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The angular distribution of the isomeric ratio of the 197Au (p, pn) 196Au reaction with 400 MeV protons
J. inorg,nucl.Chem., 1971,Vol. 33, pp. 909 to 914. PergamonPress. Printedin Great Britain
THE ANGULAR DISTRIBUTION OF THE ISOMERIC R A T I O O F T H E t 9 7 A u ( p , pn)196Au R E A C T I O N WITH 400 MeV PROTONS L. B. C H U R C H State University of N e w York, Buffalo, N.Y. 14214
(First received 25 August 1970; in revised fi~rm 29 October 1970) Abstract-The angular distribution of the isomeric ratio from the 197Au(p,pn)la6Au reaction has been radiochemically determined. T h e average ~96"Au to lg6"Au isomeric ratio is 0-18_+ 0-06 and appears to be rather constant with respect to the laboratory recoil angle. This is interesting because the reaction m e c h a n i s m has been postulated to change as a function of this recoil angle. It is therefore concluded that the two predominant m e c h a n i s m s must give approximately the s a m e isomeric ratio. A calculation of the isomeric ratio which a s s u m e s a clean knockout m e c h a n i s m agrees rather closely with the experimental value. A n o t h e r calculation which a s s u m e s the inelastic scattering followed by evaporation m e c h a n i s m indicates that the excited ( p , p ' ) nucleus is in a spin state which differs from the target nucleus by about 4.5 h units. INTRODUCTION
THE STUDY of the nuclear isomerism resulting from the reactions induced by high energy protons has been shown to be an important tool in the determination of the reaction mechanisms involved. A number of workers have analyzed the mechanisms of some simple reactions [ 1-3] by first assuming a particular reaction mechanism, calculating the expected isomeric ratio using the format of Benioff[4] and Vandenbosch and Huizenga[5], and then comparing this with their experimentally observed ratio. A favorable comparison is generally acknowledged to support to the assumed mechanism. This work on the isomeric ratios of simple reactions has been extended to a measurement of the 197Au(p, pnY96Au isomeric ratio as a function of the laboratory recoil angle. Independent of any isomeric ratio considerations, the mechanism for this reaction has previously been studied as a function of the recoil angle [6]. Thus the purpose of the present work is to study the relationship between the isomeric ratio and the various mechanisms involved. Two mechanisms each contribute about 50 per cent to the total reaction cross section. These are thought to be either a one-step direct knockout of a bound neutron by the incident proton in such a way that the residual energy is too low for further particle emission, or a two-step inelastic scattering of the incident proton with a bound nucleon resulting in sufficient excitation energy for the evaporation of one neutron. The former is often referred to as the clean knockout 1. I. Levenberg, V. Pokrovsky, R. D e - H o u , L. T a r a s o v a and I. Yutlandov, Nucl. Phys. 51, 673 (1964). 2. N . T . Porile and S. T a n a k a , Phys. R ev. 130, 1541 (1963). 3. A. A. Caretto, Nucl. Phys. 92A, 133 (1967). 4. P . A . Benioff, Phys. R ev. 119, 324 (1960). 5. R. V a n d e n b o s c h and J. R. Huizenga, Phys. Rev. 120, 1313 (1960). 6. Y.-W. Yu, A. A. Caretto and L. B. C h u r c h , Nucl. Phys. 152A, 295 (1970). 9O9
910
L.B. CHURCH
