Russian], Moscow, Russia, Modified (MOD) Library of
Photonuclear Data [Biblioteka Fotoyadernykh Dannykh(BOFOD), in Russian], BOFOD(MOD), evaluations from the
IAEA Photonuclear Data Library,126 as well as with calculations by two older versions of CEM, namely, the CEM95 photonuclear 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,J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005

CEM03 and LAQGSM03

12

16

γ+ C

1

10

A7

γ+ O
1

σabs /mb

σabs /mb

10

0

10

LANL
AHR85
BRU73
BIA96
BUR63
ARA83
ARA85
MUC99
WYC65
CEM95
CEM2k mod. in MCNPXGABS.FOR

-1

10

10

1

10

2

10

3

0

10

LANL
AHR75
AHR85
ARA83
ARA85
ARE81
CEM95
CEM2k mod. in MCNPXGABS.FOR

-1

10
10

4

10

1

Projectile Energy / MeV

10

2

10

3

10

4

Projectile Energy / MeV

2

10

2

27

40

10

γ + Alγ + Ca1

10

σabs /mb

σabs /mb

1

LANL
AHR75
AHR85
ARA85
BRO73
BIA96
MIC77
MUC99
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10

-1

10

10

1

10

2

10

3

10

0

10

LANL
AHR85
CEM95
CEM2k mod. in MCNPXGABS.FOR
-1

10

10

4

10

1

Projectile Energy / MeV
2

10

63

γ + Cu

10

2

10

3

10

4

Projectile Energy / MeV
γ+

109

Ag

2

σabs /mb

σabs /mb

10
1

10

LANL
WYC65
ARA78
ARA83
BIA96
BRU73
CAL73
MIC77
MUC99
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10

10

1

10

2

10

3

1

10

KAERI
WYC65
MIC77
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10
10

Projectile Energy / MeV

4

10

1

10

2

10

3

10

4

Projectile Energy / MeV

Figure 4. Examples of total photoabsorption cross sections for 12C, 16O, 27Al, 40Ca, 63Cu, and 109Ag as functions of photon energy. The thick solid lines
marked as “GABS.FOR” are from our subroutine written to reproduce Kossov’s18 systematics, as described in the text. The thin solid line marked
as “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

KAERI, and the BOFOD evaluations, especially for heavy
targets. For 12C, 27Al, and 63Cu (and several other nuclei wetested but did not include in Figures 4 and 5) the agreement in
the GDR region is not so good. This is because we use here
the “global” approximation given by the Kossov systematics to
calculate the photoabsorption cross section in the GDR region
for 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 separately. 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, Kossov
did 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 of
the GDR photoabsorption on light nuclei using all available

experimental data.
5. Illustrative Results
In this Section, we present several illustrative results from
CEM03 and LAQGSM03 extended to describe photonuclear
reactions. Let us start with photofission cross sections. We
have compiled from the literature all reliable experimental dataon photofission cross sections that we could identify and haveanalyzed them with both CEM03 and LAQGSM03. Figure 6
shows a comparison of such data for 197Au, 208Pb, 209Bi, 232Th,
233
U, 235U, 238U, and 237Np with the results of CEM03, as well as
to several earlier versions, namely, the photonuclear versions of
CEM95,34 CEM98,158 CEM2k+GEM2,8 and by the modified
version of CEM2k incorporated into MCNPX by Gallmeier.31
The CEM03 results agree well with the experimental fission
cross 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 describe
the fission cross section, not only for photon energies from ~ 30

MashnikJ. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005
118γ+

σabs /mb

10

10

10

2

10

1

KAERI
BIA96
BRU73
LEP81
MUC99
FUL69
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10

1

10

2

10

3

10

10
10

197

LANL
GUR81
TAV93
TER96
TER98
BRU76
LEP91
CEM95
CEM2k mod. in MCNPXGABS.FOR

1

0

4

10

1

10

10

2

10

KAERI
GUR81
MAR89
MAR91
TER96
TER98
MIC77
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10

