Cross-Section Evaluations to 150 MeV for Accelerator...

Cross-Section Evaluations to 150 MeV for Accelerator-DrivenSystems and Implementation in MCNPX

M. B. Chadwick,* P. G. Young, S. Chiba,† S. C. Frankle, G. M. Hale, H. G. Hughes, A. J. Koning,‡R. C. Little, R. E. MacFarlane, R. E. Prael, and L. S. Waters

Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received April 24, 1998Accepted July 30, 1998

Abstract –New accelerator-driven technologies that utilize spallation neutrons, such as the production oftritium and the transmutation of radioactive waste, require accurate nuclear data to model the perfor-mance of the target/blanket assembly and to predict neutron production, activation, heating, shieldingrequirements, and material damage. To meet these needs, nuclear-data evaluations and libraries up to150 MeV have been developed for use in transport calculations to guide engineering design. By usingadvanced nuclear models that account for details of nuclear structure and the quantum nature of thenuclear scattering, significant gains in accuracy can be achieved below 150 MeV, where intranuclearcascade calculations become less accurate. Evaluations are in ENDF-6 format for important target/blanket and shielding materials (isotopes of H, C, N, O, Al, Si, P, Ca, Cr, Fe, Ni, Cu, Nb, W, Hg, and Pb)for both incident neutrons and incident protons. The evaluations are based on measured data as well aspredictions from the GNASH nuclear model code, which calculates cross sections using Hauser-Feshbach,exciton, and Feshbach-Kerman-Koonin preequilibrium models. Elastic scattering distributions and directreactions are calculated from the optical model. All evaluations specify production cross sections andenergy-angle correlated spectra of secondary light particles as well as production cross sections and en-ergy distributions of heavy recoils and gamma rays. A formalism developed to calculate recoil energydistributions is presented. The use of these nuclear data in the MCNPX radiation transport code is alsobriefly described. This code merges essential elements of the LAHET and MCNP codes and uses these newdata below 150 MeV and intranuclear cascade collision physics at higher energies. Extensive compari-sons are shown between the evaluated results and experimental cross-section data to benchmark and val-idate the evaluated library. In addition, integral benchmarks of calculated and measured kerma coefficientsfor neutron energy deposition and neutron transmission through an iron slab compared with MCNPXcalculations are provided. These evaluations have been accepted into the ENDF/B-VI library as Re-lease 6.

I. INTRODUCTION

High-current proton accelerators are being designedat Los Alamos National Laboratory~LANL ! and otherlaboratories for accelerator production of tritium~APT! ,transmuting long-lived radioactive waste into shorter-

lived products @accelerator transmutation of waste~ATW !#, converting excess plutonium, and producing en-ergy. These technologies make use of spallation neu-trons produced in~ p, xn! and ~n, xn! nuclear reactionson high-Z targets. New nuclear cross-section data areneeded to improve theoretical predictions of neutron pro-duction, shielding requirements, activation, radiation heat-ing, and materials damage. Such predictions can guidethe design of the target0blanket configurations and canreduce engineering overdesign costs.

To address these needs, a program is under way todevelop new evaluated nuclear data libraries for inci-dent protons and neutrons up to 150 MeV for a range of

*E-mail: [email protected]†Permanent address: Advanced Sciences Research Cen-

ter, JAERI, Tokai, Ibaraki 319-11, Japan.‡Permanent address: ECN, P.O. Box 1, 1755 ZG Petten,

The Netherlands.

NUCLEAR SCIENCE AND ENGINEERING:131, 293–328~1999!

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high-priority elementsa in the ENDF-6 format.2,3 Theseevaluations are based on a combination of nuclear modelcalculations and measured data to evaluate cross sec-tions. The MCNP radiation transport code4 is being de-veloped to utilize these evaluated libraries, as well as toinclude charged-particle transport, and is being mergedwith the LAHET intranuclear cascade code5 for model-ing nuclear reactions above 150 MeV. The extendedmerged code is referred to as MCNPX~Ref. 6!. This pa-per describes methods and results of the neutron and pro-ton cross-section evaluations and briefly summarizes theirimplementation in the MCNPX code.

Since the APT program has been the primary sourceof support for this research, the evaluations described hereare for high-priority elements in that program: H, C, N,O, Al, Si, P, Ca, Cr, Fe, Ni, Cu, Nb, W, and Pb, as well asfor Hg, owing to its importance as a spallation target forneutron-scattering material science studies. While theseelements are also likely to be of high priority in otheraccelerator-driven applications, there are some notableomissions in this work, such as actinides. Future re-search is needed, therefore, to extend the usefulness ofthis work for ATW applications. In the case of tritiumproduction, the current design consists of a 1.7-GeV pro-ton beam incident on a split tungsten target surroundedby a lead blanket. Through~ p, xn! and ~n, xn! nuclearreactions, neutrons are produced and are moderatedby heavy water in the target region and light water inthe blanket region. These moderated neutrons are sub-sequently captured on3He, which flows throughout theblanket system, to produce tritium via the~n, p! reaction.

The GNASH nuclear model reaction code7,8 is usedextensively in this work to predict nuclear reaction crosssections for particle and gamma-ray emission becausemeasured data at higher energies are relatively sparse.However, extensive use is made of existing experimen-tal data to guide and benchmark the model calculations,and numerous comparisons between the evaluated re-sults and experimental data are shown in this paper forvalidation purposes. Furthermore, the evaluated data forthe total cross sections and the total nonelastic cross sec-tions are usually primarily determined from measure-ments, since there are often a sufficient number of suchexperimental data to constrain the evaluations. An eval-uation based on experimental data, in addition to nuclearmodel predictions, can be expected to be more accuratethan that based solely on model calculations. The opticalmodel codes ECIS~Ref. 9! and SCAT~Ref. 10! wereused to predict elastic scattering angular distributions. Fulldetails of the calculation and evaluation methods usedare described in Sec. II.

The LAHET Code System has been instrumental inguiding the design of spallation targets. Until now, theLAHET intranuclear cascade code has been used to modelthe nuclear interactions as well as the radiation transportfor neutral particles above 20 MeV and for charged par-ticles of all energies. Below 20 MeV, the nuclear reac-tions and the transport of neutral particles are performedby the MCNP code,4 which uses ENDF0B-VI-evaluatednuclear data libraries. The intranuclear cascade model inLAHET is most accurate above 150 MeV, where semi-classical approximations become more applicable. Be-low 150 MeV, however, nuclear interactions are moresensitive to specific details of nuclear structure along withquantum effects in the scattering. For this reason, the eval-uated data libraries are being extended up to higher en-ergies~150 MeV!, since the libraries can be based on theGNASH, ECIS, and SCAT nuclear modeling codes, whichbetter account for this physics.

The upper data-library energy of 150 MeV was cho-sen for the following reasons:

1. It corresponds approximately to the pion thresh-old, and pion production is not included in the GNASHmodel code used to evaluate the cross sections.

2. The INC model works fairly well above thisenergy.

3. The GNASH code system has been benchmarkedextensively below this energy and has been shown to per-form well in an international code intercomparison,11 butfor use at higher energies, additional improvements wouldbe desirable, such as including more than two multiplepreequilibrium particles.12,13

A summary of the information included in the ENDFevaluations is given in Table I. For incident neutrons,the new evaluations to 150 MeV have been built on theexisting ENDF0B-VI evaluations, which usually extendup to 20 MeV. For protons, the new evaluations extendfrom 1 to 150 MeV. Total, nonelastic, and elastic scat-tering cross sections are given, as are production crosssections for light particles and heavy nuclides. For thelight particles, angle-integrated production spectra~in-clusive emission spectra! are tabulated along with thepreequilibrium fractions to allow angle-energy corre-lated double-differential emission spectra to be deter-mined. For heavy nuclides~recoils! and gamma rays,only angle-integrated emission spectra are provided, andisotropic angular distributions are assumed. For gammarays, this is a reasonable approximation; for recoils, theangular distributions are unimportant for most applica-tions due to the very small recoil ranges.

Figures 1 and 2 provide three-dimensional illustra-tive examples of the emission spectra information avail-able from the evaluations. These examples, for neutronsincident on lead and on carbon from 20 to 150 MeV, wereobtained by combining the nonelastic cross sections,

aThe new 150-MeV evaluated cross sections, collectivelyreferred to as the LA150 library, are available via the internetat http:00t2.lanl.gov0data0he.html. They can be augmented withother evaluations~e.g.,9Be and238U! to 100 MeV developedin the late 1980s by Young et al.1

294 CHADWICK et al.

NUCLEAR SCIENCE AND ENGINEERING VOL. 131 MAR. 1999

multiplicities ~yields!, and probability energy distribu-tions tabulated in the ENDF file. Figure 1 shows the emis-sion spectra of the light ejectiles and gamma rays and thetrends of increasing high-energy preequilibrium emis-sion with increasing incident energy. The effect of theCoulomb barrier in suppressing low-energy charged-particle emission is also evident.~The low-energy evap-oration peaks seen for tritons and alphas are significantlysmaller than those for protons—they appear pronouncedin Fig. 1 due to the smaller cross-section scales used inthe graphs and the small magnitude of cluster preequi-librium emission.! In Fig. 2 the recoil spectra are shownfor only a few of the many product nuclides formed forneutrons on carbon. The heavier mass of the recoil nu-clides results in the extension of their emission energiesto lower values than seen for the light particles in Fig. 1~note that the emission energy axes in Fig. 2 only extendto 15 MeV, unlike those in Fig. 1 that extend to 150 MeV!.Three-dimensional pictures of this type, along with sim-ilar pictures of the preequilibrium ratio~used for obtain-ing angular distributions! and of light-particle productioncross sections, are shown for every isotope evaluation ina laboratory report.2 They provide an important compo-nent to the validation of the evaluations because trendsin the large amounts of evaluated data can be quicklyobserved.

Prior to the present work, high-energy neutron andproton data libraries up to 100 MeV were first developedin the late 1980s for a range of elements.1 More recently,high-energy libraries were generated for particle radio-therapy simulations in the Lawrence Livermore NationalLaboratory~LLNL ! PEREGRINE project, through anLLNL-LANL collaboration.14,15 The present evaluateddata libraries represent an advance over these earlier worksbecause they also include energy-distribution and yieldinformation for the heavy-recoil product nuclides and arebased on the latest version of the GNASH code.7 In re-cent years, other groups have initiated programs to de-

velop high-energy nuclear data libraries, mainly for ATWand medical applications.16–19

This paper is organized as follows. Section II pro-vides an overview of the nuclear models used in this work.Section III ~and the Appendix! discusses the calculationof nuclear recoil spectra, a new capability we have re-cently developed. Section IV describes the evaluationsfor each of the elements studied and provides detailedcomparisons with experimental cross-section data. Sec-tion V describes recent extensions to the MCNP-LAHETcode system, as embodied in the new MCNPX code, toutilize the ENDF libraries in the calculations of radiationtransport and energy deposition and shows some integralbenchmark results that have been obtained to validate thecross-section evaluations.

II. NUCLEAR MODEL CALCULATIONS

II.A. General

The latest version of the GNASH code has been de-scribed in Ref. 7, and its recent application in nuclearreaction evaluation work has been described in Refs. 14,15, and 20. For this reason, here we provide only an over-view of the models used in the calculations, concentrat-ing on new features.