mechanism ( C K O ) and the recoiling products form a rather featureless angular distribution[7-9]. The latter mechanism is referred to as inelastic scattering f o l l o w e d by evaporation (ISE) and these recoil products have been observed to have a fairly narrow angular distribution which in this case peaks about 85 ° [6, 10]. Thus the experimental isomeric ratio in the region of 85 ° should represent that ratio which primarily results from an ISE mechanism, while the ratio in the 0 ° to 60 ° or the 110 ° to 180 ° region is indicative of the C K O mechanism. EXPERIMENTAL The work described in this paper is very similar to the previously described determination of the angular distribution of high-energy nuclear recoils [6, 10, 11]. The target, 50 tzg cm -2 gold evaporated onto 0.008 cm thick aluminum foil, was placed at 45 ° in the internal beam of the Carnegie-Mellon University synchrocyclotron at a radius corresponding to 400 MeV protons. The (p,pn) reaction recoils were caught on a cylindrically shaped aluminum catcher foil placed above or below the proton beam. After the irradiations, the catcher foil was cut into strips corresponding to 10° segments and the 196Au from each strip was separated, purified and mounted using standard radiochemical techniques [12]. The 196mmuwas determined by counting either the 0-15 MeV y-ray or the X-rays with a 7.5 cm or a 2 mm NaI crystal respectively. The small (p,pn) cross-section to the 9.7 hr 196mAustate and the lack of a specific manner to accurately count this decay led to an average estimated uncertainty in this count rate o f ± 12 per cent [13]. The yield of the 6-2 d 196gAuwas determined by counting the 0.36 MeV y-ray with the 7.5 cm Nal crystal. Because of the larger cross section and specificity of counting, these count rates had an average uncertainty of only ± 1 per cent. The specific yield for each isomer state was determined by extrapolating the count rates back to the end of the bombardment, correcting for the chemical yields, branching ratios, counter efficiencies and the saturation factor[14]. The individual runs were then normalized to each other by summing the activity in the 60 ° to 120 ° region. In Fig. 1 the 196mAuto ~96OAuisomeric ratio is plotted as a function of the laboratory angle for each 10° segment of the angular distribution. The uncertainties associated with each point were estimated using the standard deviation from the average value of the ratio at that point and include an estimate of the systematic errors ascribable to uncertainties in the decay schemes and counting efficiencies. RESULTS AND DISCUSSION
The data presented in Fig. 1 shows that the isomeric ratio does not vary as a function o f the recoil angle nearly to the extent that both o f the previously reported 197Au(p,pn)19nAu cross sections do [6]. This is especially true in the region near 85 ° . Over the w h o l e angular distribution the mean value o f the isomeric ratio with its standard deviation is 0.18 + 0.06 and as can be seen from the dashed line in Fig. 1, the mean value is within the limits of uncertainty for each point. 7. J. A. Panontin, L. L. Schwartz, A. F. Stehney, E. P. Steinberg and L. Winsberg, Phys. Rev. 169, 851 (1968). 8. P . A . Benioffand L. Person, Phys. Rev. 140B, 844 (1965). 9. J. R. Grover and A. A. Caretto,A nn. Rev. Nucl. Sci. 14, 51 (1964). 10. L. P. Remsberg, Phys.Rev. 174, 1338(1968). 11. M. K. Dewanjie, G. B. S a h a a n d L. Yaffee, Can.J. Chem. 46,3551 (1968). 12. J. F. Emery and G. W. Leddicotte, The Radiochemistry o f Gold. US Nat. Res. Coun., Rep. NAS-NS-3051 (1961). 13. J. B. Cumming, Applications o f Computers to Nuclear and Radiochemistry. U.S. Nat. Res. Coun. NAS-NS-3051 (1961). 14. C. M. Lederer, J. M. Hollander and I. Perlman, Table o f Isotopes. Wiley, New York (1967).
The 197Au(p,pn)~96Au isomeric ratio
911
:5 o'~
3 o~
&-
c) m 13" Ld
1,0
0.8 0.6
CO
J
0.4
lTf
o'~
g_
d_ 0.2 v
.
.
.
.
.
i_
± 1 L, i
0
i
i
50"
60*
1 i
90 °
120°
150°
180"
RECOIL ANGLE, 0 Fig. I. The angular distribution of the isomeric ratio of the 19rAu(p,pn)196Au reaction. The dashed line is the average value of 0.18.
