IL NUOVO CIMENTO VoL. 40A, N. 4 21 Agosto 1977

Pre-Equilibrium Decay of Nuclei with A ~ 200

at Excitation Energies to 90 MeV (').

E. GADIOLI and E. GADIOLI ]~RBA

I s t i tu to d i F i s i ca dell' Universi th - Mi lano , I t a l i a I s t i tu to Naz ionale di F i s i ca Nuclea te - Sezione di Mi lano , I ta l ia

J . J . ]=[OGA~

Depar tment o] Chemistry, McGil l Universi ty - Montreal , Que., Canada

(riccvuto il 4 Apri le 1977)

Summary . - - Calculations using t i le exciton model of pre-equil ibrium decay have been made of the exci tat ion functions and part ic le spectra of reactions induced by (10--90)MeV protons on 197Au and 2~ The results of the calculations have been compared in all cases with appropri- ate exper imental data. The agreement between theoret ical predictions and exper imental measurements is quite sat isfactory if we use parameters which are unchanged from previous work on medium-weight target nuclei. The very low cross-sections for charged-part icle emission from heavy nuclei provide a rigorous test of the theory. Emphasis in the discussion is, therefore, on the discrepancies, par t icular ly as they relate to reaction mechanisms which are not at present accounted for by the theory. Of par t icular note is the agreement between calculation and experiment of the very complcx reactions in which the effects of nuclear s tructure are minimized and the model provides excellent results.

1 . - I n t r o d u c t i o n .

This p a p e r is t h e s econd of a ser ies w h i c h is i n t e n d e d t o i n v e s t i g a t e w h e t h e r

t h e e x c i t o n m o d e l a l lows one t o e v a l u t a t e w i t h a f ixed se t of p a r a m e t e r s

t h e c ross - sec t ions of t h e m a j o r i t y of t h e r e a c t i o n s i n d u c e d b y p r o t o n s w i t h

e n e r g y u p to a b o u t one h u n d r e d M e u on a g i v e n t a r g e t nuc leus .

(*) To speed up publ icat ion, the authors of th is paper have agreed to not receive the proofs for correction.

383

3 ~ E. GADIOLI, E. GADIOLI ERBA a n d J . J . HOGAN

This s tudy is m o t i v a t e d b y the fact tha t , a l though no sys temat ic analyses

of the k ind we propose have been repor ted up to now, the model has p roved to be successful in reproducing the cross-sections of m a n y different reac- t ions (see papers (1-3) and references therein).

An invest igat ion like the one we propose relies on the avai labi l i ty of appro- pr ia te exper imenta l data . I n the first paper of the series, which hereaf ter will be referred to as I (4), we considered 30 different reactions induced on

A ~_~ 90 nuclei; the model allowed us to correct ly eva lua te the cross-sections of all the processes considered including some with cross-sections of the order of one mb. The ta rge t nuclei we considered, 8SSr, 8~y and especially ~~ were

neu t ron deficient. This fact and their relat ively low Coulomb barr ier made the

emission of charged particles compet i t ive with neu t ron emission. In fact ,

a t exci ta t ion energies exceeding ___ 50 MeV, the major i ty of de-exci ta t ion processes included the emission of a t least one charged particle (4,5). The

nuclei we consider in this paper (197Au and ~~ present a much higher Coulomb barr ier to chargerd-part icle emission. I n addition, ~9~Hg is neut ron rich. This

means t h a t the emission of charged particles occurs main ly during the pre- equi l ibr ium stage of the de-exci ta t ion process, and the s tudy of those react ions in which charged particles are emi t t ed allows one to m a k e a ve ry significant tes t of the predict ions of the exei ton model.

As was the case in paper I , the overall fit of bo th the exci ta t ion functions

and the par t ic le spectra is highly sat isfactory. In this paper , however, we have t r ied to delve more deeply into the discrepancies which do exi t in an

effort to fur ther define the s t rengths and weaknesses of the exci ton model. I f a t t imes we discuss secondary effects a t greater length than m a y ~ppear necessary, i t is largely due to the general agreement of the theory with exper iment coupled with the detailed discussion of pape r I. I n sect. 2 the reactions we have con- sidered are summarized; sect. 3 is devoted to the comparison of the theoret ical predict ions wi th the exper imenta l da ta and sect. 4 to the conclusions.

2. - Summary of the experimental data considered.