The GNASH code calculates nuclear reaction crosssections using the Hauser-Feshbach theory for equilib-rium decay and the exciton model for preequilibrium de-cay. Direct reactions to low-lying residual nucleus statesare precalculated and included as input into the GNASHcalculations. The preequilibrium emission cross sectionscan also be calculated according to the quantum mechan-ical Feshbach-Kerman-Koonin~FKK ! theory.21,22How-ever, for calculations of the large number of nuclear dataneeded, the exciton model was generally utilized be-cause of the shorter computational times needed, and

TABLE I

Contents of LA150 Data Library for Incident Neutrons and Protons

Reaction Type Cross SectionAngle-IntegratedEmission Spectra

Angle-Energy-CorrelatedEmission Spectra

Total Yes~for neutrons! – – – – – –Nonelastic Yes – – – – – –Elastic Yes – – – ~c.m. angular distributions!Neutron production Yes Yes, in c.m. Yes, using Kalbach preequilibrium ratiosProton production Yes Yes, in c.m. Yes, using Kalbach preequilibrium ratios

Deuteron production Yes Yes, in c.m. Yes, using Kalbach preequilibrium ratiosAlpha production Yes Yes, in c.m. Yes, using Kalbach preequilibrium ratiosTriton production Yes Yes, in c.m. Yes, using Kalbach preequilibrium ratiosGamma Production Yes Yes, in lab No~isotropy assumed!Nuclide production Yes Yes, recoils in lab No~isotropy assumed!

CROSS-SECTION EVALUATIONS TO 150 MeV 295


Fig. 1. Three-dimensional graphical representations of light-particle angle-integrated emission spectra from the ENDF eval-uation for neutrons on lead. The spectra are in the c.m. reference frame. Pictures of this type are available in Ref. 2 for all isotopesevaluated.

296 CHADWICK et al.


Fig. 2. Three-dimensional graphical representations of recoil angle-integrated emission spectra from the ENDF evaluationfor neutrons on carbon. The spectra are in the laboratory reference frame.



comparisons with the FKK theory were made only in se-lect cases for validation purposes~see Sec. II.D!.

The system of computer codes used to produce theevaluated cross sections is shown in Fig. 3. The steps inthe evaluation involve~a! setting up the input informa-tion using the PREGNASH code23; ~b! calculating elas-tic scattering, transmission coefficients, and directinelastic scattering with an optical mode code such asECIS; ~c! running GNASH to determine emission crosssections and spectra; and finally~d! running GSCAN, acode that scans the GNASH output, calculates recoilemission spectra for the heavy isotope products, and gen-erates data in ENDF-6 format.

Where secondary particle emission experimental dataexist, certain input parameters, such as level density pa-rameters and the preequilibrium matrix element, are some-times adjusted within their ranges of validity to optimizeagreement with the measurements.

Details of the nuclear models used are described inSecs. II.B, II.C, and II.D.

II.B. Optical Models

Evaluations begin with the development, and in somecases selection from the literature, of an optical model

~deformed or spherical, depending on the nucleus understudy! to describe measured total, reaction, and elasticscattering cross sections. In many cases, if a specificnucleus-dependent potential does not exist, we have madeuse of a modified version of Madland’s global medium-energy nucleon potential24 above an energy of, typically,30 to 50 MeV. The revised expression for medium-energy potential is given in Table II, where the symbolsare defined in a conventional way. Generally, this globalpotential gives a good description of measured total andreaction cross sections and elastic scattering distribu-tions up to;160 MeV. Note that the potential in Table IIis a nonrelativistic approximation to that presented inRef. 24, which uses relativistic kinematics, allowing it tobe used in the nonrelativistic SCAT code.

For evaluation of Cr, Ni, and Cu, we have searchedfor new nucleon optical potentials to reproduce in moredetail the isotopic data for elastic scattering angular dis-tributions,s-wave strength function25 and total cross sec-tions for neutron projectiles, and total reaction crosssections for proton projectiles. The parameter search wascarried out based on the Bayesian generalized least-squares method for Cr and Ni and by ECISVIEW~Refs. 16 and 26! for Cu. In these cases, the energy de-pendencies of potential depths are expressed in the

Fig. 3. Schematic flowchart of the computer codes usedin the nuclear model calculations.

TABLE II

Global Nucleon Optical Potential*

Parameter Expression

VR 105.57 16.5h 2 17.14375 ln~E!2 0.4Z0A103~ 1

2_ 1 tz!

rR 1.1251 0.001EaR 0.6751 0.00031EWD 0.0WV 2.43461 0.1016E 2 9.2883 1024E2

1 3.873 1026E3

rV 1.6502 0.0024EaV 0.3281 0.00244EVso 19.06 3.75h 2 3.154 ln~E!Wso 0.0

rso H0.9201 0.0305A103

0.98~A # 40!

aso 0.7682 0.0012Erc 1.25

*For energies from;30 to 50 MeV up to 160 MeV, basedon Madland’s24 potential but modified for use in a nonrel-ativistic calculation. The potential depths and projectile energyE are expressed in mega-electron-volts, while the geometricparameters are given in femtometres. The symboltz denotesthe z component of projectile isospin, i.e.,1

2_ for neutrons and

2 12_ for protons,h 5 ~N 2 Z!0A, whereN, Z, andA represent

the neutron, proton, and mass numbers of the target nucleus,respectively. In7 or 6, the upper sign corresponds to neu-trons and the lower one to protons.

298 CHADWICK et al.


following way, which is similar to that proposed byDelaroche et al.27:

VR 5 Ve2lR~E2EF ! 1 V0 1 V1E ,

WD 5 WD0e2lWD

~E2EF !~E 2 EF !4

~E 2 EF !4 1 WD1

4 ,

WV 5 WV0

~E 2 EF !4

~E 2 EF !4 1 WV1

4 ,

Vso 5 6.0e20.005E

and

Wso 5 0.22 0.011E . ~1!

The symbolEF denotes the Fermi energy and was calcu-lated as

EF ~n! 5 2 12_~Sn~A! 1 Sn~A 1 n!!

and

EF ~ p! 5 2 12_~Sp~A! 1 Sp~A 1 p!! , ~2!

where

EF ~n! 5 neutron Fermi energy

EF ~ p! 5 proton Fermi energy

Sn~A! 5 neutron separation energy from targetnucleusA

Sp~A! 5 proton separation energy from targetnucleusA

Sn~A 1 n! 5 neutron separation energy from tar-get1 n nucleus

Sp~A 1 p! 5 proton separation energy for target1 pnucleus.

The potential form factor was chosen to be of Woods-Saxon form forVR andWV, derivative Woods-Saxon forWD, and Thomas-Fermi form for the spin-orbit parts. Thecalculation was performed with ECIS making use of rel-ativistic kinematics.

The following global potentials were employed inthe evaluations for composite particles, which are neededfor the inverse process of composite particle emission:

1. deuterons—the Lohr-Haeberli28 and the Pereypotential29

2. tritons—the Becchetti-Greenlees30 potential

3. alpha particles—the McFadden-Satchler31 poten-tial.

Recent work in nuclear reaction theory has empha-sized the importance of calculating direct inelastic scat-tering cross sections to low-lying states and indicated thatcollective direct excitations often persist into the contin-

uum.32 For this reason, the GNASH code has been mod-ified to allow the inclusion of direct scattering crosssections for large numbers of states~sometimes as manyas 100!, including those that are embedded within the“continuum” region, where a statistical level density pre-scription is used, such as excitation of giant resonances.For such direct reactions, nuclear deformation param-eters are obtained from the literature, and the ECIS codeis used to calculate the distorted wave Born approxima-tion ~DWBA! cross sections. These are then included asinput to GNASH so that the effects of their subsequentgamma-ray decay, as well as the removal of flux fromother reaction mechanisms, are incorporated into theresults.

Gamma-ray transmission coefficients are deter-mined using the Kopecky-Uhl33 formalism, whichmodifies the Brink-Axel hypothesis to include anexcitation-energy dependence of the giant dipole~andother multipole! strength.

II.C. Level Densities

The Ignatyuk et al.34 nuclear level densities are used,which include the washing out of shell effects with in-creasing excitation energy, and are matched continu-ously onto low-lying experimental discrete levels. TheIgnatyuk model for describing the statistical level den-sity properties of excited nuclei is particularly appropri-ate for the relatively high energies studied in this work.For instance, it has been shown35 that the larger leveldensity parameter at high excitation energies that resultsfor nuclei near closed shells causes a lower nuclear tem-perature, and therefore a lower average ejectile evapora-tion energy, which in turn significantly influences thedistribution of isotope production yields after the reac-tion. Our implementation of this formalism, using aconstant-temperature region just above the discrete lev-els before the Fermi-gas region begins, also allows it tobe applied at low excitation energies.

In this approach, the level density parameter is en-ergy dependent:

a~U ! 5 a@11 f ~U !dW0U# , ~3!

wherea is the asymptotic high-energy value. Shell ef-fects are included in the termdW, which is determinedvia dW5 Mexp~Z,A! 2 Mld~Z,A, b!, whereMexp~Z,A! isthe experimental mass andMld~Z,A, b! is the liquid-drop mass at deformationb. The exponential damping ofshell effects is given by

f ~U ! 5 12 exp~2gU ! , ~4!

whereg 5 0.05 MeV. The asymptotic form ofa~U ! r ais given by

a

A5 h 1 bA . ~5!



By fitting s-wave resonance data at the neutron separa-tion energy, the valuesh 5 0.1375 andb 5 28.3631025 were obtained.1

In some cases, level density analyses were per-formed for all residual nuclei to determine the maximumnumber of discrete levels that should be used~e.g., forlight nuclei such as C, N, and O, where the number ofresidual nucleus products is relatively small!. However,since many different residual nuclei can be produced innuclear reactions up to 150 MeV, exceeding 100 in manycases for heavy targets, in some cases we automate thisprocedure by always using a maximum of 10 to 15 ex-perimental levels. This procedure is expected to be ade-quate for nuclear reactions induced at these relatively highincident energies—it has the merit that the nuclear levelsincluded for each nucleus are likely to be complete up tothe highest level’s energy, which is important whenmatching a statistical level density theory onto the den-sity of known low-lying levels.

II.D. Preequilibrium Emission

After the aforementioned steps have been completed,all input parameters are available for the GNASH calcu-lations. An input parameter that is sometimes adjusted isthe exciton model damping matrix element that governsthe relative probability of emission from different stepsin the preequilibrium cascade. To determine the best valueto use, experimental emission spectra measurements arecollected, and trial calculations are performed. The ma-trix element is then adjusted within the range from 140to 175 MeV3 ~Ref. 8! to optimize the global agreementwith measurements.

