Journal of Nuclear and Radiochemical Sciences, Vol. 3, No. 2, pp. 7-12, 2002

ArticlesMost Probable Charge of Fission Products in Proton-Induced Fission of 238U and 232Th
D. Kaji,a S. Goto,a M. Fujita,b T. Shinozuka,b M. Fujiokab, and H. Kudo*, aaDepartment of Chemistry, Faculty of Science, Niigata University, Niigata 950-2181, Japan
Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japanb

Received: October 20, 2002; In Final Form: December 6, 2002
The charge distributions of fission products in proton-induced fission of 238U and 232Th were measured in a widemass range. The most probable charges lay on the proton-rich side in the light fragment region and on the protondeficient side in the heavy one compared with the unchanged charge distribution hypothesis. This result implies
that the charge polarization occurs in the fission process. The charge polarization was examined with respect tothe ground-state Q values. The estimations by the Q values fairly well reproduced the experimental most probablecharges. These results suggest that the fission path to the most favorable charge division may go through the mostenergetically favorable path at scission point.

1. INTRODUCTION
Since nuclear fission was discovered, many experiments
have been accumulated to reveal the mechanism of fission
process. However, no theory has been successful in a complete
elucidation of those data. The nuclear charge division of afissioning nucleus between two fragments results in a charge
distribution of fission products. Accordingly, the charge distribution of fission products provides important information about
nuclear fission. Many experimental studies have been carriedout to determine the charge distribution in various fissioning
systems. Wahl et al.1 proposed that the charge dispersion offission products in low-energy fission is empirically well represented by a normal Gaussian function which is characterized by
two parameters, the most probable charge and the charge
dispersion width. These parameters have been discussed forrevealing the mechanism of nuclear charge division during
fission process. There are some suggestions about the dependence of the width parameter on the excitation energies,
fissioning systems, and mass chains.2−6 Baba et al.6 reported
that the width of the charge dispersion changes at some incident energy in proton-induced fission of 238U. But the widthparameter in α-induced fission of 232Th exhibits no dependence
on the excitation energy and is about the same with that in thethermal-neutron-induced fission of 235U.2 As for the most probable charge, a few hypotheses have been proposed so far.
According to the unchanged charge distribution (UCD) model,
primary fission fragments have the same proton-to-mass ratio
as in a fissioning nucleus. If the charge in the fissioning
nucleus is distributed homogeneously and the redistribution of
the charge does not occur in the course of fission process,charge densities of fission fragments will be the same as that of
the fissioning nucleus. In this sense, the UCD hypothesis isstraightforward and permits a simple method to estimate themost probable charge. 7−9 The equal charge displacement(ECD) model states that the most probable charges for one
fission fragment and for its complementary fragment lie anequal number of charge units away from the β stability line.
This ECD hypothesis was empirically suggested by Glendenin
et al.10 and seems to reproduce the most probable charge in low
excitation fission.1, 11 In the minimum potential energy (MPE)model, a nucleonic redistribution occurs such that a minimum*Corresponding author. E-mail: hkudo@sc.niigata-u.ac.jp. FAX:
+81-25-262-6171.

in the sum of the nuclear potential and Coulomb repulsion
energy is attained and fission proceeds along the minimum
potential energy surface. This MPE hypothesis was proposedby Present12 and found to describe the fission of 197Au with 112
MeV 12C rather well.13 However, none of these postulates havesucceeded in becoming a general rule.
Kudo et al.14 examined the charge polarization in 24 MeV
proton-induced fission of 238U and concluded that the experimental most probable charge was fairly well reproduced by theestimation from production Q values. And it is also reported
that some structure in the charge polarization was recognizedin the vicinity of A = 142 and they attributed it to the deformed
shell, N = 86 − 88. In order to see whether these findings are
the universal evidence, the charge distribution of fission products was measured in the systems of proton-induced fission of238
U and 232Th at various incident energies. The charge distribution is discussed from the view point of charge polarization.
2. EXPERIMENTAL
The experiments were performed by using an azimuthally
varying field (AVF) cyclotron and an ion-guide isotope separator on-line (IGISOL) at the Cyclotron and Radioisotope
Center in Tohoku University. The Tohoku IGISOL iscomposed of an ion-guide chamber, a mass separator, and atape transport system. The details of the Tohoku IGISOL
system are described in References 14−16. The ion-guidechamber consists of an ion-guide vacuum chamber and an ionguide target chamber. The target in the ion-guide target
chamber consisted of two self-supported foils of 238U and 232Th
in thickness of 20 and 100 mg/cm 2 , respectively. The twotargets kept the angle of 45˚ and 135˚ with respect to the incident beam direction. The bombarding energies were, 13, 18,
and 24 MeV for 238U and 13, 20, and 24 MeV for 232Th at the
point between the two target foils. The data for light fragment
mass region in the system of 24 MeV proton-induced fission of238
U were re-obtained because of large errors in Reference 14.
The beam energy losses in the window foils and target material
were evaluated from the range-energy relationship. 17 The
beam intensity was monitored by a Faraday cup equipped witha current integrator, and was checked at both the entrance andexit points of the target chamber. The beam current was typically about 2 µA on target.
Mass-separated fission products were collected on analuminized Mylar tape. The mass calibration was performed at© 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 12/28/2002

8

Kaji

J. Nucl. Radiochem. Sci., Vol. 3, No. 2, 2002

The obtained radioactivities were converted to either cumulative yields or independent yields as follows. After the end ofcollection, the radioactivities of the members of a given decay
chain at time t are given by
A1 = A10 exp(−λ 1t)(1)

λ2
A2 = A10{exp(−λ 1t) − exp(−λ 2t)} + A20 exp(−λ 2t) (2)λ2− λ 1...
where A10, A20, . . . are the activities at the end of collection.
The obtained activities at the end of collection were converted
to corresponding cross sections by correcting for saturation
conditions. The next differential equations hold during theperiod of collection.