1

10

2

10

3

10

10
10

10

4

Pb

LANL
ARA78
BIA96
BRU73
CHO83
GAL73
MAR89
MAR91
TER96
TER98
AHR85
MUC99
CEM95
CEM2k mod. in MCNPXGABS.FOR

0

10

1

10

2

10

3

10

4

Projectile Energy / MeV

232

γ+

Th
10

10

1

0

10

1

10

2

10

3

10

Projectile Energy / MeV

4

10

238

U

2

σabs /mb

2

BOFDM
BIR76
AHR85
GUR74
GUR76
MAR91
SHE85
TAV91
MIC77
ARA90
235
ARA90: U
BIA93
CEM95
CEM2k mod. in MCNPXGABS.FOR1

BOFODM
GUR76
CEM95
CEM2k mod. in MCNPXGABS.FOR

10

208

1

4

σabs /mb
10

3

3

γ+

10

10

2

Projectile Energy / MeV
10

2

γ+

Au

1

10

Projectile Energy / MeV

σabs /mb

σabs /mb

10

Ta

2

Projectile Energy / MeV
γ+

181

γ+

Sn

σabs /mb

A8

0

10

1

10

2

10

3

10

4

Projectile Energy / MeV

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’s 18 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) are
from: 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

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 MeV
to 5 GeV.
This is an example of getting reasonably good results
outside the region where the model is justified, as discussed in
the previous section. Results of LAQGSM03 for these fission
cross sections practically coincide with the ones by CEM03
above 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 the
GDR 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 default
and fixed values of all parameters, without fitting anything. We
only specify the energy of the incident photons and A and Z of
the target in the inputs to CEM03 (and CEM2k+GEM2) and
LAQGSM03, and then calculate. CEM95, CEM98, and CEM2k

use a parameter whose value affects drastically the calculated
fission cross sections, just as in many similar statistical models:This is the ratio of the level density parameters used in the fission
and evaporation channels, af /an (or, Bs, in the case of CEM98,
see details in Reference 158). The fission cross sections calculated by any code employing the statistical evaporation andfission models depend so much on af /an that by fitting this ratio
to 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 any
particular measured reaction. This is why some publishedpapers that analyze fission cross sections or even pretend toobtain “experimental fission barriers” without addressing thequestion of a f /a n are of low significance. In our CEM95,
CEM98, and CEM2k calculations, we use the default options
for nuclear masses, pairing energies, and fission barriers (the“recommended” options, in the case of CEM95, where several
options are available in its input; see details in Reference 27),
but we still need to define (more exactly, to fit) the values of

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

CEM03 and LAQGSM03

A9

2

10

197

Au

0

10

TER98
TER96
MAR91
LU89
AND72
CEM98, BS=1.22
CEM95, af/an=1.095
CEM2k mod. in MCNPX, af/an=1.154
CEM03

-1

10

-2

10

-3

10

100

Fission Cross Section/mb

Fission Cross Section/mb

10

γ+

1

γ+

0

10

MAR91
MAR89
TER92
TER96
TER98
CET02
CEM95, af/an=1.151
CEM2k mod. in MCNPX, af/an=1.151
CEM03

-1

10

-2

100

γ+

1

209

Bi

LEM80
MAR89
MAR91
TER92
TER96
TER98
BEL83
MOR69
MIN57
TER96a
RAN67
GUA87
JUN57
CEM2k+GEM2
CEM03

0

10

-1

10

-2

10

100

Th

1

CAL80
CET02
KAP69
LEP87
VEY73
ZHA86
CEM95, af/an=1.073
CEM2k mod. in MCNPX, af/an=1.073
CEM03

0

10

-1

10

100

1000

Projectile Energy / MeV

3

3

10

10

γ+

233

U

2

10

BER86
CET02
KAP69
DEM93
HUI62
OST78
CEM2k+GEM2
CEM03

1

10

0

10

-1

10

100

Fission Cross Section/ mb

Fission Cross Section/ mb

232

10

10

1000

γ+

2

10

Projectile Energy / MeV

10

1000

Projectile Energy / MeV
Fission Cross Section/mb

Fission Cross Section/mb

Projectile Energy / MeV

10

Pb

10

10

1000

208

1

γ+

U

2

10

1

10

VAR87
CET02
CEM2k+GEM2
CEM03

0

10

-1

10

1000

235

10

Projectile Energy / MeV

100

1000

Projectile Energy / MeV
3

238

U

2

10

Varlamov’s evaluation
REI84
LEP87
CET02
FRO94
CEM95, af/a=1.05
CEM2k mod. in MCNPX, af/an=1.06
CEM2k+GEM2
CEM03

