LA-UR -85-4056

REUMI)BYKJl %C 06M35

Los Alamos Nallonal Labormofy H opofmed by lI!o LJnMrq of Caldofnl.gfor Ihg Umlcd Stalca Dapartmant of Energy under contracl W.740$ENG.M

LA-UR--85-4C56

DE86 003660

TITLE: NON - E LAST I C CROSS - SECT I ONS FOR NEUTRON I NT ERACT I ONS W I THCARBON AND OXYGEN ABOVE 1 4 Me V

AUTI+OR(S]: 0. J. B r e n n e rR . E . P r a e l

SUBMITTEDTO P r o c e e d i n g s o f t h e I AEA Ad v i s o r y G r o u p Me e t i n g o n h u c l e a r a n dA t om i c Da t a f o r Ra d i o t h e r a p y a n d Ra d ~ i o l o g y ( I AEA P a n e lP r o c e e d i n g s S e r i e S ) - Sept. 1 6 - 2 0 ,

& Ra d i o b i o l o g i c a lI n s t i t u t e , T . N . O . R i j sw i j k , THE NE THERLANDS

D~ [ _

LosAllanrm) v’LosAkmos NationalLab~atoryLosAlamos,NewMexico 87545

Uwrm

Non-ElasticCross-sectionsfor NeutronInteractionswith Carbonand OxygenAbove 14 MeV

D. J. BrecnerRadiologicalRedearchLaboratory

ColumbiaUniversity630 West 1 6 8 t h S t r e e t

New York,NY 1 0 0 3 2 , USA

R. E. PraelLos AlamosNationalLaboratory

GroupX6Los Alamos,NM 8 ’ 7 5 4 5 , USA

,

-2-

Abstract

In the light of the new generation of high energy

(S 80 MeV) neutron therapy facilitiescurrentlybeing tested,

the need Fcr neutronkerma factors in the range from 15 to

80 MeV on carbon and oxygenhas becomeof urgentimportance.

Not enoughexperimentaldata currentlyexist or are likelyto be

measuredsoon,so a nuclearmodel is essentialfor interpolation

or, less satisfactorily,extrapolationof available data. The

use of a suitablemodel,applicableto light nuclei,is shown to

be crucial. Sucha model is described, and good agreement

between its results and the experimentaldata in the energy

rangeof interestis reported. Comparisons between the model

predictions and the ENDF/B-V evaluation of the non-elastic

cross-sectionfor carbonbetween15 and 20 MeV indicate that a

re-evaluationof ENDFis required.

.- 3 -

Introduction

The use of high energy (S 8 0 MeV) n e u t r o n r a d i o t h e r a p y

facilitiesat variouscentersaroundthe world is beginning to

increase[lj. In order thatmeaningfulintercomparisonsbe made

between the different neutron facilities, etich with a

characteristicneutronenergyspectrum,it is essentialthat the

same estimated dose at different facilities should indeed

correspond,as precisely as possible, to the same energy

depositionper unit mass of tissue. This requirement in turn

necessitatesa precise k,lowledgeof’neutronkermafactorsand

ratiosover the energyrangeof interest[2].

However,due to lack of nuclear data above 14 MeV, only

kerma factors for hydrogenare knownwith acceptableprecision

(a few percent). The other two elementsof importance, carbon

and oxygen,have considerableuncertainties,due to our lackof

knowledgeof’detailedcross-sectionsfor the various possible

neutron-inducedreactions.

To rectifythis situationa largeamountof nucleardata is

required. It 1s not sufficient,for example,to know the total

oross-sectionfor a particularrnartion,for the kerma f’~ctor

rofcmsto tho cnorgy of cmittnd secondury particles. Thus,——

detallod reaction mochilnlumsor, equivalently,Corirpleto

secondarych;rscflpurtlc]espectra,muot bc known. Tt 1s not

practlaalto expectcompletodata of this typo to becomecxperio-

montfillyav:JIJablcover thu whole energy f’anguof interest

(111< En < 80); thio lo jn part boc:luseof difflcult,lcsin

meil~uroment,tuchntquwsnnd bunmavull:+billty,hut al~O t.MIJilUSf3

-4-

of the enormous expense tliatwould be involved. A more

practical possibility, thereFore, is to develop model

calculatfonaltechniques,which have been validatedby whatever—

nucleardata are availablein the energyrange of interest, and——

serve ideally to interpolate (but sometimesof necessityto

extrapolate)the experimentaldata that do exist. It is the

purposeof this contributionto describesuch a technique.