The constancy of the isomeric ratio especially in the region where the mechanism appears to be rapidly changing implies for this reaction and proton energy, both the CKO and ISE mechanisms lead to about the same isomeric ratio. Various consequences of this 'idea will be investigated in further detail by calculating the ratio of the (12--) to the (2--) states of the 196Au product assuming first a CKO mechanism and then an |SE mechanism. The well known approach of Vandenbosch and Huizenga [5, 15] and the shell model calculation of the neutron levels of the ~97Au nucleus by Ross et al.[16] were used in both sets of calculations. Only the top four neutron levels shown in Fig. 2 were considered because deeper neutron levels would have involved excitation energies large enough to permit further particle evaporation. The isomeric ratio calculated on the assumption o f the clean knockout mechanism
The relative probability of the clean knockout of a neutron from the above mentioned 197Au neutron levels was calculated from the product of the number of neutrons in the level, n, and BeniotVs fractional availability coefficients, Mnt[4]. Although these Mnl values were calculated at multi-GeV energies, the error introduced into the present calculations by using them with data at 400 MeV is thought to be small. The removal of a neutron with angular momentum Jn results in a set of states having angular momentum Jr = IJn+3/21 to Js = IJn-3/21 (the 3/2 comes from the ground state spin of 197Au) and with relative weights, Rj, varying for each neutron level as (2Jr+ 1). The deexcitation of nuclei with this set of spins was assumed to occur with quadrupole y-rays averaging 2 MeV each. The calculation was performed using a spin parameter, o-, of 4.0 and assuming that the last y-ray resulted in the population of either the (12--) or (2--) isomer of 19nAu depending on which transition involved a smaller spin change. This calcula15. W. L. Hafner, J. R. Huizenga and R. Vandenbosch, USA EC Rep. A N L-6662 (1962). 16. A. A. Ross, H. Mark and R. D. Lawson, Phys. R ev. 102, 1613 (1956).
L. B. CHURCH
912
TOP OF NUCLEAR WELL FOR NEUTRONS
45.8
40
3P3/z 35
l i 13/2
> iii Z
2f7/z
I h9 / 2 - ~
>(-9 ta3 Z I,i
.
.
.
.
.
3S ~/2 2d3/2___
30
---I h ulz-
Fig. 2. The top neutron levels in J97Au(Ref. [16]). tion is quite similar to previous calculations of Porile and Tanaka[2] and Caretto [3]. T h e results of this calculation are outlined in T a b l e 1. While the very close agreement between the calculated and experimental ratios is probably s o m e w h a t fortuitous, nevertheless it does lend general support to the statistical validity of this calculation and to the assumptions which went into it.
The isomeric spin calculation assuming an I S E mechanism As was previously mentioned, the interpretation of the angular distribution curve indicated the | S E m e c h a n i s m accounted for most of the recoils in the 85 ° region. T h e large n u m b e r of excited bound neutron and proton levels which would be populated after an inelastic scattering event makes an accurate calculation of the resulting spin distribution almost impossible, If this distribution is not known, then the calculation of the isomeric ratio assuming an I S E m e c h a n i s m and a comparison with with the experimental ratio to support the existence of this mechanism is not possible. It was therefore decided to use the experimental ratio and c o m p a r e it with a set of calculated ratios to determine the nuclear spin after an inelastic (p,p') event. It was arbitrarily assumed that the ( p , p ' ) event always left 12 M e V excitation energy in the 197Au nucleus. A neutron from the same four upper levels shown in Fig. 2 was then assumed to be e v a p o r a t e d with a probability proportional to the n u m b e r of neutrons in the level, N, times the transmission coefficient for neutrons, Tt, from the work of Feld et al.[17]. T h e spin distribution after the 17. B. T. Feld, H. Feshbach, M. L. Goldberger, H. Goldstein and V. Weisskopf, USAEC Rep. NYO-636 (1951).
