Photodisintegration of light and medium-weight nuclei at intermediate energies—II Photoproduction of 11C and 7Be from 40Ca

.I. inore, natl. ('hem., 1976, VoL 38, pp. I-s

Pergamon Press. Printed in Great Britain

PHOTODISINTEGRATION OF LIGHT AND MEDIUM-WEIGHT NUCLEI AT INTERMEDIATE ENERGIES--II PHOTOPRODUCTION

O F '1C A N D VBe F R O M 4°Ca*

V. di NAPOLI, G. ROSA, F. SALVETI'I and M. L. TERRANOVA Istituto di Chimica Generale e Inorganica dell'UniversitL Roma, Italy and H. G. de CARVALHO, J. B. MARTINS and O. A. P. TAVARES Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil (Received 13 November 1974) Abstract--Mean cross sections for the photoproduction of "C and 7Be from 4°Ca targets have been measured using bremsstrahlung beams in the energy range 0.3-1 GeV. The values obtained turned out to be much larger than those expected from a simple spallation mechanism. A fragmentation-like process has therefore been suggested to explain such a discrepancy. INTRODUCTION A PREVIOUS paper[l] reported cross section measurements of the photoproduction of '8F, 22Na and 24Na from targets having masses between 23 and 40, in the energy range 0-3-1 GeV. In that paper (henceforth referred as I) measured cross sections were compared, in the absence of data from Monte Carlo calculations on photon-induced cascade-evaporation processes up to 1 GeV, with the charge-distribution-mass-distribution (CDMD) formula of Rudstam[2], modified by Jonsson and Lindgren[3] to account for the different kind of bombarding particles. This formula, which will be referred to in the course of the paper as CDMD-RJL formula, has been shown[I,3] to predict, with a fairly good accuracy, the cross section for any spallation reaction in the region of intermediateenergy photons. By comparing the experimentally determined cross sections in I with the predictions of the CDMD-RJL formula, some deviations from the spallation patterns have been found when the production of radionuclides implied the ejection from the nucleus struck of a large fraction of target nucleons. We found, in fact, that when the outgoing particles represented more than 40% of all the target nucleons, production cross sections were always larger than those predicted by the formula, thus indicating other mechanisms were effective which were different from the spallation one. It is the purpose of the present paper to confirm the trend already found in 1 by investigating the formation cross section of the two radionuctides ~C and 7Be from 4°Ca. These radionuclides are very far indeed from the target nucleus and, consequently, their photoproduction should somehow imply either the emission of 72.5 and 82.5%, respectively, of the nucleons of the target nucleus or the splitting off of ~C and 7Be as nucleon clusters (these may well be the final products of the decay of different initially ejected fragments, but this does not *Work supported by the Italian Consiglio Nazionale delle Ricerche and the Brazilian Conselho Nacional de Pesquisas and Comiss~o Nacional de Energia Nuclear.

significantly alter what has just been said.) In both cases, large deviations from the spallation patterns would indicate that their formation might not be ascribed to evaporation (spallation) processes only. Also, in this paper, we shall discuss in a deeper manner some results not completely analysed in I. EXPERIMENTAL As regards the experimental irradiation conditions, dose measurements and counting techniques, they were quite similar to those reported in l, to which the reader is referred. The targets consisted in analytical grade calcium hydride, in powder form, with a density of about 102' nuclei of 4°Ca per cm2. Five end-point bremsstrahlung energies have been used from 0.3 up to I GeV. The bremsstrahlung intensity varied from 5x 109 equivalent quanta per sec at Eo = 1 GeV to 109 equivalent quanta per sec at E,,= 0.3 GeV. The spectroscopic characteristics of the two radionuclides under investigation are the following: tm = 5Y6d, E~ = 0.447 MeV, 10.3 photons per 100 disintegrations for 7Be, and t,/2 = 20.34 m, E~ = 0.511 MeV, 200 photons per I00 disintegrations for "C. The integrated doses were, as an average, 1,D~4 equivalent quanta for the production of 7Be and 3x10 '~ equivalent quanta for t'C. Fluctuations in the beam intensity have been taken into consideration in correcting counting rates for the decay of 'LC during the irradiations. Such corrections were found to be unnecessary for 7Be. RESULTS The yields of photoproduction of the two radionuclides "C and 7Be, expressed as cross sections per equivalent quantum o'o, are presented in graphical form in Figs. 1 and 2 (semilog plots). Least-squares fits have been drawn, which gave the straight lines in the figures. For a brief discussion about the errors affecting the o-~'s the reader is referred to I. From the straight lines in Figs. 1 and 2, the two equations have been deduced o-o(Eo) = {(70 + 30) In Eo + (90 _+20)}/~b

(1)

~ro(Eo/= {(70 -+ 30) In Eo + (85 - 20)}/~b

(2)

and for the production of "C and 7Be, respectively.