The da ta we considered are a) the exci ta t ion functions of the react ions

summar ized in table I (~.8), b) the spectra of the ~-particles emi t t ed in the re-

(1) E. GADIOLI and E. GADIOLI ERBA: Acta Phys. Slov., 25, 126 (1975). (2) E. GADIOLI, ]~. GADIOLI ERBA, L. SAJO BOHUS and G. TAGLIAFERRI: RiV. N~OVO Cimento, 6, 1 (1976). (8) E. GADIOLI: ~Vukleonika, 21, 385 (1976). (4) E. GADIOLI, ]~. GADIOLI ERBA and J. J. HOGAN: submitted to Phys. Rev. (5) G. B. SAHA, N. T. PORILE and L. YAFFE: Phys. Rev., 144, 962 (1966). (6) G. ALDERLIESTEN, O. BOUSSHID, P. JAHN, H.-J. P~OBST and C. MAY~R-BORICKE: KFA-IKP 10/76 (1976), unpublished. (~) T. ~V[. KAVANAGH and R. E. BELL: Can. Journ. Phys., 39, 1172 (1961). (s) M. V. KANTELO and J. J. HOGAN: Phys. Rev. G, 13, 1095 (1976).

PRE-EQUILIBRIUM DECAY OF NUCLEI ETC.

TABLE I .

385

Reaction (E~)mL n ~MeV) (ED)m~ ~ (MeV) References

197Au(p, 3n)lg~Hg 18 42 (9)

197Au(p, 4n)lgaHg 27 45 (a)

197Au(p, 5n)lgaHgm 36 45 (s)

197Au(p, pn)199Au 18 86 (7)

197Au(p, p2n)195Au 23.2 86 (7)

197Au(p, p3n)194Au 32.4 86 (7)

~92Hg(p, 2p)2OlAu 34 86 (s)

292Hg(p, 2pn)2~ 30 86 (s)

2~ 2p2n)199Au 12 86 (s)

292Hg(p, 2p3n)lgSAu 15 86 (s)

292Hg(p, 2p5n)199Au 34 86 (s)

29~Hg(p, 2p7n)194Au 56 86 (s)

~~ 2pSn)lgZAu 68 86 (8)

~92Hg(p, 2p9n)192Au 74 86 (s)

action 197Au(p, x~) measured at Ep-----20, 23.7, 26.6, 30.15, 33.85, 36.8, 39.8, 41.5 MeV by GADIOLI et al. (9) an at Ep = 28.8 and 61.5 MeV by BERTRAND and PEELLE (lo), 9~nd e) the spectra of protons emi t ted ia the reaction 197Au(p, xp) measured at 28.8 and 61.5 MeV by :BERTRAND and t)EELLE (10).

The analysis of the exci ta t ion functions of the ~~ 2pxn) reactions (9) and of the energy distributions of the ~-particles emi t ted iu (p, x~) reactions induced ou gold and neighbouring nuclei (Ta, Bi and Pb isotopes) (9.n) allowed one to est imate the cross-section for the product ion of ~-particles in reactions induced by protons on A _~ 200 nuclei. This quan t i ty is repor ted in fig. 1 as a funct ion of the incident-proton energy.

A discussion of the most re levant features of these reactions has been pre- sentend in each of the papers which repor ted the exper imenta l measurements , bu t a theoretical in terpre ta t ion of these data has not bcea published up to n0W.

(9) E. GADIOLI, I. IORI, ~]'. ~r and L. ZETTA: Phys. 1~ev. C, 4, 1412 (1971). (lo) F. E. BERTRAND and R. W. PEELLE: Oak Ridge National Laboratory Report, ORNL 4460 (I969), unpublished. (11) E. GADIOLI, I. IORI, N. MOLHO and L. ZETTA: Report INFN/BE 73/5 (1973), unpublished.

26 - I l N u o v o G i m e n $ o A .

386

60

50

40

~ 3 0

20

10

~4

I I

E. G A D I O L I , :E. G A D I O L I E R B A and J . J . H O G A N

I I I I /1

a)

0 ~ I I I I I I 20 30 40 50 60 70 80

~p (MeV)

Fig. 1. - Cross-section for production of alpha-particles as a function of the incident- proton energy. The experimental points are from KANTELO and HOGAN (s) (• ~O2Hg), :BERTRAND and P E E L L E (10) ( , 197Au ) and G A D I O L I et al. (11) (A l a T A u , * 2 ~ �9 2~

~ogpb, [] ~ogBi, o 181Ta). The two lines represent the result of theoretical predictions: a) in the case of proton bombardment of 2O2Hg utilizing a value of the performation factor of 0.075, b) in the case of proton bombardment of 197Au utilizing a value of the preformation factor of 0.05.

3. - Theoretical calculations and comparison with the experimental data.

3"1. General considerat ions. - The calculations tha t are reported here have

been performed by means of the same procedure and the same parameters

we utilized and described in I. Here, for the sake of completeness, we will

limit ourselves to presenting a brief outline of the procedure followed. The

cross-sections have been calculated by means of a Monte Carlo tecnique by generalizing the procedure suggested by DOST~OVSKY et al. (12). Two main

stages contribute to the de-excitation process: the pre-equilibrium decay stage

and the evaporat ive stage. I n both stages the emission of neutrons~ protons

(1~) I. DOSTROVSKY, Z. I~RAENKEL and G. FRIEDLANDER: .Phys. Rev., 116, 683 (1959).