913
The 197Au(p,pn)196Au isomeric ratio Table I. Calculation of the isomeric ratio assuming a C KO mechanism
Neutron shell
No. of 7
Product spin, Je
Fraction to (-2) state, f(2--)
3p:~/2
3
3 2 1 0
1.0130 1-000 1.000 1-000
0.133 0.095 0.057 0.019
0.000 0.000 0'000 0.000
li131z
4
8 7 6 5
0.505 0.700 0.846 0,939
0.112 0"136 0" 143 0.134
0.110 0'058 0,026 0,009
l h.~12
5
6 5 4 3
0-847 0'928 0"972 0'992
0'082 0.076 0'066 0.052
0.013 0.006 0.002 0.000
lfT/~
5
5 4 3 2
0-928 0.972 0-992 0.999
0'153 0' 131 0.104 0'075
0.012 0.004 0-001 0.000
~, 1.568
0.241
Isomeric ratio -
Total production probability N × M,,~ × Rj N × M,a × R j ×f(2--) ×f(12-)
2~(12-) (2-)
0.154
neutron evaporation and during the subsequent y-ray deexcitation was calculated in a manner outlined in Ref. [5] and [15]. All other assumptions made in this set of calculations were the same as in the above C K O set. A typical calculation is illustrated in Table 2. T h e calculated ratios are plotted in Fig. 3 as a function of the assumed spin after the inelastic (p,p') event. Using the experimental ratio of 0-18+0.06, it appears that the spin after the (p,p') event is about 6.0 ± 1.0. This is to be compared with the 197Au target spin of 3/2. The fairly steep slope of the curve in Fig. 3 implies that the inelastic scattering part of the ISE mechanism determines to a very large extent the final spin distribution, and hence the final isomeric ratio. It would be interesting to see if this is also true in other simple reactions which involve the 1SE mechanism. It would also be interesting to compare this rather indirect calculation of the spin change attributed to the (p,p') inelastic scattering event with a more direct method of estimating nuclear spin change. One possible avenue of approach would be to radiochemically measure the cross section of a series of (p,p') reactions. T w o possible targets might be 113In and HSln. In summary, the approach of this study has been to examine the isomeric ratio as a function of the recoil angle and hence the reaction mechanism. With 400 MeV protons, the reaction studied appears to occur via two different mech-
914
L.B. CHURCH Table 2. A typical calculation assuming an ISE mechanism with a spin of 7/2 after the (p,p') event
3P3/2
li,.3/.2
lh9/2
2f7/2
0.142
0.276
0.314
0.268
3
2
1
1
Fraction of events to (2-) state
0"938
0-857
0.904
0.949
Fraction of events to (12-) state
0-062
0.143
0-096
0.051
Total production probability (2-)
0.133
0.236
0.284
0.254
Total production probability (12-)
0-008
0-033
0.027
0,013
Neutron shell Weighted probability for neutron evaporation; N × Tt N umber of y's after neutron evaporation
1someric ratio
(to 12--) 1~ (to 2--)
0.081 0.907
= 0-089
O" o~ (D i,i
0.3
~E
o oo 0.2 uJ
j
o.I
o
0
0~0----~0~
,io
zi0
310
jo1~---°-/ 0b 76
46
50
86
SPIN AFTER A (P,P') EVENT Fig. 3. The calculated isomeric ratio assuming the |SE mechanism as a function of the 19~Aunuclear spin after the (p,p') event.
anisms, both of which give close to the same isomeric ratio. A calculation of this ratio assuming the clean knockout mechanism agrees very well with the experimental results. A similar calculation assuming the ] S E mechanism indicates that the change in spin o f the 197Au target nucleus resulting f r o m the inelastic scattering event is about 9/2 units ofh. Acknowledgements--The author appreciates the cooperation received from the staff of the Carnegie-Mellon University synchrocyclotron staff. In addition the generosity of Professor A. A. Caretto for sharinghis laboratory and counting facilities is gratefully acknowledged.
