IEEE Transactions on Nuclear Science, Vol. NS-30, No. 2, April 1983

EFFECTS OF A NUCLEAR SCATTERING RESONANCE ON BREMSSTRAHLUNG

PRODUCTION AND K-SHELL IONIZATION

C.C. Trail, P.M.S. Lesser and M.K. LiouBrooklyn College of CUNYBrooklyn, New York 11210

Summary

While the effects of nuclear resonances onnuclear bremsstrahlung emission have been the focusof current bremsstrahlung studies in nuclear physics,such effects on atomic K-shell ionization haveattracted much attention recently. In this paper, wereview the recent developments of these two topicswith the emphasis upon their common features. Specialattention is given to the effect of the nuclearresonance near 461 keV in p+l2C where experimentalresults are available for bremsstrahlung productionand K-shell ionization.

In the past, since nuclear processes played norole in most atomic-collision studies, the reasonsfor studying K-shell ionization were quite differentfrom those for studying nuclear bremsstrahlung.Recently, however, a common feature of these studieshas emerged. That is the possibility of extractingmore detailed information about (compound) nuclearreactions, such as nuclear time delay, either throughmeasurements of the nuclear bremsstrahlung spectrumin the vicinity of a nuclear resonance or throughmeasurements of K-shell ionization across a nuclearresonance.

The idea of using bremsstrahlung emission as atool for investigating nuclear reactions was firstproposed by Eisberg, Yennie and Wilkinson in 1960.1Their classical treatment was extended later to aquantum mechanical treatment by Feshbach and Yennie.2Briefly, the amplitude which represents the photonemission before nuclear scattering and the amplitudewhich represents the photon emission after scatteringadd coherently. Since these two amplitudes differ inphase by W-4 ( 1W = radiation frequency, a = timedelay), the bremsstrahlung cross section evaluatedfrom these two amplitudes (and an internal amplitudeobtained through the gauge invariant condition) willcontain an interference term which depends upon thetime delay -C . For small values of 1Ct , one obtainsa typical bremsstrahlung spectrum with 1/K dependence(K = photon energy). As Wt increases, interferencebetween the two amplitudes is altered, causing a

change in the bremsstrahlung spectrum. For example,when a long-lived resonant state is formed, thebremsstrahlung spectrum will show structure. Aquantitative measurement of the bremsstrahlung cross

section can then provide a measure of the time delay.This information about the time delay can be used todistinguish unambiguously between direct nuclearreactions and compound nuclear reactions. It is well-known that the nuclear bremsstrahlung process is alsoan ideal process for the study of off-shell effects.Since the off-shell effects produce no special struc-

ture which depends upon the incident bombardingenergy, the structure due to the resonance can beidentified very easily from the experimental data.

A serious attempt to measure the proton-carbonbremsstrahlung cross sections near the 1.7-MeV andO.5-MeV resonances and to extract important informa-tion about the time delay was made by the Bolognagroup3 and the Brooklyn group,4'5 and these resultshave been confirmed by a group from Tokyo.6 Thesegroups have clearly observed the resonance structure

in the measured p12C bremsstrahlung spectra and haveused these spectra to extract a delay time of theorder of 10-20 secs. Some typical p12C bremsstrahlungspectra with resonant structure are shown in Fig. 1.

3.5 P 2C

3.0 E, 1 .795 MeV7

2.5-

105

1.0*- 7

15 ' \ro I-10 20 30 40 50 60 70 80 90 100 110 120

k (keV)

Fig. la: The proton-carbron bremsstrahlungcross section in the lab. system as a functionof photon energy at Ei = 1.795 MeV. The solidcurve represents the calculation using theFeshbach-Yennie approximation which includesboth the principal term and the correction term.

The dashed curve represents the calculationusing the principal term of the Feshbach-Yennieapproximation. The dotted curve represents thecalculation using the leading term of the soft-photon approximation. The experimental dataare from Ref. 3.

32

28

24

20

16

12

8

4,

P C -

0,. iss5E1, -I.88 MeV

20 40 60 80 100 120 140 160 180 200 230 240

k (KeV)

Fig. lb: The proton-carbon bremsstrahlungcross section relative to the elastic scatter-ing cross section as a function of photonenergy at Ei = 1.88 MeV. The solid curve

represents the result calculated from theFeshbach-Yennie approximation, which includesboth the principal term and the correctionterm, and averaged over the solid angle of thephoton detector. The dash-dotted curve

represents the result calculated from thesame approximation but without averaging over

the solid angle of the photon detector. Thedashed curve represents the result, averagedover the solid angle of the photon detector,of the calculation using the principal termof the Feshbach-Yennie approximation. Thedotted curve represents the result,averagedover the solid angle of the photon detector,of the calculation using the leading term of

the soft-photon approximation. The experi-mental data are from Ref. 4.