PRE-EQUILIBRIU1K DECAY OF NUCLEI ETC. 387

and alphas has been considered. The emission of alphas ia the pre-equilibrium stage can occur only ff a nucleon interacts with an ~ substructure pre-existing in the composite excited system (1~). The probability for a nucleon to interact with a preformed g substructure is indicated by T. The possibility of up to four sequential pre-equibibrium emissions has been considered. At the end of the pre-equilibrium stage r an excited compound state is left which subsequently decays by particle evaporation. The expressions of the decay rates correspond- ing to the different decay modes have been reported in paper I and ref. (l-s), to which the reader interested in an exhaustive description and a careful dis- cussion of all the computational procedure is referred. The parameters entering the calculations are the ones reported in these references.

In the calculations of the excitations functions, the presence of shell effects which could influence the state and level densities appearing in the expressions of the decay rates for particle emission is not considered. Altough both ~"TAu and 20~Hg lie near the doubly-magic-nucleus region~ we expect such effects to have only minor influence on most of the results of the calculation. In the majority on the reactions studied~ ~.t least one charged particle is emitted by the excited composite nucleus created in the interaction of projectile and tar- get. Due to the high Coulomb barrier, the predominant reaction mechanism is one in which the charged particle~ or particles~ is emitted during the pre- equilibrium stage of the de-excitation process, which is little affected by the presence of shell effects. However, the yield and energy distribution of alpha- particles having kinetic energies approximating the Coulomb barrier are poorly reproduced by these calcualtions, which utilize semi-classical inverse cross- sections. Since alphas with such an energy are mainly evaporated by the com- pound nucleus, the presence of shell effects has a nonnegligible influence on the results of a calculation aiming at reproducing their distribution. In order to eliminate these shortcomings, in the case of the analysis of the spectra of the alphas emitted in the ~97Au(p, xg) reaction~ the evaporative contribution has been calculated by means of the analytical expressions reported in ref. (9).

Though at the highest proton energies considered the excitation energy of the composite nucleus reaches a value of the order of one hundred 1VIeV, the competition of fission processes has not been included in the calculation. In fact, as has been previously stated, the majority of the reactions considered starts with the pre-equilibrium emission of charged particles and~ during this stage of the process~ fission does not compete with the other decay modes of the excited system. When the evaporative stage begins, the excitation energy is greatly decreased, neutron evaporation predominates and the importance of fission competition is reduced.

(13) L. ~r COLLI and 1~. G. BRAG)~ ~ARCAZZAI~: Riv. Nuovo Cimento, 3, 535 (1973).

~ ~.. GADIOLI~ E. GADIOLI E R R A and J . J . HOGAN

3"2. Tota l a lpha-par t i c le y ie ld . - The experimental cross-sections for pro- duction of alpha-particles, ~ , reported in fig. 1, show a linear dependence on the incident-proton energy E~. The theoretical prediction for this quantity also displays a linear dependence on Ep except at the lowest energies, but its slope in the energy range 30 < Ep < 85 MeV is slightly steeper than the exper- imental one. This discrepancy is due to the underestimation, in the theoret- ical calculations, of the alpha-particle yield at low proton energies (E~<30MeV). This point is discussed in subsect. 3"4 and 3"5.

The two lines reported in fig. 1, which enclose the majority of the experi- mental alpha-particle yields at proton energies exceeding approximately 37 MeV, represent the result of calculations of a~ in the case a) of proton bombardment of ~~ and V = 0.075, b) of proton bombardment of ~ A u and 9 = 0.05.

The excitation functions of the reactions induced on ~~ discussed in subsect. 3"4, have been calculated by assuming for ~ the value 0.075. The best fit to the spectra of the alpha-particles emitted in proton bombardment of gold at energies exceeding ~-- 35 MeV has been obtained by assuming 9 = 0.5.

The results of the calculation of the cross-sections of the reactions ~~ xn) and (p, pxn) are almost unaffected by a variation, within the intervel consid- ered, of the value of ~, but for consistency the results shown in subsect. 3"3 have been obtaine4 by assuming ~ = 0.05.

3"3. E x c i t a t i o n f u n c t i o n s o/ 197Au(p, xn) and (p, pxn) react ions . - The com- parison of calculated and measured (B.7) excitation functions of the reactions 197Au(p, xn) and (p, pxn) is reported in fig. 2-5. The agreement between the measured and calculated excitation functions in the case of (p, xn) reactions is very satisfactory. In the case of (p, pxn) excitation functions the dashed line represents the results of our calculations, the dot-dashed line in all the cases gives the contribution of the (p, d(x--1)n) reactions which our calculations do not take into account and which has been estimated by the integration of appropriate sections of the deuteron spectra measured at 28 < Ep < 62 MeV on 197Au and ~o~ by BERTRAND and PEELE (10,14). Only in the case of the (p, pn) reaction at the rise of the excitation function does this contribution exceed 10% of the cross-section we evaluated. The full line represents the sum of the two contributions.

