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Independent yields of Rb and Cs isotopes from the fission of natural uranium induced by protons of energy 80 and 100 MeV
3 inor~,, nucl. Chem.. 1975, Vol. 37, pp. 2035-2038. Pergamon Press. Printed in Great Britain
INDEPENDENT YIELDS OF Rb AND Cs ISOTOPES FROM THE FISSION OF NATURAL URANIUM INDUCED BY PROTONS OF ENERGY 80 AND 100 MeV* J. K. P. LEEr, G. PILARt, B. L. TRACYt and L. YAFFE~ McGill University, Montreal, Canad~t
(Received 25 November 1974) Abstract~The independent yields or production cross sections of rubidium isotopes from mass 86 to 97, and of cesium isotopes from mass 129 to 144, have been measured for the fission of natural uranium induced by 80 and 100 MeV protons. The results were obtained by means of an on-line mass spectrometer. The rubidium distributions are quite symmetric, whereas the cesium distributions show a definite skewness toward the heavy mass side. Comparison with other results at 40, 50, 60 and 150 MeV proton energies shows that the heavy mass sides of the isotopic distributions are relatively insensitive to proton energy, whereas the light mass sides shift downward with increasing proton energy. The average total number of neutrons emitted has been estimated for each fission reaction. The mechanism of nuclear charge division in 80 and 100 MeV proton fission in the mass split studied here appears to be similar to that operating in thermal-neutron and low-energy proton fission.
INTRODUCTION
DURING the past few years extensive radiochemical investigations[I--4] have been carried out at this university on the production cross sections of various elements from fission by 10-100 MeV protons. This work has now been extended to the study of much shorter lived isotopes by the acquisition of an online mass spectrometer of the the type described by Klapisch et al.[5]. With this mass spectrometer one can measure the independent yields or cross sections of essentially all the isotopes of a given alkali element to a high degree of precision. The shape of the complete isotropic distribution curve can thus be accurately determined, and important new information can thereby be obtained, particularly on the neutron-rich side of the curve where half-lives are the order of a second or less. The rubidium and cesium yields from the fission of natural uranium have been measured with this type of mass spectrometer for protons of 4 0 - 6 0 M e V energy[6] and 150MeV energy[7]. The present investigation was undertaken in order to fill a gap in the experimental data in the energy range of 80-100MeV. It should then be possible to make some generalizations about the variation of the isotopic distributions with proton bombarding energy. In particular it is hoped that the present results will help to clarify the mechanism of charge distribution in fission at these energies. Some authors have claimed that their results from charged particle induced fission support the postulate of U C D (unchanged charge distribution) (e.g. Colby and Cobble[8]), whereas others find that their results are intermediate between the prediction of U C D and ECD (equal charge displacement) (e.g. Benjamin et al.[3]). Tracy et al.[6] concluded that their mass spectrometric results in 40-60 MeV proton fission were consistent with ECD, the same mechanism which seems to operate in thermal neutron fission. It would be interesting to see if *Supported in part by grants from the Atomic Energy Control Board of Canada and the National Research Council of Canada. tFoster Radiation Laboratory. +~Department of Chemistry.
this conclusion remains valid up to 100 MeV bombarding energy. EXPERIMENTAL
The on-line mass spectrometer used in this investigation was obtained from Gamma lndustrie of Paris. Further details on this type of instrument can be found in the literature [5, 7, 9]. Basically, the target material is contained directly in the ion source of the mass spectrometer. During irradiation by a beam of particles, recoiling reaction products are stopped in hot graphite (1700°C). Members of the alkali family diffuse out quickly and are ionized by surface ionization. The ions are then accelerated by a potential of 5kV, mass-analyzed in a 90° sector magnetic field, and individually detected by means of an electron multiplier. The diffusion and ionization processes are highly selective toward elements of the alkali family; hence this method is well suited to the measurement of rubidium and cesium fission yields. Furthermore, since a significant fraction of the diffusion takes place in less than a second, the yields of even the shortest rived isotopes, that are produced in any appreciable abundance, can be measured. For the purpose of this experiment U~O8 was deposited to a thickness of 1.5 mg/cm2 on to strips of graphite, each measuring 0,07ram thick and 15x4.3mm 2 in area. The entire target consisted of 20 such strips enclosed in a tantalum oven. Irradiations were carried out in the external beam of the McGill Synchrocyclotron, which delivers about 30 nA of protons at 100 MeV energy to the experimental