The semiclassical exciton model in combination withthe Kalbach angular-distribution36 systematics providesa reliable method to predict double-differential outgoingspectra for all the nuclides considered here. Since the high-energy tail of the continuum spectrum is so important—certainly for high incident energies it accounts for themajor part of the reaction cross section—we have vali-dated the exciton model’s predictions through compari-sons with quantum preequilibrium calculations. Thisapproach enables a realistic prediction of angle-integratedspectra and the angular distributions without using anyexperiment-based phenomenology. We use the recent two-component extension37 of the multistep direct~MSD!model of Feshbach-Kerman-Koonin.21 It comprises acombination of DWBA matrix elements and a statisticaldescription of the excited states of the nucleus. When areaction proceeds by the MSD mechanism, at least oneparticle is in the continuum throughout the process, andat each subsequent step of the reaction, a new particle-hole pair is created. After one or a few collisions, thecontinuum particle is emitted in a direction that still hasretained some coupling to the initial direction and is there-fore forward-peaked. The main difference with conven-tional direct-reaction theories is the high density of final

and intermediate states, which necessitates statistical pos-tulates in the direct-reaction formalism so that the com-putation of these processes remains tractable. In Ref. 37we presented a formalism for calculating MSD cross sec-tions in a fully two-component theory, where all possibleneutron and proton particle-hole excitations are explic-itly followed for all orders of scattering.

Figure 4 shows comparisons of double-differentialcross sections as calculated with the FKK method withexperimental data38 for the Fe~ p, xn! and Pb~ p, xn! re-actions at 113 MeV. The good agreement obtained be-tween the FKK predictions and experiment, and betweenFKK and exciton model predictions,11 provides some con-fidence in the use of the exciton model in GNASH forthe large-scale calculations of nuclear data described inthis paper. Theoretical studies using the FKK preequilib-rium theory have played another useful role in thiswork—a number of theoretical nuclear reaction physicsdevelopments have been made and tested within the con-text of the quantum multistep theory, such as multiple

Fig. 4. Comparison of quantum mechanical FKK predic-tions of continuum preequilibrium emission spectra with ex-perimental data.38

300 CHADWICK et al.


preequilibrium emission12 and preequilibrium spin ef-fects,39 before being included in the GNASH code fornuclear data evaluation calculations.

III. CALCULATION OF RECOIL SPECTRA

The calculation of the energy spectra of secondary re-coils in this work represents an advance in the complete-ness of high-energy ENDF files. Previous high-energyevaluationworkshaveeitheromitted this information,sincetransport effects were the main focus of study,1,16or havetabulated the total energy per reaction deposited by the re-coils but have neither specified recoil energy spectra norhow this energy is divided among individual recoils.14,15

Our more complete treatment facilitates detailed calcula-tions of radiation damage and heating. In addition, inapplications that use these data in simulations of heavy-particle radiotherapy, one could utilize the recoil spectrato determine relative biological effectiveness in additionto absorbed dose because the linear energy transfer prop-erties of the ionizing radiation are known. Clearly, kine-matics determine that energy deposition by recoils~definedas all nuclides withA. 4! is most important for reactionson light target nuclei. Indeed, we calculate that for 20-MeVneutrons on oxygen, approximately 30% of the total en-ergy deposition~kerma! is due to the recoils.40

The basic physical principles influencing recoil en-ergies were elucidated in the 1960s by Blann and Ewart,41

who measured recoil ranges and made use of the Lindhard-Scharff-Schiott theory for the range-energy relationship.Their findings can be briefly summarized:

1. In the formation of a compound nucleus, full mo-mentum transfer from the projectile occurs. Compound-nucleus evaporation of a particle leads to a new recoilthat has, on average, a higher kinetic energy than the ki-netic energy before emission.

2. Where preequilibrium reactions occur in the firststages of the reaction, there is only a partial momentumtransfer from the projectile, which results in lower ki-netic energies of the first recoil nucleus after preequilib-rium emission.

A more recent work by Gadioli et al.42 also nicely dem-onstrates these effects.

Full details of our calculational method for recoilsare described in Ref. 20. Briefly, the GSCAN code is usedto read emission spectra from each decaying compositenucleus in the GNASH output. Kinematic transforma-tions from the center of mass~c.m.! to lab reference framesare performed analytically to determine recoil lab ener-gies, taking advantage of the simple analytic functionalform of the angular distributions embodied in the Kal-bach systematics.36 Equations for these kinematic trans-formations are provided in the Appendix.

Since the recoiling nucleus after particle emission isfrequently particle-unstable and undergoes further parti-cle emissions, the calculation of the recoil spectra of agiven product nuclide requires following the sequentialparticle decays in a coupled manner. The c.m.-to-lab boostvelocity changes during the evolution of the reaction.41

The initial composite nucleus lab velocity after the pro-jectile strikes the target nucleus is rather large. However,since the first ejectile is often a preequilibrium emissionwith a large kinetic energy in a forward direction, the labrecoil speeds after this primary emission are reduced~which is another way of saying that only partial momen-tum transfer occurs!. During further sequential com-pound nucleus decays, the recoiling nuclei tend to pickup speed again as internal excitation energy is convertedto particle emission energy and recoil kinetic energy.

The resulting calculated recoil spectra are tabulatedas angle-integrated spectra in the laboratory frame in thefile-6 section of the ENDF evaluation. Since recoil rangesare small, a detailed representation of angle-energy-correlated recoil spectra is unnecessary for most appli-cations. Also, the recoil spectra are represented inhistogram format for ten equally sized emission energybins. Such a coarse representation of the calculated spec-tra prevents the evaluated file from becoming too long,and this level of detail for the recoil information is suf-ficiently accurate for calculations of radiation heating anddamage. We checked that the average energy of thecoarsely binned recoil spectra agreed well with the exactresults, which is important for ensuring that the nonelas-tic recoil kerma coefficients are accurately defined. Il-lustrative examples of recoil spectra are shown in Fig. 2.

An example of the variation in calculated recoil ve-locities with particle emission is shown in Fig. 5 for 80-MeV protons on28Si for processes involving sequential

Fig. 5. Variation in average velocity of recoiling nucleias neutrons are emitted from decaying phosphorus isotopes inthe 80-MeVp 1 28Si reaction.



neutron emission. The initial reduction in recoil velocitydue to first-particle preequilibrium emission is evident,followed by increasing average recoil velocity with se-quential equilibrium neutron decay.

IV. RESULTS AND COMPARISONSWITH MEASUREMENTS

IV.A. General

This section describes the evaluation methods and nu-clear model calculations used for each element under study.The methods used depend on the nature of the target, andin particular, they depend on the extent to which statisti-cal assumptions implicit in the nuclear models are valid.For this reason, the cross-section evaluations of the light-est nuclei studied here, hydrogen and deuterium, werebased almost entirely on experimental data and on nu-clear theoryR-matrixandphase-shift representationsofex-perimental data.The evaluations for targets such as carbon,nitrogen, and oxygen used GNASH nuclear model calcu-lations, but they also relied heavily on measured data. Eval-uations of targets heavier than oxygen were based almostexclusively on GNASH model calculations.

The comparisons in this section between the evalu-ated results and experimental data are critical for bench-marking the evaluations, for validation purposes, and forassessing the accuracy of the evaluated data library. Eventhough these comparisons are rather extensive, numer-ous comparison figures have been omitted due to limita-tions on space~which can be provided on request by thefirst author!. The figures that we use are representativeand have been chosen to emphasize nuclear reactions ontargets that are most important for accelerator-driven sys-tems, such as Pb, W, and Fe. Fewer comparisons are pro-vided for other targets that are somewhat less importantor that are documented elsewhere.14,15,43

IV.B. The206,207,208Pb Evaluations

The development of high-quality nuclear data for leadis particularly important due to lead’s role as a spallationtarget and neutron multiplier in many accelerator-drivensystem designs.

Measurements for the total, elastic, and nonelasticcross sections for lead are shown in Figs. 6, 7, and 8,compared with our evaluated results. In the case of thetotal cross section, we were guided mainly by the Lisowskiet al.45 and Finlay et al.46 data. The elastic scattering an-gular distributions~Fig. 7!, calculated with a deformedoptical potential developed for lead,47 are seen to ac-count for the measurements well. The total nonelasticcross section obtained from this coupled-channel calcu-lation was modified slightly to better agree with the ex-perimental data, as shown in Fig. 8. Figure 8 also showsthe proton nonelastic cross section compared with mea-

surements. An accurate representation of the nonelasticcross sections is important because the production crosssections of secondary ejectiles are directly proportionalto this quantity~being the product of the nonelastic crosssection and the ejectile yield, or multiplicity!. The eval-uated total and nonelastic cross sections were taken to beidentical for all the lead isotopes, a good approximationdue to the small relative mass differences.

Direct inelastic scattering to low-lying levels in leadisotopes was calculated using the ECIS code, usingDWBA theory. Excitation of states in the discrete levelregion, as well as states within the continuum region, wasconsidered. Ninety-eight states were considered for208Pbup to an excitation energy of 7.114 MeV; 59 states wereconsidered for207Pb up to an excitation energy of 6.483MeV; and 13 states were considered for206Pb up to anexcitation energy of 6.423 MeV. Deformation lengths forthe DWBA transitions were obtained from the NuclearData Sheets and from Refs. 48 and 49.

The only neutron-induced emission spectra measure-ment above 20 MeV is that of Hjort et al.50 for the65-MeV Pb~n, xn! reaction at forward angles. These dataare extremely useful for benchmarking the neutron-induced GNASH calculations, and Fig. 9 demonstratesthat the GNASH predictions are in good agreement withthese data. The fall-off in the experimental data below20-MeV emission energy is an artifact and due to thehigh detector threshold energy. Some of the fluctuationsseen in the measured data are due to the excitation ofgiant resonances high in the continuum not included inour calculations.

Numerous data for neutron production via Pb~ p, xn!reactions exist. Comparisons between the evaluated re-sults and angle-integrated emission spectra measurementsat 26, 45, and 80 MeV are shown in Fig. 10. Agreement

Fig. 6. Evaluated neutron total cross section for208Pb com-pared with measurements.

302 CHADWICK et al.


with the measured data is good with the exception of the80-MeVreaction, where the calculations underpredict neu-tron emission in the 20- to 40-MeV energy range. At113 MeV, the evaluation is compared to the double-differential experimental data of Meier et al.38 in Fig. 11.Agreement is fairly good over the whole emission energyrange, except at 150 deg. The magnitude of the calculatedback-angle preequilibrium emission is determined by theextent of forward-backward asymmetry from the Kal-bach angular-distribution systematics36 and is thereforeonly as accurate as these systematics are accurate. How-ever, the small magnitude of the back-angle cross sectionimplies that the practical impact of the back-angle under-prediction is expected to be small.

The increasing importance of preequilibrium emis-sion with incident energy is evident in Fig. 10, as canbe seen from the significant contribution of high-energy

Fig. 7. Evaluated neutron elastic scattering cross sectionfor 208Pb compared with measurements.44

Fig. 8. Evaluated neutron and proton nonelastic cross sec-tion for 208Pb compared with measurements.44

Fig. 9. Evaluated208Pb~n, xn! neutron emission spectraat 65 MeV compared with experimental data.50



ejectiles for the higher incident energy reactions. In addi-tion, this figure also shows the increased neutron emis-sion in the evaporation regime with increasing incidentenergy due to energy conservation~more energy is avail-able toovercomeseparationenergies forparticleemission!.

IV.C. The196,198,199,200,201,202,204Hg Evaluations

Mercury is currently receiving a great deal of inter-est as a spallation neutron source, particularly at accel-

erator facilities used in material science studies. NoENDF0B-VI evaluation exists for mercury, though re-cently Shibata et al.51 have produced neutron evalua-tions below 20 MeV for seven mercury isotopes for theJapanese JENDL-3.3 file. Through a collaboration withthese authors, we have extended their neutron evalua-tions up to 150 MeV using GNASH model calculationsand have produced new proton evaluations from 1 to150 MeV.

