Photon-induced nuclear reactions above 1 GeV

Nuclear Physics A197 (1972) 71--80; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

PHOTON-INDUCED NUCLEAR REACTIONS ABOVE 1 GeV

(II). Spallation reactions K. L I N D G R E N and G. G. JONSSON

Department of Nuclear Physics, Lund Institute of Technology, Professorsgatan 3, S-223 63 Lund, Sweden Received 16 May 1972 Abstract: Previously reported studies on spallation reactions in I and Au at intermediate energies

have been extended to the GeV region. The yield and cross-section distributions in iodine are analysed with the five-parameter formulas given by Rudstam and the values of the parameters obtained are discussed. At intermediate energies, some Monte Carlo calculations based on the cascade-evaporation model have been carried out and agreement between calculations and experiment is obtained. The experimental (~, xn) cross sections in gold are compared to estimates from the Rudstam CDMD formula.

1. Introduction High-energy reactions are often treated as two-step processes: a cascade step followed by an evaporation step. Compared to proton-induced reactions the primary interactions in the photon case are quite different, but the memory of how the cascade residuals were produced is lost so the de-excitation processes are probably very much alike. In this paper the experimental yields and cross sections in iodine presented in part I of this work ~) are analysed with the five-parameter formulas given by Rudstam [ref. 2)] and the parameter values obtained are discussed. It is very interesting to compare these parameters to those for proton-induced reactions since this may give information about differences in the reaction mechanisms. From the analysis the average number of nucleons and charged particles emitted is obtained, which gives information about the excitation energy involved in the photonuclear process at different energies. The experimental photonuclear absorption cross section is compared to the total free-nucleon absorption cross section. The experimental results from this work and from the experiment at intermediate energies reported previously 3) are compared to cascade-evaporation calculations carried out with the Gabriel-Alsmiller Monte Carlo program 4). This program can unfortunately only be used for photon energies up to 400 MeV. From the calculations we deduce the kind and number of particles emitted in the cascade, the excitation energy distributions as well as the mean excitation energy of the cascade products, the number of nucleons and charged particles evaporated, etc. Furthermore, the calculations give the cross sections for different spallation products. 71

72

K. LINDGREN AND G. G. JONSSON

Finally, the Rudstam formula ( C D M D ) has been used with appropriate parameters to estimate the (~;, xn) cross sections in gold at different energies.

2. Analysis of the iodine spallation yields and cross sections A useful tool in analysing spallation reactions are the five-parameter formulas given by Rudstam 2). One of these formulas ( C D M D ) represents the cross sections in terms of charge distributions and a yield-mass distribution, and is written: ~pR ~

~(Z, A) - 1.79( ePa:- 1)exp

[PA-RIZ-SA+TAZI~].

Another way of describing the cross sections of the reaction products is in terms of isotopic distributions and an elemental distribution (IDED). The parameter values are determined by fitting the formulas to experimental data. Rudstam has analysed many proton- (also some n-, d- and ~-) induced spallation reaction data and deduced values of the parameters. There exist some earlier investigations with bremsstrahlung and electrons in the GeV region 5-8), but for the bremsstrahlung data the yields have not been unfolded to give the cross sections. In the energy region below 1 GeV, Jonsson and Persson 3) have investigated both spallation yields and mean cross sections in iodine. In this analysis we have used both the C D M D and IDED distributions but for most parameters we have restricted ourselves to presenting the results obtained from the C D M D distribution found most appropriate by Rudstam. For some of the reactions studied here only one of an isomeric pair could be measured. To obtain the total yields and cross sections for these reactions, we used the isomeric ratios found below 1 GeV [ref.3)]. All the measured yields and the cross sections deduced except those for which only one isomer could be determined were included in the analysis. For the (7, 3n) and (7, 4n) reactions, we used the mean cross sections in the energy range 250-900 MeV [ref. 3)]. This was done since the unfolding procedure 9) gives very inaccurate cross sections for reactions with such low thresholds. For energies above 1 GeV, an upper cross-section limit of 0.5 mb was used for both reactions. In tables 1 and 2 the parameters obtained from fitting the C D M D distribution to the yields and the cross sections at different energies are given. The lower photon energy limit for fitting to the cross sections was taken as 350 MeV. Above 3 GeV the cross sections are small and the errors large, which resulted in negative P-values and unreasonable total inelastic cross sections. Parameter P. From tables 1 and 2, it is clear that at E~ = Em,x the P-values obtained from fitting to the yield data are larger than the values obtained from the cross-section data. The different behaviour is due to the fact that the mean energy of the interacting photons is much less than Emax in the yield case.