area. Protons of 80 MeV energy were obtained by placing 1.75 cm of berylium degrader after the exit of the cyclotron. Independent yields were accumulated in the following manner (see Fig. 1): Clock pulses from the PDP-15 computer were used to switch the cyclotron on and off. Another pulse turned on the sweep generator, which applied a 50 Hz triangular modulation to the accelerating voltage of the mass spectrometer. This allowed a region of several mass units wide to be scanned at one time. Output pulses from the electron multiplier were accumulated in the computer memory in the multi-scaling mode. Synchronization pulses from the sweep generator kept the scan through the computer memory in phase with the scan of the high voltage. In this way the results of many scans were added together to give better statistics. Typically, the cyclotron bombardment lasted from 1 to lO secs. A mass spectrum was accumulated during the bombardment and stopped shortly after the end of the bombardment. Several seconds later, a second mass spectrum was accumulated. This spectrum contained the constant background of naturally-
2035
J . K . P . LEE et aL
2036
Table 1. Rb production cross sections (m.b.) from the proton fission of natural uranium
/V~A
Proton Energy Mass Number
MuLr, SCALING
PDP-15
~ J-
I~uLT'~'ER I ]
80 MeV
I00 MeV
86
0.70 -+ 0.07
1.00 + 0,04
87
3.3
+ 0.2
3.12 -+ 0.ii
88
6.1
+ 0.3
6.15 + 0.16
89
13.1
+ 0.4
10.36 + 0.17
90
19.6
-+ 0.4
14.9
+ 0.5
91
20.9
-+ 1.0
17.1
+ 0.5
92
21.0
+ 0.9
16.49 + 0.i0
93
14.0
+ 0.6
11.70 -+ 0.09
94
7.4
+ 0.4
5,82 +- 0.08
95
4.3
+ 0.3
3-94 + 0.07
96
1.5
+ 0.2
1.22 -+ 0.04
CYCLOTRON
START&STOP
Fig. 1. Schematic diagram showing the data acquisition system used for the independent yield measurements. occuring isotopes together with the cumulative rubidium and cesium yields resulting from the /3-decay of precursors in the target. The differences between the mass peaks in the two spectra were then directly proportional to the independent yields of the respective rubidium and cesium isotopes. It was necessary to correct the yields of isotopes with half-lives of a few seconds or less for partial decay inside the target. For this purpose the diffusion rates of the relatively long-lived isotopes 9°Rb and "2Cs were measured by following their count rates as a function of time after bombardment. It was then assumed that all isotopes of the same element diffuse out of graphite at the same rate. Such an assumption appears to be justified on the basis of other experimental work (Chaumont[7]). Correction factors were then calculated on the basis of the measured diffusion rates of the long-lived isotopes and the known half-lives of the short-lived isotopes. The experimental yields were also corrected for a slight degree of mass discrimination in favor of lighter masses. From the measurement of the count rates of stable isotopes of known abundances, this discrimination was found to be - 1.0 _+0.5% for a 1% mass difference. RESULTS AND DISCUSSION The independent cross sections for the production of rubidium and cesium isotopes from the fission of natural uranium by protons of 80 and 100MeV energies are shown in Tables 1 and 2 and in Figs. 2 and 3. The mass spectrometric measurements gave only the relative isotopic yields; absolute yields were obtained by normalization to the radiochemical measurements of the absolute cross sections of S6Rb and '3°'3'~32'34'36'3SCsby Davies and Yaffe [2] at 80 MeV and by Friedlander et al. [10] at 100 MeV. The error quoted for each measurement in Tables l and 2 indicates only the precision relative to the measurements of the yields of other isotopes of the same element and at the same bombarding energy. The absolute error or error of normalization, is indicated separately for each isotopic distribution. The large normalization errors for the rubidium cross sections result from the difficulty in obtaining an accurate absolute cross section of 18-day a6Rb. Normalization errors for cesium are taken from the weighted means of individual normalization values. Tables 1 and 2 also show the mean mass number, or centroid, of each isotopic distribution. The results at 80 MeV are somewhat less precise than those at 100 MeV, because of the reduced intensity of the degraded proton beam. The larger uncertainty at mass 138 results from a high degree of contamination by natural 13~Ba'
97
0.43 + 0.02
Normalization Error Mean Mass Number
T30%
T30%
91.133 ~ 0,025
91.112 T 0.012
Table 2. Cs production cross sections (m.b.) from the proton fission of natural uranium Proton Energy Mass Number
80 MeV
129
I00 MeV 0.09 + 0.03
130
0.49 + 0.04
131
0.61 + 0.08
1.54 -~ 0.08
132
2.33 + 0.19
3.81 ~+ 0.15
133
6.5
+ 0.5
8.2
+ 0.3
134
13.2
-+ 0.6
ii.0
+ 0.3
135
17.6
-+ 1.0
13.8
+ 0,4
136
21.3
-+ 1.0
15.2
+ 0.4
137
23.5
+ 1.3
15.9
T 0.6
138
18.0
+ 2.7
18.4
+ 2.0
139
15.6
-+ 1.0
12.1
+ 0.3
140
11.9
-+ 1.3
8.8
~- 0.4
141
7.7
-+ 1.0
7.2 + 0.4
142
6.3 -+ 0.7
6.3 -+ 0.6
143
3.0 + 0.5
3.0 -+ 0.3
144
1.6 + 0.3
0.97 -+ 0.ii
Normalization Error
~ 3%
~ 7%
Mean Mass Number
137.26 ~ 0.06
137.10 ~ 0.04
