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Fractional independent yields of 111mPd and 112Ag from thermal-neutron-induced fission of 249Cf
J. inor~', nuel. Chem., 1973, Vol. 35, pp. 11-17.
Pergamon Press.
Printed in Great Britain
FRACTIONAL INDEPENDENT YIELDS O F 111mpd A N D "ZAg F R O M T H E R M A L - N E U T R O N - I N D U C E D FISSION O F 249Cf* D. E. T R O U T N E R ? and R. M. H A R B O U R Savannah River Laboratory, E. I. du Pont de Nemours and Company, Aiken, South Carolina 29801
(First received 3 January 1972; in revised form 27 March 1972) Abstract-The fractional independent yields of mmpd and "2Ag from thermal-neutron-induced fission of 249Cf were measured. The yields of ~''~Pd and HZAg are 0-083 ± 0.005 and 0.035 ± 0.008, respectively. The yield of "~"Pd is consistent with an isomer yield ratio for which the low-spin ground state isomer '"~Pd is favored. INTRODUCTION
EXeEmMENTS are under way in this laboratory[l, 2] to measure independent yields of products of thermal-neutron-induced fission of 249Cfin order to compare nuclear charge distribution for that process with those for thermal-neutroninduced fission of 233U and 235U. In the light mass region, it is possible to measure independent yields for the A = 11 1 and A = 112 mass chains. '12Ag is shielded by 2 1-hr l~2pd so that the independent yield of t12Ag can be measured if it is separated soon after fission, xxlmpdis not shielded, but since only - 0.4% of short-lived "~Rh decays through that isomer [3], the independent yield of 'nmpd can be calculated from the measurement of its cumulative yield. Aumann et al. [3] have reported independent yields of ""nPd from ~33U, z35U and z~gPu fission; Roche et al. [4] have reported yields of "2Ag from 233U and e35U fission; and Troutner et al. [5] have reported yields of "~Ag from 2'~2Cffission. This work reports yields of 'nmPd and H2Ag from 249Cffission. Fission product decay chains of interest are shown in Fig. 1. Half-lives and branching ratios for A = 111 are from Aumann et al. [3]. Others are from Lederer et al. [6]. EXPERIMENTAL One microgram of 249Cf was electroplated on a high-purity aluminum foil. The source was covered with another aluminum "catcher" foil, and the two foils were roiled together. The rolled foils were *Part of the information in this article was developed during the course of work under Contract AT(07-2)-1 with the U.S. Atomic Energy Commission. CAEC Faculty Research Participant for Summer 1970. Permanent address: Department of Chemistry, University of Missouri, Columbia, Missouri 65201. 1. D. E. Troutner and R. M. Harbour, Phys. Rev. C, 4(2), 505 (1971). 2. D. E. Troutner and R. M. Harbour, J. inorg, nucl. Chem. 34,801 (1972). 3. D. C. Aumann, K. F. Flynn, J. E. Gindler and L. E. Glendenin, J. inorg, nucL Chem. 31, 1935 (1969). 4. M. F. Roche, D. E. Troutner and R. L. Ferguson, Radiochim. Acta. In press. 5. D. E. Troutner, M. Eichor and C. Pace, Phys. Rev. C, 1(3), 1044 (1970). 6. C. M. Lederer, J. M. Hollander and I. Perlman, Table of Isotopes, 6th Edn. John Wiley, New York (I 967). 11
12
D . E . T R O U T N E R and R. M. H A R B O U R
short
10.933
mCd
7.5 day
,,,.. 22 min n2Rh short
tt2 Pd =~
21 hr
m=,
IrZAg
112Cd
3"2 hr
0.005 =.- ~mCd 1.2 rain ~
H3pd ~
9
u~Cd
5.3 hr Fig. 1. Decay chains of interest.
sealed in a quartz capsule which was irradiated for 2 min in a flux of greater than 101~neutrons/cm~/sec. Two pairs of foils were irradiated. After irradiation, the catcher foils were dissolved in 50 ml of 10 M HNO~ containing - 4 mg/ml of Ag + carrier. At various times after fission, silver was precipitated from 5 ml aliquots of the solution with HCI. The silver was separated and purified as in Ref. [5] using the method of Glendenin[7]. The supernatant liquids from the separation of silver from the first three aliquots were saved, and 10 mg of Pd 2+ carrier was added to each. After 5-8 hr, palladium was separated from silver by four precipitations as palladium dimethyiglyoxime. The final precipitate was dissolved in HNO~, and 20 mg ofAg + cartier was added. After 2 days, silver was separated and purified from these solutions. Samples were collected as AgCI, mounted on flat planchets, and covered with thin polyester tape. Beta activities were measured with thin stilbene scintillation counters. As in Ref. [5], samples being measured to determine the independent yield of 112Ag were counted through a 0.06 in. aluminum absorber to reduce the 113Agactivity to the same order of magnitude as that of aa2Ag. Samples being counted to determine the H2Ag activity in equilibrium with ~12pd, as part of the measurement of the yield of H2~Pd, where also counted through a 0.10 in. aluminum absorber. After decay of ~12Ag, the absorbers were removed, and ~a2Ag was measured. Decay of a~2Agand H3Ag was followed for 2 or 3 days. Decay of "~Ag was followed for about one month. After that time, samples were transferred to a low-background scintillation counter and followed for about one month to ensure the absence of significant amounts of long-lived contaminants. These later counts were not used in the calculations.