The calculations reproduce quite satisfactorily the measured excitation functions. The discrepancy between calculated and experimental cross-sections which occurs in the case of the (p, pn) reaction, starting approximately from Ep ___ 50 MeV, could be, at least in part, due to a systematic experimental error leading to an over-estimation of the measured values.

This conclusions is the result of a detailed comparison of the cross-sections

(14) F. E. BERTRAND and R. W. PEELL~: Oak Ridge National Laboratory Report, 0RNL 4638 (1971), unpublished.

PRE-EQUILIBRIUM DECAY OF NUCLEI ETC. 3 8 9

103

10 2

E

10 ~

1 I I I i I

�9 ',p ~ 3 n ) [

! (P, 5n) m

10 o I I I . I I I 15 20 25 30 35 40 45

E(MeV)

Fig. 2. - Exci ta t ion functions of the reactions 197Au(p, 3n), (p, 4n), (p, 5n). The full lines give the exper imental values a.s reported by ALDERLIESTEN et al. (e). The dashed lines give the theoret ical predictions.

10 ~

b

10

1 1 I I I I I

+. ' #

; \

+ i "\ ; x

\

I I l I 1 t J J 2O 4.0 60 80 100

Ep(MeV)

Fig. 3. - Exci ta t ion function of the ~97Au(p, pn) reaction. The exper imental da ta are from KAVAXA(m and BELL (~). The dashed lille represents our theoretical predictions, the dot-dashed line the contr ibut ion of the (p, d) reaction, the solid line the sum.

390 E. GADIOLI , E. GADIOLI ERBA a n d j . J . I IOGAN

measured b y KAVA~Ae~ and BELL at __~ 61.5 MeV with the p ro ton and deu- te ron spectra repor ted by BERTRAND and 1)EELLE at the same energy. I f we

assume t h a t the react ion pa th contr ibut ing to (p, pxn) processes is the one in which the p ro ton or the deuteron is emi t ted a t the beginning of the de-

exc i ta t ion cascade, and the contr ibut ion of second-chance p ro ton emissions to the p ro ton spec t rum is negligible, the in tegra t ion of appropr ia te sections of

p ro ton and deuteron spectra should give cross-sections direct ly comparab le

wi th the ones measured by KAVANAGH and BELL. The results we obta in in

this way, b y following the procedure suggested in appendix I of ref. (~5), are

123.4 and 143 m b in the cases, respectively, of (p, p2n)iand (p, p3n) reactions,

in excellent agreement with the values measured by KAVANAGH and BELL (136 and 150 mb). However , the yield of the (p, pn) react ion obta ined b y in tegra t ing the spectra (110.5 mb) is much lower t h a n the one obta ined b y

means of the ac t iva t ion technique (165 mb).

10 2

+ E b

10'

10 o ~I 2O

I I I I 1 1 1

\ . \ .

\ \ \

10 2

E b

10 ~

I I I I I I I

t

I I I I I I 10 ~ 1 I I I I I I 40 60 80 100 20 40 60 80

E (MeV) Ep (MeV)

Fig. 4. Fig. 5.

100

Fig. 4. - Excitation function of the 197Au(p, p2n) rcaction. The experimental data are from KAVANAGH and BELL (v). The dashed line represcnts our theoretical predic- tions, the dot-dashed line the contribution of the (p, dn) reaction, the solid line thc sum.

Fig. 5. - Excitation function of thc t97Au(p, p3n) reaction. The exper"mcntal data are from KAVASA6~I and BELL (v). The dashed line represents our theoretical predic- tions, the dot-dashed line the contribution of the (p, d2n) reaction, the solid line the sum.

(15) C. BIRATTARI, E. GADIOLI, A. M. G-RASSI STRINI, Cr. STRINI, G. TAGLIAFEI{RI and L. Z~TTA: Nucl. Phys., 166A, 605 (1971).

P R E - E Q U I L I B R I U M DECAY OF N U C L E I ETC. 391

3"4. Exci tat ion /unctions o/ 2~ (p, 2pxn) reactions. - The ~~ 2p) exci ta t ion funct ion (see fig. 6) rises monotonical ly s tar t ing f rom approximate ly

an incident-proton energy of 30 MeV. As previously pointed out by KANTEL0 and HoeA~ (s), the main contr ibut ion to this react ion is due to the reaction pa th in which both protons are emi t ted in the pre-equilibrium stage. The monotonic rise of this exci ta t ion funct ion is reproduced b y the calculation; however, above E p _ 50 MeV, the calculation over-estimates the measured cross-sections~by as much as a factor 2.