THE ANGULAR DISTRIBUTION OF THE ISOMERIC R A T I O O F T H E t 9 7 A u ( p , pn)196Au R E A C T I O N WITH 400 MeV PROTONS L. B. C H U R C H State University of N e w York, Buffalo, N.Y. 14214
(First received 25 August 1970; in revised fi~rm 29 October 1970) Abstract-The angular distribution of the isomeric ratio from the 197Au(p,pn)la6Au reaction has been radiochemically determined. T h e average ~96"Au to lg6"Au isomeric ratio is 0-18_+ 0-06 and appears to be rather constant with respect to the laboratory recoil angle. This is interesting because the reaction m e c h a n i s m has been postulated to change as a function of this recoil angle. It is therefore concluded that the two predominant m e c h a n i s m s must give approximately the s a m e isomeric ratio. A calculation of the isomeric ratio which a s s u m e s a clean knockout m e c h a n i s m agrees rather closely with the experimental value. A n o t h e r calculation which a s s u m e s the inelastic scattering followed by evaporation m e c h a n i s m indicates that the excited ( p , p ' ) nucleus is in a spin state which differs from the target nucleus by about 4.5 h units. INTRODUCTION
THE STUDY of the nuclear isomerism resulting from the reactions induced by high energy protons has been shown to be an important tool in the determination of the reaction mechanisms involved. A number of workers have analyzed the mechanisms of some simple reactions [ 1-3] by first assuming a particular reaction mechanism, calculating the expected isomeric ratio using the format of Benioff[4] and Vandenbosch and Huizenga[5], and then comparing this with their experimentally observed ratio. A favorable comparison is generally acknowledged to support to the assumed mechanism. This work on the isomeric ratios of simple reactions has been extended to a measurement of the 197Au(p, pnY96Au isomeric ratio as a function of the laboratory recoil angle. Independent of any isomeric ratio considerations, the mechanism for this reaction has previously been studied as a function of the recoil angle [6]. Thus the purpose of the present work is to study the relationship between the isomeric ratio and the various mechanisms involved. Two mechanisms each contribute about 50 per cent to the total reaction cross section. These are thought to be either a one-step direct knockout of a bound neutron by the incident proton in such a way that the residual energy is too low for further particle emission, or a two-step inelastic scattering of the incident proton with a bound nucleon resulting in sufficient excitation energy for the evaporation of one neutron. The former is often referred to as the clean knockout 1. I. Levenberg, V. Pokrovsky, R. D e - H o u , L. T a r a s o v a and I. Yutlandov, Nucl. Phys. 51, 673 (1964). 2. N . T . Porile and S. T a n a k a , Phys. R ev. 130, 1541 (1963). 3. A. A. Caretto, Nucl. Phys. 92A, 133 (1967). 4. P . A . Benioff, Phys. R ev. 119, 324 (1960). 5. R. V a n d e n b o s c h and J. R. Huizenga, Phys. Rev. 120, 1313 (1960). 6. Y.-W. Yu, A. A. Caretto and L. B. C h u r c h , Nucl. Phys. 152A, 295 (1970). 9O9
910
L.B. CHURCH