In order to elucidate the general trends of the isotropic distributions, expressions of the form
Y(A ) = exp {(Co + C~A + C2A 2+ C3A 3)} were fitted to the experimental data, where Y(A) is the yield at mass A, and Co, C,, C2 and C3 are adjustable coefficients. It was found that the rubidium distributions could be reasonably well fitted by exponentials of second degree polynomials, and that no improvement was to be gained from a higher degree fit. This implies essentially a
Yields of Rb and Cs isotopes from the fission of nalural uranium [~ CsrYi~ld [:)istP~bu~ion ~ 140~ - ' ~ ' ~ x .x ~ , / UPPER HALF-MAX
:Rb Yield
/,/ //
XIO0 MeV 1 ,---'v"-,\ \
// /
o
~: 80
2037
[
"~
LOWERHALF MAX
MeV
x ~ 132
~:
© _
| 94 r
Rb Yield Distribution - . - - . - - ~ - - x - - x
uPPER HA~F MAX
!
86
90
94
,
-i
98 90 ]
MASS NUMBER
J
Fig. 2. Independent cross sections for the production of rubidium isotopes from fission of natural uranium induced by protons of energy 80 and 100 MeV. 40 10; Cs Yield
~ ' ~ " ~ .//
Fig. 4. Higher and lower mass numbers at which the tilted mass distribution curves of (a) rubidium and (b) cesium falls to half ils maximum values at various proton bombarding energies
100 MeV ~'~Nxxl/3
zlO ©
w :!
\\
///
k,
t: . .132 . . 136. . . 140
128
6Q 80 1QO 150 PROTON E N E R G Y (M~V',
A
144
MASS N U M B E R
Fig. 3. Independent cross sections for the production of cesium isotopes from fission of natural uranium induced by protons of energy 80 and 100 MeV.. ..... , second order polynomial fit; third order polynomialfit. symmetric, gaussian shape to the rubidium isotopic distributions. On the other hand, third degree polynomial fits to the cesium yields were considerably better than the second degree fits, thus implying a net skewness or asymmetry to the cesium distributions. In particular these distributions fall off more quickly on the neutron-deficient side than on the neutron-rich side. Figure 2 shows the second degree polynomial fits to the rubidium yields, whereas Fig, 3 shows both second and third degree polynomial fits to the cesium yields. Second degree polynomial fits to rubidium yields and third degree fits to cesium yields were also carried out on the data at 40, 50, 60[6] and 15017] MeV. The results are combined with the present results and are shown in Fig. 4 in terms of the higher and lower mass numbers at which the fitted curves fall to one-half of their maximum values. It is seen that the higher sides of the distributions remain more or less fixed while the lower sides shift downward with increasing bombarding energy. In other words the broadening of the curves with increasing bombarding energy is almost entirely caused by the production of more neutron-deficient isotopes. The increased production of neutron-deficient isotopes with increasing proton energy can of course be understood in terms of increased neutron evaporation, either
before or after fission, as a result of the higher degree of excitation energy imparted to the nucleus. However, the persistence of the neutron-rich isotopes, even up to 150MeV proton energy, indicates that a significant fraction of the fission events are of the low energy or thermal type, where only a small fraction of the total proton energy is absorbed by the nucleus. From the mean mass numbers in Tables 1 and 2 it is possible to estimate the average total number of neutrons released in these fission events and to draw some conclusions about the partition of nuclear charge between light and heavy fragments. To do this one can make use of the fact that rubidium and cesium are nearly complementary in the proton induced fission of uranium. 1! is assumed that the most probable fissioning nucleus is some isotope of neptunium, i.e. that the probability of proton knock-out or evaporation before fission is small. Thus rubidium fragments are to be paired with barium fragments, and cesium fragments with strontium fragments. The mean mass number of the barium fragments can be estimated by multiplying that of the cesium fragments by 56/55. Alternatively, the mean mass number of the strontium fragments can be estimated by multiplying that of the rubidium by 38/37. Either way, the mean mass numbers of complementary fragments can be added together and subtracted from the mass number !239) of target plus projectile to obtain the average total number of emitted neutrons. The results are 8.13 +_0.10 for 80 MeV, and 8.32 +0,10 for 100 MeV proton fission. These results can be compared with the values of 7.62-10.19 obtained by Diksic, McMillan and Yaffe[1] for the fission of natural uranium by 80 X,leV protons. Before conclusions can be drawn about the division of nuclear charge between two fragments of given masses (or what is equivalent, the division of mass between two fragments of given charges), the mean mass numbers in Tables 1 and 2 must be corrected for the effects of post-fission neutron emission. The total numbers of emitted neutrons obtained in the previous paragraph must be divided between pre- and post-fission neutrons; the post-fission neutrons must then be divided between the rubidium and cesium fragments. It is then possible to