10 ~

10 o

S

b

f 1 0 - I _

1 0 - ~ 3O

I I I I I I I I I ~ :

+

+

10 "1

10 o

+ E

+

10 -1

+

10 -2 I I 90 30 40

I I I I I I I I I 40 50 60 70 80 50 60 70 80

Ep (MeV) Ep (PleV) 90

Fig. 6. Fig. 7.

Fig. 6. - Excitation function of the 2~ 2p) reaction. The experimental data are from KANTELO and HOGAN (s). The full lille represents our theoretical predictions.

Fig. 7. - Excitation function of thc 2~ 2pn) reaction. The experimental data are from KANTELO and HOOA~ (8). The full line represents our theoretical predictions. The two triangles give the contributions of the (p, 3He) reaction at 28.8 and 61.5 MeV, as deduced from BERTRAND and PFELLE (10).

The ~~ 2pn) exci ta t ion function, as is shown in fig. 7, also rises mo- notonically start ing from approximate ly 30 MeV. The calculation satisfactorily reproduces the exper imental da ta start ing f rom E , _~ 60 MeV. At lower en- ergies, it underest imates the measured cross-sections. The disagreement is due to the fact t ha t the calculation does not take into account the contr ibut ion of the ~~ SHe) react ion which, a t p ro ton energies lower than 50 MeV,

3 9 2 E. GADIOLI~ 1~.. GADIOLI ERBA a n d J . J . HOGAN

gives the predominant contribution to the measured axcitation function. The spectra of 3He emitted in proton bombardment of gold at E~ ~-28.8 and 61.5 ~r have been measured by B~RTRA~D and PE~LLE (lo). The values for the cross-sections of the (p, SHe) reaction at the two energies, deduced from their data, are, respectively, 0.03 and 0.49 mb. These values agree very sat- isfactorily with the ones one could deduce looking at the excitation function of the (p, 2pn) reaction measured on 2O~Hg. Before discussing new data we want to stress that the shape of the energy distribution of 3He measured by BEBTBAN]) and PEELLE seems to indicat~ that the reaction mechanism responsible for the emission of these particles cannot be described in the framework of the exciton model.

++ ++++ ++ /

+

E b

10 o

I I I I

10 1 10 ~

E Io

10 o

10-11 I I I I 10 -I 20 40 60 80

Ep (MeV)

+

I I I I I I I

++

I I I I I I I 20 40 60 80

E (MeW

Fig. 8. Fig. 9.

Fig. 8. - As fig. 6 for the reaction ~~ 2p2n).

Fig. 9. - As fig. 6 for the reaction 2~ 2p3n).

The excitation function of the reaction ~~ 2p2n), reported in fig. 8, shows a peak at Ep=25 l~IeV which is to be ascribed to the reaction ~~ a) (8). The measured and calculated cross-sections noticeably disagree at Ep < 34 MeV~ at which, on the contrary, the measured and calculated cross-sections of the re- action 2~ an) agree stasfactorily (see fig. 9). This consideration indicates that the calculations do not accurately reproduce the highest-energy part of

PRE-EQUILIBRIUM DECAY OF NUCLEI ETC. 3 9 3

the spectrum of the alphas emitted at proton energies in the interval 20 <E~ < < 34 MeV. At lower energies of the emitted alphas~ however, the calculations reproduce satisfactorily the emitted-alpha spectrum and, as a consequence~ the

E

10 0

I I I I I

+

10 -~ I I I I I 30 40 50 60 70 80 90

Ep(MeV)

Fig. 10. - As fig. 6 for the reaction 2O~Hg(p, 2pSn).

10 ~

E

100

f 1 1

./ 10 -1 I I I

50 60 70 80 90 Ep (MeV)

Fig. 11. - As fig. 6 for the reaction ~O~Hg(p, 2p7n).

~9~ ]~. GADIOLI, E. GADIOLI ERBA and J. J. HOGAN

theoret ical (p, ~n) cross-section satisfactorily agrees with the measured one. The same result is obtained in the analysis of the spectra of the alphas emi t ted in (p, x~) reactions on gold (see subsect. 3"6). In tha t case the comparison

10 1

E b

10 ~

I I

b

10

1 lO

+

S +

10-1l I I J 101 I I I I 60 70 80 90 60 70 80 90

Ep(MeV) Ep(MeV)

Fig. 12. Fig. 13.

Fig. 12. - As fig. 6 for the reaction S02Hg(p, 2p8n).