Appropriateand InappropriateApproaches

As described above,the calcul.at!onsmust agree w~bh such

experimental

non-elastic

and oxygen.

data that are available:we are concernedhere with

neutron cross-sectionsfor the lightr,ucleicarbon——

As describedin an earlierreview [ 3 ] , the nature

of these light nuclides is sdch that theiruniquenuclear

structuresmust be taken intoaccountin any model calculation,

as the effectsof theirstructuresare not maskedby the statis-

ticalbehavior caused by a large number of nucleons. In

addition,of course,both carbonand oxygenexhibitconsiderable

alpha-particleclustering: for example, the calculations of

Kurath [4] and F3alashovet al. [5] both indicate large—.

spectroscopic?factorsfor alpha particlesin carbonand oxygen;

also, experimentallythere io some evidencefrom alpha transfer

and knockoutreactions,in carbonand oxygen,that there 1s con-

siderablealphoclustering[62.

These conulde~atlonuthen, lead us to concludethat a

‘general purpone’ nuclear reaction model--of’which several

evidenceto supportthis

calculationsbelow,but

-5-

thesls will be given from our own

for the moment,we Illustratethe point

by referenceto some data from the literature.

The de-excitationby particleemlsslonof excited compound

nuclei i3 usually calculated usinga statisticalevaporation

model,firstdescribedby Weisskopf[ 7 ] i n which the probability

that an excitednucleuswith excitationEc will emit a particle

with energyE is proportionalto EU(EC-E), where @(Ec- E) IS

the density of energy levels of the residual nucleus at

excitationEc- E. The analytlcform of the densityor levelsis

usuallytakento

u(c) -

be [ 8 1

exp(26G~) , (1)

wtierea is a cuns~ant.for a givennucleusand 6 is the pairing

energy. From such considerations,Le Couteur [9] calculated

that the energyspectrumot’eva;c?atedparticlc~to bu propo-

rtionalto

5 -12FJT CTIT s (~)

wherj T 1s the initial nuclear ‘tomperaljure’. Thus, a

logarithmic plot of Lhe productioncross-scctlonfor low energy

(evaporated)secondaryparticles,dividedby E~T shouldyield a

straight line. Such a relflesentatinn,takenfrom the work of’

Cross L1O],for the productionof low energysecondary neutrons

from 190-MeVprotonbombardmentof variousnuclides,is shown in

Flgme 1. It can

(2) doesseem to

- 6 -

b e s e e n t n a t for the h e a v i e r nuclei, Equation

apply,but the agreementbecomecprogressively

worseas the targetmass dscreases,and 1s very poor for carbon.

This may be understood by l’eferenceto Figure2, where the

energylevelsfor a light nucleus and a heavy nucleus are

compared. It is clearthat the use of an analyticPorm such as

Equation(2) to describethe densityof energy levels, whilst

potentiallyreasonablefor gold, is entirelyinappropriatefor a

nuci.cussuch as carbon,which has its own unique, and non-

analyticallydescribable,energylevels.

Having established that whatevermodel is to bc used, it

must specificallytake intoaccountthe special properties of

llght nuclei, we considerwhat mightbe an appropriatemodel.

It has been clearfor about 40 yearsthat the angle and energy

of particlescomingout of a high energynuclearreactionresult

from a two-stepprocess[11]. In the first ‘direct!stage,

incident particle energy 1s sharedprogressivelyamongst

and more degreesof freedomof tha system. In other words

the

more

the

incident particle makescollisionswith individualnucleonsor

groupsof nucleonswithinthe nucleusand the3e,in turn, have

further collisions in the same nucleus,generatingan intra-

nuclearcascade. Some of the productsof such collisions may

acquiresufficientenergyto escapefrom the nuoleus,thesehigh

energyparticlesbolngreferredto aa ‘direct’ products, being

predominantlyemittedin Lhe forwarddltectlon. In the second,

‘equilibrium’3tag0, the remaining energy 1s statistically

.

-7-

distributedin a compoundnucleusand resultsin the emissionof

lowerener~yparticles,isotropicin the cenkerof mass system.

For the firstIntra-nuclearoascadepart of the reaction,

we follow the technique first suggestedby Goldberger[12].

Here the targetnucleusis treatedas a degenerate Fe~Bmigas,

and the nucleon-nucleonor nucleon-clustercollisionswithinthe

nucleusare determinedby experimentallydeterminedfree (i.e.,

on-shell) differential cross-sections. The path of these

nucleonsand clustersis then tracedby Monte-Carlo techniques,

i.e., sampling distributionsbased on theseon-shellcross-

sectionstogetherwith assumptions about nuclear density and

nucleonor clustermomenta. All primaryand secondaryparticles

are followeduntileitherthey escapefrom the nucleusor thetr

energybecomessmall.

Our particular implementationof the Goldbergertechnique

will be deswibed ir, the next section. It is worthwhile,

however, to mention briei’lythe inherentassumptionsof the

technique.