CALCULATIONS
The use of ~13Ag as a fission monitor has been described in Ref. [5]. Although there is a shorter-lived isomer, 1-2 min, of l~3Ag, its decay was essentially complete by the time at which separation of silver from palladium was made. Therefore, the number of atoms of ~13Ag present was directly related to the number of fissions. The relation between the activities of ~2Ag and ~13Ag at the time of separation and the number of atoms of ~zPd and l~2Ag at the time of fission is 7. L. E. Glendenin, In Radiochemical Studies: The Fission Products (Edited by C. D. Coryell and N. Sugarman), National Nuclear Energy Series, Plutonium Project Record, Vol. 9, Div. IV, p. 1580. McGraw-Hill, New York ( 1951).
Fractional independent yields of m'Pd and H2Ag
13
given by [A2exp (X2t)][[A,,exp (Xmt)] = {~zh2/e,,hm}{ [N~°[Nm°] [h~/(h2--X~)] [exp (Xzt--h~t) -- 1] + [Nz"/N,,,°]}.
(1)
Subscripts 1, 2 and m refer to t~zPd, ~V'Ag and HaAg, respectively. A and represent activity and decay constant. N ~' is the number of atoms at time of fission, e is counting efficiency, and t is the interval between the mean irradiation time and time of separation of "2Ag from "2Pd. Equation (I) can be rewritten as
(la)
Y = k (NI°/N,,°)X + k (N~°IN,, °) where Y = [A2exp (h2t)]/[Amexp (h,,t)], X = [h~/(h2--ha)] [exp (X2t--h~t) -- 1], ~md k = {E~X~/E~X,.}.
A plot of Y as a function of X results in a straight line with slope k(Na°/N,, °) and intercept k(N.,_°/N~°). The intercept of this line divided by the sum of the slope and intercept reduces to [N2°/(Nt°+ Nz°)]. N~ ° represents the total number of atoms formed directly as l~2Pd or its precursors and N2° the number formed directly as ~2Ag. Therefore, the ratio [N2°/(N('+N2°)] is the fractional independent yield of ~ZAg. The activity of "2Ag in equilibrium with z~2Pd can be used as a monitor for the yield of "z'Pd, in which case [A., exp (hd+ hzr) ][[A,, exp (hpat + hpa~-) ] [A2exp (X2"r')][[Amexp (Xt,~V)]
[Nl°[N°a ] -
[(NO+N
o ~ j ~ r o 3" 2 //z~pdJ
(2)
The subscripts I, 2, rn and Pd refer to *11"Pd, "lAg, 112Agand l*2pd, respectively. Time t is the interval between mean irradiation time and the time at which Pd was separated as the dimethyl glyoxime; time r is the interval between that separation time and the time at which Ag was separated from that Pd. The time r' is the time interval between mean irradiation time and time of separation of Ag for those samples which were used to measure the total amount of 1*lAg produced. The numerator of the left-hand side of Eqn (2) is a measure of the HIAg which grew from H~"Pd and will be called (A2~%d. The denominator is a measure of the total t11Ag and will be called (A2°)tom,. Because the right side of the equation is the fractional cumulative yield of *11mpd, that yield is therefore equal to (A2~%a/ (A 2°)total. Average values of (A 2(')edand (A 2°)total were used to calculate the yield. RESULTS Data from two experiments to measure the yield of l*2Ag from 24'~Cffission are shown in Table 1. Uncertainties in Y, which range from 0.7 to 2-6% were estimated from uncertainties in the values of As and Am determined by computer analysis of the decay curves. Since these uncertainties are nearly the same for
14
D . E . T R O U T N E R and R. M. H A R B O U R Table I. Data for computation of independent yield of l~2Ag by Eqn (1)
Experiment la Ib Ic ld 2a 2b 2c 2d
t (min) 130 160 265 327 121 150 212 397
A2exp (A2t) Amexp (h,.t) (c/m) (c/m) 47,360 70,730 133,430 162,800 62,000 77,100 112,800 274,000
27,460 34,630 36,700 36,520 40,770 41,320 41,720 42,650
X
Y
0.088 0.114 0.228 0.315 0.081 0-106 0.166 0.438
1.73 2.04 3.64 4.46 1-52 1.87 2.70 6.40