Fig. 13. - As fig. 6 for the reaction 2O~Hg(p, 2p9n).

between theoret ical calculations and exper imental da ta indicates that, for

20 < Ep < 30 MeV 9 the measured spectra are harder t han the calculated ones. I t should be also ment ioned t ha t recently ~ h Z Z O COLLIet al. (16) have concluded tha t effects different f rom pre-equilibrium decay seem to contr ibute to (p, x~) reactions induced by (20--30) MeV protons on near doubly magic nuclei. These authors have not a t t empted a detailed analysis of these effects, which in high- resolution experiments are easily distinguishable f rom pre-equilibrium con- tr ibutions, since they selectively populate a few residual-nucleus levels and disappear almost completely at angles near or greater t han 90 ~ . However , on

(is) L. MILAZZO COLLI, M. G. BRAGA I~[ARCAZZAN and M. MILAZZO: Nuovo Cimento, 30, 632 (1975).

PRF.-:EQ~)'ILIBRIUM DECAY OF NUCLEI ETC. 3 ~ 5

the basis of previous work by l=[oP~x~s (17) and GLASHAUSSER (18) they suggest t ha t the effects observed are to be in terpre ted as t r i ton pick-up.

An excellent agreement bcetwen calculations and exper imental da ta is found in the case of all the other measured exci ta t ion functions~ as shown in fig. 9-13. We limit ourselves to recalling t h a t for the 2~ 2pxn) reactions (x > 2) the first peak is to be a t t r ibu ted to the reaction (p, ~(x--2)n), while the second peak comprises a small contr ibut ion from this mode of dec~y ~nd a larger one f rom (p, 2pxn) (8).

3"5. Spectra o] the protons emittend in the l'TAu(p, xp) reaction. - The com- parison (see fig. 14) between calculated ~nd measured spectra of protons emi t ted in the l*TAu(p, xp) react ion at E~ = 28.8 MeV shows that~ apar t f rom the lowest energies 9 at which the presence of contaminant copper could produce the ab- normally high exper imenta l p ro ton yield (lO), the calculated differential cross- section is systematical ly lower than the measured one. In the outgoing-proton energy interval (13--22) MeV the calculated yield is (30--40) % smaller t han the measured one. At outgoing-proton energies f rom 22 MeV up to the maxi-

E

b

101 _

o 10 -

10 -~

I 1 I I 1

_2

5 l 1 L

10 15 20 25 Ep,(MeV)

30

Fig. 14. - Spectrum of the protons emitted in the 19VAu(p, xp) reaction a.t Ep = 28.8 MeV. The heavy-line histogram gives the experimental spectrum as measured by BERTRAND and P~:LLE (~0), the thin-line histogram our theoretical prediction.

(17) F. F. HOPKINS, W. J. CO~:RT~J.:Y, W. R. Co•:.'R, C. F. MOORE and P. RICIIARD: Zeits. Phys., 243, 446 (1971). (18) C. GLASnAVSSl.m, D. L. Iib:.','D~I~: and E. A. MCCLATCIIIE: .~'ud. Phys., 222 A, 65 (1974).

~ ~ . G A D I O I , I , E . G A D I O L I E R B A a n d J . J . H O G A N

mum available energy, the calculated spectrum steeply decreases with increas- ing proton energy, while the measured one remains relatively constant . A closer inspection of the ~TAu(p, pxn) exci tat ion functions confirms t h a t at

I I I I l I

+ / E "~ 10 o

10 -~ I I I I I 10 20 30 40 50 60 70

Ep,(MeV)

Fig. 15. - As fig. 14 for the l~TAu(p, xp) reaction at E~= 61.5 McV.

Ep < 30 l~IeV the calculated proton yield is really smaller than the measured one. While the discrepancy between measured and calculated yields at E , < 22 MeV is within the limits of aceurancy we can achieve by using a priori fixed para- meters in the exciton model, the flat energy distribution of the measured pro- tons at the higest energies is at variance with the energy distribution of neutrons in (p, It) reactions, tha t decreases with the energy. This suggests the presence of effects not described by the exciton model (1.3).

A flat distribution of the highest-energy protons was also revealed by (p, p') spectra measured at E~ ~ 18 MeV on A ~ 100 nuclei by KhI~ACH et al. (19).

Co~E~ et al. (=), measuring (p, p') spectra on nickel and isotopes at E~ ~ 17 MeV, showed tha t low-energy collective levels of the residual nucleus were excited, by means of a reaction mechanism tha t hardly could be described by the pre-

+

equilibrium models. The same result has been reached by BEIr and t)EELLE ia the bombardment of bismuth by 39 and 62 MeV protons (14). The last measurements clearly indicate tha t the yield of these high-energy protons

(19) C. KALBACII, S. 5[. GRIMES and C. WO.~G: Zeits. Phys., 275A, 175 (1975). (20) B. 1,. ColtJ~x, G. R. RAp, J. II. DItGNAN and K. C. CHAN : Phys. Rev., 7, 331 (1973).