0018 -9499/83/040- 1124$01.00(' 1983 IEEE

1124

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4.0

,; 3

11 3.0

2-0

a 2a

a,,IDII

b

0

X200D200 ~~~835 keV

b-o

100 200K (keV)

Fig. lc: The proton-carbon bremsstrahlungcross section multiplied by K in the C.M.system as a function of photon energy atEi = 1.835 MeV. The solid curve representsthe calculation using the principal term ofthe Feshbach-Yennie approximation. CTakenfrom Ref. 6).

These experimental data are compared with the theoret-ical predictions calculated from the Feshbach-Yennieapproximation7 and the soft-photon approximation.8Since the elastic scattering amplitude, determinedfrom the elastic scattering data, has been used asinput, these types of calculations are modelindependent.

The bremsstrahlung cross section can be simplywritten in the form

K 0Kwhere OUz/K , which depends only upon theelastic scattering amplitude, is called the principalterm and C0o , which depends upon the elasticscattering amplitude and its derivatives, is calledthe correction term. MI and (0 are evaluated atthe incident energy Ei in the soft-photon approxima-tion. In the Feshbach-Yennie approximation, G_and CIO are evaluated at two energies: theincident energy Ei and the final energy Ef = Ei - K.For small K, the contribution from the correctionterm is small compared with the principal term exceptin the region of the resonance. In the past, thecorrection term had been ignored without justification,and the data were compared with the simplifiedFeshbach-Yennie approximation which included only theprincipal term of the approximation. Fig. lb showsclearly that the correction term is indeed importantin the energy region of the resonance. However, asshown in Fig. 2, for the case of p12CV near the461-keV resonance, the calculation using theprincipal term alone is in better agreement with theexperimental data than the full Feshbach-Yenniecalculation. This unusual result, for which thereare several possible explanations, is not well under-stood and warrants further study.

The original formula derived by Feshbach andYennie (or by Eisberg et al.) for the calculation ofthe time delay was rather simple; it was based uponthe assumption that the principal term of theapproximation dominated the bremsstrahlung crosssection and the correction term was negligible. Underthis assumption, the time delay can be determineddirectly from the bremsstrahlung and elastic scatter-ing data. However, as shown in Fig. lb, the correc-tion term is not negligible in the region of theresonance, and we must take into account the correc-tion term in the extraction of the time delay fromthe p12CIdata near 1.7 MeV. The expression for thetime delay is very complicated if the contributionfrom the correction term is included.9 Furthermore,the time delay cannot be determined directly from theelastic scattering and bremsstrahlung data. Fig. 3shows a set of the results obtained by the Brooklyn

group .

w-

4'a) 3'° 2'

H1.(

K (keV)

Fig. 2: The proton-carbon bremsstrahlungcross section relative to the elasticscattering cross section as a function ofphoton energy at Ei = 591 keV, 696 keV and796 keV. Three sets of data are plottedon the same photon energy scale in orderto show the shift of the resonant structurewith the incident proton energy. The dashedcurves represent the cross section calculatedfrom the full Feshbach-Yennie approximation,which includes both the principal term andthe correction term. The dash-dotted curvesrepresent the calculation using the principalterm of the Feshbach-Yennie approximation.The solid curves represent the calculationusing the leading term of the soft-photonapproximation. The experimental data arefrom Ref. 5.

-53U);0, .5

_

20 40 60 80 100 120 140 160 180k (keV)

Fig. 3: Cos ( OT) and nuclear time delayst extracted from the p12C Y data atEi = 1.88 MeV. The solid curves are thetheoretical predictions. (Pef. 9)

1125

I I' 1

E[.88 MeV

i II} I i i.

1126

The nuclear time delay associated with a reson-ance formed in a nuclear reaction can also alter theprobability for K-shell ionization (-K). The variationin the inner-shell ionization probability is analogousto the change in the probability for bremsstrahlungproduction due to nuclear time delay, as discussed inthe preceding paragraphs. In the ionization case, thevariation of PK is due to the interference between theatomic amplitudes for ionizing the K-shell electron bythe projectile on the way in (incoming) and on the wayout (outgoing). This time delay effect on PK, whichwas suggested by Ciocchetti and Molinari in 1965,10was experimentally verified very recently by severalexperimental groups. The first experimental evidencewas obtained by a group from the University ofWashington. They observed a change in probability forproduction of K-shell X-rays across the Si nuclearresonance at Ep = 3.151 MeV in p+58Ni elastic scatter-ing.11 Significant variations in PK have also beenobserved in the elastic scattering of protons from88Sr at Ep = 5.06 MeV by the Stanford group12 and from12C at Ep = 461 keV by the Utrecht group.13 Someresults of these measurements are shown in Fig. 4.