Because of the very limited number of experimentaldata for nucleon reactions on mercury, the evaluated dataare heavily based on model calculations. An optical modeloriginally developed by Chiba for neutron scattering onlead was adapted for use on mercury. This potential wasused for the total, nonelastic, and elastic scattering dis-tributions. For protons, the medium energy potential~Table II! was used above 20 MeV, and the Becchetti-Greenlees potential,30 at lower energies. Deformationlengths for inelastic scattering were obtained from theanalyses performed for the JENDL-3.3 evaluations.

IV.D. The182,183,184,186W Evaluations

Tungsten is a particularly important element in theAPT program due to its use as the spallation neutron tar-get. Its high melting point enables it to withstand largeproton beam currents, and a high number of spallationneutrons are released per incident proton. Because low-energy neutrons have a high neutron capture cross sec-tion on tungsten, a split-target design is used to minimizeneutron self-absorption.

Prior to a recent LANL total cross-section measure-ment,52 only two measurements of the total cross sectionon tungsten existed above 20 MeV: those of Peterson,Bratenahl, and Stoering53 and Hildebrand and Leith.54

The new total cross-section data were taken at the Weap-ons Neutron Research white neutron source facility andextend from 6 to 600 MeV. Our evaluated results from 20to 150 MeV follow these new data for elemental tung-sten, which are in good agreement with the Peterson mea-surements~Fig. 12!. Since the total cross section isexpected to vary by less than;2% among the naturallyoccurring tungsten isotopes, our evaluation uses the sameelemental total cross section for all the isotopes.

No measurements exist for the neutron nonelasticcross section on tungsten, though there is a 90-MeV mea-surement of the proton nonelastic cross section by Kirbyand Link.55 Our evaluated nonelastic cross section makesuse of optical model calculation results. Below 80 MeV,the neutron potential of Young and Arthur was used,1

and above 80 MeV, the global Madland potential wasused~Table II!. The calculated neutron nonelastic crosssection agreed well with the Kirby proton-induced mea-surement~after scaling by the calculated optical modelratio of neutron-to-proton nonelastic cross section at90 MeV!. The shapes of the calculated results are alsoconsistent with measurements at other energies: data at

Fig. 10. Evaluated208Pb~ p, xn! angle-integrated neutronemission spectra compared with experimental data44 at inci-dent energies of 26, 45, and 80 MeV.

Fig. 11. Evaluated208Pb~ p, xn! double-differential neu-tron emission spectra compared with experimental data38 at113-MeV incident energy.

304 CHADWICK et al.


14 MeV ~Ref. 56!, and systematics from neutron-induced measurements on other targets at higher ener-gies~interpolated using a mass dependence ofa1 bA203 !,as shown in Ref. 57. Optical model calculations usingthe medium energy potential~Table II! above 20 MeVand the Becchetti-Greenlees potential at lower energieswere performed for protons, with a small renormaliza-tion to better account for the measurements. The datashown in Fig. 12 include Kirby’s 90-MeV value, mea-surements on tantalum~which would be expected to besimilar since tantalum is adjacent to tungsten in the pe-riodic table!, and systematics from measurements onother targets.44

Direct inelastic scattering reaction mechanisms wereconsidered for the tungsten isotopes calculated with theECIS code. Reaction mechanisms studied included~a!excitation of low-lying rotational levels and~b! excita-

tion of giant isoscalar 1-, 2-, and 3-~LEOR! resonances.Our calculation of these collective excitations followedthat of Marcinkowski, Demetriou, and Hodgson.58

At 26 MeV, Marcinkowski et al.59 have measured184W~n, xn! neutron emission spectra. Their angle-integrated data are compared in Fig. 13 with our calcu-lations, and the agreement is excellent. This is due, inpart, to the theoretical description of collective excita-tions. The GNASH calculation without collective en-hancements is shown by the dashed line and substantiallyunderpredicts the high-energy cross sections. The exci-tation of the giant isoscalar broad resonances account forthe cross section given by the difference between the solidand dashed lines in Fig. 13; the calculated peak at thehighest emission energies is due to the excitation of ro-tational levels. The agreement seen in Fig. 13 is signifi-cantly better that that found in the model calculationscontributed to the 1988 Code Intercomparison60 becauseof the inclusion of continuum collective effects in thiswork.

A measurement of neutron production in the 113-MeV proton-induced reaction on tungsten was made byMeier et al.38 ~see Fig. 14!. The only other existing mea-surement for neutron production is from Skyrme.61 Anumber of factors, however, suggest that the double-differential Meier et al. data may be;50% too high:

1. Skyrme’s data61 for tungsten are significantlylower and in good agreement with our evaluation~Fig. 15!.

2. Comparisons with other Meier data, such as datafor a lead target,38 indicate that the tungsten data appearto be anomalously high for all emission energies andangles.

(a)

(b)

Fig. 12. Comparison of tungsten evaluation and elemen-tal measurements for~a! total neutron cross section44,52 and~b! proton nonelastic cross section.

Fig. 13. Comparison of the evaluated 26-MeV184W~n, xn!emission spectrum with measurements.59



3. Energy balance arguments argue against the highneutron emission multiplicity implicit within the Meieret al. data.

These factors are discussed in detail in Ref. 62. Fig-ure 14 shows our calculated emission spectra at four an-gles, and when the Meier et al. measurements are scaledby a factor of 203, the agreement is seen to be good. Thecalculated neutron production spectra in the low-emission-

energy evaporation region are compared with Skyrme’smeasurements at 42 and 150 MeV in Fig. 15. Again, theMeier et al. data appear to be inconsistent with both ourcalculations and the Skyrme data.

No W~ p, xp! measurements exist, but Richteret al.63 have recently measured Ta~ p, xp! emission spec-tra at 120 MeV at the National Accelerator Center inFaure, South Africa. These data are useful for bench-marking our calculations because continuum emissionspectra for tungsten and tantalum would be expected tobe similar at this energy. Figure 16 shows calculatedangular distributions at various emission energies com-pared with these data. The increase in forward peakingwith increasing emission energy is evident, and the cal-culations using Kalbach angular-distribution systemat-ics36 are seen to describe the variations in the data withangle over many orders of magnitude. At the highestemission energy~100 MeV!, our calculations overpre-dict the measured proton emission at the forward angles.

IV.E. The93Nb Evaluation

Niobium is present at the 5.5% level, by weight, inInconel-718.a This is a structural alloy used in the LANLAPT design in the proton beam window. It is also usedfor structural support of the tungsten spallation neutrontarget tubes and for cladding the tungsten tubes to pre-vent water corrosion. Furthermore, niobium is present inthe superconducting cavities in the proton accelerator, andnuclear reactions on niobium must be understood to sim-ulate accidental beam-spill scenarios.

Global optical potentials described in Sec. II.B, in-cluding the medium energy potential in Table II, were

aInconel is a trademark of the Inco family of companies.

Fig. 14. Evaluated W~ p, xn! double-differential neutronemission spectra compared with experimental data38 at 113-MeV incident energy. The measurements have been decreasedby a factor of 0.66~see text!.

Fig. 15. Comparisons between calculated W~ p, xn! back-angle emission spectra in the evaporation regime with mea-surements by Meier et al.38 and Skyrme.61 The calculations areconsistent with the Skyrme data but not the Meier et al. data.

Fig. 16. Comparison between calculated 120-MeVW~ p, xp! angular distributions with experimental data for the120-MeV Ta~ p, xp! reaction.

306 CHADWICK et al.


used. The total cross-section evaluation was based onFinlay et al.’s46 data. The evaluation of secondary pro-duction cross sections was based on GNASH nuclearmodel calculations, along with ECIS calculations describ-ing the direct excitation of vibrational states~excitationof 21 and 32 phonon states coupled to the 4.51 core!.Our results are compared in Fig. 17 with experimental26-MeV Nb~n, xn! angle-integrated data64 and withdouble-differential 65-MeV Nb~ p, xp! data.65 Good agree-ment is observed. The 26-MeV neutron scattering datawere analyzed by many researchers for an internationalcode intercomparison, organized by Gruppelaar andNagel66—the level of agreement between calculation andmeasurement evident in Fig. 17 is an improvement onthe calculations performed for this intercomparison, pri-marily because of our inclusion of collective excitationsat the highest emission energies. Our evaluation is alsoconsistent with new~ p, xp! data at 14 MeV obtained byWatanabe.67

IV.F. The63,65Cu Evaluations

The neutron total cross section above 20 MeV wasobtained by evaluating experimental data, with a partic-ular emphasis on the Finlay elemental data.46 This re-sulted in an evaluated elemental Cu total cross section;to obtain isotopic63,65Cu total cross sections, it was as-sumed that63Cu and65Cu have total cross sections in anA203 ratio to one another. The total neutron nonelasticcross section was obtained directly from an optical modelcalculation after verifying that it was in good agreementwith the experimental data.

A neutron optical potential with a functional formdescribed by Eq.~1! was obtained by a least-squares pa-rameter search to fit experimental total cross-sectiondata46 and elastic scattering distributions from 1.6 to96 MeV ~Ref. 44!. This optical potential was used forECIS calculations of neutron transmission coefficients andDWBA cross sections for the entire energy region above20 MeV.

Due to the lack of proton elastic scattering data innumerical form, we used a combination of global opticalmodels for the proton channel. The Becchetti-Greenleespotential30 was adopted below 47 MeV, and the nonrel-ativistic version of the Madland potential~Table II!, above47 MeV. At this particular energy, the two potentials joinsmoothly. Following Delaroche et al.,67,68we adopted theweak-coupling model for direct collective inelastic scat-tering for63,65Cu, using even-even62,64Ni cores, respec-tively. For the calculation of the cross sections, ECIS wasused in DWBA mode. Deformation lengths were ob-tained from the literature.

The copper isotope evaluations are documented indetail in Ref. 69; therefore, further details are not re-peated here. Reference 69 provides numerous compari-sons against experimental total, reaction, elastic, andemission spectra data to benchmark the evaluations.

IV.G. The58,60,61,62,64Ni and 50,52,53,54Cr Evaluations

Nickel and chromium are important structural ele-ments in steel. A significant number of experimental dataexist to benchmark our 150-MeV evaluations, particu-larly for Ni, where proton-induced emission spectra areavailable at 60-, 90-, 120-, and 150-MeV incident ener-gies, and neutron-induced alpha production data exist upto ;50 MeV. The methods used to evaluate the chro-mium isotope cross sections followed closely those usedfor nickel and are therefore not described in this paper.Furthermore, apart from total, total nonelastic, and elas-tic scattering data, few measurements exist for Cr.

The Ni neutron total cross sections were evaluatedbased on the least-squares method, taking into accountthe experimental data,44 including the recent elementalNi results from LANL by Dietrich et al.52 The total cross-section data for natural Ni were transformed to those forNi isotope cross-sections according to anA203 dependence.

Fig. 17. Comparison between calculated and measuredemission spectra for niobium.