I'R:E-:EQUILIBRIUBI DECAY OF NUCLEI :ETC. 3 ~ 7

not accounted for by the exciton model is mainly confined at forward angles lower than approximately 75 ~ :No simple explanation of this reaction mech- anism, most likely a surface process, can be given according to Com~. The importance of effects of this kind steadily decreases with increasing incident- proton energy. At E = 61.5 MeV, as shown in fig. 15, the calculated proton spectrum reproduces very satisfactorily the measured one at the high energies (in this case, also the measured yield of low-energy protons is abnormally high).

3"6. Spectra o] alphas emittend in the ~TAu(p, x~) reaction. - The agreement of calculated and measured spectra of alphas emittend in the 197Au(p, xcr re- action is reasonably good. However, a closer inspection reveals that, at low

10~ I- 1 I I I I

10 -1 _':- ,-,J~

. . , - ~ i -

- ~ .

b -

10 -2 _

10 3 I 15

i I I II [

20 25 30 35 E (MeV)

Fig. 16. - As fig. 14 for the 197Au(p, xa) reaction at Ep= 28.8 McV.

proton energies, as shown e.g. in fig. 16, the measured alpha spectrum is slightly harder than the calculated one. As was mentioned in subsect. 3"4, M/LAZZO COLLI et al. (1~) found that in proton bombardment of lead isotopes at 20 < E, <

30 NIeV a substantial contribution to alpha emission has to be attributed to a reaction mechanism, presumably triton pik-up, not described by the exeiton model. Though to a much lesser extent, the presence of alphas with energy greater than the one predicted by the exciton model seems to be revealed also by the data here considered. At 30 < E < 40 MeV the agreement of calculated and measured spectra is satisfactory, as shown e.g. in fig. 17. At higher energies,

~8 E. GADIOLI, E. OADIOLI ERBA and J. y. I{OGAN

the calculated spec t rum becomes increasingly flatter than the measured one. The effects is jus t appa ren t a t E ~ 41 MeV, as shown in 18, bu t becomes no-

t iceable a t Ep ~ 61.5 MeV (see fig. 19). Before di'awing definite conclusions

f rom this discrepancy, it should be recalled t ha t the density of those s ta tes of

the composi te and residual nuclei in which a lpha substructures and a lpha

10 3 I I I I I I

2

b

J 10 ~ I I I I I I

10 15 20 25 30 35 40 45 E (MeV)

Fig. 17. - Spectrum of tile alphas emitted in thc 197Au(p, x~) reaction at E~=36.8 MeV. The continuous lille gives the experimental spectrum ms measured by GADIOLI et al. (u), the histogram our theoretical prediction.

I I I I 1 I

] i

b

10 3

101 I 1 I I I 15 20 25 30 35 40 45

E (MeV)

Fig. 18. - As fig. 17 for the 197Au(p, x~) reaction at ED= 41.2 McV.

PRE-EQUILIBRIUM DECAY OF NUCLEI ETC. 39~

holes are involved is calculated by irLdroducing the naive assumption that the single-alpha-particle state density is one quarter of the single-nucleon state density. The whole of the data considered shows that this assumption con- stitutes a not unrealistic approximation. Its introduction, however, could prevent a too detaliled fit of the alpha-particle spectra.

1 I I t I

10

E

B10-

1 0 2 ~ , 10 20 30 40 50 60 70

Eo(MeV)

:Fig. 19. - Spec t rum of the a lphas emi t t ed in t he 19~Au(p, xc~) react ion ~t E p : 3 6 . 8 MeV. The thin-line histogram gives the experimental spectrum as measured by BERTRAND and PEELLE (lo), the heavy-line histogram our theoretical prediction.

4. - S u m m a r y and conc lus ions .

This paper reports the results of calculations of the cross-sections of pro- cesses induced by (10--86) MeV protons on 197Au and :~ The experimental

data considered allow a detailed study of the charged-particle emission from heavy excited composite nuclei. Since iu the case of these nuclei charged- particle emission occurs mainly ia the pre-equilibrium stage, analyses like the

one here reported allow a very detailed test of the predictions of the exciton model. The calculations have been done by using an a priori fixed set of para- meters (4) with the only exception being the preformation factor ~, whose value was found to be in the interval 0.05--0.075.

Though some discrepancies between the calculated and measured cross- sections exist which seem to confirm the existence of reaction mechanisms not

400 E. GADIOLI , E. GADIOLI ERBA and J . J . HOGAI~

d e s c r i b e d b y t h e e x c i t o n mode l , as s u g g e s t e d in ref . (1-a.~6) t h e b u l k of t h e d a t a

is r e p r o d u c e d w i t h a fa i r a c c u r a c y .