(3)

dN1
= N0σ iε iφ + Ni−1λ i−1 − Ni λ idt(4)

i = 2, 3, . . .
where N0 is the number of target nuclei, σ i is the cross section,
ε i is the transport efficiency in IGISOL, and φ is the proton
beam flux. These differential equations can be easily solved
and the relative yields in the form of N0σ iε i are obtained bysubstituting Ai0's in eqs 1 and 2 for the resulting equations.
The transport efficiency may be affected by both the operating
conditions of the mass separator and the chemical properties of
elements. But the differences in transport efficiencies can beeliminated by taking an appropriate ratio of the obtained yields
as described in Reference 14. The measured nuclides and thenuclear data used for the analysis are summarized in Table 1
with quated References 18−54.
Empirically, the charge dispersion of fission products has
been well represented by a Gaussian function.1 The theoretical
calculations with the asymmetric two-center shell model55, 56
and the statistical model by Fong et al.57 also give a Gaussianfunction. At low energy fission, a certain deviation from theGaussian curve was observed because of an odd-even effect.4
But in a charged-particle-induced fission, the odd-even effectis presumed not to appear because high excitation energy offissioning nuclei washes out the effect. It is reported that the
odd-even effect is reduced when an extra 3 MeV is added tothe system of neutron-induced fission of 238U.58 Therefore, theanalysis of the charge dispersion was performed assuming thefollowing function
P(A, Z) =−(Z − ZP)2
P(A)
exp
,
C
πC

678

3. RESULTS AND DISCUSSION

dN1= N0σ 1ε 1φ − N1λ 1
dt123

A = 16, 32, and the mass numbers of interest. The mass
resolving power M/dM was determined by measuring the γ -rayactivities of fission products at each mass number. The typicalmass resolving power was about 150.
The radioactivities of fission products collected on the tapewere identified and determined by γ -ray spectrometry. Twohigh-purity germanium (HPGe) detectors coupled with 4096channel pulse height analyzers were used for the detection ofγ -radiations. One detector was positioned just behind thecollecting point of transported fission products and used for themeasurement of accumulating radioactivities. The other was
set about 38 cm away from the first detector along the collection tape and used for a growth and decay measurement. It
took 0.6 s to move the collection tape between the two
measuring positions. The time interval of the tape transportation was varied from 5 s to 30 min according to the half-livesof the nuclides of interest. In order to reduce statistical errors,
the counting cycle was repeated appropriate times. In order toavoid the counting loss from the photopeak through coincidence summing, the detectors were placed at positions which
are more than 2 cm away from the source positions. The
typical energy resolutions (FWHM) of the two HPGe detectors
were 2.1 and 2.8 keV for 1332 keV γ -ray of 60Co, respectively.
The energy and efficiency calibrations for γ -ray energy range
from 50 to about 2500 keV were performed using a set of γ ray reference sources (133Ba, 57Co, 137Cs, 54Mn, 22Na, and 60Co)
of Amersham, a mixed radionuclide γ -ray reference sources ofAmersham (containing 108Cd, 57Co, 139Ce, 208Hg, 113Sn, 85Sr,
137
Cs, 88Y, and 60Co), and handmade sources of 56Co and of152
Eu. The γ -ray spectral data were recorded event by event
together with time information.
The charge distribution of fission products in 13 and 20
MeV proton-induced fission of 232Th was also measured by adirect collection technique. In this measurement, 232Th targets
were prepared by electrodeposition onto a 6.7 mg/cm 2 thickaluminum backing foil from an isopropanol solution. The
thickness of each target was about 500 µg/cm2 and the precise
amount of 232 Th was determined by α spectrometry with asurface barrier detector of a known counting efficiency. The
obtained 232Th targets were wrapped with 6.7 mg/cm2 thickaluminum cover foils for a complete collection of fission products. Two of the wrapped targets were stacked for irradiations.
Irradiations were carried out with the proton beams from the
JAERI tandem Van de Graaff accelerator. The proton energy
in each target was calculated from the range-energy relationship. 17 Beam intensity was monitored with a Faraday cup
during the irradiation. The beam intensity from the accelerator
was in the range of 0.3 to 0.4 µA. The irradiation duration was
5 min for short-lived products and 30 min for long-lived ones.
The radioactivities of fission products were identified anddetermined by γ -ray spectrometry.