Ep (MeV)Fig. 4a: (a) Observed and calculatedexcitation function for protons elasti-cally scattered by 58Ni. (b) Ratio ofproton yield in coincidence with K X-raysto the singles-proton yield, normalizedto unity off resonance. The solid curverepresents the result of a detailedcalculation performed by the Washingtongroup. (Taken from Ref. 11).

1.4

1.2

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0.8-

0.6-

V.' 0.8

a 0.7

0.6

0.5

2.0

1.5

1.0

c 4000

° 2000

,T T T I I ,- T

b

L a0A~~~~~~

I

400 450 500 5500 Ep(K eV)

Fig. 4c: (a) Measured and calculatedp+14C elastic scattering cross section.(b) The yields of backscattered protonsin coincidence with a K-shell electron.The solid curve represents the resultof a calculation using a formula derivedby the Utrecht group (Taken from Ref. 13).

A fully quantum-mechanical theory of K-shellionization near nuclear resonances has been developedby Blair et al. for the special case of an S-waveresonance.11 The theory was extended later by Blairand Anholt,14 Feagin and Kocbach,15 and McVoy andWeidenmuller16 to more general cases. These theoriesshow that the magnitude of the variation of PK dependsupon the ratio of the binding energy of the K-electron,UK, to the width of the nuclear resonance, r , andalso on the ratio of the resonant part of the nuclearscattering amplitude to the Coulomb part of thescattering amplitude, lfr4fcl M In order for PK tovary significantly near a nuclear resonance, thesetheories tell us that r' must be smaller than UK andthe angle of the scattered particles (protons) must belarge.

The experimental results of the Washington groupand the Stanford group are in satisfactory agreementwith the theoretical predictions, but the result ofthe Utrecht group is a controversial case. In ameasurement of PK near the 461-keV resonance inp+12C elastic scattering, the Utrecht group found a

large variation (about 70%) of the PK with protonenergy. Since the ratio of UK to r is very smallcompared with unity (about 0.008), PK is expected tobe nearly independent of proton energy. All theoreti-cal calculations 14,15,16 predict very small variation.For example, Anholt and Blair found theoretically a 4%dip in PK near the resonance energy. Thus, a largediscrepancy exists between theory and the experimentalresult of the Utrecht group.

In an effort to resolve this discrepancy,Meyerhof et al.17 have repeated the experiment of theUtrecht group and have found only a small variation inPK across the 461-keV resonance as expected. Asshown in Fig. 5, this new result of Meyerhof et al.agrees in angular and energy dependence with alltheoretical calculations.

5.0 5.1 5.2

Ep (MeV)

Fig. 4b: (a) The measured 88Sr K-shellionization probability as a function ofthe incident proton energy. The solidcurve represents the result of the calcu-lation using a formula derived by Blairet al. and by Blair and Anholt. (b) Measuredand calculated p+88Sr elastic scatteringcross section at 900 (Taken from Ref. 12).

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1127

References

t=

co

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a:

PK(14?)PK(16°)K 1

S

1.4

1.2

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0.8

06

Np(142°)Np(16°)

0.06

0.04

002

.(b)

-(a), A \i i

350 400 450 500Epf(keV)

Fig. 5: (a) Observed and calculatedsingles proton ratio in 1420 to 160.(b) Ratio of ionization probabilitiesat 1420 to 160. The solid curverepresents the theoretical predictioncalculated by Blair and Anholt.14 Thedashed curve is a fit to the data ofDuinker et al. using a modified formula.(Taken from Ref. 17.)

In nuclear scattering, where UK/r7( 1, brems-strahlung production appears to be a more sensitiveway to measure nuclear time delay. However, in orderto get a complete understanding of the bremsstrahlungprocess, much more experimental and theoretical workneeds to be done.

ACKNOWLEDGEMENTS

This work is supported in part by the Departmentof Energy under Contract No. DE-AC02-81ER40023 and bythe CUNY PSC-BHE Faculty Research Award Program. Weare grateful to Professor W. E. Meyerhof who providedus with results of his work prior to publication.

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12. J.F. Chemin, R. Anholt, C.L. Stoller,W.E. Meyerhof, and P.A. Amundsen, Phys. Rev. A24,1218 (1981); R. Anholt, Bull. Am. Phys. Soc. 27,29 (1982) and private communication.

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17. W.E. Meyerhof, G. Astner, D. Hofmann, K.O.Groeneveld, and J.F. Chemin, Z. Phys. A, to bepublished; W.E. Meyerhof, private communication.

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