mechanism ( C K O ) and the recoiling products form a rather featureless angular distribution[7-9]. The latter mechanism is referred to as inelastic scattering f o l l o w e d by evaporation (ISE) and these recoil products have been observed to have a fairly narrow angular distribution which in this case peaks about 85 ° [6, 10]. Thus the experimental isomeric ratio in the region of 85 ° should represent that ratio which primarily results from an ISE mechanism, while the ratio in the 0 ° to 60 ° or the 110 ° to 180 ° region is indicative of the C K O mechanism. EXPERIMENTAL The work described in this paper is very similar to the previously described determination of the angular distribution of high-energy nuclear recoils [6, 10, 11]. The target, 50 tzg cm -2 gold evaporated onto 0.008 cm thick aluminum foil, was placed at 45 ° in the internal beam of the Carnegie-Mellon University synchrocyclotron at a radius corresponding to 400 MeV protons. The (p,pn) reaction recoils were caught on a cylindrically shaped aluminum catcher foil placed above or below the proton beam. After the irradiations, the catcher foil was cut into strips corresponding to 10° segments and the 196Au from each strip was separated, purified and mounted using standard radiochemical techniques [12]. The 196mmuwas determined by counting either the 0-15 MeV y-ray or the X-rays with a 7.5 cm or a 2 mm NaI crystal respectively. The small (p,pn) cross-section to the 9.7 hr 196mAustate and the lack of a specific manner to accurately count this decay led to an average estimated uncertainty in this count rate o f ± 12 per cent [13]. The yield of the 6-2 d 196gAuwas determined by counting the 0.36 MeV y-ray with the 7.5 cm Nal crystal. Because of the larger cross section and specificity of counting, these count rates had an average uncertainty of only ± 1 per cent. The specific yield for each isomer state was determined by extrapolating the count rates back to the end of the bombardment, correcting for the chemical yields, branching ratios, counter efficiencies and the saturation factor[14]. The individual runs were then normalized to each other by summing the activity in the 60 ° to 120 ° region. In Fig. 1 the 196mAuto ~96OAuisomeric ratio is plotted as a function of the laboratory angle for each 10° segment of the angular distribution. The uncertainties associated with each point were estimated using the standard deviation from the average value of the ratio at that point and include an estimate of the systematic errors ascribable to uncertainties in the decay schemes and counting efficiencies. RESULTS AND DISCUSSION
The data presented in Fig. 1 shows that the isomeric ratio does not vary as a function o f the recoil angle nearly to the extent that both o f the previously reported 197Au(p,pn)19nAu cross sections do [6]. This is especially true in the region near 85 ° . Over the w h o l e angular distribution the mean value o f the isomeric ratio with its standard deviation is 0.18 + 0.06 and as can be seen from the dashed line in Fig. 1, the mean value is within the limits of uncertainty for each point. 7. J. A. Panontin, L. L. Schwartz, A. F. Stehney, E. P. Steinberg and L. Winsberg, Phys. Rev. 169, 851 (1968). 8. P . A . Benioffand L. Person, Phys. Rev. 140B, 844 (1965). 9. J. R. Grover and A. A. Caretto,A nn. Rev. Nucl. Sci. 14, 51 (1964). 10. L. P. Remsberg, Phys.Rev. 174, 1338(1968). 11. M. K. Dewanjie, G. B. S a h a a n d L. Yaffee, Can.J. Chem. 46,3551 (1968). 12. J. F. Emery and G. W. Leddicotte, The Radiochemistry o f Gold. US Nat. Res. Coun., Rep. NAS-NS-3051 (1961). 13. J. B. Cumming, Applications o f Computers to Nuclear and Radiochemistry. U.S. Nat. Res. Coun. NAS-NS-3051 (1961). 14. C. M. Lederer, J. M. Hollander and I. Perlman, Table o f Isotopes. Wiley, New York (1967).
The 197Au(p,pn)~96Au isomeric ratio
911
:5 o'~
3 o~
&-
c) m 13" Ld
1,0
0.8 0.6
CO
J
0.4
lTf
o'~
g_
d_ 0.2 v
.
.
.
.
.
i_
± 1 L, i
0
i
i
50"
60*
1 i
90 °
120°
150°
180"
RECOIL ANGLE, 0 Fig. I. The angular distribution of the isomeric ratio of the 19rAu(p,pn)196Au reaction. The dashed line is the average value of 0.18.