Firstly,in orderto use the two--bodyinteractionmcdel for

each colllslon in the cascade,the averageintranuclearmean

freepath shouldbe largerthan the wavelengthof the particles

in the cascade. Roughly, this appears to be the case at

particleenergies of about 100 McV and above, though the

rapidity and degreeof’breakdownof the modelbelow 100 MeV 1s

not known, and can only really be evaluated by detailed

comparisonwith experiment. Secondly,the use of oxperlmentally

dotermlncdnucleon-nuclnunand nucleon-clustercross-scctlons

implies that the

the nucleuscan be

- 8 -

off-shellinteractionmatrix elementsinside

approximatedby on-shellvalues:the separa-

tion energy of an

about7 NeV; however,

These rather large

alpha clusterin carbonor oxygen Is only

for nucleons,lC variesfrom 12 to 1 9 MeV.

nucleonic separationenergiesmight imply

that f’reenucleon-nucleoncross-sectionsare not completely

appropriate;however,the magnitudeof this effectis difficult

to asseasa priori.

The IntranuclearCascadeCode, INCAl

Our intranuclearcsscadecode is based on the one described

by Chen et al. [13], although without provision for pion——

production,implyingan upperenergylimit of around 300 MeV.

It allowsfor a

alpha clusters

clustering is

descriptionof the nucleusin termsof nucleons,

and two-nucleon clusters. (The two-nucleon

for a description of ‘bN.) We have taken

spectroscopic

nucleus--from

tions in turn

factors--themeasureof findinga cluster in the

the work of Balashovet al. [5],whose calcula-——

agree with the results of cluster ‘knockout’

experiments on carbonand oxygen. For example,the ~60nucleus

is taken to be a timeaverageof 2.52 alpha clusters plus 5.92

nucleons, whilst the ‘ZCnucleus1s taken to be representedby

1.64 alphaclu9tersplus 5.44 nucleons. The nucleusis assumed

to be spherically symmetric and t.>consistof a seriesof 13

anhularsphericalshells,each with a densityobtainedfrom two-

or three-parameterFermi distributionsderivedfrom electron

elastlcScattering”[lU].In each shell Fermi-momentumdlstri-

.

- 9 -

butions for nucleons are calculated, based on the nucleon

densityin thatregion. For the clusters,whichare bosons, a

Fermi momentum ciistributionappropriateto the densitynormal-

ized ta a singleparticle is used. For nucleon scattering,

Paull blocking is enforced, such that a colllsionis only

allowedif both nucleonshave a finalenergygreaterthan their

Fermi energies. Particleemissionis restrictedby one and two

particle separation energies, which are updated on a

time-dependent basis to take into account prior particle

emissions, and to ensure energy conservation. Finally,

particles are allowed to escape freely when their radial

position

nucleus.

We

in part,

deuteron

approximatelyexceedsthe half-densityradius of the

have also includeda simplemodelfor nucleontransfer,

cular, the nucleon pickup reaction yielding the

a crocess known to contributesignificantlyto the

chargedparticleyield [15]. In the spiritof the intra-nuclear

cascade we have followed the conceptual approach used in

Ref. 1 5 , wherebyorl-shelltransfercross-sectionswere success-

fully used. As a firstapproach,thesetransfercross-sections

are estimated using the plane-wave Born zpproximatlon as

describedby Selove[16].

When no furtherdirectemissionis energeticallypossible,

the typ9,energyand directionof all emittedparticlesand the

compound nucleus are recorded, and anotherincidentparticle

treated. Typically10’ incidentparticlesare used for INCA1,

taking, for oxygen at 20 MeV, around 1 hour on a CRAY X-MP

-10-

c omp u t e r . The cnupoundnucleiare then allowed to decay by

‘Fermi-breakup‘ as describedIn the next section.

Fermi Breakupof the CompoundNucleus,INCA2

As discussed above, the use of an evaporationmodel to

describethe particle emission from an equilibrium compound

nucleusis not realisticfor lightnuclei. Therefore,we use an

approach,termed‘Fermibreakup’,suggestedinitially by Fermi

[ 1 7 1 , and subsequentlyused by, among others, Zhdanuvand

Fedotov[8] and Gradszta.jn~t al. [19]. Fermipointedout that.—

if the energy of the collisionIs dumpedinto a smallnuclear

volume,it will be rapidlystatisticallyredistributedamongthe

degrees of freedomof the system. This conclusionwill be true

independentof the numbe? of particles in the volume. Al1

possible finalstateswill then appearwith frequenciespropor-

tional to their s~atistical weights which, excluding spin

factors,will be

sn = dQ(w)air” S@, ( 3 )

for a state of n non-relativisticparticleswith momenta~i,

Here Q is the volumeof phasespace correspondingto the total

energy, w. This integral,with the constraintsof energyand

mcmentum conservation,was calculated analytically--~hough

incorrectly--by Rozental[20],and subsequentlyby Brenner[21]:

.

-11-

(4)

where T is the totalkineticenergyand pi the mass of particle

i. Thus, the breakupprobabilityfor all possiblechannels may

be computed, and a particularchannelchosenby random-number

techniques.

In contrastto earlierimplementationsof the Fermibreakup

technique, we have recognized that a considerablenumberof

decaysgo throughparticle-unstableintermediatestates,and we

have thusallowedmultiple,sequent~aldecays.