The evaluated total cross-section data,s-wavestrength functions,25 and elastic scattering angular dis-tribution data44 were used to obtain the neutron opticalpotential parameters, with a potential functional formgiven by Eqs.~1! and~2!. The parameter estimation wascarried out based on the Marquart-Bayesian approach,where the ECIS code was used for the optical modelcalculations. The initial potential parameters were takenfrom Koning, Delaroche, and Bersillon.70 This poten-tial was used for the calculation of neutron transmissioncoefficients and DWBA cross sections in the entire en-ergy region above 20 MeV. Below 20 MeV, the Harperneutron potential71 was used. For protons, above 50 MeVwe obtained a potential after performing a parametersearch on experimental elastic and nonelastic data. Be-tween 5 and 50 MeV, the results from Ref. 70 were used,and below 5 MeV, the Harper potential was used.71 Fordeuterons, the Lohr-Haeberli28 global potential was used;for alpha particles the McFadden-Satchler potential31 wasused; and for tritons the Becchetti-Greenlees30 poten-tial was used.

Direct collective inelastic scattering to levels in theNi isotopes was calculated using the DWBA mode inECIS. The deformation lengths were taken from Nu-clear Data Sheets or from Ref. 70. However, for60Niwe just included inelastic scattering to the 21 vibra-tional state, with a deformation length that resulted in amatch with the ENDF0B-VI inelastic scattering at20 MeV because the use of deformation parameters givenin Ref. 70 appeared to overestimate the magnitude ofinelastic scattering.

Above 20 MeV, new measurements from Haightet al.72 exist for alpha production on the Ni isotopes. Be-cause alpha emission represents a small fraction of thetotal reaction cross section, its prediction by a nuclearmodel calculation is sensitive to the level density and op-tical potential parameters used. This fact allows such datato be used to infer level densities in the residual nucleusfollowing alpha emission and in the residual nucleus fol-lowing neutron emission, the dominant competition chan-nel.72 Our results, which include a fine-tuning of leveldensity parameters to match both measureds-wave res-onance spacings and~n, xa! data, are shown in Fig. 18.This provides a good example of the important role thatexperimental data can play in guiding a model calcula-tion for an evaluation. If default parameters were used, itis likely that these alpha-production data would not bewell predicted.

Other measurements exist for proton-induced reac-tions, primarily for the58Ni target. At 90 MeV, our cal-culations of proton, neutron, deuteron, and alpha emissionagree well with measured data from the Universityof Maryland,73,74 as shown in Fig. 19. At the highestemission energies, preequilibrium alpha emission is over-predicted; however, cross sections for preequilibriumcluster emission are difficult to predict accurately, andeven though the data are overpredicted, their magnitude

is very small, so the impact of this on applications suchas energy deposition is small. Where the alpha cross sec-tion is high, at low emission energies, the calculated crosssection from compound nucleus decay agrees with themeasured data. At 65 MeV, our results are in excellentagreement with the proton emission spectra of Sakaiet al.65 Finally, continuum proton emission spectra havebeen measured75 at the National Accelerator Center atFaure, South Africa, at 100-, 120-, and 150-MeV inci-dent energies. Our results, shown in Fig. 20, are in ex-cellent agreement with these data.

Fig. 18. Comparison between calculated and measured72

alpha-particle production from Ni isotopes.

Fig. 19. Comparison between calculated and measured73,74

angle-integrated emission of neutrons, protons, deuterons, andalpha particles for 90-MeV protons on58Ni.

308 CHADWICK et al.


IV.H. The54,56,57Fe Evaluations

Because of the abundance of iron in target0blanketdesigns, the 150-MeV neutron and proton evaluations arediscussed in some detail in this section.

Figure 21 shows the evaluated neutron total cross sec-tion compared with data. Below 40 MeV, we have placeda particular emphasis on the Larson Oak Ridge NationalLaboratory measurements rather than the higher valuesmeasured by Cierjacks.44 Elastic scattering angular dis-tributions for neutrons are also shown in Fig. 21, calcu-lated from the Arthur-Young optical potential76 below50 MeV and the medium energy potential~Table II! athigher energies. Agreement is good, except that the cal-culations underpredict the scattering data beyond the firstminimum for the 65-MeV data. This failing is due to ouruse of a global potential at this energy, rather than a po-tential that has been fitted to the iron elastic scatteringdata. However, the practical impact of this underpredic-tion is likely to be small because the cross section is lowhere, and where the cross section is large~at small an-gles!, the agreement with experiment is good.

The total nonelastic cross section is shown in Fig. 22for incident neutrons and protons. Only three neutron

Fig. 20. Comparison between calculated and measured75

secondary proton angular distributions for 100-, 120-, and150-MeV protons incident on58Ni.

(a)

(b)

Fig. 21. Comparison of iron evaluation and elemental mea-surements for~a! total neutron cross section44,52 and~b! neu-tron elastic scattering cross sections.



measurements exist between 20 and 150 MeV; therefore,we also show existing proton nonelastic cross-section datain Fig. 22a for incident neutrons.~We expect the protonand neutron nonelastic data to be comparable at energieswell in excess of the Coulomb barrier.! The calculatedneutron nonelastic cross section from the optical modelwas slightly modified above 50 MeV to smooth the tran-sition between the two potentials used. The total protonnonelastic cross-section evaluation is also compared withexperimental data in Fig. 22, obtained from the compi-lation by Carlson.77

Two measurements of neutron-induced neutronemission spectra exist above 20 MeV: The 26-MeVMarcinkowski et al.64 measurement at Ohio Universityand the recent 65-MeV~n, xn! measurement at forwardangles by Hjort et al.50 at the University of California-Davis. From Fig. 23 it is evident that our calculationsdescribe the 26-MeV angle-integrated data well, includ-ing the collective excitations at higher energies~somediscrepancies between experiment and theory exist in

the 20- to 23-MeV region, but the calculations do re-produce the general features of the experimental data!.This is due to our DWBA direct reaction calculations oftransitions to all states where deformation-parameter in-formation exists. We also include the fragmented low-energy-octopole-resonance state, which accounts for thebroad peak at 17.5 MeV in Fig. 23a. Our calculationsalso agree well with the 65-MeV double-differential mea-surements of Hjort et al., where we applied Kalbach an-gular distribution systematics and converted the resultsinto the laboratory frame of reference.

Secondary particle emission spectra following proton-induced reactions are shown in Fig. 24. The upper graphshows the calculated 113-MeV Fe~ p, xn! differential spec-tra at four angles, compared with the Meier et al. data.38

Agreement is seen to be reasonable, even at the back-ward angle. However, the calculations overpredict neu-tron emission in the evaporation regime. At 60 MeV

(a)

(b)

Fig. 22. The evaluated neutron and proton nonelastic crosssection for Fe compared with measurements.44

(a)

(b)

Fig. 23. Comparison of evaluated56Fe~n, xn! emissionspectra with measurements:~a! 26-MeV angle-integrated data64

and~b! 65-MeV double-differential data.50

310 CHADWICK et al.


~Fig. 24b!, ~ p, xp! experimental78 and calculated angle-integrated spectra are shown for54Fe, and again the agree-ment is seen to be good. For comparison, results for theemission spectra for56Fe are also shown—the differ-

ences in magnitude of proton compound nucleus emis-sion evident in the figure are mainly due to the differentQ values for the two isotopes.~DifferentQ values meansthat after particle emission, the respective residual nu-clei are populated at different levels of excitation energy,where the level density is very different.! Figure 24cshows the angle-integrated Svirin 22.4-MeV56Fe~ p, xn!data.44 The calculations underpredict the measured low-energy neutron production by;20%.

In 1997, Watanabe et al. presented~ p, xp! spectra foriron isotopes at 14 and 26 MeV at the International Con-ference on Nuclear Data for Science and Technology, inTrieste, Italy.79 Our calculated results, obtained prior tothe measurement, are in good agreement with these data.

As discussed earlier, the evaluated cross-section li-braries include results for isotope production to facilitatestudies of activation, energy deposition, and radiationdamage. As an illustrative example of the informationincluded in the files, Fig. 25 shows evaluated isotope pro-duction cross sections compared with experimental datafor incident protons. The same axis scales are used forall the curves shown, and the results are ordered accord-ing to decreasing magnitudes of maximum productioncross section. The calculated excitation functions are seento agree with the measured data best where the produc-tion cross sections are large~at the;20% level!, but thediscrepancies become larger for the small cross sections~a factor of 5 to 10 for cross sections below 1 mb!. Theseresults are comparable to the best results shown in therecent international code comparison on intermediate en-ergy activation yields.81

IV.I. The28,29,30Si Evaluations

The neutron total cross section above 20 MeV wasobtained by evaluating the experimental data44,46 ~seeFig. 26!. Since28Si comprises 92% of elemental silicon,the 28Si total cross section was obtained by evaluatingthe elemental data. Total cross sections for29,30Si iso-topes were obtained from the28Si evaluation after scal-ing the values by anA203 dependence.

The global medium-energy optical potential inTable II was used for neutrons above 46 MeV, and theWilmore-Hodgson potential was used for lower neutronenergies. The global medium-energy optical potential wasused for protons above 28 MeV, and the Becchetti-Greenlees potential was used for lower proton energies.In both cases the transition region to the medium-energy potential was chosen to give approximatecontinuity in the reaction cross section. While the afore-mentioned optical potentials did describe the experimen-tal proton nonelastic cross-section data fairly well, wemodified the theoretical predictions slightly to betteragree with the measurements and renormalized the trans-mission coefficients accordingly. In addition to using Sinonelastic proton cross-section measurements, we alsowere guided byp 1 Al nonelastic data scaled byA203.

(a)

(b)

(c)

Fig. 24. Comparison of evaluatedp1Fe emission spectrawith measurements:~a! 113-MeV~ p, xn! double-differentialemission spectra,38 ~b! 60-MeV ~ p, xp! angle-integrated spec-tra,78and~c!22-MeV~ p, xn!angle-integratedemissionspectra.44



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312 CHADWICK et al.


Coupled-channel optical model calculations were per-formed to determine inelastic scattering on28Si for the01, 21, and 41 states as well as a DWBA calculationof the inelastic scattering to the 32 vibrational state, allperformed with the ECIS code. To produce continuityin the calculated inelastic cross sections up to 150 MeV,we performed a rotational band~01, 21, 41! coupled-channel calculation using the global medium-energy po-tential in Table II~with its imaginary potential reducedby 20%, to approximately account for the coupling! overthe whole neutron energy range. Deformation param-eters were chosen to reproduce the ENDF0B-VI crosssections at 20 MeV, resulting in values ofb2 5 20.365andb4 5 10.22, in reasonable agreement with Alarcon

and Rapaport’s values of20.37 and 0.17, respective-ly.82 A vibrational DWBA calculation was performedfor the 32 state resulting inb3 5 0.235 ~Alarcon andRapaport obtained 0.23! ~Ref. 8!. These sameb valueswere used for the proton inelastic scattering calcula-tions. For30Si, inelastic scattering to the 21 ~2.24 MeV!and 41 ~5.95 MeV! states was also determined usinga coupled-channel ECIS calculation. Deformation pa-rameters were chosen to reproduce the JENDL-3 eval-uation at 20 MeV~Ref. 83!. The resulting deformationparameters~b2 5 20.33 andb4 5 0.20! were close tothose used for28Si. Due to the small natural abun-dance of29Si, a coupled-channel calculation was notperformed. Instead, the JENDL-3 evaluated results forinelastic scattering to the 5021 ~2.03-MeV! and 3021~2.43-MeV! states at 20 MeV were extrapolated to higherenergies using an inverse-incident energy variation.84

Only two measurements exist for neutron-inducedemission spectra above 20 MeV for Si. New data havebeen published by the Louvain group for 63-MeV Si~n,xz!double-differential spectra~z 5 p,d,a ejectiles!.85 Ourcalculations agree reasonably well with these measure-ments~Fig. 27!. The angle-integrated data were ob-tained by performing an angle integration of the resultspresented by Lambert et al. in Ref. 85. In addition, Bate-man et al. have preliminary data for Si~n, xp!, for neu-trons up to 50 MeV, including emission spectra at fourangles, which are compared to our calculations inRef. 86. While default level density parameters~usingthe Ignatyuk model! were utilized, in the case of28Al thelevel density parameter was slightly modified to opti-mize agreement with the Abfalterer et al.87 total level den-sity measurements based on fluctuation analyses.