(5)

where P(A, Z) is the independent yield of the nuclide with an
atomic number Z and a mass number A, P is the chain yield of
the mass chain A, ZP is the most probable charge, and C is thewidth parameter of the charge dispersion.
There are several indications about the dependence of thewidth parameter on the excitation energies, fissioning systems,
and mass chains. Baba et al.6 reported that the charge dispersion width in proton-induced fission of 238U changes with theincident-proton energy. On the other hand, there are also
contrary evidences that the width parameter is independent of
the excitation energies. For example, McHugh and Michel2
indicated that the fractional yield data of 135I, 135Xe, and 135Cs
obtained in α-induced fission of 232Th with the various excitation energies up to 39 MeV are well represented with a single
charge dispersion curve. The value of C that best fits all energies was 0.95 ± 0.05. This value was quite similar to thevalue, C = 0.94 ± 0.15, determined in thermal-neutron-induced
fission of 235U.3, 4 Since the same compound nucleus (236U*)
was produced in both systems, the above results indicate that asingle charge dispersion function is maintained through a wide
range of excitations. Umezawa 59 reported that the charge
dispersion is identical for all investigated mass chains obtainedin the system of proton-induced fission of 238 U. Besides,
Blann13 has reported that the width of the charge dispersion
curve is 0.9 ± 0.1 in the fission of gold with 112 MeV 12C ions.
These results suggest that the width of the charge dispersion is
identical for any mass chains in various fissioning systems. In
the present analysis, the width parameter is assumed to be
independent of excitation energies, mass numbers, andfissioning systems investigated. If more than two same Z
nuclides of mass number, A, are observed at different protonenergies, E 1 and E 2 , the difference of the most probablecharges between E1 and E2 can be expressed as follows

Most Probable Charge of Fission Products

J. Nucl. Radiochem. Sci., Vol. 3, No. 2, 2002

9

TABLE 1: Nuclear Data Used for the Analysis Only a Main Characteristic Gamma Ray of Each Nuclide is Listed
Nuclide
82

Ge
82b
As
82a
As
84
As
84
Se
84m
Br
84g
Br
88
Se
88
Br
88
Kr
88
Rb
89
Kr
89
Rb
90
Br
90
Kr
90m
Rb
90g
Rb
91
Kr
91
Rb
91
Sr
92
Kr
92
Rb
92
Sr
92
Y
93
Kr
93
Rb
93
Sr
94
Rb
94
Sr
95
Sr
95
Y
97
Sr
97m
Y
97g
Y
99
Y
99
Zr

T1/2

Eγ /keVIγ /% Ref. typea) Nuclide

4.6 s
1091.9 90 [18] C
13.6 s343.5 57.6 [18] I
19.1 s654.4 15.1 [18] I
5.5 s
1455.1 49 [19] C
3.1 min
408.2 100 [19] I
6 min
424
100 [19] I
31.8 min 1897.6 14.7 [19] I
1.52 s159.2 10.6 [20] C
16.5 s775.3 63 [20] I
2.84 h
196.3 26 [20] I
17.78 min 1836
21.4 [20] I
3.15 m586
16.6 [21] C
15.15 m1248.1 42.6 [21] I
1.92 s707.1 38 [22] C
32.3 s1118.7 36.2 [22] I
4.3 min
824.2
8.64[22] I
2.6 min
831.7 27.8 [22] I
8.57 s108.8 43.5 [23] C
58.4 s93.6 33.7 [23] I
9.52 h1024.3 33.4 [23] I
1.85 s142.4 66 [24] C
4.5 s
814.7
8 [24] I
2.71 h1383.9 90 [24] I
3.54 h934.5 13.9 [24] I
1.29 s266.8 20.3 [25] C
5.7 s
986.2
4.43[25] I
7.423 min 590.3 65.7 [25] I
2.702 s836.9 87.1 [26] C
75.1 s1427.6 94.2 [26] I
25.1 s
685.9 24 [27] C
10.3 min954.2 19 [27] I
0.42 s1905
28 [28] C
1.23 s161.4 70.7 [28] I
3.5 s
3287.7 18.1 [28] I
1.47 s121.8 43.8 [29] C
2.1 s
469.1 55.2 [29] I

99m

T1/2

Eγ /keVNb 2.6 min
253.3
99g
Nb 15 s137.7
101
Mo 14.61 m
590.9
101
Tc 14.22 m
306.8
102
Mo 11.2 min
211.7
102m
Tc 4.35 min
628.1
102g
Tc 5.28 s
475.1
105
Tc
7.6 m
143.3
105
Ru 4.44 h
469.7
107
Ru 3.75 m
194.1
107
Rh 21.7 m
302.8
108
Tc
5.17 s242.2
108
Ru 4.55 min (434.1
108b
Rh 6 min581.1
108a
Rh 16.8 s
434.1
116
Pd 12.72 s
114.7
116m
Ag 10.4 s
1028.9116g
Ag 2.68 min
699.3
116m
In 2.18 s
162.4
116m
In 54.15 min
416.9
119
Ag 2.1 s
626.4
119m
Cd 2.2 min 1025
119g
Cd 2.69 min
292.9
120
Cd 50.8 s(1172.5120c
In 47.3 s
89.9120b
In 46.2 s
863.7
120a
In 3.08 s
1172.5121
Ag 0.72 s
341.6
121m
Cd 8.3 s
1020.9121g
Cd 13.5 s
324.2
121g
In 23.1 s
925.6
122
Cd 5.24 s
1140.3122c
In 10.8 s
407.3
122b
In 10.3 s
1190.3122a
In 1.5 s
1013.1124
Cd 0.9 s
179.9Iγ /% Ref. typea) Nuclide
3.71[29] I
90.6 [29] I
15.66[30] C
88 [30] I
3.82[22] C
25.2 [22] I
6.25[22] I
15.7 [31] C
17.55[31] I
9.85[32] C
66 [32] I
82.4 [33] C43.)b) [33] I
59 [33] I
43 [33] I
88 [22] C
30 [22] I
10.9 [22] I
36.6 [22] I
26.2 [22] I
10.7 [22] C
25 [22] I
41 [22] I20.)b) [34] C
77.6 [34] I
32.5 [34] I
19 [34] I
30.9 [35] C
18.9 [36] I
49.5 [36] I
87 [22] I
39 [37] C
7.8 [37] I
20 [37] I
2.7 [37] I
49.9 [38] C