Some othernovel fea~bi-es of INCA2are the use of a.Coulomb

barrier~enetrat;.onfactor,derivedfromCculombwave functions,

for two-bodybr{:akup(themost commontype);for mult~-particle

breakup,a simple threshold is used, adjusted for Coulomb

energy. Again ‘or the most commonlyfoundtwo-bodybreakup,

parj:yand Lsospin conservation1s enforced, as well as a

res’;rictionof’ particleemissionby a ncut)’al-particleangular

mor,er,t,umbarrier. For cilrbonand oxygen ir, the range below

a’~ollt100 MeV, aig}~.-bodybreakupis sufficientlyunlikelyto

allow restriction of calculating probabilitiesonly up to

seven-body breakup. Ir much higherenergiesare requlrcd,the

code couldbc extended,thoughwith an increiissin runningtime.

Finally,and vc!ryimportantly,up--to-elateexperimentaldata

are used as the data”-b;l~efor Milsg exccsws, excitation

-12-

energies,spins,isospins,and paritiesof all availablenuclear

levels.

As discussed above, the utilityof a nuclearmodel as an

interpolatingor, less ideally, extrapolating device for

available nuclear data depends on a detailedcomparisonwith

experimentwhere it is available. By far the most detailed

experimentaldata availablein the energyrange of interestare

the resultsof measurementsof double-differentialhydrogen and

heliumspectraproducedby neutronreactionson carbon,nitrogen

and oxygenat 27.4, 3 9 . 7 and 60.7 MeV. For carbon,a comparison

has been published elsewhere [221, so only a few pertinent

detailswill be discussed here. (For oxygen, similar ~om-

parisofisare currently being undertaken,preliminaryresults

indicatinga degreeof agreementsimilarLo that for carbon.)

When evaluating these comparisons,it shouldbe born in mind

that the INC.4model does not have any free parameters, so the

calculationis in no sensea ‘fit’to the data.

Figures3 and 4 show some typicalcomparisonsfor carbonat,

27,4 and 60.7MeV incidentnelltronenergy, at varlou~ angles.

Also shown in these figuresare the charge-aymrnetricproton-

incluceddata measuredby Bertrandand Peel’e[23] at, the sam~

energie9. Overall, the agreement for all particletypes is

quite mtisfying,

Figure5 illustrates the effects of not treating the

particularpropertiesof the lightnucleicor’rcctly,Tho short-

- 1 3 -

d a s h e d lines art? the results of INCA runs where a) the

spectroscopicfactor for a-clusteringwas get to zero, and

b) the cross-sectionf~r deuteronpickupwas set to zero. It is

clear that the yield of deuteronsand alphas--whichtogether

(Seebelow)are responsiblefor almosthalf the total kerma--ls

not reproducedin this case.

The resultsof this comparisongive greatconfidencein the

model at energies above 27 MeV. Between this energy and

15 MeV--wherepresumablythe modelwill becomeincreasinglyless

realistic--nosuch complete experimentaldata are available.

However, a recentemulsionexperiment[25]has the potentialto

yieldmore limited,but in some casesiore specific,data. This

work involvesan incidentspectrumof neutr9nenergiesimpinging

on an emulsioncontainingc~rbon,nitrogen,oxygen arlc!silver.

If the finalstatecontainsno more t,hanone neutralparticle,

the reaction can in principle be uniquely ~dentified, and

f’mtherDalitz-plotanalysiscallalso revealintermediatestates

for particularreactions. This approachwas used to measurethe

cross-sectionsfor the reaction ‘2C(n,n’)3abetween 11 and

3 5 MeV. Circuitously,however, such an approach requires

corrections for phenomenu such an three-prongedeventsnot

causedby threealphas,and rc!actionsin whichan alpha is not

detectedas it is belowthe dct.ectlonthresholdin the emulsion:

such corrections,of couroc, presuppose the measurements in

question. Our INCA codes appear to be an idealcoolfor such

correctionsand when applied to tho data, aa discussed in

Ref. 26, yield cross-sec.tlonu10 to 30:tlowerthan or’iglnally

- 1 4 -

report.ed.Figure6 showsa comparisonof the reviseddata with

INCA predictionsfor the 12C(n,n’)3areaction.

Dalitz-plot analysis of emulsion data can also yield

partialcross-sections,and comparison with calculati.1s then

becomes a particularlysensitivetest of the model. Figure 7

s h ows a comparison of the revis~d emulsion data for the

~2C(n,n~)12C*(g.63MeV)+30 reaction,with INCAresults,and also

with some recenttime-of-flightmeasurements at 20 to 26 MeV

[27].

This latter time-of-flight experiment also reported

cross-sectionsfor the 12C(n,n’)~2C*(4,43MeV)reaction, which

are comparedwith INCApredictionsin Table I.

Overall, then, it appears that satisfactory agreement

betweentheoryand experinlt?ntex.stsin the 14 to 6 5 MeV rani{e.