The a g r e e m e n t b e t w e e n t h e o r e t i c a l p r e d i c t i o n s a n d t h e e x p e r i m e n t a l f ind-

ings is e spec i a l l y s a t i s f a c t o r y in t h e case of c o m p l e x r e a c t i o n s to wh ich t h e

emis s ion of s eve ra l pa r t i c l e s c o n t r i b u t e , i n c l u d i n g t h o s e w i t h p e a k c ross -sec t ion

of on ly a few rob. This resu l t , wh ich is t h e s a m e t h a t was o b t a i n e d also in t h e

case of r e a c t i o n s i n d u c e d on A ~ 90 nuclei , i n d i c a t e s t h e s u b s t a n t i a l co r rec t -

ness of t h e m o d e l a n d of t h e a v e r a g e p a r a m e t e r s u t i l i zed .

Two of us (E. G. a n d J . J . I t . ) wish to t a n k t h e N o r t h A t l a n t i c T r e u t y

O r g a n i z a t i o n for m a k i n g th i s w o r k poss ib l e t h r o u g h ~ T r a v e l G r a n t . The ex-

p e r i m e n t a l w o r k was s u p p o r t e d b y a g r a n t f r o m t h e ~ a t i o n a l R e s e a r c h Counci l

of C a n a d a .

R I A S S U N T O

Si sono calcolate, usando il modello a eccitoni, lc funzioni di eccitazione e gli spettr i dcllc part icel le emesse in reazioni indot te da protoni di energia variabile t ra 10 e 90 MeV su 197Au e ~9~Hg. L'accordo t ra le previsioni teoriche e i r i sul ta t i sperimentali , ot tenuto usando nei calcoli gli stcssi paramet r i gi~ ut i l izzat i in un nostro precedente lavoro su nuclei con A ~ 90, b soddisfacente. In part icolare, le sezioni d 'ur to relat ive all 'emissione di part icel le cariche sono molto piccole e permettono un test molto rigoroso della teoria. Nella discussione si ds part icolare rilicvo alle discrepanze sopra t tu t to quando sere- bruno indicate mcccanismi di reazione c h e l a tcoria qui svi luppata non ~ in grado di r iprodurre. Di part icolare rilievo b l 'cccellente ~ccordo t ra calcoli c ~isultati sperimenCali re la t iv i a reazioni molto complessc in cui gli effetti legati alla part icolare s t ru t tura dei nuclei considerati sono minimizzati .

Ilpe~lpannoBecmafi pacna~ a~ep c A--~200 npH 3neprnax Boa6y~lenna ~Io 90 M3B.

Pe3mMe (*). - - ]/[cnonb3ya MOj~eJIb 3KClITOHa ~JI~I npe~paBHoBecaoro pacaa~a, np0- BO~.qrc.q BblqnCneHng ~byHrttn~ BO36y~eHna n cncKTpOB qacrnu ~ pearun~, I4aay- tmpoBaHHUX npOTOHaMn C aneprnaMa (10- -90)MaB na ~pVAu n 2~ PeaynbTaTbI BblqHC~eHnff[ cpaBHI4BaIOTC~I C HMelOI~nMHC~ 3KCrtepHMeHTa~bHbIMH ~aHHbIMH. I-[o~Iy- qaeTc~i y~OBfleTBOpnTeJTbHOe cor~acne M e ~ y TeopeTHqeCKHMH rtpe~cKa3aHrIgMH 14 3KClleplIMeHTa.rlbHbLMH H3MCpeHH~IMH, eC.rlH HCnO.rlb3y/OTCfl napaMeTpbi, KOTOpbte He orJn~qa~oTc~t oT HapaMeTpOB H3 npe,a~,~,ayme~ pa60 ' r~ Ha M~IUIeHaX H3 cpe.RRHX a,~ep. O~lerlb Manbm nonepe~H~ie ceqeH~a ~ n ncnycKaHH~ 3apa~renn~x qaCTI4II H3 T~eYlblX a~ep o6ecneqnBamr cTporym nposepry Teopnn. IIprt o6cy~aeHmt oco6oe BnnManne y~e~aeTca paaJ~HqnaM, rOTOpbm CBa3aHb~ C MexaHn3MOM pearunn n KOTOpbte ~0 nacTo~mero BpeMenn He MOryT ~blTb O67~CHenbt B paMrax 3TO~ Teopnm OTMeqaeTca coraacne Me~r~y Bb~qnCneHneM n 3KcnepnMeHTOM ~ oaeH~ CnO~H~tX pearttni~, r~e aqbqberrbt ajxeprlo~ cTpyKTypb~ aB.rlflrOTCfl MnnnMaabm,~Mn n npe~J~O~eHHa~t Mo~eab ]laeT xopom~e pe3yJ~bTaTbL

(*) IIepeaec)eno pec)amlueft.