Fig. 26. Comparison between evaluated neutron total crosssection and proton nonelastic cross section for silicon com-pared with measurements.44,77

Fig. 27. Comparison between evaluated angle-integrated63-MeV Si~n, xp! spectra with measurements.85



IV.J. The27Al Evaluation

The neutron total cross section was evaluated fromavailable experimental data. From 20 to 40 MeV, the ex-isting ENDF0B-VI ~release 5! total cross-section evalu-ation of Young et al.56 was adopted; from 40 to 150 MeV,the evaluation was based primarily on Finlay’s 1993 mea-surements.46 Figure 28 shows our evaluation comparedwith the experimental data.

The optical potential of Petler et al.,88 specially de-veloped forn 1 Al elastic scattering, was used for neu-trons up to 60 MeV, and above this energy, the medium-energy potential was used~Table II!. For incident protons,the Petler neutron potential was modified to account forproton scattering up to 60 MeV using a Lane transfor-mation, and again the medium-energy potential was usedat higher energies. The DWBA calculations were per-formed for inelastic scattering to low-lying states. Fig-ure 28 also shows our evaluated neutron and protonnonelastic cross sections compared with experimentaldata. For incident neutrons, the figure illustrates the pre-dictions obtained from optical model analyses and howthese predictions were modified, on the basis of mea-sured data, to obtain an evaluated nonelastic cross sec-tion. The evaluated neutron elastic scattering distributionsare shown in Fig. 29 in a comparison with experimentaldata.

A measurement of the emission spectra forp, d, t,and a ejectiles in the 63 MeVn 1 Al reaction has re-cently been performed by Benck et al.89 at Louvain-la-Neuve. These data are important because few suchmeasurements exist for neutrons above 20 MeV. De-tailed comparisons between our evaluated cross sectionsand the measurements are presented in Ref. 89 and are,therefore, not repeated here. In addition, our evaluatedneutron-induced cross sections on aluminum are com-pared to discrete gamma-ray cross-section measure-ments from decaying product nuclei in Ref. 90.

The evaluated double-differential emission spectra,after conversion into the laboratory frame of reference,are compared in Fig. 30 with experimental measure-ments at 90 MeV and 113 MeV~Refs. 38, 73, and 74!.The 90-MeV measurements from the University of Mary-land are of particular interest because they are for bothemitted protons and neutrons and, therefore, present astringent test of the model calculations. Agreement withthe GNASH calculations is seen to be reasonable, exceptfor proton emission at the most forward angles and forparticle emission near 20 MeV just above the evapora-tion peak. In particular, the calculations agree with theexperimental results, showing an approximate ratio of pre-equilibrium proton-to-neutron emission of 2:1.

IV.K. The12C, 14N, 16O, 31P, and40Ca Evaluations

Evaluated cross sections for these elements were orig-inally developed by one of the authors~M.B.C.! in the

LLNL format for neutron and proton radiotherapy appli-cations. The new evaluations, in ENDF-6 format, repre-sent an extension of that earlier work. In addition to theirimportance in medical applications, these elements are

Fig. 28. Comparison of evaluated neutron total cross sec-tion and proton and neutron nonelastic cross sections with ex-perimental data44,77 for Al.

314 CHADWICK et al.


also important in accelerator-driven systems~for exam-ple, carbon is a beam-stop material, oxygen is present inwater and heavy water moderators, and calcium and ox-ygen are abundant in concrete shielding!. The earlier eval-uations were documented in detail in Refs. 14, 15, and43; therefore, only additional details are presented here.The main additions and extensions in the current workwere ~a! inclusion of nuclide production and recoil en-ergy spectra,~b! inclusion of direct inelastic scatteringto low-lying collective states for Ca and inclusion of tri-ton emission for P and Ca, and~c! utilization of theENDF-6 format and the ENDF0B-VI evaluations below20 MeV.

There is an important difference in these evalua-tions compared to the previous LLNL work14,15 thataffects the evaluated kerma coefficient: The present eval-uations make use of our new recoil calculationalmethod, described in Sec. III. Since the fractional

kerma due to the recoils is significant for light targetnuclei, the calculated total kerma coefficients for car-bon and oxygen differ~slightly! from our previous re-sults, which were based on energy-balance estimates.

Fig. 29. Comparison of elastic scattering distributions forn 1 Al, calculated using the optical model, with experimentaldata.44

Fig. 30. Comparison of aluminum~ p, xn! and ~ p, xp!double-differential emission spectra with experimental data, at90 and 113 MeV~Refs. 38, 73, and 74!.



The total kerma coefficients derived from our evaluatedmicroscopic cross sections~in the lab reference frame!are compared with measurements in Sec. V.A, and theagreement is good.

Other minor modifications were made to the earliercarbon and oxygen neutron evaluations. For neutron re-actions on carbon, the model calculations were modi-fied at 20- and 23-MeV incident energies to increasethe abundance of high-energy alpha preequilibrium emis-sion, resulting in a higher12C~n,a!9Be cross section~40 mb at 20 MeV and 18 mb at 23 MeV!. This modi-fication was made to obtain better agreement with themeasurement by Stevens91 and with Axton’s evalua-tion.92 Also, for oxygen at 20- and 23-MeV neutron en-ergy, the fraction of alpha preequilibrium emission wasreduced to be more comparable with the results at27 MeV, where experimental data exist. The motivationfor this modification was to reduce the alpha-particlepartial kerma coefficient to compensate for the largernonelastic recoil kerma coefficient obtained in the presentwork compared to Ref. 15 so that agreement with totalkerma coefficient data in the 20- to 23-MeV region isimproved.

IV.L. The Deuterium Evaluation

Deuterium is present in the LANL APT design inthe heavy water moderator in the target region.

Our evaluation of then 1 2H cross sections extendsto an incident neutron energy of 200 MeV. The neutrontotal cross section is based on ENDF0B-VI below 100MeV and on experimental data between 100 and 200 MeV.Our evaluated total cross section from 10 to 200 MeV iscompared to the available experimental database44 inFig. 31a.

Several neutron elastic scattering angular distribu-tion measurements exist above 20 MeV, which were fit-ted with Legendre expansions to obtain integrated crosssections and to establish the evaluated angular distribu-tions. The measurements of Romero et al.,93 Wang,94

and Howard et al.95 as well as the partial distribu-tions of Yountz96 and Palmieri97 were especially impor-tant for determining the neutron elastic scattering data~Fig. 31b!.

The elastic scattering, nonelastic, and2H~n,2n! 1Hcross sections were determined above 20 MeV in paral-lel, using the fact that the nonelastic cross section es-sentially equals the~n,2n! cross section aboveEn '1 keV, and the elastic and nonelastic cross sectionsmust sum to the total cross section. We revised theexisting ENDF0B-VI ~n,2n! cross section at most ener-gies between 10 and 100 MeV to improve the agree-ment with experimental data. The evaluated2H~n,2n!1Hand n 1 2H nonelastic cross sections are comparedto measurements44 in Fig. 32. In the course of evalu-ating the nonelastic cross section at higher energies,experimental proton reaction cross-section data for

2H were found to be consistent with the neutron non-elastic cross-section measurements above;20 MeV.The proton reaction cross-section measurements ofCarlson et al.98 are included with the nonelastic data inFig. 32.

For p 1 2H reactions, we utilized the results of anR-matrix analysis for proton energies up to 4 MeV. Wecompiled a selection ofp 1 2H elastic angular distribu-tion measurements up to;65 MeV and used the resultsdirectly in the evaluation.

We utilized the Faddeev calculations of Sloan99 atlower energies and the results of ourn 1 2H evaluationat higher energies for the2H~ p,2pn! cross section, tak-ing advantage of the near equality of the proton and neu-tron reaction cross sections above 20 MeV. Finally, weevaluated the2H~ p,g!3He cross section using experi-mental data below 2 MeV, assuming equality with the2H~n,g!3H cross section above 4 MeV, with a smoothmatch at intermediate energies.

IV.M. The1H Evaluation

Hydrogen is an important element in many applica-tions. It is abundant in water moderators and in plasticmaterials and is present at the;10% level~by weight! inhuman tissue, which makes it an important material infast-neutron and -proton cancer therapy studies. An ac-curate evaluation of the total cross section, and theneutron-proton elastic scattering angular distributions isimportant for determining the kinetic energy imparted tosecondary recoil protons, which affects the energy de-posited by neutrons in matter~kerma!. In addition, theback-angle neutron-proton scattering cross section is animportant quantity as it is used as a “standard” to deter-mine neutron fluences.

Prior to the present work, an evaluation by Haleet al. for neutrons on hydrogen existed in the ENDF0B-VI library up to 100 MeV. This evaluation was based onan R-matrix representation of measured data up to 26 MeVand a phase-shift analysis by Arndt at higher energies.However, it has some limitations: The Arndt analysis usedwas an interim analysis available at the time of the eval-uation~1988!, and the matching to the R-matrix solutionbelow 26 MeV was rather crude. After the completion ofthis earlier hydrogen evaluation, a standards committeeof the Nuclear Energy Agency~NEA! recommended100

that for hydrogen, ENDF0B-VI should be used below20 MeV, but at higher energies, cross sections shouldbe taken from Arndt’s more recent VL40 phase-shiftsolution.101

We have implemented this NEA recommendationin a new hydrogen evaluation that extends to 150 MeVin ENDF-6 format. The R-matrix solution from ENDF0B-VI and Arndt’s VL40 phase-shift solution were mergedat 26 MeV, where a smoother transition could beachieved. Furthermore, the merging was performed in away that resulted in relatively smooth cross sections

316 CHADWICK et al.


from one region to the other, not just in the totalcross section but in the scattering cross sections at dif-ferent angles. This is described in more detail inRef. 40.

For proton scattering on hydrogen, a new R-matrixanalysis was performed up to 150 MeV, extending aprevious evaluation to 100 MeV that was the basis of theexisting ENDF0B-VI p-p evaluation.

(b)

(a)

Fig. 31. The evaluatedn 1 2H total cross section and total elastic cross section up to 200 MeV, compared with measure-ments.44



V. INTEGRAL BENCHMARKS: TRANSPORTAND ENERGY DEPOSITION

V.A. Kerma Calculations for Energy Deposition

It has been necessary to extend the NJOY NuclearData Processing System102 in a number of ways to pro-

cess the new 150-MeV neutron and proton data for useby radiation transport codes. One set of extensions is de-signed to provide accurate kerma coefficients for the de-termination of radiation heating from neutrons. Heatingis important in a variety of applications, including accel-erator technologies and calculations of absorbed dose in

Fig. 32. The evaluated2H~n,2n! cross section and then 1 2H nonelastic cross section up to 200 MeV, compared withmeasurements.44

318 CHADWICK et al.


radiation therapy. The fluence-to-kerma conversion co-efficient, or “kerma coefficient,”b is given by the ratio ofthe kerma~an acronym for kinetic energy released in mat-ter! to the neutron fluence.