T1/2

Eγ /keV124b

In 2.4 s
124a
In 3.17 s
126Cd 0.51 s
126b
In 1.45 s
126a
In 1.5 s
128b
In 0.9 s
128a
In 0.9 s
128m
Sn 6.5 s
128g
Sn 59.1 min
128m
Sb 10.4 min
128g
Sb 9.01 h
130m
Sn 1.7 min
130g
Sn 3.72 min
130b
Sb 6.3 min
130a
Sb 40 min
130m
I
9 min
130g
I 12.36 h
132
Sn 40 s132b
Sb 2.8 min
132a
Sb 4.2 min132
Te 78.2 h
132m
I 83.6 min
132
g
2.3 h
134
Te 41.8 min
134m
I
3.69 min134g
I 52.6 min
135
Te 19 s135
I
6.57 h135m
Xe 15.29 min
135g
Xe 9.14 h
136
Te 17.5 s
136b
I 46.9 s
136a
I 83.4 s136
Cs 13.16 d
138
I
6.41 s138
Xe 14.08 min

Iγ /% Ref. typea) Nuclide1359.9 38.8 [38] I
997.8 21.1 [38] I
260.1 89.6 [39] C
111.8 88 [39] I
969.6 14.9 [39] I
1867
32.3 [40] C
1168.8 50.3 [40] C
831.5 100 [40] I
482.3 58 [40] I
314
91.6 [40] I
526.5 45 [40] I
144.9 34 [22] C
192.5 71 [22] I
1017.5 30 [22] I
330.9 78 [22] I
536.1 16.7 [22] I
668.5 96.1 [22] I
340.8 43.2 [22] C
989.6 15 [22] I
1041.5 18 [22] I
228.2 88.1 [22] I
599.8 13.2 [22] I
522.7 16.1 [22] I
210.5 22.5 [41] C
271.9 79 [41] I
1072.5 15 [41] I
603.5 37 [42] C
1260.4 28.9 [42] I
526.6 80.5 [42] I
249.8 90.2 [42] I
334
18.8 [43] C
381.4 99.8 [43] I
1321.1 24.8 [43] I
818.5 99.7 [43] I
588.8 60 [44] C
258.4 31.5 [44] I

T1/2

138m

Cs 2.9 min
138g
Cs 32.2 min139
Xe 39.68 s
139Cs
9.27 min139
Ba
1.38 h140
Xe 13.6 s
140
Cs 63.7 s141
Xe 1.73 s
141
Cs 24.94 s
141
Ba 18.27 min
142
Ba 10.6 min142
La 91.1 min
143Cs
1.78 s143
Ba 14.5 s
143
La 14.2 min143
Ce 33 h144
Ba 11.5 s
144
La 40.8 s
145
Cs
0.594 s145
Ba
4.31 s145
La 24.8 s
145Ce
3.01 min
146
Ba
2.2 s
146m
La 10 s146g
La 6.27 s
146
Ce 13.52 min
146
Pr 24.15 min
147
La
4.48 s147
Ce 56.4 s
148
La
1.05 s148
Ce 56 s148b
Pr 2 min148a
Pr 2.27 min
149
Pr
2.26 min149
Nd 1.72 h

Eγ /keVIγ /% Ref. typea)

191.7
1009.8218.61283.2
165.8
805.5
908.4
909.4
561.6
190.3
255.3
641.3
195.5
211.5
643.7
293.3
388.2
397.4
175.4
96.6
355.8
724.2
251.2
409.9
258.5
316.7
453.9
117.6
268.7
158.5
269.5
450.8
301.7
138.5
211.3

15.4 [44] I
29.8 [44] I
52 [45] C
7.7 [45] I
23.8 [45] I
20 [46] C
7.89[46] I
13.3 [47] C
4.7 [47] I
47 [47] I
21.1 [48] C
47.4 [48] I
12.6 [49] C
24.9 [49] I
1.55[49] I
42.8 [49] I
13.5 [50] C
94.3 [50] I
15.6 [51] C
7.73[51] I
3.83[51] I
58.9 [51] I
18 [52] C87 [52] I
76 [52] I
51 [52] I
48 [52] I
15 [22] C
5.5 [22] I
56 [53] C
17 [53] I
50 [53] I
61 [53] I
1.02[54] C
25.9 [54] Ia) C: cumulative yield, I: independent yieldb) Used daughter activitydZP (Energy) ≡ ZP(E1) − ZP(E2)6565(a) 238U+p (24 MeV)