all runs, k(N~°/Nm °) and k(N2°/N,n °) were calculated by unweighted least-squares analysis to be 13.33__+0.35 and 0.49±0.08, respectively. The fractional independent yield of ~12Ag calculated from these results is 0.0354±0.0058. An additional uncertainty due to uncertainties in the half-lives of l~2Ag and ll3Ag and in the time of separation is estimated to be less than 0.004 [5]. Taking the total uncertainty to be the square root of the sum of the squares of both uncertainties, the final value is 0-035 ± 0-008. Data for the fractional cumulative yield of ~11mpd are shown in Table 2. The yield calculated from these data is 0.094 ± 0.005. However, two corrections are necessary. During a similar measurement[8] of the yield of ~ " P d from 252Cf fission, palladium was separated as usual, but at a time such that all mmpd had decayed; results indicated that - 0.07% of the mAg was carried down with the palladium. For our experiments, palladium was separated at times such that 4% of the chain was present as ~Hmpd. Therefore, the calculated value is too high by a factor of ~ (0.0407/0-04). In addition, at the time of separation, some Table 2. Data for computation of fractional cumulative yield of 111"Pd by Eqn (2) I
T
T'
A2
Am
Experiment
(rain)
(rain)
(rain)
(c/m)
(c/m)
(Af)r,d
la lb lc le If 2a 2b 2c 2e 2f 2g
459 489 519
2393 2363 2356
44 63 50 8,000 7,700 30 42 24 12,200 11,200 13,200
480 655 590 1520 1600 85 144 84 630 600 670
0.062 0.070 0.064
4274 4274 469 496 516
5068 5075 5038 6912 6912 696l
0.67 0.60 0.063 0.055 0.056
0-062 Average ± 0.003 8. C. H. Pace, M. A. Thesis, University of Missouri, 1971.
(Ae°)tom~
0.68 0-66 0.67 0.66 ± 0.02
Fractional independent yields of m'~Pd and ~ZAg
15
Hlmpd was in equilibrium with muPd. Assuming that 93% of 111mpd decays to m-"Pd, it can be shown that only 93.4% of the total palladium for A = 111 at the time of separation is m'~Pd. When these two corrections are applied, the yield is lowered to 0.086 ± 0.005. In deriving Eqn (2), the slight amount of hold-up of mAg due to decay of t " " P d and moPd was neglected. The resulting error is less than 0.0005 and was ignored. Any uncertainties in the corrections for branching and incomplete separations were ignored because they are small compared to the error already shown. The yield of m"~Pd can be estimated in a manner similar to that of Aumann et al. [3] for fission of 233U and 235U. They showed that the fractional cumulative yield of HmPd from fission of Z3ZTh, 0.004, may be taken as a measure of the fraction of a short-lived mRh precursor decaying to ~l'~Pd. Subtracting this value results in a fractional independent yield of 0.083 for 1Hmpd. DISCUSSION
The independent yields of mmpd and 112Ag determined in this work are the first independent yields measured in the light mass region for fission of "49Cf. A few independent yields have been measured in the complementary mass region for fission of 24°Cf[1]. It is not possible, therefore, to make a very precise estimate of Zp, the most probable charge, for A = 112. However, the fractional cumulative yield of ~34Te has been found[l[ to be - 0.30, from which an independent yield of - 0.01 is estimated for 134Sb. If F, the average number of prompt neutrons per fission, for this mass split is - 4, 1~4Sb should be the complement of 1~ZAg. The yield reported here is therefore consistent with that of 134Te if v is somewhat higher than 4 for this mass region. The reported value of t, for thermal-neutroninduced fission of 24°Cf is 4.6±0.2[9]. If o-, the Gaussian width parameter, is assumed to be 0.56 ___0.06, Zp is 46.5 ± 0-2 [ 10]. There are a number of other pairs of chains for which independent yields of both an odd-Z nuclide and the nuclide with one-less proton have been measured. An example is 4~Nb and ~Zr from fission of 2~3U.These pairs of nuclides and their yields are shown in Table 3. Only those pairs for which the yield of the odd-Z member falls between about 0.001-0.05 have been included. These bracket the yield of U2Ag from fission of 249Cf. Two yields, those of 14°Ba and 92y from fission of 23~U, have not been considered because of the large uncertainties in their reported values. The yields of the lighter members of each pair, (~a-1)(Z- 1), are plotted on probability paper as a function of [ (Z - 1) - (H)Zp] in Fig. 2. Values of Zp for A were calculated assuming a o- of 0.56 and using the reported independent yields for 'aZ. Values of (a-~)Zv are then estimated to be equal to A(Z.) -- [A' -- (A -- 1)' ] (ZHAr), where the primes indicate masses before neutron emission, and Zp and A F are the atomic and mass number, respectively, of the fissioning nucleus. 