The constancy of the isomeric ratio especially in the region where the mechanism appears to be rapidly changing implies for this reaction and proton energy, both the CKO and ISE mechanisms lead to about the same isomeric ratio. Various consequences of this 'idea will be investigated in further detail by calculating the ratio of the (12--) to the (2--) states of the 196Au product assuming first a CKO mechanism and then an |SE mechanism. The well known approach of Vandenbosch and Huizenga [5, 15] and the shell model calculation of the neutron levels of the ~97Au nucleus by Ross et al.[16] were used in both sets of calculations. Only the top four neutron levels shown in Fig. 2 were considered because deeper neutron levels would have involved excitation energies large enough to permit further particle evaporation. The isomeric ratio calculated on the assumption o f the clean knockout mechanism
The relative probability of the clean knockout of a neutron from the above mentioned 197Au neutron levels was calculated from the product of the number of neutrons in the level, n, and BeniotVs fractional availability coefficients, Mnt[4]. Although these Mnl values were calculated at multi-GeV energies, the error introduced into the present calculations by using them with data at 400 MeV is thought to be small. The removal of a neutron with angular momentum Jn results in a set of states having angular momentum Jr = IJn+3/21 to Js = IJn-3/21 (the 3/2 comes from the ground state spin of 197Au) and with relative weights, Rj, varying for each neutron level as (2Jr+ 1). The deexcitation of nuclei with this set of spins was assumed to occur with quadrupole y-rays averaging 2 MeV each. The calculation was performed using a spin parameter, o-, of 4.0 and assuming that the last y-ray resulted in the population of either the (12--) or (2--) isomer of 19nAu depending on which transition involved a smaller spin change. This calcula15. W. L. Hafner, J. R. Huizenga and R. Vandenbosch, USA EC Rep. A N L-6662 (1962). 16. A. A. Ross, H. Mark and R. D. Lawson, Phys. R ev. 102, 1613 (1956).
L. B. CHURCH
912
TOP OF NUCLEAR WELL FOR NEUTRONS
45.8
40
3P3/z 35
l i 13/2
> iii Z
2f7/z
I h9 / 2 - ~
>(-9 ta3 Z I,i
.
.
.
.
.
3S ~/2 2d3/2___
30
---I h ulz-
Fig. 2. The top neutron levels in J97Au(Ref. [16]). tion is quite similar to previous calculations of Porile and Tanaka[2] and Caretto [3]. T h e results of this calculation are outlined in T a b l e 1. While the very close agreement between the calculated and experimental ratios is probably s o m e w h a t fortuitous, nevertheless it does lend general support to the statistical validity of this calculation and to the assumptions which went into it.
The isomeric spin calculation assuming an I S E mechanism As was previously mentioned, the interpretation of the angular distribution curve indicated the | S E m e c h a n i s m accounted for most of the recoils in the 85 ° region. T h e large n u m b e r of excited bound neutron and proton levels which would be populated after an inelastic scattering event makes an accurate calculation of the resulting spin distribution almost impossible, If this distribution is not known, then the calculation of the isomeric ratio assuming an I S E m e c h a n i s m and a comparison with with the experimental ratio to support the existence of this mechanism is not possible. It was therefore decided to use the experimental ratio and c o m p a r e it with a set of calculated ratios to determine the nuclear spin after an inelastic (p,p') event. It was arbitrarily assumed that the ( p , p ' ) event always left 12 M e V excitation energy in the 197Au nucleus. A neutron from the same four upper levels shown in Fig. 2 was then assumed to be e v a p o r a t e d with a probability proportional to the n u m b e r of neutrons in the level, N, times the transmission coefficient for neutrons, Tt, from the work of Feld et al.[17]. T h e spin distribution after the 17. B. T. Feld, H. Feshbach, M. L. Goldberger, H. Goldstein and V. Weisskopf, USAEC Rep. NYO-636 (1951).