60

55

55

Similarly, if more than two identical nuclides at different
targets, 232Th and 238U, are observed, the difference can be
expressed by the following function

50

50

45

45

40

40

35

35

123

60

123

PE1(A, Z1) · PE2(A, Z2)C=
ln P (A, Z ) · P (A, Z ) , (6)2(Z1 − Z2)
E1
2
E2
1

dZP (Target) ≡ ZP(Th) − ZP(U)

30

123

123

PTh(A, Z1) · PU(A, Z2)C
ln P (A, Z ) · P (A, Z ) , (7)2(Z1 − Z2)
Th
2
U
1

As a result, the dZP (Energy) and dZP (Target) were given in aunit of the width parameter C. So far, the most probablecharge was precisely reported in the 24 MeV proton-induced
fission of 238U,14 where the value of the width parameter was
given as 1.00 ± 0.12. The most probable charges for othersystems were evaluated by converting the obtained data usingeqs 6 and 7. The resulting information is based on their differences, but the transport efficiency in IGISOL is eliminated. In
the course of the analysis, the width parameter was intentionally varied from 0.90 to 1.10, but the most probable charges
were almost unaffected with variation of the width parameter.
In the case of the direct collection technique, 13 and 20 MeV
proton-indeced fission of 232 Th, the most probable charges
were directly obtained using a fixed width parameter, C = 1.00.
Mass distributions calculated with these parameters wellagreed with reported ones. 60 Therefore, the most probablecharges obtained in the present work can be regarded asreasonable ones. The evaluated most probable charges areplotted against the product mass number in Figure 1. The
linear broken lines depicted in the figure show the most probable charge expected from the unchanged charge distribution(UCD) hypothesis. According to the UCD hypothesis, theprimary fission fragments have the same proton-to-mass ratioof the fissioning nucleus.

80

100

120

140

160

65
60

ZP

=

30

(b) 238U+p (18 MeV)

60
55

50

50

45

45

40

40

35

35
80

100

120

140

160

30

(c) 238U+p (13 MeV)

60

55

55

50

50

45

45

40

40

35

35

30

100

120

140

160

(e) 232Th+p (20 MeV)

80

100

120

140

160

65

65
60

80

65

55

30

(d) 232Th+p (24 MeV)

80

100

120

140

160

30

A

(f) 232Th+p (13 MeV)

80

100

120

140

160

Figure 1. The most probable charge, ZP, plotted as a function of
product mass number, A. The linear broken line shows the most probable charge expected from the unchanged charge distribution hypothesis.

10

Kaji

J. Nucl. Radiochem. Sci., Vol. 3, No. 2, 2002
239

The fissioning nuclei were assumed to be Np for the 13
MeV p + 238U system, 237Np for the 18 and 24 MeV p + 238U
systems,61 233Pa for the 13 MeV p + 232Th system, and 231Pa forthe 20 and 24 MeV p + 232Th systems.60 The most probablecharges gradually increase with an increase of the fragment
mass number in all the systems. It is necessary to elucidate
masses of primary fragments for the precise comparison. The
primary fragment mass can be estimated by adding the numberof emitted neutrons, ν , but they were reported only in alimmited number of systems. In the present analysis, thecorrection for the emitted neutrons was performed by using thedata of 12.7, 22.0, and 25.5 MeV62, 63 for the 13, 18, and 24
MeV p + 238U systems, respectively. And for the 13, 20, and
24 MeV p + 232Th systems, the data of 13.2, 14.7, and 14.7
MeV,64 respectively, were used. The comparison revealed thedistinct deviation of the experimental Z P from the charge
expected from UCD, ZUCD. The deviations of ZP from ZUCD are
displayed as a function of the fragment mass number, A', inFigure 2. As seen in the figure, ZP's mainly lay on the protonrich side in the light fragment mass region and on the neutronrich side in the heavy mass region in all the systems. These
results imply that the charge polarization occurs in fission
process. The nuclides of higher charge density are formed in
the light fragment region, while those of lower charge density
are produced in the heavy fragment region compared with the
UCD hypothsis. As the neutron-to-proton ratio of stable nuclei
increases with an increase of the mass number, the present
results suggest that the nuclear stability of fission fragments
reflects the charge polarization in fission.
The deviation of ZP of the complementary fragment fromthe corresponding ZUCD should be the same but with an opposite sign because the probability of charged particle emission isquite small in low energy fission. This can be ascertained bysuperimposing the complementary light fragments to the heavy
ones. The results are shown in Figure 3, where the primary
2

2

1

1

0

0

-1

-1
-2

(a) 238U+p (24 MeV)

2

100

120

140

3

3

2

2

1

1

-2

(b)

238

100

120

140

-2

-2

2

100

120

140

3

3

2

2

1

1

0

0

-1

-1

140

150

160

232

Th+p (20 MeV)