9. Y. S. Zamyatnin, N. I. Kroshkin, A. K. Melnikov and V. N. Nefedov, Nuclear Data for Reactors, Vol. II, p. 183. IAEA, Vienna (1970). 10, A. C. Wahl, A. E. Norris, R. A. Rouse and J. C. Williams, In Second Symposium on Physics and Chemistry of Fission, p. 813. IAEA, Vienna (1969),
16
D. E. T R O U T N E R and R. M. H A R B O U R Table 3. Independent yields of product pairs AZ and (A-I~( Z - 1 ) Fission process 235U(n,f)*
AZ Yield
Nuclide
a~t" 94y '321 133I 13~s
(1"6---0"2)10 -2 (6'0 +_2) 10-2 (3"9+--0"3)10 -2 (2.5 ± 0.3) 10-2 (9.3+0.5)10 -~ ( 1"7 ± 0"4) 10-2 (1.3 ±0.3) 10-3~ (1 "4 ± 0"4) 10-3t (3 "7 -I-0" 1) 10--3~ (1'0±0"7)10-2t (3.5 ±0.8)10-~¶
a2Sr 93Sr(+ 93y) 131Te 13z'l'e 135Xe 141Ba 9zZr 135Xe 139Ba 135Xe ,~l,~pd
142La 2~U(n,f)
~Nb
136Cs 14°La 239Pu(n,f) ~49Cf(n,f)
~A-I~(Z-- I) Yield
Nuclide
136Cs l~2Ag
0.14±0.04 0.44 ±_0.04 0.124+__0-014 0"20 +--0'03 (4.04±0.01) 10-2 0'26 ± 0.05 (3.4±0.9)10-2:1: 0' 195 + 0.006§ (8 "4 ± 0 "7) l 0 -21~ 0.15±0.01§ (8.3 ±0.5)10-~¶
*Ref. [10]. tRef. [14]. SRef. [15]. §Ref. [16]. rhRef. [17]. ~Fhis work.
Values of A' and (A -- 1)' for 23~U were taken from Wahl et al. [10], and those for 233U and 2Zgpufrom Apalin et al. [1 1]. A plot such as this is a method for comparing yields of the even-Z nuclides to those of the odd-Z. If the same charge distribution applied for both odd- and evenZ products, all points would fall on the line as discussed in Ref. [12]• That they do not demonstrates the odd-even effect noted earlier[10, 12]. This comparison is not very sensitive to absolute values of A' since the difference between A' and (A -- 1)' is very similar for most pairs of adjacent chains• Neither is it very sensitive to the value chosen for tr. The point for 11mpd from fission of 249Cf is shown on the graph. Values of A' were estimated from the neutron emission results for 25~Cffission of Bowman et al. [13]. The yields are much less than those predicted by comparison with the other yields or with the line. If there is no odd-even effect, i.e. if yields can be predicted from the line, the ratio of the independent yield of 111mpdto 111gPdis - 0.6. If the odd-even effect does exist for these chains, the same ratio is - 0.4. • Aumann et al. [3] noted that the low-spin (5[2) isomer 'l'uPd appears to be favored over the higher-spin (1 1/2) ~"~Pd in fission of 23aU, 23~U and 239pu, and 11. V. F. Apalin, Y. N. Gritsyuk, I. E. Kutikov, V. I. Lebedev and L. A. Mikaelian, NucL Phys. 71, 553 (1965). 12. N. G. Runnalls and D. E. Troutner, Phys. Rev. C, 1(1), 316 (1970). 13. H. R. Bowman, J. C. D. Milton, S. G. Thompson and W. J. Swiatecki, Phys. Rev. 129(5), 2133 (1963). 14. K. Wolfsberg, Phys. Rev. 137, (4B), B 929 (1965). 15. L. H. Niece, D. E. Troutner and R. L. Ferguson, Phys. Rev. C, 1, (1), 312 (1970). 16. A. Okazaki, W. H. Walker and C. B. Bigham, Can. J. Phys. 44, 237 (1966). 17. M. Eichor and D. E. Troutner, J. inorg, nucl. Chem. 33, 1543 (197 I).
Fractional independent yieldsof mmPdand H2Ag
0.o01 -o.~0.005 ~' O-Ol
17
/
0'02
iill
I
2
[ (z-,)-~.-,,zp]
3
Fig. 2. Independent yields of nuclides ( ' I - " ( Z - 1 ) listed in Table 3 as a function of [ ( Z - 1)-(A-1)Zp] on probability paper.
pointed out that this is in disagreement with most other measurements of independent yields of isomeric pairs. Although the results of this work cannot be compared directly to their results, because A --- 111 and 112 are in the symmetric region for uranium and plutonium fission and in the asymmetric region for z49Cf fission, we also conclude that the yield of the low-spin ~11"Pdis favored.