73

P H O T O N - I N D U C E D REACTIONS (II) TABLE 1 Parameter values obtained from the yield data with the C D M D formula Ema, (MeV)

8q(mb/eq. q.)

P

100 250 400 600 800 1000 985 1280 1580 1980 2480 3190 4000 5000 6000 7400

104- 4 494-14 744- 9 934-29 1024-28 1224-14 137-4-12 1464-12 1604-11 1724-12 1574-11 1864-14 1994-17 1924-19 209 4-14 2264-14

~ 0.5 0.244-0.03 0.134-0.03 0.124-0.06 0.104-0.08 0.10:t:0.03 0.134-0.02 0.134-0.02 0.11 ~:0.02 0.114-0.02 0.134-0.02 0.104-0.02 0.094-0.02 0.10d:0.03 0.09 4-0.02 0.094-0.01

R

1.51.41.41.51.61.31.21.21.2-

-0.2 -0.2 -0.2 -0.3 -0.4 -0.2 -0.2 -0.2 -0.2

1.1--0.1 1.1--0.2 1.24-0.2 1.24-0.2 1.24-0.2 1.24-0.2

S

T

0.574-0.02 0.544-0.02 0.544-0.04 0.534-0.05 0.524-0.02 0.574-0,02 0.634-0,02 0.60 4-0.02 0.57 4-0,02 0.62 i 0 , 0 2 0.57 4-0.02 0.574-0.02 0.574-0,02 0.564-0.01 0.564-0,01

0.00114-0.0002 0.00094-0.0002 0.00094-0.0004 0.00084-0.0004 0.00074-0.0002 0.0011 4-0.0002 0.0017 :i:0.0002 0.0013 4-0.0002 0.0011 4-0.0002 0.0015 4-0.0002 0.0012 4-0.0001 0.0011 4-0.0001 0.00124-0.0002 0.0011 4-0.0001 0.0011 4-0.0001

The data for energies below I GeV are taken from ref. 3). Other data are from this work. TABLE 2 Parameter values obtained from the cross-section data with the CD MD formula E;, (MeV) 350 500 700 1000 1500 2000 3000

t~(mb)

P

R

S

T

844-30 644-11 50 4-20 404- 7 37 4-14 314-14 18± 4

0.074-0.06 0.094-0.04 0.09 4-0.06 0.084-0.03 0.04 4-0.04 0.044-0.04 0.064-0.04

0.94-0.3 1.14-0.3 1.2 4-0.2 1.34-0.2 1.3 4-0.3 1.34-0.3 1.34-0.3

0.534-0.06 0.564-0.03 0.564-0.05 0.554-0.03 0.53 4-0.03 0.534-0.03 0.554-0.03

0.0008±0.0005 0.0010:L0.0003 0.0011 4-0.0004 0.00104-0.0002 0.0008 4-0.0003 0.00084-0.0003 0.00094-0.0003

The parameter Pc (from CDMD) as a function of the incident photon energy is plotted in fig. 1. The Pc value obtained from an analysis of electron-induced spaUation cross sections in iodine 7) is also given. The hatched area gives the result from fitting to the mean cross sections in the energy range 250-900 MeV [ref. 3)]. The solid lines give the result for proton-induced reactions in medium-heavy nuclei 2). It is interesting to note that the photon points fall below the solid lines. This is probably not only an effect of the larger target mass number 2) but also an indication of the presence of different reaction mechanisms 3). The parameter Pi (from IDED) can be compared to results from cascade-evaporation calculations by Gudima et al. 10) for maximum bremsstrahlung energies between 50 and 1300 MeV. They have calculated the cross section per equivalent quantum for events with n > 2 and n __> 3 charged particles emitted as a function of the maxi-

74

K. L I N D G R E N I

I

L

~

i

~

i

A N D G. G. J O N S S O N t I

1 ~ 10-1

1

I

g_

10-2

I

t

I

t I Illl

10 2

i 103 Energy (MeV)

I

[

[

I I

Fig. 1. P a r a m e t e r Pc as a function o f the incident energy: o this work, the h a t c h e d area s h o w s the result f r o m ref. 3), [] electron d a t a f r o m ref. 7). T h e solid lines give results for p r o t o n - i n d u c e d reactions 2).