One exception is the recenttime-of-flightmeasurementof the

~2C(n,n~)3across-sectionat IllMe’J[28],yielding 110 A 15 mb.

This is in totaldisagreementwithother experimentalmeasure-

mentsat this energy(?jO, 287, 230 mb) and with our cal-

culations (262 mb). The discrepancy is extremelylargeand

shouldbe investigatedfurther.

PredictedKeactlonMechanismsat 20 MeV--

There 1s currentlymuch debatoovernot only the reaction

cross-sectionsfor neutron Interactionson lightnucl~i,but

also the reactionmechanl:m. In this seotion, we show some

predictions for carbon and oxygenat 20 MeV. I!?the lightOf

the comparisonsin’ the previous section, thase results are

.-15-

clearly predictive of the basic reactionmechanismfeatures

though,based

are estimated

about25$.

Table 11

on

to

thosecomparisons,the actualbranching ratios

ha”{ean uncertainty,due to the model,of up to

showsthe yield

where all directemissionhas

nucleihas occurred. It can

outcome

or no em

emission

of compoundnuclei,at the point

ceased,but no breakupof compound

be seen that the most common

of the directreactionis the emissionof one neutron,

ssion at all; howev~r,as seen in Figure5, the direct

of chargedparticlesis certainlysigrlificantand in-

creasinglyso with increasingenergy. The mechanisms for the

breakup of l=C* and “CM are shown in Figures8 and 9 . The

lowestexcitedstateof ‘*C simplydecaysby gamma emission,but

the higherstatesmostlydecayby sequentialtwo-bodydecaysto

yield Sa, The deoayof i‘C is much more complex; for clar~ty,

decays leading to 3a + n (the majority)have been displayed

separatelyfrom thoseleadingto other finalstates, Table III

sums up thosemechanismsthat lead to the 12C(n,n1)3areaction

at 20 MeV, Only thooechannelowith cross-sectionsmoro than 1%

of the totalare shown,but evenwith this restrictiont,hcreare

13 distinctmechanisms--a difficultuituatlon fur an analytic

calculation!As tho cnorgyincreaaou,so Lht!numberof chtmnels

increilses.

Table IV shows the+yluld of cumpo’mclnucl.cl

equlllbrlum sto~o ~ftor20-MoVnoutronnare ineidonton

F~gures 10 and 11 then ohow t}lemochanlamsfor the decay

at the

oxygen.

of the

- 1 6 -

predominantcompoundnuclei leO*and I’O*. Again,the diversity

of reactionsis notable.

Perusalof thesefiguresreveals an interesting contrast

between carbonand oxygenat 20 MeV. Whilstfor carbon,almost

al1

85%

As

( 9 9% ) the yieldof alphasis from multiple alpha emission,

of the alpha yieldof oxygenis from singlealpha emission.

more channels open at higher energies, this contrast

decreases, and at 3 5 Me v , o n l y 3 5% of the alpha yield is from

singlealphas. Such considerationsare, of course,of consider-

ablemicrodosimetricimportance.

Comparisonswith ENDF for Carbon

The latest evaluationcf neutroncross-sectionsin carbon

was undertakenin 1978by Fu and Pereyfor ENDF/B-V [29]. The

non-elastic cross-section above 14 MeV was estimated by

subtractingthe elasticfrom the.totalcross-section;@valuation

of the predominantalpha-productioncross-sectionwas apparently

guidedby this and by the old emulsiondata of Frye~ ~. [30]

and Vasllev et al. [ 3 1 ] , i l l u s t r a t e d in Figure 6. The——

evaluatedalphaproductionis shown in Figure12, toG ~her with

the INCA prediction, Comparisonwith F i g u r e 6 illustrate that

the large rise in the evaluated alpha-productioncross-section

appetirsto be based on two datapointsby Vasilevet al. [31],—. —

at 1’/a n d 1 8 MeV, each with over 30$ error”bars,and which have

had rathe:auncertaincorrectionsmade for’low-energyalphasthat

were not detectablein the emulsion.

Tablg V il.lus~rutesthntsuch n maosiverise in the a-pro-

- 1 7 -

d u c t i o n a n d t h u s t h e n o n - e l a s t i c

s a r i l y i mp l i e d by the most r e c e n t l y

cross-sectionis not nece9-

available elastic [27,32]

and total [33]

predictionsare

together with

cross-sections.Both at 14 and 20 MeV, the INCA

consistent with the available data, This,

the resultsof the more recentemulsionexperi-

ment, indicatethat the non-elastic cross-sectionis p?obably

continuouslydecreasingabove 15 MeV.