Pergamon Press.
Printed in Great Britain
FRACTIONAL INDEPENDENT YIELDS O F 111mpd A N D "ZAg F R O M T H E R M A L - N E U T R O N - I N D U C E D FISSION O F 249Cf* D. E. T R O U T N E R ? and R. M. H A R B O U R Savannah River Laboratory, E. I. du Pont de Nemours and Company, Aiken, South Carolina 29801
(First received 3 January 1972; in revised form 27 March 1972) Abstract-The fractional independent yields of mmpd and "2Ag from thermal-neutron-induced fission of 249Cf were measured. The yields of ~''~Pd and HZAg are 0-083 ± 0.005 and 0.035 ± 0.008, respectively. The yield of "~"Pd is consistent with an isomer yield ratio for which the low-spin ground state isomer '"~Pd is favored. INTRODUCTION
EXeEmMENTS are under way in this laboratory[l, 2] to measure independent yields of products of thermal-neutron-induced fission of 249Cfin order to compare nuclear charge distribution for that process with those for thermal-neutroninduced fission of 233U and 235U. In the light mass region, it is possible to measure independent yields for the A = 11 1 and A = 112 mass chains. '12Ag is shielded by 2 1-hr l~2pd so that the independent yield of t12Ag can be measured if it is separated soon after fission, xxlmpdis not shielded, but since only - 0.4% of short-lived "~Rh decays through that isomer [3], the independent yield of 'nmpd can be calculated from the measurement of its cumulative yield. Aumann et al. [3] have reported independent yields of ""nPd from ~33U, z35U and z~gPu fission; Roche et al. [4] have reported yields of "2Ag from 233U and e35U fission; and Troutner et al. [5] have reported yields of "~Ag from 2'~2Cffission. This work reports yields of 'nmPd and H2Ag from 249Cffission. Fission product decay chains of interest are shown in Fig. 1. Half-lives and branching ratios for A = 111 are from Aumann et al. [3]. Others are from Lederer et al. [6]. EXPERIMENTAL One microgram of 249Cf was electroplated on a high-purity aluminum foil. The source was covered with another aluminum "catcher" foil, and the two foils were roiled together. The rolled foils were *Part of the information in this article was developed during the course of work under Contract AT(07-2)-1 with the U.S. Atomic Energy Commission. CAEC Faculty Research Participant for Summer 1970. Permanent address: Department of Chemistry, University of Missouri, Columbia, Missouri 65201. 1. D. E. Troutner and R. M. Harbour, Phys. Rev. C, 4(2), 505 (1971). 2. D. E. Troutner and R. M. Harbour, J. inorg, nucl. Chem. 34,801 (1972). 3. D. C. Aumann, K. F. Flynn, J. E. Gindler and L. E. Glendenin, J. inorg, nucL Chem. 31, 1935 (1969). 4. M. F. Roche, D. E. Troutner and R. L. Ferguson, Radiochim. Acta. In press. 5. D. E. Troutner, M. Eichor and C. Pace, Phys. Rev. C, 1(3), 1044 (1970). 6. C. M. Lederer, J. M. Hollander and I. Perlman, Table of Isotopes, 6th Edn. John Wiley, New York (I 967). 11
12
D . E . T R O U T N E R and R. M. H A R B O U R
short
10.933
mCd
7.5 day
,,,.. 22 min n2Rh short
tt2 Pd =~
21 hr
m=,
IrZAg
112Cd
3"2 hr
0.005 =.- ~mCd 1.2 rain ~
H3pd ~
9
u~Cd
5.3 hr Fig. 1. Decay chains of interest.
sealed in a quartz capsule which was irradiated for 2 min in a flux of greater than 101~neutrons/cm~/sec. Two pairs of foils were irradiated. After irradiation, the catcher foils were dissolved in 50 ml of 10 M HNO~ containing - 4 mg/ml of Ag + carrier. At various times after fission, silver was precipitated from 5 ml aliquots of the solution with HCI. The silver was separated and purified as in Ref. [5] using the method of Glendenin[7]. The supernatant liquids from the separation of silver from the first three aliquots were saved, and 10 mg of Pd 2+ carrier was added to each. After 5-8 hr, palladium was separated from silver by four precipitations as palladium dimethyiglyoxime. The final precipitate was dissolved in HNO~, and 20 mg ofAg + cartier was added. After 2 days, silver was separated and purified from these solutions. Samples were collected as AgCI, mounted on flat planchets, and covered with thin polyester tape. Beta activities were measured with thin stilbene scintillation counters. As in Ref. [5], samples being measured to determine the independent yield of 112Ag were counted through a 0.06 in. aluminum absorber to reduce the 113Agactivity to the same order of magnitude as that of aa2Ag. Samples being counted to determine the H2Ag activity in equilibrium with ~12pd, as part of the measurement of the yield of H2~Pd, where also counted through a 0.10 in. aluminum absorber. After decay of ~12Ag, the absorbers were removed, and ~a2Ag was measured. Decay of a~2Agand H3Ag was followed for 2 or 3 days. Decay of "~Ag was followed for about one month. After that time, samples were transferred to a low-background scintillation counter and followed for about one month to ensure the absence of significant amounts of long-lived contaminants. These later counts were not used in the calculations.