2038
J. K. P. LEE et al.
calculate the mean mass numbers, and hence the mean N [ Z ratios, of the prompt rubidium and cesium fragments. Table 3 shows the results for the case at 100 MeV (the 80 MeV case is quite similar). The first column, labelled z,-fission/v-total, is the fraction of the total number of neutrons emitted after fission. The calculations of Diksic, McMillan and Yaffe [1] for fission in this energy range indicate that 0.50 is a reasonable value for this fraction. However, it will be seen that the final result does not greatly.depend on whether half, all or none of the neutrons are assumed to be emitted after fission. The next column, labelled v(Cs)/v(Rb), is the ratio of neutrons emitted from cesium fragments to those emitted from rubidium fragments. The value of 2.0 for this ratio is based on experimental measurements by Cheifetz and Fraenkel[ll], Britt and Whetstone[12] and Cheifetz et a/.[13]. The columns labelled (Cs) and (Rb) are the resulting mean N / Z ratios of the prompt isotopic distributions, and the last column gives the differences between these N / Z ratios. The UCD mechanism of charge division would give equal N [ Z ratios to prompt rubidium and cesium fragments. It is seen that the only way to obtain this equality from the present data is to assume ~,(Cs)/u(Rb)= 0.78, a value which is not consistent with the experimental measurements. On the other Table 3. Mean N/Z ratios of prompt Rb and Cs fragments from the 100 MeV proton fissionof natural uranium ~-fission 9-total
9 ~
_~Rb > a)
0.50
2.0
1.500
1.543
+0.043
1.00
2.0
1.537
1.594
+0.057
0.00
2.0
1.462
1.493
+0.031
0.50
0.78
1.526
1.526
0.000
These values are compared to +0,048 for 50 MeV proton induced fission of natural U and +0.055 for thermal neutron induced fission of 235U.
hand it is seen that the first value of (Cs)-(Rb) is similar to the values obtained in the 50MeV proton fission of natural uranium[6] and the thermal-neutron fission of 235U[14]. Thus we are led to conclude that the mechanism of charge division in fission induced by protons of up to 100MeV energy in the mass split studied here is not markedly different from that operating in fission at thermal energies. In particular there appears to be no significant shift toward UCD at higher bombarding energies. However, our results are limited to one particular charge split--that leading to rubidium and cesium. It would be interesting to carry out similar mass spectrometric measurements on other elements besides those of the alkali family. REFERENCES
1. M. Diksic, D. K. McMillanand L. Yaffe, J. Inorg. Nucl. Chem. 36, 7 (1974). 2. J. H. Davies and Y. Yaffe, Can. J. Phys. 41,762 (1963). 3. P. P. Benjamin, D. A. Marsden, N, T. Porile and L. Yaffe, Can. Z Chem. 47, 301 (1%9). 4. L. D. Miller and L. Yaffe, 3. Inorg. Nucl. Chem. 35, 1805 0973). 5. R. Klapisch, J. Chaumont, C. Philippe, I. Amarel,R. Fergeau, M. Salom6and R. Bernas, NucL Instr. Methods 53,216(1%7). 6. B. L. Tracy, J. Chaumont, R. Klapisch, J. M. Nitschke, A. M. Poskanzer, E. Roeckl and C. Thibault, Phys. Rev. C5, 222 (1972). 7. J. Chaumont, Ph.D. Thesis, Facult6 des Sciences Orsay (1970). (unpublished). 8. L.J. Colby,Jr. and J. W. Cobble, Phys. Rev. 121, 1410(1%1). 9. R. Klapisch, Ann. Rev. NucL Sci. 19, 33 (1%9). 10. G. Friedlander, L. Friedman, B. Gordon and L. Yaffe, Phys. Rev. 129, 1809 (1963). 11. E. Cheifetz and Z. Fraenkel, Phys. Rev. Lett. 21, 36 (1%8). 12. H. C. Britt and S. L. Whetstone, Jr., Phys. Rev. 133, B603 (1%4). 13. E. Cheifetz, Z. Fraenkel, J. Galin, M. Lefort, J. P6ter and X. Tarrago, Phys. Rev. C2, 256 (1970). 14. A. C. Wahl, R. L. Ferguson, D. R. Nethaway, D. E. Troutner and K. Wolfsberg, Phys. Rev. 126, 1112 (1%2).