KermaFactors

The INCA codesare capableof predictingonly non-elastic

and compound-elasticcro3s-3ections. Shape-elastic cross-

sections, which,at 14 McV, contributeabout30% and 20% to the

totalkerma for carbonand oxygen respectively (decreasing to

about 5% at 60 MeV), must be estimated separately. Above

14 MeV, appropriatedatn are sparseand optical model analyses

of availabledata sucklas thosereportedin Refs,27 and 3 4 must

of necessitybe consideredratheruncertain. For example, in

Ref. 27 at 40 MeV, the kermafactorfor elasticscatteringof

carbonderiveddirectlyfrom the data,and derivedfrom the best

opticalmodel fit to the samu data,differby about 10~! In part— ——

this is due to the fact that,becauseof the energyweightingin

the definition of’ kerma, midclluand b~ck angleswhichhave

smallercross-sectionsand tend not to bc meauuredso Well (if

at all),make the largestcontributionto the kermafactor. The

situationappearaoven worm for oxygen,where it seems to be

the case that (cf Ref. 35), at leastin the onm’gyrange from 20

t o 2 6 MeV, there i~ a deep hack-angle minimum a t around 120°

- 1 8 -

t h a t o a n n o t be reproduced by any c o n v e n t i o n a l p a r ame t e r i s a t i o n

o f t h e a p h e r i o a l o p t i c a l p o t e n t i a l .

W i t h t h e s e c a v e a t s , E q u a t i o n ( 5 ) a n d T a b l e VI show fits to

our calculated kerma factors, included our best estimate of’

elastic scattering, Further details and c0mpar190n9 with other

works can be f o u n d i n Re f . 3 4 .

K(E) - p, + p2 E - P3 exp(-p4E)J ( 5 )

where E is the neutron energy in MeV, and K is the kerma factor

in 10-’B Gy m~. The formula was fitted to our predictions

between 1 6 a n ~ 8 0 MeV.

Conclusions

We conclude firstly that a nuclearmodel is essentialto

interpolatewhat experimentaldata thatdo exist, in order to

caloulate non-elastic kerma factors for oarbon and oxygen.

Secondly,we have arguedthat a nuolear model must be specific

to llght nuclei. Such a model has been described and fits well

with experimental double-differential secondarychargedparticle

spectra for incident neutrong between 27 and 6 0 MeV on carbcn

and oxygan. The model ha~ us~antially no free parameters. It

also f i t g reasonably well with the limited data available

between 15 and 27 MeV,

Given that the modtil has been shown to be reasonably

reliable, WQ have argued that tho ENDF/B-V-valuation of non-

elasLlc crosn-section~and a-production crosb-sections for

.,?

- 1 9 -

carbon must be in considerable error’ between 15 and 20 MeV,

perhaps by as much as 30% at some energies. It is in urgent

need of re-evaluation.

Finally, kerma factors based on our model calculations are

given for carbon and oxygen and tissue. !Iore elastic scattering

data and modelling, particularly for oxygen between 15 and

‘5 MeV, are, however, required to improve these predictions.

Acknowledgement

This investigation was in part supported by Contract DE-

AC02-83Eff60142 from the US Department of Energy and by PHS Grant

CA 1530’1 awarded by the National Cancer Institute, DHHS, to the

Radiological Researoh Laboratory.

-20-

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JACKSON, D.F., BRENNER, D.J., Prcg. ParE. Nucl. Phys.

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ROOS, P.G., CHANT, N.S., COWLEY,A.A., GOLDBERG, D.A.,

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BLATT, J.M., WTISSKOPF, V.F., “TheoreticalNuclear

Physicstt, Wiley & Sons, New York (1952).

LECOUTEUR, K.J., Proc. Phys. Sot. 6 5 ( 1 9 5 2 ) 7 1 8 .

GROSS , E . , The Absolute Yield of’ Low-mergy Neutrons

from 190-MeV Proton Bombardment oi’ Cold, Silver, Niakel,

Aluminum and Carbon, Univ. of CA Rep. UCRL-3330

(1956). I

[11] SERBER, R,, Phys. Rev. 72 (1947) 1114.—

[12] GOLDBERGER,M,L.,Phys. R(?v. 7 4 ( 1 9 4 8 ) 1 2 6 9 .—

L 1 3 ] CHEN, ~., FRAENKEL, Z., FRIEDLANDER, G., GROVES, J,p.,

MILLER, J.M., SHIMAMOTO,Y., Phy9, Rev. 166 (1968)

949.

[14] DE JAGER, C,W., DE VRIES,H., GZ VRIES,C., At. Data

Nucl, Data Tables 14 (1976) 479.—

-21-

[ 1 5 1

[16]

[171

[18]

[ 1 9 1

[ 2 0 1

[ 2 1 ]

[22]

[ 2 3 ]

[24]

[251

[ 2 6 ]

[27]

[281

HACHENBERG,F., CHIANG, H.C., HtiFNER, J., Phys. Lett.

97B (1980) 183.

SELOVE,w., phys. w. Iol ( 1 9 5 6 ) 2 3 1 .

F ERM I , E . , P r o g . T h e o r . Phys. q(1950) 570.

ZHDANOV, A.P., FEDOTGV, P.I., SOV. Phys . JETP ~

( 1 9 6 4 ) 3 1 3 .