1

10

0

10

10

100

1000

Projectile Energy / MeV

Fission Cross Section / mb

Fission Cross Section / mb

10

γ+

γ+

237

Np

2

10

1

BER86
CET02
CES83
HUI62
OST78
SOL97
VEY73
CEM2k+GEM2
CEM03

10

0

10

-1

10

10

100

1000

Projectile Energy / MeV

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

af /an (or, Bs, in the case of CEM98): These values are listed on
our plots in Figure 6. Naturally, CEM2k+GEM2, CEM03, and
LAQGSM03 also had the problem of af /an in the beginning, but
this problem was solved in Reference 8 by fitting these parameters for proton-induced measured fission cross sections for all
targets for which we found data, at all incident energies, and by
their extrapolation/interpolation for unmeasured targets. The
fitted values are fixed and are used in all our further CEM03 and
LAQGSM03 calculations without subsequent variation; thisallows us not only to describe well most of the measured data
but 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 as
possible all available proton-induced measured fission crosssections; this is why the fission cross sections calculated by CEM03
practically 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 secondary
particles 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 186
to “create” high-energy d, t, 3He, and 4He by final-state interactions 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 is
the 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-equilibrium
decay followed by the equilibrium evaporation/fission stage ofthe reaction. Generally, all four components may contribute toexperimentally measured particle spectra and other distributions. But if the residual nuclei after the INC have atomic
numbers with A ≤ 12, both CEM03 and LAQGSM03 use theFermi break-up model described in Reference 10 to calculate
their further disintegration instead of using the preequilibriumand evaporation models. The Fermi break-up is much faster
than, 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 calculated by CEM03 and LAQGSM03 compared with the experimental data for the reactions 300 MeV γ + Cu187 and 198 MeV
γ + C, 188 respectively. Both codes describe quite well the
proton spectra in the case of copper, but less well for carbon.

Mashnik

A10 J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005
10

5

3

10

10

300 MeV γ + Cu → p + ...

4

3

Pb(×10 )2
Sn(×10 )Ca(×10)
C(×1)
CEM03

+

213 MeV γ + A → π + ...

64

10
10
10
10

dσ/dΩ/mb sr -1

d 2 σ/ (dT·dΩ) /µb MeV-1sr-1

2

10

3

2

1

0

1

10

0

10

-1

-1

10

45 deg × 100
90 deg × 10
135 deg × 1
CEM03
LAQGSM03

10

-2

10

-2

10

-3

10

0

50

100

150

200

250

300

0

30

60

90

Tp /MeVFigure 7. Proton spectra at 45˚, 90˚, and 135˚ from the reaction 300
MeV γ + Cu. Symbols are experimental data from Ref. 187,
histograms and dashed lines are results of CEM03 and LAQGSM03,
respectively.

10d 2 σ/(dT·dΩ) /µb MeV-1sr-1

10
10

5

γ(198 MeV) + C → p + ...

4

10
10

150

180

Figure 9. Energy-integrated angular distributions dσ/dΩ of π + emitted
from 213 MeV γ interactions with Pb, Sn, Ca, and C. Symbols show
experimental data by Fissum et al.189 while histograms show CEM03
results.

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

3

/

E
1 E
E·N(E, E0)dE ∫ N(E, E0)dE.
∫
0
E0 0
0

10

120

Θ Lab /deg

Q=

2

0

(12)

1

0

-1

10

32.5 deg x 10000
55 deg x 1000
80 deg x 100
105 deg x 10
130 deg x 1
CEM03
LAQGSM03

-2

10

-3

10

0

50

100

150

Tp / MeV

Figure 8. Proton spectra at 32.5˚, 55˚, 80˚, 105˚, and 130˚ from thereaction 198 MeV γ + C. Symbols are experimental data from Ref.
188, histograms and dashed lines are results from CEM03 and
LAQGSM03, respectively.