INDEPENDENT YIELDS OF Rb AND Cs ISOTOPES FROM THE FISSION OF NATURAL URANIUM INDUCED BY PROTONS OF ENERGY 80 AND 100 MeV* J. K. P. LEEr, G. PILARt, B. L. TRACYt and L. YAFFE~ McGill University, Montreal, Canad~t
(Received 25 November 1974) Abstract~The independent yields or production cross sections of rubidium isotopes from mass 86 to 97, and of cesium isotopes from mass 129 to 144, have been measured for the fission of natural uranium induced by 80 and 100 MeV protons. The results were obtained by means of an on-line mass spectrometer. The rubidium distributions are quite symmetric, whereas the cesium distributions show a definite skewness toward the heavy mass side. Comparison with other results at 40, 50, 60 and 150 MeV proton energies shows that the heavy mass sides of the isotopic distributions are relatively insensitive to proton energy, whereas the light mass sides shift downward with increasing proton energy. The average total number of neutrons emitted has been estimated for each fission reaction. The mechanism of nuclear charge division in 80 and 100 MeV proton fission in the mass split studied here appears to be similar to that operating in thermal-neutron and low-energy proton fission.
INTRODUCTION
DURING the past few years extensive radiochemical investigations[I--4] have been carried out at this university on the production cross sections of various elements from fission by 10-100 MeV protons. This work has now been extended to the study of much shorter lived isotopes by the acquisition of an online mass spectrometer of the the type described by Klapisch et al.[5]. With this mass spectrometer one can measure the independent yields or cross sections of essentially all the isotopes of a given alkali element to a high degree of precision. The shape of the complete isotropic distribution curve can thus be accurately determined, and important new information can thereby be obtained, particularly on the neutron-rich side of the curve where half-lives are the order of a second or less. The rubidium and cesium yields from the fission of natural uranium have been measured with this type of mass spectrometer for protons of 4 0 - 6 0 M e V energy[6] and 150MeV energy[7]. The present investigation was undertaken in order to fill a gap in the experimental data in the energy range of 80-100MeV. It should then be possible to make some generalizations about the variation of the isotopic distributions with proton bombarding energy. In particular it is hoped that the present results will help to clarify the mechanism of charge distribution in fission at these energies. Some authors have claimed that their results from charged particle induced fission support the postulate of U C D (unchanged charge distribution) (e.g. Colby and Cobble[8]), whereas others find that their results are intermediate between the prediction of U C D and ECD (equal charge displacement) (e.g. Benjamin et al.[3]). Tracy et al.[6] concluded that their mass spectrometric results in 40-60 MeV proton fission were consistent with ECD, the same mechanism which seems to operate in thermal neutron fission. It would be interesting to see if *Supported in part by grants from the Atomic Energy Control Board of Canada and the National Research Council of Canada. tFoster Radiation Laboratory. +~Department of Chemistry.
this conclusion remains valid up to 100 MeV bombarding energy. EXPERIMENTAL
The on-line mass spectrometer used in this investigation was obtained from Gamma lndustrie of Paris. Further details on this type of instrument can be found in the literature [5, 7, 9]. Basically, the target material is contained directly in the ion source of the mass spectrometer. During irradiation by a beam of particles, recoiling reaction products are stopped in hot graphite (1700°C). Members of the alkali family diffuse out quickly and are ionized by surface ionization. The ions are then accelerated by a potential of 5kV, mass-analyzed in a 90° sector magnetic field, and individually detected by means of an electron multiplier. The diffusion and ionization processes are highly selective toward elements of the alkali family; hence this method is well suited to the measurement of rubidium and cesium fission yields. Furthermore, since a significant fraction of the diffusion takes place in less than a second, the yields of even the shortest rived isotopes, that are produced in any appreciable abundance, can be measured. For the purpose of this experiment U~O8 was deposited to a thickness of 1.5 mg/cm2 on to strips of graphite, each measuring 0,07ram thick and 15x4.3mm 2 in area. The entire target consisted of 20 such strips enclosed in a tantalum oven. Irradiations were carried out in the external beam of the McGill Synchrocyclotron, which delivers about 30 nA of protons at 100 MeV energy to the experimental area. Protons of 80 MeV energy were obtained by placing 1.75 cm of berylium degrader after the exit of the cyclotron. Independent yields were accumulated in the following manner (see Fig. 1): Clock pulses from the PDP-15 computer were used to switch the cyclotron on and off. Another pulse turned on the sweep generator, which applied a 50 Hz triangular modulation to the accelerating voltage of the mass spectrometer. This allowed a region of several mass units wide to be scanned at one time. Output pulses from the electron multiplier were accumulated in the computer memory in the multi-scaling mode. Synchronization pulses from the sweep generator kept the scan through the computer memory in phase with the scan of the high voltage. In this way the results of many scans were added together to give better statistics. Typically, the cyclotron bombardment lasted from 1 to lO secs. A mass spectrum was accumulated during the bombardment and stopped shortly after the end of the bombardment. Several seconds later, a second mass spectrum was accumulated. This spectrum contained the constant background of naturally-