CRADSZ TA JN , E.p YIOU, F., KLAPISCH, R., BERNAS, R.,

Fhys. Rev. Lett. ~(1965) 436.

RG7ENTAL,I.L.,SOV. Phys. JETP~ (1955) 166.

BRENNER, D.J., IIpion Interactionswith LightNuclei and

Applications to Radiotherapy”, Rutherford Laboratory

Report, RL-79-032 (1979).

SUBRAMANIAN, 7;S., ROMF.1{0, J.L., BRADY, F.P., WATSON,

J.W. , FITZGERALD, D.H., GARRZTT, R., NEEDHAM,

ULLMANN, J.L., ZANEL1.1, C.I., BRENNER, D.J.,

R.E., Phys. Rev. C~(1983) 521.

BERTRAND, F.E., PEELLE, R.W., Phys. Rev. C 9

1045.

G.A.,

PRAEL,

(1973)

DIMBYLOW,P.J., Phys. Med. Biol. ~(1980) 6 3 7 .

ANTO I KOV I C , D . , SLAUS, 1., PLENKOVIC, D., MACQ, P.,

MEULDERS,J.P., Nucl. Phys . ~(1983) 87.

BRENNER,D.J., PRAEL, R.L., Pluc:l. Scl. Eng. 88 (1384)—

97.

MEICOONI, A.S., PETLER, J.S., FINLAY, R.W., Phys. Med.

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-22-

[29] KINSEY, R., ENDF/B Summary Documentation, Brookhaven

National Laboratory Report BNL-NCS-17541 (ENDF-201)

( 1 9 7 9 ) .

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( 1 9 5 5 ) 1 3 7 5 .

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Phys . Rev. C32 (1985) 673.

-23-,

Table 1. Cros3 Sections for ‘aC(n,n’)lzC(2+) 20-26MeV.

Energy Experiment [27] INCA/FBMeV mb mb

20 92 9624 79 7926 73 63

Table 11.IntermediateYieldof’CompoundNuclei (20-MeVNeutronson Carborl).

n+ 12(J + 13C* 117mb 26%+ 12C* + n 279mb 61s+ 12B* + p 18mb 4%+ IIB* ~ d 24mb 5%+ ‘i3e* + a 6mb+eBe*+a+n 12mb ;;

-24-

Table 111Mechanisms of 12C(n,n’)3a at 20 MeV.

n+ 12c ● n ~ 12CX ● ~ + oBe + z=

+ 13c* + ‘He + ‘Be+ ~ + a + Za

+ 13C* + n + 12c* + a + ‘Be + Za

+ l~cit + a + ‘Be* + n + ‘Be + Za

+n+a+ ‘Be + 2a+ 13C* + a + gBe* + a + ‘He.~+n

+ 13ciI + ~ + ‘Be* + n + Za

+]3C*+za+ ‘He+n+a.. n + ‘2C*+ 3a

+ l~c*+ n + a + ‘Be + 2a

+(Y+ 9Be* + n + ‘Be + 2a

+a+ 9Be*+ a + ‘He + a + n

+a+ 9Be*+ n + 2a

585

1 3%

6%

5%

5%

4%

2%

2%

1%

1%

1%

1%

1%

TableIVIntermediateYieldof CompoundNuclei (20-MeVNe~trons on Oxygen).

n + 16(-J + 170* 150mb 25$+ 160* + n 31On!b 52$+ ~GN* + p 31mb 5%+ ISN* + d 67mb 11%+ 15N~+np 9mb 2$+ IsC*+ a 1‘i’mb 3%+ 12C* + an 14mb 2$

,-25-

Table VEvaluatedExperimentalTotal and ElaaticCross-Sections

(in Barns)for Neutronson Carbon.CornDaredwithINCA Non-ElasticPredictiong:—

INCATotal Elastic Non-ElasLic

14 MeV 1.32 t .02 .86 f .06 .47

20 MeV 1.48 t . 0 6 . 9 5 * . 1 0 . 4 6

Table VI. Parameters for Equation (5). T h e r e s u l t s a r e v a l i d from16 to 80 MeV and yield kerma per unit fluence values in 10-lS Gy IT12.

ICRUlH 12C 14N 130 mu9cle

PI 5 1 . 7 9 2 . 3 5 5 1 2 . 0 8 2 2 . 7 3 0 6 . 5 8 7

P2 -0.2563 0 . 0 3 8 8 6 - 0 . 0 2 6 5 6 0 . 0 3 0 8 5 0 . u 1 8 7 7

P1 - 0 . 0 4 2 4 6 7 . 9 9 0 1 1 . 3 2 5 3 . 5 3 2 4 . 6 8 3

P , - 0 . 0 6 0 . 1 4 4 5 0 . 0 1 2 1 1 0 , 0 5 8 2 S 0 . 1 3 1 4

-26-

Figure Captions

1) Low Energy Neutrons emitted after bombardment of various

targets by 190-MeV protons [10]. In this representation,

if Equation (2) is valid, the data should fall on 9trai8ht

lines.