CALCULATIONS
The use of ~13Ag as a fission monitor has been described in Ref. [5]. Although there is a shorter-lived isomer, 1-2 min, of l~3Ag, its decay was essentially complete by the time at which separation of silver from palladium was made. Therefore, the number of atoms of ~13Ag present was directly related to the number of fissions. The relation between the activities of ~2Ag and ~13Ag at the time of separation and the number of atoms of ~zPd and l~2Ag at the time of fission is 7. L. E. Glendenin, In Radiochemical Studies: The Fission Products (Edited by C. D. Coryell and N. Sugarman), National Nuclear Energy Series, Plutonium Project Record, Vol. 9, Div. IV, p. 1580. McGraw-Hill, New York ( 1951).
Fractional independent yields of m'Pd and H2Ag
13
given by [A2exp (X2t)][[A,,exp (Xmt)] = {~zh2/e,,hm}{ [N~°[Nm°] [h~/(h2--X~)] [exp (Xzt--h~t) -- 1] + [Nz"/N,,,°]}.
(1)
Subscripts 1, 2 and m refer to t~zPd, ~V'Ag and HaAg, respectively. A and represent activity and decay constant. N ~' is the number of atoms at time of fission, e is counting efficiency, and t is the interval between the mean irradiation time and time of separation of "2Ag from "2Pd. Equation (I) can be rewritten as
(la)
Y = k (NI°/N,,°)X + k (N~°IN,, °) where Y = [A2exp (h2t)]/[Amexp (h,,t)], X = [h~/(h2--ha)] [exp (X2t--h~t) -- 1], ~md k = {E~X~/E~X,.}.
A plot of Y as a function of X results in a straight line with slope k(Na°/N,, °) and intercept k(N.,_°/N~°). The intercept of this line divided by the sum of the slope and intercept reduces to [N2°/(Nt°+ Nz°)]. N~ ° represents the total number of atoms formed directly as l~2Pd or its precursors and N2° the number formed directly as ~2Ag. Therefore, the ratio [N2°/(N('+N2°)] is the fractional independent yield of ~ZAg. The activity of "2Ag in equilibrium with z~2Pd can be used as a monitor for the yield of "z'Pd, in which case [A., exp (hd+ hzr) ][[A,, exp (hpat + hpa~-) ] [A2exp (X2"r')][[Amexp (Xt,~V)]
[Nl°[N°a ] -
[(NO+N
o ~ j ~ r o 3" 2 //z~pdJ
(2)
The subscripts I, 2, rn and Pd refer to *11"Pd, "lAg, 112Agand l*2pd, respectively. Time t is the interval between mean irradiation time and the time at which Pd was separated as the dimethyl glyoxime; time r is the interval between that separation time and the time at which Ag was separated from that Pd. The time r' is the time interval between mean irradiation time and time of separation of Ag for those samples which were used to measure the total amount of 1*lAg produced. The numerator of the left-hand side of Eqn (2) is a measure of the HIAg which grew from H~"Pd and will be called (A2~%d. The denominator is a measure of the total t11Ag and will be called (A2°)tom,. Because the right side of the equation is the fractional cumulative yield of *11mpd, that yield is therefore equal to (A2~%a/ (A 2°)total. Average values of (A 2(')edand (A 2°)total were used to calculate the yield. RESULTS Data from two experiments to measure the yield of l*2Ag from 24'~Cffission are shown in Table 1. Uncertainties in Y, which range from 0.7 to 2-6% were estimated from uncertainties in the values of As and Am determined by computer analysis of the decay curves. Since these uncertainties are nearly the same for
14
D . E . T R O U T N E R and R. M. H A R B O U R Table I. Data for computation of independent yield of l~2Ag by Eqn (1)
Experiment la Ib Ic ld 2a 2b 2c 2d
t (min) 130 160 265 327 121 150 212 397
A2exp (A2t) Amexp (h,.t) (c/m) (c/m) 47,360 70,730 133,430 162,800 62,000 77,100 112,800 274,000
27,460 34,630 36,700 36,520 40,770 41,320 41,720 42,650
X
Y
0.088 0.114 0.228 0.315 0.081 0-106 0.166 0.438
1.73 2.04 3.64 4.46 1-52 1.87 2.70 6.40