100

120

140

(b) 238U +p(18 MeV)

2

80

100

120

140

-1
Z Qgg

120

130

140

150

160

-3

120

130

140

150

3

(c) 238U+p(13 MeV)
Z=50

N=82 N=86-88 N=502(f) 232Th+p(13 MeV)
N=82 N=86-88 N=50

1
0

-1

-1

-2

-2

Z Qgg

(f) 232Th+p (13 MeV)
80

160

N=82 N=86-88 N=50

Z Qgg

100

120

140

120

130

140

150

160

-3

120

130

140

150

Ah'

-3

-3

(e) 232 Th+p(20 MeV)

Z=50

-3

-2

150

-2

0

(c) 238U+p (13 MeV)

140

0
Z Qgg

1

-2

130

1

-1

2

120

Z=50

N=82 N=86-88 N=50

3

160

-3
3

0

-3

80

160

130

1

-3
80

120

3

160

Z Qgg

-1

-2

(e)

-3

N=82 N=86-88 N=50

0

Z=50

-2

U+p (18 MeV)

Z=50

1

-1

-3

(d) 232Th+p (24 MeV)

-1

-1(d) 232 Th+p(24 MeV)

Z Qgg

0

0

N=82 N=86-88 N=50

0

80

160

2
Z=50

Z P - Z UCD803(a) 238 U+p(24 MeV)

1

-3

-3

ZP-Z UCD

3

3

3

-2

heavy fragment mass number, Ah', is taken as an abscissa. The
deviations of the complementary fragments are nearly consistent. These results indicate that the most probable charge is
not seriously affected by neutron emission from fission fragments.
For a given mass split, many combinations of charge division are possible. The most probable charge was examined inconnection with the most energetically favorable combination.
The most energetically favorable charge, ZQgg, was estimatedby the ground-state Q value as in Reference 14. In this estimation, the Q value was defined as the difference between themass of the fissioning nucleus and the ground-state masses offission fragments.65, 66 The results are shown in Figure 3 bysolid curves. The experimental ZP seems to agree with theevaluated ZQgg in the systems of 18 MeV protons on 238U, 24
MeV protons on 238U, and 20 MeV protons on 232Th. But theagreement between the experimental and evaluated ZP's is notgood in the case of other systems showed in Figures 3(c), 3(d),and 3(f). The data in Figure 3(c) and 3(f) are for the lowest
proton-energy studied in the present work. The effect such asshell effect, which is emphasized in low energy region, may
influence of the most probable charge. For example, in
A = 135 the charge of nuclide with N = 82 shell is larger thanZ Q g g . As the yield of nuclide with N = 82 shell may beenhanced, the most probable charge increases and consequently deviates from ZQgg. The same kind of explanation isapplicable to the disagreement at other nuclear shell anddeformed shell, N = 86-88, which is suggested by Wilkins etal.67 The existence of the nuclear shell effect in this energy
region was also reported in the isomeric yield ratio measurement.68 On the other hand, the reason why ZP dose not seem toagree with ZQgg in the 24 MeV proton + 232Th system is probably because of the inadequate correction of emitted neutrons.

160

A'
Figure 2. Deviation of ZP from ZUCD plotted versus primary fragment
mass number, A'.

Figure 3. Same as Figure 2, but folded at the symmetric mass withsuperimposing the complementary light fragments. The light mass
products are indicated by colsed symbols. The solid curve is the resultof the estimation by using production Q values.

Most Probable Charge of Fission Products

J. Nucl. Radiochem. Sci., Vol. 3, No. 2, 2002

11

232

1

ZP - Z UCD

0

Z EX

-1

ZQgg
-2
-3

120

130

140

150

160

Ah'
Figure 4. Comparison of ZQgg estimated from ground state masses
with Z EX estimated by considering deformation at scission for thefissioning nucleus of 239Np.

Because the number of the emitted neutrons were not reported
for 24 MeV proton-induced fission of 232Th, we used the dataof the 14.7 MeV protons on 232Th. The dependence of ν on the
excitation energy was demonstrated by Bishop et al.62 and by
Strecker et al.,63 and according to them, there are two striking
features. The first one is the disappearance of the sawtooth
structure with increasing excitation energy. The other one is
the tendency for ν to increase more rapidly with an increase of
excitation energy for heavier fragment than for the light fragment, even in the mass region away from closed shells. If thedependence of ν on excitation energy for the 232Th + p system
is similar to that for the 238U + p system, Z P is expected toapproach to ZQgg in Figure 3(d).
If the shape of the β stability vs. nuclear charge curve at agiven mass number is about the same for the complementaryfragment pair, the maximum energy is available for the pair at
which the differences between the most stable charge and thefragment charge are the same. In this sense, the ECD modelhas the similar meaning as the present consideration by the Q
values.
It is generally considered that fission fragments are highly
deformed at scission point. Accordingly the masses at scission
point are expected to be different from the ground-state masses
and the explanation by the ground-state masses seems to be
unrealistic. As the deformation at scission point is not wellunderstood, two-spheroid model by Quentin69 was assumed forscission point configuration. Assuming that the degrees of thedeformation of complementary fragments are the same andthat the kinetic energy, TKE, of fission fragments is purely
originated from the Coulomb repulsion between two fragments
at scission, the deformation energy at scission was calculated
after the method of Brossa et al. 7 0 The values of TKE
presented by Strecker et al.63 for proton-induced fission of 238U
and by Croall and Cuninghame71 for proton-induced fission of232
Th were used in the calculation. For a given mass split, thedeformation energies, Edef, at scission point were calculatedwith varying combinations of charge division. The charge
expected from the most energetically favorable combinationsat scission point, ZEX, was determined from the largest (Q −Edef) for a given mass sprit. It was found that ZEX is not largely
different from ZQgg. An example of the results is shown in
Figure 4 for the fissioning nucleus of 239Np. This result indicates that the ground-state masses can be used for the estimation of the most energetically favorable charge.
4. CONCLUSIONSThe charge distributions of fission products were measured
in the systems of 13, 18, and 24 MeV proton-induced fission of238
U and of 13, 20, and 24 MeV proton-induced fission of