2) Energy levels of the compound n u c l e i of ‘SC and ‘smAu.

Note the energy scale for lB@Au has been expanded by about

2 5 compared with that of l’C.

3) Yield of hydrogen and helium isotopes after bombardment of

carbon by 27.4-MeV n e u t r o n s . The row3 A,B,C,D,E

correspond to production angles of 15°, 35°, 65°, 90° and

130”. The points are results of a measurement [22], the

h i s t o g r ams a r e t h e p r e d i c t i o n s o f t h e INCA oode and the

smooth curves are the results of a measurement of the

charge-symmetric proton-induced reaction [231.

4) As Fig, 3, for 6 0 . 7 - Me V incident neutrons. Tho rows

A,B,C,ll,E correspond to production angles of’ 20°, 40°,

650, 9 0 ” and 150”.

5) Comparison of prodictlons for incident 60.7-MoV neutrons

(at 20°) whcm a-clustering and deuteron pickup are

~ncluuu~ (full histograms) md wh e n e x o l u d e d (dashed

hlstogramn) ,’” Tho moanured dnt~ ire ~hown as points.

-27-

6 ) C r o s s - s e c t i o n f o r the lzC(n,n’)3a r e a c t i o n . The open

circles are the results of an emulsion experiment [ 2 5 ] , a s

r e v i s e d i n Re f . [ 2 6 1 . The squarea and crosses are,

respectively,

reported in

prediction of

7 ) C r o s J - . s e c t i o n

The trii’ngles

the results of the emulsion experiments

Refs. [30] and [31]. The curve 1s the

the INCA oode.

for the 19C(n,n’ )1aC*(9.63MeV)+3a reaction.

are the results of the emulsion experiment

[25] as revised in Ref. [26]. The circles are the results

of a recent time-of-flight measurement [27]. The curve is

the prediction o!’ the INCA code.

8) Predicted

carbon by

9) As /1s. 8

10) Predioted

oxygen by

in mb.

decay scheme for ‘aC* formed by bombardment of

20-MeV neutruns.

f o r “ C* . The numbers are cross-seotions in mb.

decay scheme for ‘GO*

20-MoV noutrona. The

formed by bombardment of

numberfl are cross-aectlong

11) An Fig. 10 for “O*.

12) Alpha nroductlon cro!!o-section for mutrons incident on

o a r b o n , T h e f u l l curve 1s the prediotlon of thn INCA

coda; the d a s h e d curve 1s the ENl)F/U-V ovaluution [x!].

-. .,.

●

●

v

h:!?

‘Vvw

-f

+●

v

10’I I 1 1 1 I 1 1 I I 1 10 2 4

,6 8 10 1 2

v

Vv

NEUTRON ENERGY (MW)

,

F i g 1

.

t T .4-L

Iii>

-F-3e,.

!,1.

. 4 -—~-==.f$y ! ,r’,,T——--——-. - nw, , ,, ,

1 cI;c

,,,,I LR..

illftlllltll-a

1+ - [11111

4“ ‘ lllllll!l/i

,

.

F i g 2

b a.]d

1o”’

I d

10-’

I d

I d

10-’

l d

Io-’-

0 1 0 2 0 0 1 0 2 0 0 1 0 2 0 0 10 20 3 0

ENERGY (MeV)

F i g 3

P d t He-3 a.Id

10”

Id

10”

Id

10’

Id

I(S

Id

10.

310”0 2 0 4 0 0 2 0 4 0 ’ 0 2 0 4 0 0 2 0 4 0 0 2 0 4 - 0

II:NIHWY f MGV I

rlg4

.

Ki

Id

73~ ]fj

\J 3T J 10

10

310

rJfJ

n

.,.*..., ,,,$

,,,

,,, ,

:,, ..

—.

—

r———r———

P

L:.$..,,.;,*BU-’%.:

$. . % 1]:,!, ., ! “j~t,.,:

:a ; . . , , ,

, : LI I10 2 0 3 0 4 0 5 0 6 0 ‘— - - 2 = 0 - % 5 0 6 0t 1 0

E N ER G Y ( M e V )fl

F i g 5

c 115 20 25 30 35

ENERGY (MeV).F i g 6

1 0 0

50

0

.

15 .20 25 30 35#,’ ENERGY (MeV)

lig7

3a

k mb~ 118mb ~“ 3mb .p+llB

153mb

I‘Be + a

I2a

. F i g 8

z~+~e+n a+5He+a+n

b’ ‘Y/a+n+%e+za

‘He + ‘Be-~ %’ -%e” -ta4 $

n+a2a [> n+a+~Be+2a

Fig 9 ,

------ .. .

n

15N

a

n

q p -—m_—

168

“1a+

\

2

12c

P + 15N

a + 12C

F i g 1 0

.

I

3

—

12-

0.9 “#

0 . 6“ .14 16 18 20

NEUTRON ENERGY (MeV)

F i g 1 2

.

,,. .