As discussed above, CEM03 and LAQGSM03 do not describe
properly photonuclear reactions in the GDR region, we cancalculate bremsstrahlung reactions with our codes while limiting
ourselves 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 the
GDR region in our calculations, and we need to use Emin for the
lower limits of the integrals in eq 12 instead of 0 in calculating
the 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=+

Figure 9 shows examples of π angular distributions from213 MeV γ ’s interacting with Pb, Sn, Ca, and C targets. One
can see that the π+ angular distributions calculated by CEM03
agree reasonably well with the experimental data189 for C, Ca,
and Sn targets, but underestimate by a factor of 2 to 3 the Pb
data. We do not have a good understanding of this disagreement. One possible explanation of this would be if CEM03
absorbs too strongly the low-energy pions produced in γ pcollisions inside the target. The heavier the target the bigger
would be this effect, therefore we may see it with Pb but notobserve it for C, Ca, and Sn targets. There also could be problems with the experimental data for Pb. As noted in Reference
189, 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 experimental
cross 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 reactions
induced by monoenergetic photons of a given energy E, thebremsstrahlung beam is produced by monoenergetic electrons
and has a spectrum of photon energies E of the form N(E, E0) ~1/E, 190 from 0 to E 0 , where the end-point energy E 0 is the1<E>∑E = E ,Nin E0 i i
0(13)where the mean energy of the bremsstrahlung photons <E> isequal toE0

<E > =∫ E· N(E, E )dE
0

Emin

E0

∫

N(E, E0)dE

∑ Ei
= i
,
Nin

(14)

Emin

and Emin ≤ Ei ≤ E0. In the present paper, we use Emin = 30 MeV
for all the reactions we discuss. The total inelastic (photoabsorption) cross section σ in in the case of bremsstrahlung
photons is calculated as following:
E0

σin =

∫ σ (E) ·N(E, E )dE
γ
in

Emin

∫

0

E0

N(E, E0)dE∑ σ inγ (Ei)

= i

Nin

,

(15)

Emin

γ
in

where σ (Ei) is the photoabsorption cross section by a nucleus
of 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, we
will miss the products from interaction of γ with energies

J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005 A11

CEM03 and LAQGSM03

CEM03
Direct knockout
Quasideuteron

2

10

-1

-1

10 1

12

=1050 MeV) + C → p + X

43° (× 100)310d σ/(dT·dΩ) /µb MeV sr /eq.q.

max

90° (× 10)

10(a)Total fission yields / mb/eq.q.

γ(E

4

10

This work
Jungerman and Steiner
Ranyuk and Sorokin
Methasiri and Johansson
Kroon and Forkman
Andersson et al.
David et al.
Vartapetyan et al.
Emma et al.
Kiely et al.
PICA3/GEM
CEM03

10 -1

10 -2

10 -3
0

500

1000

1500

2000

E0 / MeV

1

2

10 2

154° (× 1)

-2

10

0

50

100

150

200

250

300

350

400

Tp /MeV191

Figure 10. Comparison of measured differential cross section for proton photoproduction on carbon at 43˚, 90˚, and 154˚ by bremsstrahlung
photons with E max(≡ E0) = 1.05 GeV (symbols) with CEM03 calculations (histograms), and predictions by the direct knockout model192(dashed lines) and a quasideuteron calculation193 (dotted lines), respectively. The experimental data and the results by the direct knockout
and quasi-deuteron models were taken from Figure 5 of Ref. 192.

10

0

γ(E

-1

10

-2

10

-3

12

+

=305 MeV) + C → π + ...

2

10

max

data
CEM03

0

50

100

150

Tπ / MeV

Figure 11. Comparison of measured194 differential cross section for π+
photoproduction on carbon at 90˚ by bremsstrahlung photons with
E max(≡ E0) = 305 MeV (circles) with CEM03 calculations (histogram).

below 30 MeV, like the cross sections for (γ, n), (γ, 2n), and, toa certain degree, (γ, np) in our results, but this limitation does
not affect at all the description of products in the deep spallation, 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 and
305 MeV, respectively. One can see that CEM03 describes
well both the measured proton and pion spectra and agrees
with 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

Total fission yields / mb/eq.q.

(b)
-1

10

d σ / dT / dΩ / Q (µb / MeV / sr / Q)

10 0

10 1

10 0

This work
Bernardini et al.
Jungerman and Steiner
Carvalho et al.
Ranyuk and Sorokin
Moretto et al.
Vartapetyan et al.
Carvalho et al.
Emma et al.
PICA3/GEM
CEM03