1

[

i

i

I

i

r

I

I

I

I

I

200

300

I

i

I

r

]

o O-

500 1000 Maximum bremsstrahtung energy (MeV)

i

150q

Fig. 2. T h e p a r a m e t e r PI as a f u n c t i o n o f the m a x i m u m b r e m s s t r a h l u n g energy: o this work, • d a t a f r o m ref. 3). T h e solid curve s h o w s the result f r o m cascade-evaporation calculations on l ° ° R u [ref. lo)].

PHOTON-INDUCED

R E A C T I O N S (II)

75

mum bremsstrahlung energy for the target nucleus l°°Ru. A simple calculation shows that Crq(n > 2)/aq(n > 3) ~ e PI. In fig. 2 we have plotted the experimental results for P~ and the result from these calculations. G o o d agreement between experiment and theory is obtained.

20 1

I

I

I

I

i

i

~ i

I

i

I~Io

I

o

o

o

JJ_/S ____. __7.~///PZ/7////~._ •

0

.~

" .....................

"--,'-"r;;T;Tl

,

,

1

I

1

30 o

2O

I

I

102

I

I

I

I

1 1 i ~I

103 Energy (MeV)

I

104

Fig. 3. T h e average n u m b e r o f nucleons a n d charged particles emitted as a f u n c t i o n o f the incident energy: o this work. T h e d a s h - d o t curve is the p r o n g n u m b e r t a k e n f r o m ref. 11). T h e h a t c h e d areas are results t a k e n f r o m ref. 3). • a n d + are the n u m b e r o f cascade a n d totally emitted particles calculated with the Gabriel-Alsmiller p r o g r a m 4). T h e dashed curve s h o w s p r o t o n cascade data 17) a n d the dotted curve is an estimate (see text).

The parameter P is related to the average number of nucleons and charged particles emitted: A A ~ 1/P c and A Z ~ 1/Pl. The AA and A Z values obtained for photons in this experiment are plotted in fig. 3. The errors in these points are very large which can be seen from the errors in P given in table 2. The dash-dot curve gives the prong number as a function of the photon energy found in a nuclear emulsion study 11). The A-A and A---Zvalues with errors obtained in the earlier analysis 3) are given by the hatched areas. Parameters R, S and T. The parameters R, S and T are related to the evaporation

76

K. L I N D G R E N

A N D G. G. J O N S S O N

part of the reaction process. Parameter R defines the width of the charge distribution ( C D M D ) . As seen from tables 1 and 2, R is independent of both photon and maximumbremsstrahlung energy in agreement with Rudstam's result for proton-induced reactions. The mean values in the energy regions studied are R = 1.20+0.05 and R = 1.29 + 0.05 for photons and bremsstrahhmg respectively. These values are comparable to R = 1.38 obtained with protons. The parameters S and T define, in the C D M D case, the position of the charge distribution: Zp = S A - T A 2. Both parameters are independent of photon as well as m a x i m u m bremsstrahlung energy in agreement with what is found for protons. For photons we find S = 0.52+0.02 and T = 0.0009___0.0002, and for bremsstrahlung S = 0.57+_0.03 and T = 0.0011+_0.0003. For proton-induced reactions Rudstam found S = 0.486±0.001 and T = 0.00038 +0.00002. The parameters are coupled to each other so even if the S- and T-values for photons and bremsstrahlung are different f r o m the values obtained with protons, the Zp values are almost the same. In table 3 we have compiled the results on R, S and T f o r different incident particles. The proton data are taken from Rudstam and the parameters for electron-induced spallation were deduced from data in ref. 7). TABLE 3 C o m p a r i s o n o f the p a r a m e t e r s R, S a n d T f r o m C D M D for incident p h o t o n s , b r e m s s t r a h l u n g , electrons a n d p r o t o n s Irradiation photon bremsstrahlung electron proton

Element

R

I I I

1.20±0.05 1.294-4-0.05 0.7 4-0.2 1.38

S 0.54 0.57 0.52 0.486

±0.02 4-0.03 4-0.02 ± 0.001

T 0.0009 0.0011 0.0007 0.00038

4-0.0002 4-0.0003 4-0.0002 4- 0.00002

T h e p r o t o n R-value is for .4 t = 127 and the p r o t o n S- a n d T-values are for elements with Zt ~ 47.