913
The 197Au(p,pn)196Au isomeric ratio Table I. Calculation of the isomeric ratio assuming a C KO mechanism
Neutron shell
No. of 7
Product spin, Je
Fraction to (-2) state, f(2--)
3p:~/2
3
3 2 1 0
1.0130 1-000 1.000 1-000
0.133 0.095 0.057 0.019
0.000 0.000 0'000 0.000
li131z
4
8 7 6 5
0.505 0.700 0.846 0,939
0.112 0"136 0" 143 0.134
0.110 0'058 0,026 0,009
l h.~12
5
6 5 4 3
0-847 0'928 0"972 0'992
0'082 0.076 0'066 0.052
0.013 0.006 0.002 0.000
lfT/~
5
5 4 3 2
0-928 0.972 0-992 0.999
0'153 0' 131 0.104 0'075
0.012 0.004 0-001 0.000
~, 1.568
0.241
Isomeric ratio -
Total production probability N × M,,~ × Rj N × M,a × R j ×f(2--) ×f(12-)
2~(12-) (2-)
0.154
neutron evaporation and during the subsequent y-ray deexcitation was calculated in a manner outlined in Ref. [5] and [15]. All other assumptions made in this set of calculations were the same as in the above C K O set. A typical calculation is illustrated in Table 2. T h e calculated ratios are plotted in Fig. 3 as a function of the assumed spin after the inelastic (p,p') event. Using the experimental ratio of 0-18+0.06, it appears that the spin after the (p,p') event is about 6.0 ± 1.0. This is to be compared with the 197Au target spin of 3/2. The fairly steep slope of the curve in Fig. 3 implies that the inelastic scattering part of the ISE mechanism determines to a very large extent the final spin distribution, and hence the final isomeric ratio. It would be interesting to see if this is also true in other simple reactions which involve the 1SE mechanism. It would also be interesting to compare this rather indirect calculation of the spin change attributed to the (p,p') inelastic scattering event with a more direct method of estimating nuclear spin change. One possible avenue of approach would be to radiochemically measure the cross section of a series of (p,p') reactions. T w o possible targets might be 113In and HSln. In summary, the approach of this study has been to examine the isomeric ratio as a function of the recoil angle and hence the reaction mechanism. With 400 MeV protons, the reaction studied appears to occur via two different mech-
914
L.B. CHURCH Table 2. A typical calculation assuming an ISE mechanism with a spin of 7/2 after the (p,p') event
3P3/2
li,.3/.2
lh9/2
2f7/2
0.142
0.276
0.314
0.268
3
2
1
1
Fraction of events to (2-) state
0"938
0-857
0.904
0.949
Fraction of events to (12-) state
0-062
0.143
0-096
0.051
Total production probability (2-)
0.133
0.236
0.284
0.254
Total production probability (12-)
0-008
0-033
0.027
0,013
Neutron shell Weighted probability for neutron evaporation; N × Tt N umber of y's after neutron evaporation
1someric ratio
(to 12--) 1~ (to 2--)
0.081 0.907
= 0-089
O" o~ (D i,i
0.3
~E
o oo 0.2 uJ
j
o.I
o
0
0~0----~0~
,io
zi0
310
jo1~---°-/ 0b 76
46
50
86
SPIN AFTER A (P,P') EVENT Fig. 3. The calculated isomeric ratio assuming the |SE mechanism as a function of the 19~Aunuclear spin after the (p,p') event.
anisms, both of which give close to the same isomeric ratio. A calculation of this ratio assuming the clean knockout mechanism agrees very well with the experimental results. A similar calculation assuming the ] S E mechanism indicates that the change in spin o f the 197Au target nucleus resulting f r o m the inelastic scattering event is about 9/2 units ofh. Acknowledgements--The author appreciates the cooperation received from the staff of the Carnegie-Mellon University synchrocyclotron staff. In addition the generosity of Professor A. A. Caretto for sharinghis laboratory and counting facilities is gratefully acknowledged.