Th. A large number of these data enabled to get much information on the most probable charge, ZP. In all the systems
studied, ZP's mainly lay on the proton-rich side in the lightfragment mass region and on the proton-deficient side in theheavy mass region, that is, the nuclides of higher charge
density formed in the light fragment region and those of lower
charge density produced in the heavy fragment region. These
results imply that the charge polarization occurs in the fission
process and that the nuclear stability of fission fragments
reflects the charge polarization in fission. The charge polarization was examined with respect to the ground-state Q values.
The experimental ZP was fairly well reproduced by the estimation by the Q values except for the system of 13 MeV protoninduced fission of 238U and 232Th. These results suggest thatthe fission path to the most favorable charge division may go
through the most energetically favorable path.
Acknowlegements. The authors wish to express theiracknowledgement to the crews of cyclotron of Tohoku
University and JAERI tandem accelerator for splendid operation. Thanks are due to Dr. Y. Nagame, Dr. K. Tsukada, and
Dr. S. Ichikawa of JAERI for the help in a part of the measurements.
References(1) A. C. Wahl, R. L. Ferguson, D. R. Nethaway, D. E.
Troutner, and K. Wolfsberg, Phys. Rev. 126, 1112 (1962).
(2) J. A. McHugh and M. C. Michel, Phys. Rev. 172, 1160
(1968).
(3) A. C. Wahl, J. Radioanal. Chem. 55, 111 (1980).
(4) A. C. Wahl, At. Data Nucl. Data Tables 39, 1 (1988).
(5) G. R. Choppin and E. F. Meyer, Jr., J. Inorg. Nucl. Chem.
28, 1509 (1966).
(6) H. Baba, A. Yokoyama, N. Takahashi, N. Nitani, R.
Kasuga, T. Yamaguchi, D. Yano, K. Takamiya, N.
Shinohara, K. Tsukada, Y. Hatsukawa, and Y. Nagame, Z.
Phys. A 356, 61 (1996).
(7) R. H. Goeckermann and I. Perlman, Phys. Rev. 76, 628(1949).
(8) G. Friedlander, L. Friedman, B. Gordon, and L. Yaffe,
Phys. Rev. 129, 1809 (1963).
(9) J. H. Davies and L. Yaffe, Can. J. Phys. 41, 762 (1963).
(10) L. E. Glendenin, C. D. Coryell, and R. E. Edwards,
Radiochemical Studies: The fission products (McGrawHill, NewYork, 1951).
(11) A. C. Pappas, Paper P/881, Proceedings of the International
Conferencce on the Peaceful Uses of Atomic Energy,
Geneva, 1995.
(12) R. D. Present, Phys. Rev. 72, 7 (1947).
(13) H. M. Blann, Phys. Rev. 123, 1356 (1961).
(14) H. Kudo, M. Maruyama, M. Tanikawa, T. Shinozuka, andM. Fujioka, Phys. Rev. C 57, 178 (1998).
(15) M. Yoshii, H. Hama, K. Taguchi, T. Ishimatsu, T.
Shinozuka, M. Fujioka, and J. Ärje, Nucl. Instr. Meth. B
26, 410 (1987).
(16) H. Kudo, M. Maruyama, M. Tanikawa, M. Fujita, T.
Shinozuka, and M. Fujioka, Nucl. Instr. Meth. B 126, 209(1997).
(17) J. F. Janni, At. Data Nucl. Data Tables 27, 147 (1982).
(18) H. W. M uller, Nucl. Data Sheets 50, 1 (1987).
(19) H. W. M uller, Nucl. Data Sheets 56, 551 (1989).
(20) H. W. M uller, Nucl. Data Sheets 54, 1 (1988).
(21) H. Sievers, Nucl. Data Sheets 58, 351 (1989).
(22) U. Reus and W. Westmier, At. Data and Nucl. Data
Tables Part 2 29, 193 (1983).
(23) H. W. M uller, Nucl. Data Sheets 31, 181 (1980).
(24) P. Luksch, Nucl. Data Sheets 30, 573 (1980).
(25) H. Sievers, Nucl. Data Sheets 54, 99 (1988).