2035
J . K . P . LEE et aL
2036
Table 1. Rb production cross sections (m.b.) from the proton fission of natural uranium
/V~A
Proton Energy Mass Number
MuLr, SCALING
PDP-15
~ J-
I~uLT'~'ER I ]
80 MeV
I00 MeV
86
0.70 -+ 0.07
1.00 + 0,04
87
3.3
+ 0.2
3.12 -+ 0.ii
88
6.1
+ 0.3
6.15 + 0.16
89
13.1
+ 0.4
10.36 + 0.17
90
19.6
-+ 0.4
14.9
+ 0.5
91
20.9
-+ 1.0
17.1
+ 0.5
92
21.0
+ 0.9
16.49 + 0.i0
93
14.0
+ 0.6
11.70 -+ 0.09
94
7.4
+ 0.4
5,82 +- 0.08
95
4.3
+ 0.3
3-94 + 0.07
96
1.5
+ 0.2
1.22 -+ 0.04
CYCLOTRON
START&STOP
Fig. 1. Schematic diagram showing the data acquisition system used for the independent yield measurements. occuring isotopes together with the cumulative rubidium and cesium yields resulting from the /3-decay of precursors in the target. The differences between the mass peaks in the two spectra were then directly proportional to the independent yields of the respective rubidium and cesium isotopes. It was necessary to correct the yields of isotopes with half-lives of a few seconds or less for partial decay inside the target. For this purpose the diffusion rates of the relatively long-lived isotopes 9°Rb and "2Cs were measured by following their count rates as a function of time after bombardment. It was then assumed that all isotopes of the same element diffuse out of graphite at the same rate. Such an assumption appears to be justified on the basis of other experimental work (Chaumont[7]). Correction factors were then calculated on the basis of the measured diffusion rates of the long-lived isotopes and the known half-lives of the short-lived isotopes. The experimental yields were also corrected for a slight degree of mass discrimination in favor of lighter masses. From the measurement of the count rates of stable isotopes of known abundances, this discrimination was found to be - 1.0 _+0.5% for a 1% mass difference. RESULTS AND DISCUSSION The independent cross sections for the production of rubidium and cesium isotopes from the fission of natural uranium by protons of 80 and 100MeV energies are shown in Tables 1 and 2 and in Figs. 2 and 3. The mass spectrometric measurements gave only the relative isotopic yields; absolute yields were obtained by normalization to the radiochemical measurements of the absolute cross sections of S6Rb and '3°'3'~32'34'36'3SCsby Davies and Yaffe [2] at 80 MeV and by Friedlander et al. [10] at 100 MeV. The error quoted for each measurement in Tables l and 2 indicates only the precision relative to the measurements of the yields of other isotopes of the same element and at the same bombarding energy. The absolute error or error of normalization, is indicated separately for each isotopic distribution. The large normalization errors for the rubidium cross sections result from the difficulty in obtaining an accurate absolute cross section of 18-day a6Rb. Normalization errors for cesium are taken from the weighted means of individual normalization values. Tables 1 and 2 also show the mean mass number, or centroid, of each isotopic distribution. The results at 80 MeV are somewhat less precise than those at 100 MeV, because of the reduced intensity of the degraded proton beam. The larger uncertainty at mass 138 results from a high degree of contamination by natural 13~Ba'
97
0.43 + 0.02
Normalization Error Mean Mass Number
T30%
T30%
91.133 ~ 0,025
91.112 T 0.012
Table 2. Cs production cross sections (m.b.) from the proton fission of natural uranium Proton Energy Mass Number
80 MeV
129
I00 MeV 0.09 + 0.03
130
0.49 + 0.04
131
0.61 + 0.08
1.54 -~ 0.08
132
2.33 + 0.19
3.81 ~+ 0.15
133
6.5
+ 0.5
8.2
+ 0.3
134
13.2
-+ 0.6
ii.0
+ 0.3
135
17.6
-+ 1.0
13.8
+ 0,4
136
21.3
-+ 1.0
15.2
+ 0.4
137
23.5
+ 1.3
15.9
T 0.6
138
18.0
+ 2.7
18.4
+ 2.0
139
15.6
-+ 1.0
12.1
+ 0.3
140
11.9
-+ 1.3
8.8
~- 0.4
141
7.7
-+ 1.0
7.2 + 0.4
142
6.3 -+ 0.7
6.3 -+ 0.6
143
3.0 + 0.5
3.0 -+ 0.3
144
1.6 + 0.3
0.97 -+ 0.ii
Normalization Error
~ 3%
~ 7%
Mean Mass Number
137.26 ~ 0.06
137.10 ~ 0.04
In order to elucidate the general trends of the isotropic distributions, expressions of the form
Y(A ) = exp {(Co + C~A + C2A 2+ C3A 3)} were fitted to the experimental data, where Y(A) is the yield at mass A, and Co, C,, C2 and C3 are adjustable coefficients. It was found that the rubidium distributions could be reasonably well fitted by exponentials of second degree polynomials, and that no improvement was to be gained from a higher degree fit. This implies essentially a
Yields of Rb and Cs isotopes from the fission of nalural uranium [~ CsrYi~ld [:)istP~bu~ion ~ 140~ - ' ~ ' ~ x .x ~ , / UPPER HALF-MAX
:Rb Yield
/,/ //
XIO0 MeV 1 ,---'v"-,\ \
// /
o
~: 80
2037
[
"~
LOWERHALF MAX
MeV
x ~ 132
~:
© _
| 94 r
Rb Yield Distribution - . - - . - - ~ - - x - - x
uPPER HA~F MAX
!