Parameter ~. The parameter # gives the total inelastic yield or cross section. The total inelastic yield as a function of the m a x i m u m bremsstrahlung energy is plotted in fig. 4. The total inelastic cross section as a function of the photon energy is given in fig. 5. The points in fig. 5 are obtained from fitting the C D M D distribution to the cross-section data. The smooth solid curve is deduced 9) from the total yield given in fig. 4. In the figure we have also given some (interpolated) results f r o m measurements on the total photohadron cross section 12.13). The mean free path of high-energy photons in nuclear matter is very large and one would expect that the total photoabsorption cross section should be proportional to the number of nucleons in the nucleus. In fig. 5 the curve marked A ~ p gives this cross section, where ~ p is the total elementary (7, P) cross section taken from ref. 14). This estimate is found to be comparable to the experimental cross section both in shape

PHOTON-INDUCED

R E A C T I O N S (II)

77

and magnitude. However, for the energy region above 1 GeV, the vector dominance model has been discussed. In this model the A-dependence of the cross section is less than linear because here the photon interacts, at least partially, as a strongly interacting particle 15). The # values obtained are however too uncertain for observing such effects. I

I

I

I

I

I I I I

I

I

I

]

I

I i I I

I

300 12'/I('y,ypxn)

.Q

E

+++++t++ +

C

200

+II +

~ 10C f

I

I

f

I

III

I

I

I

I

I

I

III

;03 Moximum bremsstrohtung energy (MeV)

;o2

104

Fig. 4. T h e total yield as a function o f the m a x i m u m b r e m s s t r a h l u n g energy: o this work, • data from ref. 3).

|

I

I

I

1

I

I

I I ]

,

I

I

I

I

I

[

I I 1

150

127I(~,,ypxn)

.Q

E ;00

._~

"

~ 50

A~yp i

102

I

r

I

f

I I I]

I

103 Photon energy (MeV)

I

r

I

I

i Ill

104

Fig. 5. T h e total inelastic cross section as a function o f the p h o t o n energy. T h e circles give data f r o m fitting the C D M D distribution to the cross-section d a t a a n d the s m o o t h solid curve is deduced f r o m the total yield in fig. 4. • a n d ~ show (interpolated) data f r o m refs. 12. J3) respectively. T h e solid curve m a r k e d AtrTp gives the estimated cross section.

78

K. L I N D G R E N A N D G. G. JONSSON

3. Cascade-evaporation calculations To see if the number of particles emitted can be deduced from a reaction model we carried out some cascade-evaporation calculations. The Gabriel-Alsmiller Monte Carlo program was used 4). The photoabsorption cross sections used in the calculations are the quasideuteron cross section with a Levinger constant of 10.3 and the pion production cross sections. Since only single-pion production processes are included, the calculations are limited to photon energies below 400 MeV. For the evaporation calculations we used the same parameters as Dresner 4) with the exception of the level density parameter for which we used the value of ~-~-A [ref. ~6)]. 500

,

'

~

~

~

'

~

J

i

l

t

i Ill

' I

~

'

I

I

400

~300

I~

200

100

0

-

,..it.

i

i

100

200

~"

i

400 1000 Energy (MeV)

2000

4000

Fig. 6. The calculated average excitation energy for incident photons and protons 17) as a function of incident energy.

The calculated average numbers of nucleons and charged particles emitted both in the cascade and totally are given in fig. 3. There is rather good agreement between the calculated and experimentally determined values of A A and A Z where overlapping data exist. In fig. 3 the average number of cascade nucleons emitted for proton-induced reactions (the dashed curve in the lower figure) is also shown. Although the primary interaction mechanisms are different, we find that the mean number of cascade nucleons emitted is the same for photon- and proton-induced reactions. The calculated mean excitation energy ~S* given to the cascade residuals is shown in fig. 6. In this figure are also shown results from calcvlations for incident protons by Metropolis et al. 1 v). Recent calculations by Barashenkov et al. 18) on 1°°Ru give values smaller on the average by 20-40 MeV. Especially for energies above 200 MeV the excitation energy is larger in the photon case. This difference is due to pion production which is the dominating interaction process for photons at these energies. For protons the pion production processes are first of importance at energies above 400 MeV. The higher mean excitation energy may give a larger number of particles emitted in photonuclear reactions than in reactions induced by protons in the same energy region.

PHOTON-INDUCED REACTIONS (II)

79

For higher photon energies calculations are not yet available. We can however make some comparisons to cascade-evaporation calculations for incident protons 17). The AA/AZ ratio for the photon cascade is found to be constant in the energy region studied. Supposing that this also holds for higher energies together with the hypothesis that the number of cascade nucleons remains the same for photon- and proton-induced reactions at higher energies, the number of charged cascade particles can be estimated. This estimate is shown in fig. 3 (the dotted curve in the upper figure).