12

J. Nucl. Radiochem. Sci., Vol. 3, No. 2, 2002(26) H. W. M uller, Nucl. Data Sheets 44, 277 (1985).
(27) P. Luksch, Nucl. Data Sheets 38, 1 (1983).
(28) B. Haesner and P. Luksch, Nucl. Data Sheets 46, 607(1985).
(29) H. W. M uller and D. Chielewska, Nucl. Data Sheets 48,
663 (1986).
(30) J. Blachot, Nucl. Data Sheets 45, 701 (1985).
(31) D. De Frenne, E. Jacobs, M. Verboven, and P. De Gelder,
Nucl. Data Sheets 47, 261 (1986).
(32) J. Blachot, Nucl. Data Sheets 62, 709 (1991).
(33) R. L. Haese, F. E. Bertland, B. Harmatz, and M. J. Martin,
Nucl. Data Sheets 37, 289 (1982).
(34) A. Hashizume, Y. Tendow, and M. Ohsha, Nucl. Data
Sheets 52, 641 (1987).
(35) B. Fogelberg and P. Hoff, Nucl. Phys. A 391, 445 (1982).
(36) B. Fogelberg and P. Hoff, Nucl. Phys. A 376, 389 (1982).
(37) K. Kitao, M. Kanbe, Z. Matsumoto, and T. Seo, Nucl.
Data Sheets 49, 315 (1986).
(38) T. Tamura, K. Miyano, and S. Ohya, Nucl. Data Sheets
41, 413 (1984).
(39) T. Tamura, K. Miyano, and S. Ohya, Nucl. Data Sheets
36, 227 (1982).
(40) K. Kitao, M. Kanbe, and Z. Matumoto, Nucl. Data Sheets
38, 191 (1983).
(41) Yu. V. Sergeenkov and V. M.Sigalov, Nucl. Data Sheets
34, 475 (1981).
(42) Yu. V. Sergeenkov, Nucl. Data Sheets 52, 205 (1987).
(43) T. W. Burrows, Nucl. Data Sheets 52, 273 (1987).
(44) L. K. Peker, Nucl. Data Sheets 36, 289 (1982).
(45) L. K. Peker, Nucl. Data Sheets 32, 1 (1981).
(46) L. K. Peker, Nucl. Data Sheets 51, 425 (1987).
(47) L. K. Peker, Nucl. Data Sheets 45, 1 ( 1985).
(48) L. K. Peker, Nucl. Data Sheets 43, 579 (1984).
(49) L. K. Peker, Nucl. Data Sheets 48, 753 (1986).
(50) J. K. Tuli, Nucl. Data Sheets 56, 607 (1989).
(51) L. K. Peker, Nucl. Data Sheets 49, 1 (1986).
(52) L. K. Peker, Nucl. Data Sheets 41, 195 (1984); B.

Kaji
Sohnius, M. Brugger, H. O. Denschlag, and B. Pfeiffer,
Radiochim. Acta 37, 125 (1984).
(53) L. K. Peker, Nucl. Data Sheets 42, 111 (1984).
(54) J. A. Szücs, M. W. John, and B. Singh, Nucl. Data Sheets
46, 1 (1985).
(55) R. K. Gupta, W. Scheild, and W. Greiner, Phys. Rev. Lett.
35, 353 (1975).
(56) D. R. Saroha, R. Aroumougame, and R. K. Gupta, Phys.
Rev. C 27, 2720 (1983).
(57) P. Fong, Phys. Rev. 103, 434 (1956).
(58) J. P. Bocquet and R. Brissot, Nucl. Phys. A 560, 213c
(1989).
(59) H. Umezawa, J. Inorg. Nucl. Chem. 33, 2731 (1971).
(60) H. Kudo, H. Muramatsu, H. Nakahara, K. Miyano, and I.
Kohno, Phys. Rev. C 25, 3011 (1982).
(61) J. R. Boyce, T. D. Hayward, R. Bass, H. W. Newson, E.
G. Bilpuch, F. O. Purser, and H. W. Schmitt, Phys. Rev. C
10, 231 (1974).
(62) C. J. Bishop, R. Vandenbosh, R. Aley, R. W. Shaw, Jr.,and I. Halpern, Nucl. Phys. A 150, 129 (1970).
(63) M. Strecker, R. Wien, P. Plischke, and W. Scobel, Phys.
Rev. C 41, 2172 (1990).
(64) I. Nishinaka : private communication.
(65) A. H. Wapstra, G. Audi, and R. Hoekastra, At. Data Nucl.
Data Tables 39, 281 (1988).
(66) J. Jänecke and P. J. Masson, At. Data Nucl. Data Tables
39, 265 (1988).
(67) B. D. Wilkins, E. P. Steinberg, and R. R. Chasman, Phys.
Rev. C 14, 1832 (1976).
(68) S. Goto, D. Kaji, H. Kudo, M. Fujita, T. Shinozuka, andM. Fujioka, J. Radioanal. Nucl. Chem. 239, 109 (1999).
(69) Ph. Quentin, J. Phys. (Paris) 7, 32 (1969).
(70) U. Brossa, S. Grossmann, and A. Müller, Phys. Rep. 197,
402 (1990).
(71) I. F. Croall and J. G. Cuninghame, Nucl. Phys. A 125, 402(1969).