86
90
94
,
-i
98 90 ]
MASS NUMBER
J
Fig. 2. Independent cross sections for the production of rubidium isotopes from fission of natural uranium induced by protons of energy 80 and 100 MeV. 40 10; Cs Yield
~ ' ~ " ~ .//
Fig. 4. Higher and lower mass numbers at which the tilted mass distribution curves of (a) rubidium and (b) cesium falls to half ils maximum values at various proton bombarding energies
100 MeV ~'~Nxxl/3
zlO ©
w :!
\\
///
k,
t: . .132 . . 136. . . 140
128
6Q 80 1QO 150 PROTON E N E R G Y (M~V',
A
144
MASS N U M B E R
Fig. 3. Independent cross sections for the production of cesium isotopes from fission of natural uranium induced by protons of energy 80 and 100 MeV.. ..... , second order polynomial fit; third order polynomialfit. symmetric, gaussian shape to the rubidium isotopic distributions. On the other hand, third degree polynomial fits to the cesium yields were considerably better than the second degree fits, thus implying a net skewness or asymmetry to the cesium distributions. In particular these distributions fall off more quickly on the neutron-deficient side than on the neutron-rich side. Figure 2 shows the second degree polynomial fits to the rubidium yields, whereas Fig, 3 shows both second and third degree polynomial fits to the cesium yields. Second degree polynomial fits to rubidium yields and third degree fits to cesium yields were also carried out on the data at 40, 50, 60[6] and 15017] MeV. The results are combined with the present results and are shown in Fig. 4 in terms of the higher and lower mass numbers at which the fitted curves fall to one-half of their maximum values. It is seen that the higher sides of the distributions remain more or less fixed while the lower sides shift downward with increasing bombarding energy. In other words the broadening of the curves with increasing bombarding energy is almost entirely caused by the production of more neutron-deficient isotopes. The increased production of neutron-deficient isotopes with increasing proton energy can of course be understood in terms of increased neutron evaporation, either
before or after fission, as a result of the higher degree of excitation energy imparted to the nucleus. However, the persistence of the neutron-rich isotopes, even up to 150MeV proton energy, indicates that a significant fraction of the fission events are of the low energy or thermal type, where only a small fraction of the total proton energy is absorbed by the nucleus. From the mean mass numbers in Tables 1 and 2 it is possible to estimate the average total number of neutrons released in these fission events and to draw some conclusions about the partition of nuclear charge between light and heavy fragments. To do this one can make use of the fact that rubidium and cesium are nearly complementary in the proton induced fission of uranium. 1! is assumed that the most probable fissioning nucleus is some isotope of neptunium, i.e. that the probability of proton knock-out or evaporation before fission is small. Thus rubidium fragments are to be paired with barium fragments, and cesium fragments with strontium fragments. The mean mass number of the barium fragments can be estimated by multiplying that of the cesium fragments by 56/55. Alternatively, the mean mass number of the strontium fragments can be estimated by multiplying that of the rubidium by 38/37. Either way, the mean mass numbers of complementary fragments can be added together and subtracted from the mass number !239) of target plus projectile to obtain the average total number of emitted neutrons. The results are 8.13 +_0.10 for 80 MeV, and 8.32 +0,10 for 100 MeV proton fission. These results can be compared with the values of 7.62-10.19 obtained by Diksic, McMillan and Yaffe[1] for the fission of natural uranium by 80 X,leV protons. Before conclusions can be drawn about the division of nuclear charge between two fragments of given masses (or what is equivalent, the division of mass between two fragments of given charges), the mean mass numbers in Tables 1 and 2 must be corrected for the effects of post-fission neutron emission. The total numbers of emitted neutrons obtained in the previous paragraph must be divided between pre- and post-fission neutrons; the post-fission neutrons must then be divided between the rubidium and cesium fragments. It is then possible to