102127

122 I

117 J

Mass number 112 I

107 I

102 I

~27I(~',ypxn) 10

9' o (,J

10-1

10-

0

I 5

I I 10 15 Number of nucleons emitted

I 20

25

Fig. 7. Experimental a) and calculated 127I(7, ypxn) cross sections as a function of the number of nucleons emitted: o - I , • - Te, ~ - Sb, • - Sn, A - I n , V - A g . Double-marked figures indicate that only one of an isomeric pair has been measured.

From the figure it is seen that the number of cascade particles is only a small part of the total number of particles emitted which indicates a large number of particles evaporated. The average de-excitation energies per evaporated nucleon and charged particle are about 13 and 50 MeV respectively. From this, the excitation energy can be estimated. The excitation energy increases with increasing incident energy in a way similar to that for protons. The average excitation energy in the energy region E~ = 0 . 5 - 3 GeV is about 200 MeV. The calculated cross sections for different spallation products at E~ = 350 MeV is shown in fig. 7 together with the mean cross sections in the energy range 250--900 MeV as measured by Jonsson 3). Very good agreement between experiment and theory is obtained at least for products not too far away from the target.

80

K. L I N D G R E N AND G. G. JONSSON

4. Estimation of (?, xn) cross sections in gold For gold we have not sufficient data to make the same analysis with the Rudstam formulas as for iodine. We have instead tried to estimate the cross sections with the aid of the C D M D formula using appropriate parameters. For lack of other data for photon induced reactions, we have taken for P the experimental values given in table 2. For R we have used the expression given by Rudstam: R = 11.8 A - 0.45. The Rudstam values S = 0.486 and T = 0.00038 were used since they give the most reasonable Zp values. The total inelastic cross section was assumed to be a = Aarp, where arp was taken from ref. 14). With these parameters, we have calculated the cross sections at different photon energies. In table 4 we give the experimental and estimated cross sections at 1 GeV and also the overall ratio in the energy range 350-3000 MeV. F o r all reactions except (7, 1 In) reasonable agreement is obtained. TABLE 4 Experimental and estimated Au(7, xn) cross sections at E~, = 1 GeV and average ratio in the energy range 350-3000 MeV Reaction

~rexp(mb)

(7, 3n) (7, 7n) 0', 9n) ('F, l l n )

1.02:0.3 0.6-4-0.2 0.34-0.1 0.4::t:0.2

~r~st(mb) 0.6 1.0 0.3 0.1

(~r~p/a~t>

2.3 0.9 1.2 5.2

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

G. Andersson et aL, Nucl. Phys. A197 (1972) 44 G. Rudstam, Z. Naturf. 21a (1966) 1027 G. G. Jonsson and B. Persson, Nucl. Phys. A153 (1970) 32 T. A. Gabriel and R. G. Alsmiller, Jr., Phys. Rev. 182 (1969) 1035; L. Dresner, ORNL-TM-196 (1961) G. Kumbartzki, U. Kim and Ch. K. Kwan, Nucl. Phys. A160 (1971) 237 G. Kumbartzki and U. Kim, Nucl. Phys. A176 (1971) 23 F. D. S. Butement et aL, J. Inorg. Nucl. Chem. 33 (1971) 2791 C. B. Fulmer et aL, Phys. Rev. C2 (1970) 1371 K. Tesch, Nucl. Instr. 95 (1971) 245 K. K. Gudima, A. S. Iljinov and C. V. Toneev, JINR-P2-4661 (1969) [ORNL-tr-2267] C. E. Roos and V. Z. Peterson, Phys. Rev. 124 (1961) 1610 D. O. Caldwell et al., Phys. Rev. Lett. 23 (1969) 1256 V. Heynen et aL, DESY 71/5, February 1971 D. W. G. S. Leith, Proc. Third Int. Conf. on high-energy physics and nuclear structure, Columbia University, New York, Sept. 8-12, 1969 L. Stodolsky, Phys. Rev. Lett. 18 (1967) 135 G. G. Jonsson and K. Lindgren, Nucl. Phys. A141 (1970) 355 N. Metropolis et aL, Phys. Rev. 110 (1958) 204 V. S. Barashenkov et aL, Int. JINR-CERN School on high energy physics; Lectures submitted to Black Sea Summer School, Varna, Bulgaria, 13-27 June, 1971