The kerma coefficient is proportional to the total en-ergy emitted with secondary charged particles, includingthe residual nuclei~recoils!. A full calculation of radia-tion heating would have to follow the slowing down~transport! of each particle in the medium, but whencharged-particle mean paths are fairly short, folding thekerma coefficient with the neutron fluence can provide areasonably good approximation to the energy depositionby neutrons in matter. In addition, if total kerma coeffi-cients derived from evaluated cross-section data agreewell with measurements, it helps to build confidence inthe prediction of energy deposition by a transport code,such as MCNPX, that uses these same data.

V.A.1. Kerma Below 20 MeV

Below 20 MeV, kerma coefficients are calculatedfrom the ENDF0B-VI evaluated cross sections. Follow-ing the introduction of the ENDF-6 format, a number ofevaluated nuclear data files that contain explicit infor-mation on the energies of emitted charged particles havebecome available. A processing code like NJOY can eas-ily integrate these distributions, thus obtaining kermacoefficients that are directly traceable to the best judg-ment of the evaluator and that satisfy conservation ofenergy for all emitted radiations. However, even now,explicit charged-particle distributions are not availablefor many important materials. Thus, it is necessary toattempt to estimate emitted energies by using kinemat-ics, rough estimates for reaction dynamics, or energybalance. The energy-balance approach takes advantageof the fact that many ENDF-format evaluations give ex-plicit distributions for the emitted neutrons and pho-tons. The energies needed for the kerma coefficient canbe obtained by subtracting the average emitted energiesfor the neutrons and photons from the available energy~E 1 Q!.

V.A.2. Kerma Above 20 MeV

The new high-energy evaluations extend from 20- to150-MeV neutron energies. These evaluations allow to-tal neutron kerma coefficients to be determined unambig-uously because the emission spectra of all secondarycharged particles, including heavy~A . 4! recoils, arerepresented. Since the light-particle ejectile~A# 4! angle-integrated spectra are represented in the c.m. frame, NJOYperforms a transformation into the lab frame of refer-ence to obtain the partial kerma coefficients for the light

particles. Lab-frame angle-integrated spectra are pro-vided for the heavy recoils by making use of the modeldescribed in Sec. III and the Appendix. Finally, elasticrecoil partial kerma coefficients are determined from theneutron elastic scattering angular distributions after hav-ing determined theP1 component of a Legendre coeffi-cient fit to the highly forward-peaked distributions. Partialkerma coefficients for each type of secondary chargedparticle are determined using

kFi 5 N Sei si

prod , ~6!

where

kFi 5 kerma coefficient of ejectile typei

siprod 5 inclusive production cross section of ejec-

tile i ~b!

Sei 5 average energy of ejectilei ~MeV!

and all these quantities are functions of the incident neu-tron energy. The factorN5 9.648533102150MA , whereMA is the atomic mass of the target in units ofu, con-verts the partial kerma coefficient from units of mega-electron-volts{barn to Système International units off Gy m2 @femto ~f ! 5 10215, gray~Gy! 5 J0kg# .

V.A.3. Comparison with Experiments

In recent years, total kerma coefficients have beenmeasured for a number of elements, particularly thoseimportant in medical applications, allowing a test of eval-uated nuclear data and the NJOY processing methods.The measurements have been made in two ways: directdetermination of the ionization produced by the second-ary charged particles and measurements of secondarycharged-particle differential cross sections. Both meth-ods involve significant uncertainties; the latter, in partic-ular, require extrapolations for data at unmeasured angles,energies~below detector thresholds!, and for elastic andnonelastic recoils to determine the total kerma coefficient.

Figure 33 shows the total kerma coefficients deter-mined by NJOY from the evaluated ENDF data com-pared with measurements. The discontinuities seen at20 MeV arise because of the different evaluation meth-ods used in the new high-energy evaluations comparedwith the older,20-MeV evaluations. In general, theagreement is seen to be good. For C and O, there is atendency for the ENDF evaluations to overpredict kermacoefficients in the 15- to 20-MeV range. The LAHET re-sults shown were generated with a special version usingelastic cross sections from the new ENDF evaluation, andthey show reasonable agreement with the full calculation.

Additional comparisons of our calculated kerma co-efficients with experimental data relevant to medical ap-plications, such as kerma coefficients for tissue-equivalentA150 plastic, the C0O kerma ratio, and integral results

bWe follow the notation of the International Commissionon Radiation Units and Measurements40 ~ICRU! in usingkermacoefficientrather thankerma factor.



for kerma in clinical fast-neutron therapy beams, are pre-sented in Ref. 40.

V.B. MCNPX Transport Calculations

V.B.1. MCNPX Overview

A major transport code development effort is underway, primarily in support of the computational needs ofthe APT program. The main emphases of the MCNPXproject are~a! merging existing functionality of the MCNPcode4 and the LAHET Code System5 ~LCS! and~b! im-proving the physics capabilities of the merged code. Onecritical aspect of the latter is the use of the new 150-MeVdata libraries described in this paper. Therefore, for par-ticle energies above 150 MeV, MCNPX uses intranuclearcascade collision physics to simulate nuclear reactions,but below this energy, the new data libraries are used.

The starting point for the code-merger effort wasMCNP Version 4B. The MCNPX code6 expands the ca-

pabilities of MCNP by increasing the set of transport-able particles, by making use of the newly evaluatedhigh-energy nuclear data libraries described in this pa-per, and by incorporating physics models for use wheretabular data are unavailable. All of the LAHET nuclearphysics modules are included intact in MCNPX, whichexpands the capabilities of LAHET through the avail-ability of many of the variance-reduction methods ofMCNP and through the incorporation of MCNP’s verygeneral syntax for specifying geometry, sources, and tal-lies. The result of this project is a unified, general MonteCarlo transport capability to model a fully coupled cas-cade of nuclear particles over a wide energy range.

An important requirement of the MCNPX develop-ment plan is to implement the necessary tools to modelthe transport of coupled neutral and charged particles be-low 150 MeV based on nuclear-data evaluations. Thephysics capabilities of MCNPX have been upgraded toinclude the production of secondary charged particlesfrom neutron collisions, using data contained on expanded

Fig. 33. Calculated kerma coefficients compared with experimental data, for C, O, Al, and Fe. For citations to C and Oexperimental kerma coefficients, see Refs. 14, 15, and 103; for Al, see Refs. 104 and 105; for Fe, see Refs. 106 through 109.

320 CHADWICK et al.


continuous-energy neutron cross-section tables. Work isin progress on updating MCNPX to utilize the newly eval-uated high-energy data tables for incident protons.

To use the 150-MeV neutron libraries, the routinesin MCNP for reading cross sections and for sampling sec-ondary particles have been expanded. The modificationshave been managed so that the methods applicable toneutron-induced charged-particle production are very sim-ilar to the existing methods for neutron-induced photonproduction. As in the existing neutron-induced photon al-gorithm, the code performs a significant amount of pre-transport data manipulation. In particular, the list of activeparticle types for a given problem~specified on the MODEcard! is used to expunge unneeded data for the problem.Neutron heating numbers are also modified based on thecharged particles to be transported.

At every neutron collision, the possibility of produc-ing secondary charged particles exists. All data used inthe sampling process are specific to the collision isotopeand are evaluated at the incident neutron energy. The ex-pected weight of a particular charged particlei is WGTsi

prod~E!0stot~E!, whereWGT is the weight of the inci-dent neutron,si

prod~E! is the total production cross sec-tion of i at incident energyE, andstot~E! is the total crosssection. The number of charged particles produced is aninteger~possibly 0! determined by analog sampling. Ifthe code determines that a charged particle will be pro-duced, it then samples the reaction responsible for thatparticle. There is no correlation between the type of col-lision and the reactions sampled as being responsible forthe various secondary particles that may be produced.While reaction properties are not conserved on an event-by-event basis, they are accurately modeled when aver-aged over many events.

MCNPX supports several ENDF-6 representationsof scattered energy-angle distributions. Specifically, thefollowing representations for secondary charged parti-cles are allowed: tabular energy distributions, angular dis-tributions via equally probable cosine bins, Kalbachsystematics for correlated energy-angle distributions, dis-crete two-body scattering, andn-body phase-space en-ergy distributions. In all cases where necessary, kinematicsalgorithms currently incorporated in MCNP, which arespecific for~neutron-in, neutron-out! physics have beengeneralized to the~neutron-in, charged-particles-out! sit-uation. In addition, a general c.m. to laboratory conver-sion technique has been incorporated. As is currently thecase for neutron production, all such conversions are basedon the assumption of two-body kinematics, which isclearly only an approximation for many high-energy neu-tron reactions of current interest.

V.B.2. Transport Benchmarks

A number of basic quality assurance tests have beenperformed for MCNPX. These include the standard setof MCNP test problems110and a variety of problems cre-

ated to ensure internal consistency of the code and agree-ment with the new data evaluations. Here, we present newbenchmark calculations comparing both LAHET andMCNPX with experiments performed at the JapanAtomicEnergy Research Institute~JAERI!. These calculationsparticularly test the benefits of using the new evaluatedneutron data.

A number of neutron transmission experiments havebeen performed at the Azimuthally Varying Field Cy-clotron facility at the JAERI Takasaki site.111 Inci-dent 43- or 68-MeV protons impinged on convertersconsisting of 99.9% enriched7Li. The 7Li ~ p,n! reac-tion produced nearly monoenergetic neutrons, which werethen collimated and allowed to strike iron or concretetargets of various thicknesses. The neutron transmissionwas measured at several positions relative to the trans-mission target. Although the neutrons were initially al-most monoenergetic in all cases, their actual spectra weremeasured to allow for more realistic comparison withneutron transport calculations.

Before MCNPX was available, simulations of someof these experiments were performed by Hertel andEvans using the LCS. Reference 112 describes their calcu-lations in detail, and for completeness, it includes sam-ple LAHET and MCNP input files. Calculations wereperformed using LAHET versions 2.7 and 2.8, whichincludes a new elastic scattering model. The conclusionof the investigation was that simulations using LAHETversion 2.8 were in markedly better agreement with ex-periment than were simulations using LAHET version2.7 but that substantial systematic errors remained.