10 -1

10 -2
0

200

400

600

800

1000

1200

E0 / MeV

Figure 12. Bremsstrahlung-induced fission cross sections of 197Au (a)and 209Bi (b) as functions of the end-point energy E0. The experimental 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 present
CEM03 results are shown with crossed squares. We thank Haba formaking this figure for us by adding our CEM03 results to Figure 19 of
the review.195

and references therein). Thousands of useful product crosssections were measured by this group on target nuclei from 7Li
to 209Bi at bremsstrahlung end-point energies E0 from 30 MeV
to 1.2 GeV, including photopion reactions, fragmentation andfission of preactinides, deep spallation reactions, and recoil
studies (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 with
its latest version, PICA3, merged201 with the GEM evaporationfission 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 fission
cross sections of 197Au202 and 209Bi,203 compared as well withother available experimental data for Au169, 171, 204−209 and for
Bi,166, 169, 171, 207, 208, 210−212 and with results by PICA3/GEM201
from Reference 203. There is a reasonable agreement of the
CEM03 results with the experimental data in the whole intervalof E0 measured, from the threshold to the highest measured
energy.
Figure 13 presents the experimental data202, 203, 213−216 and thecalculations by PICA3/GEM201 and by CEM03 for the mass
yields of products produced by bremsstrahlung reactions on
197
Au and 209 Bi at E 0 = 1 GeV. For convenience, all theisotopes produced in these reactions were divided into fourgroups, namely: 1) spallation products produced by sequential
emission of several nucleons, positive pions, and complex

Mashnik

A12 J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005
103

10

2

2

10

Au target102

fissionYields / mb/eq.q.

101

Yields/mb/eq.q.

Experimental
PICA3/GEM
CEM03

spallation

100

fragmentation
10-1
10

24

0

10

-1

10

-2

10

-3

10

-4

1

10

0

10

All products
Forward products
Backward products

Na
28

22

0

10

photopion

Be

10-3

10-4

1

Au

Be

10-2
7

10

197

Mean energy/MeV

γ (E0 = 1 GeV) +

197

Mg

0

All products
Forward products
Backward products
-1

10
40

80

120

160

200

0

Product mass number, A

Na

20

40

60

80

100

120

140

160

180

40

80

120

160

200

Product mass number, A

0.008

100

0.006

95

200

Mean parallel velocity vz, (1/c)

103
209

Bi target

102

Experimental
PICA3/GEM
CEM03

fission101

Yields / mb/eq.q.

spallation
100

fragmentation

Mean angle Θ/deg.

Product mass number

0.004

0.002

0.000

0.002

80

CEM03, all products

0.004
-2

photopion

20

40

60

80

100

120

140

160

180

0

40

80

120

160

Product mass number, A

10-3

10-4
0

85

75

10-1

10

90

200

Product mass number

Figure 13. Comparison of CEM03 results for the mass yields of products produced by bremsstrahlung reactions on 197Au and 209Bi at E0 = 1
GeV with the experimental data202, 203, 213−216 and the calculations by
PICA3/GEM.201 The experimental yields from fission of 197Au and209
Bi 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 group
and are presented in Figure 18 of the review195 with the corresponding
citations. The mass yields for the fission products shown by black
curves represent approximations based on the experimental data obtainedin Refs. 202 and 203. We thank Matsumura for making this figure for us
by adding our CEM03 results to Figure 18 of the review.195

particles during the INC, followed by preequilibrium and evaporation processes; 2) intermediate-mass nuclides produced via
fission of excited compound nuclei; 3) light fragments emitted
either via evaporation or by “fragmentation” (Fermi break-up
model, in the case of our present results), and 4) “photopion”
products produced in (γ, π − xn) and (γ, 2π − xn) reactions, where
the charge of the products is higher than that of the initial
target. One can see that CEM03 describes quite well the yields
of products in all these groups and agrees with the experimental 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 consider
photons with energies in the GDR region (Emin = 30 MeV), as
discussed 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 or
more. We do not have yet a clear understanding of this disagreement and we plan to address it in the future. Comparing
our calculation results with experimental data isotope-by-isotope, 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 solve
this problem. We plan to perform such an analysis of isotopic
yields from photonuclear reactions in the future.
Our preliminary analysis shows that CEM03 also allows us

CEM03, all products

200

70

0

40

80

120

160

200

Product mass number, A

Figure 14. Results by CEM03 for 1 GeV bremsstrahlung-induced
reactions 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 products 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 physical 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 such
events do not have any significance.