V. DI NAPOLI, et al. ,~.

;

i

i

i

n.3

0.4

03

i

r

i

i

0,8

0.9

q

II 6O =

4O .=.,

T-

=

0 8REM.~STRAHLUNG

(1.6

03

ENERGY

[ G,,V )

Fig. 1. Cross section per equivalent quantum o-e of the photoproduction of "C from "°Ca vs the bremsstrahlung maximum energy. IUU

'--

G0

~

40

j

T

I

I

r

I

I

= ~

important to give some explanations about the symbols which will be used. We indicate with A, and A,, the mass numbers of the target nucleus and product nuclide, respectively, and with AA = A , - A p the nominal nucleon loss.* The ratio AA/A, represents then the fraction of nucleons which have left the target nucleus struck. Further, we shall indicate with ~r, the experimentally determined cross sections and with ~r, the cross sections calculated by means of the CDMD-RJL formula. Being interested in mean values of cross sections over the energy range 0.3-1GeV only, we consider it superfluous to indicate with 6~ these mean cross sections, which will be denoted simply by ~ from now on. Finally, ~rx will indicate the cross section "per nucleon", i.e. the cross section cr divided by the target mass number A, (obviously, ITN.e and crx,c will refer to experimental and calculated values, respectively.) As a first approximation we disregard in the present discussion any variation in the ~r's ascribable to differences in the N/Z ratios between the target and product nuclides, although the importance of such differences has been pointed out by Korteling and Caretto[4] (see also I). In other words, we shall restrict ourselves to the gross trend of the yield distributions, postponing to further papers a more refined treatment of the data. Taking into consideration photonuclear reactions with AA 1>3 onlyt and plotting the ratio cre/~c for the data gathered in I and in the present paper, if an evaporation mechanism had to be considered as the sole process we might expect that this ratio would be approximately constant and about unity, regardless of the value assumed by AA/A,. This is certainly true, in fact, when AA/A, is less than or equal to 0.4, but when it exceeds this latter value the ratio cr,,/o', becomes higher the higher the ratio AA/A,. This is clearly shown in Fig. 3. The highest values of ee/~r~ are reached when AA/A, assumes the values 0.725 (]]C from 4°Ca) and 0.825 (7Be from 4°Ca).

20

=

200

0

-0A

0.4

0.5

0,6

0.7

BBEMgGTRAHLUNG ENERGY

0,8

0.9

IG~VI

Before entering a detailed discussion about the results of both the present paper and paper I, we believe it *These nucleons may be ejected either as single nucleons or as nucleon clusters such as 2H, ~H, "He, and more complex aggregates. tlf AA < 3, we shall not regard the reaction as a spallation reaction.

t

-

r

~

I

~

o,5

O,G

~

~

40

Fig. 2. Cross section per equivalent quantum ~o of the photoproduction of 7Be from ~°Ca vs the bremsstrahlung maximum energy.

DISCUSSION

~

loo 70

I I

By applying the photon-difference method in the simplest form, i.e. with the approximation of a pure l/k dependence of the bremsstrahlung spectra upon the photon energy k, one obtains then the mean cross sections & in the energy range O.3-1 GeV simply by carrying out the first derivatives of eqns (1) and (2). In this way mean cross section values & (~C) = (70 +- 30)p,b and ~k (Be) = (70- 30)p,b have been found.

- -

20 Io ,:r

4

z~ zx <> 0.4

O

/

02

/

/

0,1

0.2

9.3

o,4

o,7

0.8

0,9

( At - A) / At

Fig. 3. Trend of the ratio o-~/tr, for the photoproduction of some radionuclides vs AA/A,. O, 24Na (paper 1); A, 22Na (paper 1); O, '"F (paper I); V, 'tC from "°Ca (present work); ¥, 7Be from 4°Ca (present work). The straight line parallel to the abscissa is the mean value of the experimental points up to AA/A, = 0.4. The straight line from 0.4 on is an eye-fit of the remainder experimental points.