We have now repeated some of Hertel and Evans’scalculations using MCNPX, replacing the LAHET trans-port model with the use of the new evaluated neutrondata tables throughout the energy range of the experi-ments. Specifically, we have calculated the transmissionof the quasi-monoenergetic 68-MeV neutron sourcethrough 40 cm of iron and predicted the fluence on theaxis of the beam and at 20 and 40 cm from the axis fordetectors immediately adjacent to the downstream faceof the transmission target. A typical result is shown inFig. 34, which compares the on- and off-axis experimen-tal results with the previous calculations using LAHETversions 2.7 and 2.8 and with the new MCNPX results.There is a dramatic improvement in agreement with theMCNPX calculations using the new evaluated neutrondata tables. Furthermore, the large discontinuity seen at20 MeV in the LAHET calculations, which occurs atthe transition to MCNP’s use of ENDF0B-VI data librar-ies, is largely reduced in the MCNPX calculations. Theimprovement seen in the LAHET 2.8 calculationscompared to version 2.7 is due to use of optical modelpredictions for the total elastic scattering cross sectionin LAHET 2.8; also, the earlier version used a very sim-plistic elastic angular distribution formulation, whereasthe newer version uses a black-disk diffractionformulation.113



Radiation transport simulations using MCNPX withevaluated data up to 150 MeV should be expected toexhibit a discontinuity at 150 MeV, where the transitionto INC physics occurs. However, the discontinuities at150 MeV should be significantly smaller than that pre-

viously found at 20 MeV because the INC model is knownto be more accurate at higher energies.

VI. SUMMARY

The neutron and proton reaction data that extend upto 150 MeV described in this paper have been evaluatedusing both nuclear model calculations and experimentaldata. Extensive benchmarks, both against microscopiccross-section data and integral results for transport andenergy deposition, have been performed to validate theiraccuracy. Good agreement was generally observed.

The evaluations tabulate emission spectra cross sec-tions for neutrons, gamma rays, and light charged parti-clesand, therefore, canbeused forcalculationsof transport.But because they also tabulate such information for heavycharged particles~recoils!, the data files can be used forcalculations of energy deposition, materials damage, andactivation. Therefore, they represent an advance from pre-vious high-energy data evaluations.1,14–16

These data can be used in radiation transport calcu-lations for simulations of accelerator-driven systems.They can also be used in medical applications to simu-late and optimize absorbed dose in the body by neutronand proton therapy beams. A comprehensive report onthis subject will soon be issued by the ICRU~Ref. 40!.In applications that involve energies above 150 MeV, aradiation transport code such as MCNPX~Ref. 6! canutilize intranuclear cascade physics methods “on the fly”above 150 MeV and switch to use of these data librariesfor particles whose energy has fallen below 150 MeV.

We also note that the library of 150-MeV evalua-tions described in this work can be augmented with eval-uations of other isotopes such as9Be and238U from theLANL 100-MeV evaluations1 developed during the late1980s, which can also be used in MCNPX transport cal-culations. This is important for certain applications thatmake use of beryllium as a~ p, xn! neutron source andthat use depleted uranium as a spallation target.

These new 150-MeV evaluated cross sections, col-lectively referred to as the LA150 library, are availablevia the Internet at http:00t2.lanl.gov0data0he.html. In ad-dition, they have been accepted into the ENDF0B-VI li-brary, as Release 6, and are available from the NationalNuclear Data Center.56

APPENDIX

This Appendix provides kinematic relations for thedetermination of recoil energy spectra in the laboratoryframe of reference, which are built into the GSCANcode. Their usefulness lies in the fact that, while kine-matic transformations from c.m. to lab frames are oftenperformed numerically, we show here that they can beperformed analytically when the Kalbach angular distri-bution systematics are applied. This facilitates an exact,

Fig. 34. Comparison of MCNPX calculations of neutrontransmission through 40 cm of iron with measurements of Na-kashima et al.111 The neutron source was generated via the68-MeV 7Li ~ p,n! reaction. Results are shown for neutron trans-mission on axis, 20 cm off axis, and 40 cm off axis. Calcula-tions from two versions of the LAHET-MCNP code systemare also shown.

322 CHADWICK et al.


and computationally fast, method for determining recoilenergies in the lab frame. Further details can be found inRef. 20.

The nuclear reaction models considered in this workassume a sequential chain of two-body breakup pro-cesses. In each breakup, a composite nucleus, which ismoving with a velocityva, decays into a light particle~denoted by superscriptp! and a heavy recoil~denotedby superscriptR!.

Suppose the c.m. angular distribution of the lightejectile particle is given byG~u p,f p !, where

EG~u p,f p ! dV 5 1 ,

and the superscriptp denotes the particle. Using Kalbachsystematics,36which represents the angular distribution interms of hyperbolic sines and cosines and can be rewrit-ten in terms of exponentials, this distribution can be ex-pressed as

G~u p,f p ! 5 f1 exp~a cosu p ! 1 f2 exp~2a cosu p ! ,

~A.1!

where

f1 51

4p

a

ea 2 e2a ~11 fMSD!

and

f2 51

4p

a

ea 2 e2a ~12 fMSD! , ~A.2!

wherea is the Kalbach-systematics forward-peaking pa-rameter andfMSD is the preequilibrium fraction. The sec-ondary recoil c.m. angular distribution is obtained fromthe preceding particle result because the recoil moves inthe opposite direction withuR 5 ~p 2 u p !:

G~uR,fR! 5 f1 exp~2a cosuR! 1 f2 exp~a cosuR! .

~A.3!

A.I. ANALYTIC METHOD FOR ANGLE-INTEGRATEDRECOIL SPECTRUM

In this section, we provide kinematic equations todetermine laboratory-frame recoil spectra and average en-ergies. For completeness, we also provide equivalentresults for the light-particle ejectiles. Nonrelativistic ex-pressions are currently used.

A.I.A. Light-Particle Ejectile

If u p represents the particle c.m. angle,vlp, vcp, and

va represent velocities in the lab, c.m., and the c.m.-to-lab boost velocity c.m. motion, then the cosine formulafor vector addition of these velocities yields

cos~u p ! 5vl

p2

2 va2 2 vcp2

2vapvcp5

elp 2 ea

p 2 ecp

mpvavcp, ~A.4!

where

elp 5 1

2_mpvl

p2

eap 5 1

2_mpvap

2

ecp 5 1

2_mpvcp

2.

The probability for the particle having a lab energyel

p is proportional toG~u p,f p !sin~u p !du p, and sincefrom Eq.~A.4! we have sin~u p !du p 5 ~10mpvavcp!del

p,the probability for the particle having a lab energyel

p is

P~elp! 5

2p

mpvavcpG~u p,f p ! ~A.5!

for 6~va 2 vcp!6 # vlp

# ~va 1 vcp!, and zero otherwise.Substituting the expression forG~u p,f p ! from Eqs.~A.1!and~A.2!, we obtain

P~elp! 5

2p

mpvavcpFf1 expSaS el

p 2 eap 2 ec

p

mpvavcpDD

1 f2 expS2aS elp 2 ea

p 2 ecp

mpvavcpDDG .

~A.6!

A.I.B. Heavy Recoil Ejectiles

The probability for recoils having a laboratory en-ergy el

R can be obtained in exactly the same way as inSec. A.I.A. Using the recoil angular distribution givenby Eq. ~A.3!, which is identical to Eq.~A.1! except forthe sign reversals in the exponentials, we obtain

P~elR! 5

2p

mRvavcRFf1 expS2aS el

R 2 eaR 2 ec

R

mRvavcRDD

1 f2 expS1 aS elR 2 ea

R 2 ecR

mRvavcRDDG ,

~A.7!

for 6~va 2 vcR!6 # vlR # ~va 1 vcR!, and zero otherwise,where

elR 5 1

2_mRv l

R2

eaR 5 1

2_mRva

R2

ecR 5 1

2_mRvc

R2.

We define recoil velocitiesvcR andvlR as previously forthe particles.

Equation~A.7! gives the average spectrum of lab re-coil energies given a c.m. motion addition boost velocity



va and a c.m. recoil velocityvcR. In general, however, eachof these quantities is given by a distribution of values. Theoverall lab recoil velocity spectrum can be written as a dou-ble integral over these quantities:

P~elR! 5 E

eaRE

ecR5el

R1eaR22%el

ReaR

ecR5el

R1eaR12%el

ReaR

P1~eaR!P2~ec

R! deaR dec

R

3 S 2p

mRvavcRFf1 expS2aS el

R 2 eaR 2 ec

R

mRvavcRDD

1 f2 expS1 aS elR 2 ea

R 2 ecR

mRvavcRDDGD ,

~A.8!

whereP1~eaR! andP2~ea

R! are the spectra~in energy! ofthe recoil lab motion energies and the c.m. recoil ener-gies. In the case of isotropic particle emission, thisbecomes

P~elR! isotropy in c.m. 5 E

eaRE

ecR5el

R1eaR22%el

ReaR

ecR5el

R1eaR12%el

ReaR

3 P1~eaR!P2~ec

R! deaR dec

R

3 F 1

4%eaRec

RG . ~A.9!

A simplifying assumption that we currently make isto ignore the distribution ofP1~ea

R! and just use an aver-aged value ofea

R @i.e., P1~eaR! 5 d~ea

R!# .

A.II. ANALYTIC METHOD FOR AVERAGE ENERGYOF RECOIL SPECTRUM

There are some situations where it is useful to havean analytic result for the average lab energies. This quan-tity provides a useful check on the accuracy of the de-rived lab spectra and can be used directly to obtain therecoil partial kerma coefficients.

A.II.A. Light-Particle Ejectile

Application of the cosine formula givesvlp2

5 vcp21

va2 1 2vcpva cosu p. Using the Kalbach c.m. angular dis-tribution in Eq.~A.1!, the average lab particle energy foran initial c.m. energyec

p is given by

elp 5 2pE

0

p 1

2mp @vcp

21 va2 1 2vcpva cosu p #

3 G~u p,f p !sinu p du p . ~A.10!

When substituting the expression forG~u p,f p ! fromEq. ~A.1!, solution of Eq.~A.10! involves solving inte-grals of the type

I1~a! 5 E0

p

exp~a cosu p !sinu p du p 5 F ea 2 e2a

aG

~A.11!

and

I2~a! 5E0

p

exp~a cosu p !cosu p sinu p du p

5 F ea 1 e2a

aG2

1

a2 @ea 2 e2a # . ~A.12!

These equations give the average energy of the par-ticles in the lab as

elp 5 2

12mp~vcp21 va2! 1 fMSD{mpvcpva I2~a!0I1~a! .

~A.13!

A.II.B. Heavy Recoil Ejectile

The derivation of the recoil average lab energy fol-lows that described in Sec. A.II.A for the ejectile parti-cle. The opposite direction of the c.m. recoil relative tothe c.m. particle ejectile simply results in the sign changein the exponentials in Eq.~A.3!. With this, the averageenergy for the lab recoils becomes

elR 5 2

12mR~vcR21 va2! 1 fMSD{mRvcRva I2~2a!0I1~2a! .

~A.14!

In the limiting case ofa r 0 ~isotropy!, I2~2a!0I1~2a!r0; therefore, this becomesel

R5 12_mR~vcR

21va2!,

which can be easily derived for an isotropic c.m. angulardistribution. Thus, we see that the average kinetic ener-gies of the recoils have increased through such particledecay processes. The opposite limiting case is also ofinterest—very forward peaked preequilibrium emissionthat may occur in primary particle emission—which wecan study by consideringa r large andfMSD 5 1.Here,I2~2a!0I1~2a! r 21, and Eq.~A.14! reduces toel

R 5 12_mR~va 2 vcR!2. Thus, preequilibrium emission re-

sults in a decrease in the recoil velocities, as discussedearlier.

ACKNOWLEDGMENTS

The authors are grateful to P. M. DeLuca, S. M. Grimes,R. C. Haight, D. G. Madland, P. Moller, E. Pitcher, G. Russell,H. Schuhmacher, and W. B. Wilson, for useful conversations.

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