to describe the recoil properties (forward and backward productyields, their F/B ratio, and mean kinetic energies) of nuclides
produced in bremsstrahlung-induced reactions on medium andheavy targets at intermediate energies (see Reference 196 andreference therein). We plan to publish our analysis in a future
paper. Below, we present only several predictions by CEM03
for the bremsstrahlung-induced reaction on Au at E0 = 1 GeV,
as we find such results informative and useful to better understand the mechanisms of nuclear reactions.
Due to the momentum transferred by the bombarding
gammas 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 is
not 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 of
Figure 14 shows the yield of all products as a function of A,
the same results compared in Figure 13 with the experimental
data and the calculations by PICA3/GEM. Besides the total
yield, this plot shows also its components from nuclides
produced in the forward (thick long-dashed line) and backward(thin dotted line) directions. One can see that for all the spallation isotopes, the cross sections for the forward products areabout a factor of two higher than those for backward products,

J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005 A13

CEM03 and LAQGSM03
γ (E 0 = 1000 MeV) + 197Au
53I

59Pr

65Tb

71Lu

77Ir

1

10

3

54Xe

60Nd

66Dy

72Hf

78Pt

Zaveraged F/B

10

3.0

3

γ (E0 = 1 GeV) +

2.5

197

Au

2.0
1.5
1.0
CEM03, all Zaveraged products

1

10

3

0.5
55Cs

61Pm

67Ho

73Ta

56Ba

62Sm

68Er

74W
80Hg

1

10

3

57La

63Eu

69Tm

75Re

1

3

58Ce

64Gd

76Os

70Yb

CEM03
forwardbackward1

120 130 140140

160 140

160

180

160

180

200

180

200

Mass Number, A

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 direction in the laboratory system, while the black circles show results forthe backward products.
γ(E 0 = 1000 MeV) + 197Au
10

2

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

22Ti

28Ni

34Se

40Zr

46Pd

52Te

10

-1

10

10

2

10

-1

10

10

2

10

-1

10

10

2

10

-1

10

10

2

10

-1

10

10

2

10

-1

10

40 50 60

50

60

70

60 70 80 90

80

100

100

160

200

120

100

30
CEM03 prediction

20
10
0
180

81Tl

10

120

γ (E0 = 1 GeV) + 79Au → 80Hg + ...

F/B ratio for Hg

Cross Section/ µb/Q

3

80

40

1

10

40

Product mass number, A
79Au

Cross Section/µb/Q

0120

Mass Number, A

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

185

190

195

Hg mass number, A
Figure 17. Upper plot: Z-averaged A-dependence of the F/B ratio of
the forward product cross sections to the backward ones, as predictedby CEM03 for the reaction of E0 = 1 GeV bremsstrahlung photons on
Au. 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.

in complete accordance with the available experimental data
(see the review196 and references therein). But the situation
changes 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 in
Figure 14), that is much less than the kinetic energy from several
tens 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 be
distributed isotropically in the system of the fissioning nucleus,
and the small momentum of the fissioning nuclei makes this
distribution almost isotropic also in the laboratory system. The
upper left plot of Figure 14 shows that the predicted yields forthe fission fragments in the forward and backward directions
are almost the same, i.e. the F/B ratio for the fission fragments
is almost equal to one, again in complete agreement with theavailable experimental data (see Reference 196 and references
therein).
The mean kinetic energy of the forward products shown in
the upper-right plot of Figure 14 is only very slightly higher
than that of the backward products (the momenta of fissioning
nuclei are low, as discussed above), with a little higher effectfor the spallation products than for fission fragments, as is to
be expected. Due to this fact and to the near isotropy of thefission fragments, some fission fragments may have their mean
velocity 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 problem
considering the forward and backward cross sections for every
product 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 of
two for all the spallation region (see also Figure 17), the situation changes for individual isotopes. The cross sections of theforward-emitted isotopes are still about a factor of two higher
than the backward cross sections for most of the spallation
products, but their ratio is much higher for Hg and Tl, anddepends strongly on the mass numbers of the products. Hg
and Tl are “photopion” products produced via (γ, π −xn) and (γ,2π −xn), respectively, with emission of only a few neutrons inA14 J. Nucl. Radiochem. Sci., Vol. 6, No. 2, 2005