2038
J. K. P. LEE et al.
calculate the mean mass numbers, and hence the mean N [ Z ratios, of the prompt rubidium and cesium fragments. Table 3 shows the results for the case at 100 MeV (the 80 MeV case is quite similar). The first column, labelled z,-fission/v-total, is the fraction of the total number of neutrons emitted after fission. The calculations of Diksic, McMillan and Yaffe [1] for fission in this energy range indicate that 0.50 is a reasonable value for this fraction. However, it will be seen that the final result does not greatly.depend on whether half, all or none of the neutrons are assumed to be emitted after fission. The next column, labelled v(Cs)/v(Rb), is the ratio of neutrons emitted from cesium fragments to those emitted from rubidium fragments. The value of 2.0 for this ratio is based on experimental measurements by Cheifetz and Fraenkel[ll], Britt and Whetstone[12] and Cheifetz et a/.[13]. The columns labelled (Cs) and (Rb) are the resulting mean N / Z ratios of the prompt isotopic distributions, and the last column gives the differences between these N / Z ratios. The UCD mechanism of charge division would give equal N [ Z ratios to prompt rubidium and cesium fragments. It is seen that the only way to obtain this equality from the present data is to assume ~,(Cs)/u(Rb)= 0.78, a value which is not consistent with the experimental measurements. On the other Table 3. Mean N/Z ratios of prompt Rb and Cs fragments from the 100 MeV proton fissionof natural uranium ~-fission 9-total
9
0.50
2.0
1.500
1.543
+0.043
1.00
2.0
1.537
1.594
+0.057
0.00
2.0
1.462
1.493
+0.031
0.50
0.78
1.526
1.526
0.000
These values are compared to +0,048 for 50 MeV proton induced fission of natural U and +0.055 for thermal neutron induced fission of 235U.
hand it is seen that the first value of (Cs)-(Rb) is similar to the values obtained in the 50MeV proton fission of natural uranium[6] and the thermal-neutron fission of 235U[14]. Thus we are led to conclude that the mechanism of charge division in fission induced by protons of up to 100MeV energy in the mass split studied here is not markedly different from that operating in fission at thermal energies. In particular there appears to be no significant shift toward UCD at higher bombarding energies. However, our results are limited to one particular charge split--that leading to rubidium and cesium. It would be interesting to carry out similar mass spectrometric measurements on other elements besides those of the alkali family. REFERENCES
1. M. Diksic, D. K. McMillanand L. Yaffe, J. Inorg. Nucl. Chem. 36, 7 (1974). 2. J. H. Davies and Y. Yaffe, Can. J. Phys. 41,762 (1963). 3. P. P. Benjamin, D. A. Marsden, N, T. Porile and L. Yaffe, Can. Z Chem. 47, 301 (1%9). 4. L. D. Miller and L. Yaffe, 3. Inorg. Nucl. Chem. 35, 1805 0973). 5. R. Klapisch, J. Chaumont, C. Philippe, I. Amarel,R. Fergeau, M. Salom6and R. Bernas, NucL Instr. Methods 53,216(1%7). 6. B. L. Tracy, J. Chaumont, R. Klapisch, J. M. Nitschke, A. M. Poskanzer, E. Roeckl and C. Thibault, Phys. Rev. C5, 222 (1972). 7. J. Chaumont, Ph.D. Thesis, Facult6 des Sciences Orsay (1970). (unpublished). 8. L.J. Colby,Jr. and J. W. Cobble, Phys. Rev. 121, 1410(1%1). 9. R. Klapisch, Ann. Rev. NucL Sci. 19, 33 (1%9). 10. G. Friedlander, L. Friedman, B. Gordon and L. Yaffe, Phys. Rev. 129, 1809 (1963). 11. E. Cheifetz and Z. Fraenkel, Phys. Rev. Lett. 21, 36 (1%8). 12. H. C. Britt and S. L. Whetstone, Jr., Phys. Rev. 133, B603 (1%4). 13. E. Cheifetz, Z. Fraenkel, J. Galin, M. Lefort, J. P6ter and X. Tarrago, Phys. Rev. C2, 256 (1970). 14. A. C. Wahl, R. L. Ferguson, D. R. Nethaway, D. E. Troutner and K. Wolfsberg, Phys. Rev. 126, 1112 (1%2).