all runs, k(N~°/Nm °) and k(N2°/N,n °) were calculated by unweighted least-squares analysis to be 13.33__+0.35 and 0.49±0.08, respectively. The fractional independent yield of ~12Ag calculated from these results is 0.0354±0.0058. An additional uncertainty due to uncertainties in the half-lives of l~2Ag and ll3Ag and in the time of separation is estimated to be less than 0.004 [5]. Taking the total uncertainty to be the square root of the sum of the squares of both uncertainties, the final value is 0-035 ± 0-008. Data for the fractional cumulative yield of ~11mpd are shown in Table 2. The yield calculated from these data is 0.094 ± 0.005. However, two corrections are necessary. During a similar measurement[8] of the yield of ~ " P d from 252Cf fission, palladium was separated as usual, but at a time such that all mmpd had decayed; results indicated that - 0.07% of the mAg was carried down with the palladium. For our experiments, palladium was separated at times such that 4% of the chain was present as ~Hmpd. Therefore, the calculated value is too high by a factor of ~ (0.0407/0-04). In addition, at the time of separation, some Table 2. Data for computation of fractional cumulative yield of 111"Pd by Eqn (2) I
T
T'
A2
Am
Experiment
(rain)
(rain)
(rain)
(c/m)
(c/m)
(Af)r,d
la lb lc le If 2a 2b 2c 2e 2f 2g
459 489 519
2393 2363 2356
44 63 50 8,000 7,700 30 42 24 12,200 11,200 13,200
480 655 590 1520 1600 85 144 84 630 600 670
0.062 0.070 0.064
4274 4274 469 496 516
5068 5075 5038 6912 6912 696l
0.67 0.60 0.063 0.055 0.056
0-062 Average ± 0.003 8. C. H. Pace, M. A. Thesis, University of Missouri, 1971.
(Ae°)tom~
0.68 0-66 0.67 0.66 ± 0.02
Fractional independent yields of m'~Pd and ~ZAg
15
Hlmpd was in equilibrium with muPd. Assuming that 93% of 111mpd decays to m-"Pd, it can be shown that only 93.4% of the total palladium for A = 111 at the time of separation is m'~Pd. When these two corrections are applied, the yield is lowered to 0.086 ± 0.005. In deriving Eqn (2), the slight amount of hold-up of mAg due to decay of t " " P d and moPd was neglected. The resulting error is less than 0.0005 and was ignored. Any uncertainties in the corrections for branching and incomplete separations were ignored because they are small compared to the error already shown. The yield of m"~Pd can be estimated in a manner similar to that of Aumann et al. [3] for fission of 233U and 235U. They showed that the fractional cumulative yield of HmPd from fission of Z3ZTh, 0.004, may be taken as a measure of the fraction of a short-lived mRh precursor decaying to ~l'~Pd. Subtracting this value results in a fractional independent yield of 0.083 for 1Hmpd. DISCUSSION
The independent yields of mmpd and 112Ag determined in this work are the first independent yields measured in the light mass region for fission of "49Cf. A few independent yields have been measured in the complementary mass region for fission of 24°Cf[1]. It is not possible, therefore, to make a very precise estimate of Zp, the most probable charge, for A = 112. However, the fractional cumulative yield of ~34Te has been found[l[ to be - 0.30, from which an independent yield of - 0.01 is estimated for 134Sb. If F, the average number of prompt neutrons per fission, for this mass split is - 4, 1~4Sb should be the complement of 1~ZAg. The yield reported here is therefore consistent with that of 134Te if v is somewhat higher than 4 for this mass region. The reported value of t, for thermal-neutroninduced fission of 24°Cf is 4.6±0.2[9]. If o-, the Gaussian width parameter, is assumed to be 0.56 ___0.06, Zp is 46.5 ± 0-2 [ 10]. There are a number of other pairs of chains for which independent yields of both an odd-Z nuclide and the nuclide with one-less proton have been measured. An example is 4~Nb and ~Zr from fission of 2~3U.These pairs of nuclides and their yields are shown in Table 3. Only those pairs for which the yield of the odd-Z member falls between about 0.001-0.05 have been included. These bracket the yield of U2Ag from fission of 249Cf. Two yields, those of 14°Ba and 92y from fission of 23~U, have not been considered because of the large uncertainties in their reported values. The yields of the lighter members of each pair, (~a-1)(Z- 1), are plotted on probability paper as a function of [ (Z - 1) - (H)Zp] in Fig. 2. Values of Zp for A were calculated assuming a o- of 0.56 and using the reported independent yields for 'aZ. Values of (a-~)Zv are then estimated to be equal to A(Z.) -- [A' -- (A -- 1)' ] (ZHAr), where the primes indicate masses before neutron emission, and Zp and A F are the atomic and mass number, respectively, of the fissioning nucleus. 