Photodisintegration of light and medium-weight nuclei

From the slope of the straight line, for ~ A / A , >10.4, we succeeded in deducing the following equation o-~ = o-, exp [11.5(AA IA, ) - 4.6],

(3)

which establishes a relationship among the quantities m, ~r and k A / A , and so turns out to be rather useful in evaluating the contribution of processes different from spallation to the experimental cross sections. A still deeper understanding can be obtained if one plots the cross sections per nucleon as functions of AA. All the data of Fig. 3 have been thus rearranged and are shown in Fig. 4, where values calculated by using the CDMD-RJL formula are also reported for comparison. J0

T "~7

~q

J \\

!i!

CDMD-RJL formula for spallation reactions and by comparing these distributions with the experimentally determined cross sections. The reason is that suclh a presentation gives a very clear picture of the above mentioned discrepancies and allows a direct comparison to be made between measured and calculated values of the cross sections. For the sake of simplicity we believe it preferable: to give calculated yield (cross section) distributions at fixed values of the atomic number Z. Figures 5-7 show such distributions for a ~'Ca target (Fig. 5) and for other target nuclei (Figs. 6 and 7: see also I). Measured yields have been reported for the purpose of comparison.

•

r0

\

1.45 :

2,

N o

O•

Z

;

0000 0

\i l-9

I

|

©

i

]l=4

~5 l=6 i] 3 ~ i

1

:

~ 3 NOMINIL

l ; I LI : 1 MLI~LFOH

Io LOSS

1 zo

l_ t 3o

50

30

Fig. 4. (:ross section per target nucleon vs the nominal nucleon loss. C. experimental values of paper 1: O, calculated values: A, "C from ~"Ca experimental value (present work); at, ~Be from ~°Ca experimental value (present work). The straight line is a leastsquares fit of all lhe experimental points.

The straight line in the figure has been drawn by means of a least-squares fit of the experimental points only. The least-squares analysis gives ~r,, = (30 ± 10)AA " °:°2/#b.

(4)

Z~

Z2 18 14 MASS NUMB[R

10 A

?

Fig. 5. The curves (in reality broken fines) represent the mass distributions of spallation products from 4°Ca as calculated by means of the CDMD-RJL formula. O, experimental points from paper I; ~.~, "C from "°Ca (present work); at, :Be from 4"Ca (present work). The straight line represents the slope K of the yield-surface ridge. 1000

211

a~ p

?SSi

~oo/I

A similar analysis done with the calculated
(5)

and

l:u ~'= 10 ~!-11 ~ 9

or,. - {(2" 1 + 0' I)~A c ....... } × 10~/xb.(10 ~ AA ~< 30)

(6) In this case also experimental and calculated values compare quite favourably each other when k A is not too large leqns 4 and 5), The agreement fails when AA becomes larger than 10. As a consequence, other mechanisms different from spallation have to be invoked in order to explain such trends, at least for targets in the region of the light and medium-weight nuclei. At this stage we may attempt to bring some order into the experimental data by taking into consideration the mas'; distribution curves of the product nuclides using the

=

~.I ~ 2 Z6

• • 2Z

I i I~ ~

± ~

J ZZ

MASS NUMSER

J 16 26

1

~ • ZZ

A

Fig. 6. Mass distributions o f spal]ation products f r o m 2'AI, 2~Si and ~'P targets calculated by m e a n s of the C D M D - R J L formula. The circles are experimental points from paper I.

V.

I000 ,

,

32S

i

' ' 3'5,31CI

'

DI N A P O L I ,

Owing to the lack of experimental data at Z = 4 and Z = 6 for the other target nuclei (Figs. 6 and 7), K values have been estimated from the calculated cross sections at Ap = 22.3 (Z = 11) and A, = 18 (Z = 9) by means of eqn (7). To compare these slopes with those arising from the measured yields, the cross sections of 22Na photoproduction from the different targets have been normalised to the cross sections of z:3Na by multiplying them by the constant factor 1.6, which has been deduced from the calculated values for the two masses 22 and 22.3. The results are reported in Fig. 8, which clearly shows as the "experimental" slopes always lie underneath the calculated ones. This fact is simply due to the deviations

'

+

,I

10

L-H

I

I t!/i

0,1 2[

i /Z=-l] Z=!

et al.