6. Conclusions
The 2003 versions of the codes CEM2k+GEM2 and
LAQGSM, CEM03 and LAQGSM03, are extended to describe
photonuclear reactions. Both our models consider photoproduction of at most two pions, which limits their reliable application to photon energies up to only about 1.5 GeV. The
present version of our models do not consider photoabsorption
in the GDR region, which defines the lower limit of the photon
energy to about 30 MeV. Nevertheless, developing and incorporating of a routine based on the phenomenological systematics for the total photoabsorption cross section by Kossov into
CEM03 allow us to enlarge the region of applicability of
CEM03 and to get quite reasonable results for applications
both in the GDR region and above 1.5 GeV.
As shown by several examples, CEM03 and LAQGSM03
allow us to describe reasonably well, and better than theirprecursors, many photonuclear reactions needed for applications, as well as to analyze mechanisms of photonuclear reactions for fundamental studies. But our models still have several
problems. Figure 18 shows examples of such problems on
proton and deuteron spectra from reactions induced by 60
MeV monoenergetic photons on Ca: One can see that both
CEM03 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†

d 2 σ /(dT·dΩ)/µb MeV-1sr-1

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 go
mainly forward, with a ratio F/B up to ten or higher. On thecontrary, in reactions where many neutrons are emitted
approximately isotropically, the residual nucleus has lost mostof its “memory” of the initial momentum. Therefore theneutron-deficient products from such reactions have a smaller
F/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. Approaching
the 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 for
all 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. The
lower 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 1 8 1 Hg produced by the197
Au(γ, π −16n) reaction.
We think that an analysis of such recoil characteristics isquite informative not only for photonuclear reactions, but also
for 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 may
help us to distinguish the fission processes from the fragmentation (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 on
the recoil properties from reactions with any type of projectiles,
including bremsstrahlung photons, would be very useful.

Mashnik

40

60 MeV γ + Ca → p/d (90 deg) + ...

10

2

10

1

10

0

10

-1

10

-2

10

-3

0

p datad dataLAQGSM03
CEM03

10

20

30

40

50

60

T / MeVFigure 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, respectively. The CEM03 spectra are normalized to the total absorption
cross section as predicted by Kossov’s systematics, equal to 3.49 mb
for 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.

by the Kossov systematics, which gives 3.49 mb for this reaction, while the LAQGSM03 results are normalized to the MonteCarlo-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 two
below the available experimental data at energies around 60
MeV. This explains the difference between the CEM03 and
LAQGSM03 results shown in Figure 18, and suggest that the
Kossov systematics should be further improved. Even allowing
for this normalization problem, both codes appear to underestimate 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. CEM03
and LAQGSM03 have different intranuclear-cascade models,leading after the INC stage of any reactions to different
average 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. This
explains 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 deuteron
spectrum by CEM03 is partially related with an imperfectdescription of the preequilibrium emission of d from this reaction, due to an excessively simplified estimation of the probability 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 in
the GDR region, as discussed previously, and to extend ourmodels to describe photonuclear reactions at energies of 10
GeV or more.†
Our present study suggests that analysis of characteristics ofActually, after completing the manuscript of the present paper, we have extended already LAQGSM03 to describe photonuclear reactions on
nuclei 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 γ n 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-Exciton
Model (CEM) and Los Alamos Quark-Gluon String Model (LAQGSM) Codes,” Los Alamos National Laboratory Research Note X-5-RN (U) 0511, LANL Report LA-UR-05-2686 (2005). LAQGSM03.01 will be described in details in a separate future paper.

CEM03 and LAQGSM03

recoil nuclei produced by photonuclear and other types of reactions is a powerful tool to understand mechanisms of nuclear
reactions. We encourage future measurements of such characteristics both for photonuclear and proton-or/and nucleusinduced reactions.
Acknowledgments. We thank Dr. Kumataro Ukai for providing us with numerical values of single pion photoproduction
cross sections from their compilation.36 We are grateful to Dr.
Igor Pshenichnov for sending us the γ p and γ n event generators
used in their Moscow photonuclear reaction INC.33 We thankProf. Koh Sakamoto and Drs. Hiroshi Matsumura, Hiromitsu
Haba, and Yasuji Oura for providing us with their publications
and numerical tables of their measured data, as well as for useful
discussions, help in drawing several figures for us, and theirinterest in our modeling.
This work was partially supported by the Advanced Simulation
Computing (ASC) Program at the Los Alamos National Laboratory
operated by the University of California for the US Departmentof Energy, the Moldovan-US Bilateral Grants Program, CRDF
Project MP2-3045-CH-02, and the NASA ATP01 Grant NRA01-01-ATP-066.
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