9. Y. S. Zamyatnin, N. I. Kroshkin, A. K. Melnikov and V. N. Nefedov, Nuclear Data for Reactors, Vol. II, p. 183. IAEA, Vienna (1970). 10, A. C. Wahl, A. E. Norris, R. A. Rouse and J. C. Williams, In Second Symposium on Physics and Chemistry of Fission, p. 813. IAEA, Vienna (1969),
16
D. E. T R O U T N E R and R. M. H A R B O U R Table 3. Independent yields of product pairs AZ and (A-I~( Z - 1 ) Fission process 235U(n,f)*
AZ Yield
Nuclide
a~t" 94y '321 133I 13~s
(1"6---0"2)10 -2 (6'0 +_2) 10-2 (3"9+--0"3)10 -2 (2.5 ± 0.3) 10-2 (9.3+0.5)10 -~ ( 1"7 ± 0"4) 10-2 (1.3 ±0.3) 10-3~ (1 "4 ± 0"4) 10-3t (3 "7 -I-0" 1) 10--3~ (1'0±0"7)10-2t (3.5 ±0.8)10-~¶
a2Sr 93Sr(+ 93y) 131Te 13z'l'e 135Xe 141Ba 9zZr 135Xe 139Ba 135Xe ,~l,~pd
142La 2~U(n,f)
~Nb
136Cs 14°La 239Pu(n,f) ~49Cf(n,f)
~A-I~(Z-- I) Yield
Nuclide
136Cs l~2Ag
0.14±0.04 0.44 ±_0.04 0.124+__0-014 0"20 +--0'03 (4.04±0.01) 10-2 0'26 ± 0.05 (3.4±0.9)10-2:1: 0' 195 + 0.006§ (8 "4 ± 0 "7) l 0 -21~ 0.15±0.01§ (8.3 ±0.5)10-~¶
*Ref. [10]. tRef. [14]. SRef. [15]. §Ref. [16]. rhRef. [17]. ~Fhis work.
Values of A' and (A -- 1)' for 23~U were taken from Wahl et al. [10], and those for 233U and 2Zgpufrom Apalin et al. [1 1]. A plot such as this is a method for comparing yields of the even-Z nuclides to those of the odd-Z. If the same charge distribution applied for both odd- and evenZ products, all points would fall on the line as discussed in Ref. [12]• That they do not demonstrates the odd-even effect noted earlier[10, 12]. This comparison is not very sensitive to absolute values of A' since the difference between A' and (A -- 1)' is very similar for most pairs of adjacent chains• Neither is it very sensitive to the value chosen for tr. The point for 11mpd from fission of 249Cf is shown on the graph. Values of A' were estimated from the neutron emission results for 25~Cffission of Bowman et al. [13]. The yields are much less than those predicted by comparison with the other yields or with the line. If there is no odd-even effect, i.e. if yields can be predicted from the line, the ratio of the independent yield of 111mpdto 111gPdis - 0.6. If the odd-even effect does exist for these chains, the same ratio is - 0.4. • Aumann et al. [3] noted that the low-spin (5[2) isomer 'l'uPd appears to be favored over the higher-spin (1 1/2) ~"~Pd in fission of 23aU, 23~U and 239pu, and 11. V. F. Apalin, Y. N. Gritsyuk, I. E. Kutikov, V. I. Lebedev and L. A. Mikaelian, NucL Phys. 71, 553 (1965). 12. N. G. Runnalls and D. E. Troutner, Phys. Rev. C, 1(1), 316 (1970). 13. H. R. Bowman, J. C. D. Milton, S. G. Thompson and W. J. Swiatecki, Phys. Rev. 129(5), 2133 (1963). 14. K. Wolfsberg, Phys. Rev. 137, (4B), B 929 (1965). 15. L. H. Niece, D. E. Troutner and R. L. Ferguson, Phys. Rev. C, 1, (1), 312 (1970). 16. A. Okazaki, W. H. Walker and C. B. Bigham, Can. J. Phys. 44, 237 (1966). 17. M. Eichor and D. E. Troutner, J. inorg, nucl. Chem. 33, 1543 (197 I).
Fractional independent yieldsof mmPdand H2Ag
0.o01 -o.~0.005 ~' O-Ol
17
/
0'02
iill
I
2
[ (z-,)-~.-,,zp]
3
Fig. 2. Independent yields of nuclides ( ' I - " ( Z - 1 ) listed in Table 3 as a function of [ ( Z - 1)-(A-1)Zp] on probability paper.
pointed out that this is in disagreement with most other measurements of independent yields of isomeric pairs. Although the results of this work cannot be compared directly to their results, because A --- 111 and 112 are in the symmetric region for uranium and plutonium fission and in the asymmetric region for z49Cf fission, we also conclude that the yield of the low-spin ~11"Pdis favored.