Z=ll

i I i i i i Z2 18 26 2Z 18 Z6 22 18

MASS NUNBtR

1,8

J

Fig. 7. The same as Fig. 6 for 3~S,35C1,37C1and 39Ktargets. A parameter very often useful in studying the trend of spallation yield distributions is the slope K of the yield-surface ridge [5-7] which can also be defined as K

=

(~r,/cr~)'/~,

(7)

where a, and (r2 are the production cross sections for the two nuclides 1 and 2, equally displaced from the /3-stability valley and AZ represents the difference between the charge numbers of the two nuclides. At this point the need arises to find the most probable mass number A,,p at the various values of Z (the A~, values are independent of At indeed, only depending upon the charge number Z.) Following Rudstam[2] and Jonsson and Lindgren[3] we chose A,,p = S Z + T Z 2

(8)

S = 2.080±0.007

(9)

T = 0.0032±0.0002.

(10)

with

1.0 25

I

30

I

35

I

40

Fig. 8. Values of the slope K of the yield-surface ridge calculated by means of eqn (8) as functions of the target mass number. The circles are values of K calculated from the experimental yields of 223Na and 'SF (the yields of 223Na have been obtained by normalisingthe values of 22Na, see text). The curve is a fit of K values calculated from the yield of 2Z3Naand ~SFas obtained from the CDMD-RJLformula and gives K = 2.73 exp [-0.014& ].

and

By means of eqn (8) one obtains the values of Amp listed in Table 1. Table 1. Most probable mass numbers Amp at different Z values Nuclide

Z

Am,

Be C F Na

4 6 9 11

8.3 12.6 19.0 23.3

The straight line drawn in Fig. 5 through the ridges of the mass-distribution curves for A, = 40 gives a slope K = 1.45. By using eqn (7) for the two nuclides 23Na and 8Be (AZ = 7), both displaced by 0.3 mass units from the Am, values at Z = 11 and Z = 4, respectively, a value of K = 1.52 has been obtained.

between the experimental and calculated yield values being larger for ~SF than for 22Na. Such a discrepancy further corroborates the trend already found. Moreover, the smallest K value corresponds to A, = 35.5 (average value for A, = 35 and A, = 37 in natural chlorine), where fission may contribute to a large extent to the photoproduction of 'SF. In conclusion, we wish to emphasise that the large yields of HC and 7Be from 4°Ca must be attributed to a fragmentation-like process, neither spallation nor fission being capable of explaining such high values in their photoproduction cross section. As a matter of fact, a recent study of multicharged particle emission in the high-energy electron-induced disintegration of carbon[8] shows an anomalous behaviour as far as 7Be production is concerned. Furthermore, high yields of fragments with Z/> 16 has been found in the photodisintegration of ~9Coby photons in the energy range 0.6-1.5 GeV [9]. Further papers will be dealt with "C and 7Be photoproduction from nuclei ranging between 12C and 4°Ca"

Photodisintegration of light and medium-weight nuclei

REFERENCES I. V. di Napoli, G. Rosa, F, Salvetti. M. L. Terranova, H. G. de Carvalho, J. B. Martins and O. A. P. Tavares, J. Inorg. Nucl. Chem. 37, 1101 (1975); see references therein. 2. G. Rudstam, Z Naturf. 21a, 1027 (I966). 3. G. G. Jonsson and K. Lindgren, Phys. Scripta 7, 49 (1973). 4, R. G. Korteling and A. A. Caretto, Jr., Phys. Rev. C1, 193 (1970). ~. 1. Halpern. R. J. Debs, J. T. Eisinger, A. W. Fairhall and H. G. Richter. Phys. Re~. 97, 1327 (1955).

6. C. B, Fulmer, K. S. Toth, 1. R. Williams, T. H. Handley, C. F. Dell, E. L. Callis, T. M. Jenkins and G, M. Wyckoff, Phys. Re~. C2, 1371 (1970). 7. V. di Napoli, F. Salvetti, M. L. Terranova, H. G. de Carvalho and J. B. Martins, Phys. Rev. C8, 206 (1973). 8. G. Baroni, S. Di Liberto, S. Petrera and G. Romano. lstituto di Fisica dell'Universiff~ di Roma and lstitnto Nazionale di Fisica Nucleare Report No. 555 (Apr. I974). 9. V. 1. Kasilov, A. V. Mitrofanova, Yu. N, Ranyuk and P. V. Sorokin, Kharkov Physical-Technical Institute Report No. X6TH73-31. 1973 (in Russian).