- Email: [email protected]
Mass distribution and the total fission cross section in the fission of 238U with protons of energies ranging between 13 and 55 MeV
I
2.J
I
Nuclear Physics Al75 (1971) 177-198; Not to be reproduced
MASS DISTRIBUTION
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@ North-Holland
or microfilm without
Publishing
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Co., Amsterdam from the publisher
AND THE TOTAL FISSION CROSS SECTION
IN THE FISSION OF =*U WITH PROTONS OF ENERGIES
RANGING BETWEEN
S. BABA, H. UMEZAWA Japan Atomic
Energy
Research
Institute,
13 AND 55 MeV
and H. BABA
Tokai-mura,
Naka-gun,
Zbaraki-ken,
Japan
Received 2 June 1971 Abstract: The fission of 238U with protons of energy ranging from 13 to 55 MeV was studied radiochemically. The mass-yield curve was obtained for each of the eleven incident energies, and an analysis was performed, based on the two-mode-fission mechanism. The observed total chain yields were reasonably reproduced by the combination of the three Gaussian curves with partial distortions. The deduced number of neutrons emitted in the fission was found to agree well with the postulated value in the study of the charge distribution systematics. For the three highest incident energies, the formation of the fissile nuclei through a direct process was shown to occur and the analyzing method was discussed. The peak-to-trough ratio and the total fission cross section were obtained from thus-established mass distribution curves. E
NUCLEAR
FISSION 2J8U(p, f), E = 13-55 MeV; measured fission product yields; deduced mass distribution, or, prompt n’s.
1. Introduction of the mass distriMany studies have been reported r-16) on the measurement bution and of the fission cross section in the 238U fission induced by protons with energies less than 20 MeV. Jn this energy region, the 238U fission is known to take place in both asymmetric and symmetric fission modes with comparable probabilities. Jones et al. have observed “) that the probability of asymmetric fission relative to that of symmetric fission decreases with increasing proton energy. The peak-to-trough ratio in the mass distribution is studied in detail by Butler et al. lo) and by Choppin et al. 12), as function of the proton energy, E,. They both find a prominent discontinuity in the peak-to-trough ratio at Ep z 7 MeV. The discontinuity has then been understood in relation to the threshold for the 238U(p, nf) reaction: intrusion of the 238U(p, nf) reaction causes decrease of the average excitation energy to be spent for fission, and consequently results in increase of the fission asymmetry. Ford has introduced an analyzing method “) of the mass distribution curve by means of the vector representations of the asymmetric and the symmetric mass distribution. He postulates that any mass distribution must be represented by the linear combination of the above two normal vectors, if the fission follows the two177
178
H. BABA et al.
mode-fission mechanism. Choppin et al. have applied ’ “) the method to the massyield curve of the 238U fission with protons of energies below 12 MeV. The limitation of this analyzing method lies in the fact that the basic two vectors must be fixed while energy changes. Therefore, it can not be applied for a wide range of the energy. For very high proton energies, the mass-yield curve and the fission excitation function have been studied by Lavrukhina et al. ‘), by Stevenson et al. “) and by Hagebo et al. 14). Th eir results indicate that the trough in the mass distribution disappears above about 100 MeV excitation, and the fission cross section remains constant above 30 MeV. Available data of the mass distribution and the fission cross section are rather scarce for the proton-induced fission of 238U in the energy range between 20 to 100 MeV. In this work, we, therefore, intended to supply those data in this energy region, connecting the low- and high-energy data. We expect in the present work to observe the continuous transition from the asymmetric fission at low excitation to the equivalent mixing of the symmetric fission into the asymmetric fission at high excitation. The energy dependence of each mass distribution and of the number of the prefission neutrons are also the object of our interest. 2. Experimental The uranium targets were prepared by sedimenting the purified U30, powder, suspended in liquid paraffin, onto the Al backing foil by means of the centrifugal force ‘*). Slightly depleted uranium (99.3 % of 238U and 0.68 % of 235U) was used. With this technique, targets ranging from 20 to 60 mg/cm’ in thickness were obtained with sufficient uniformity. Each stacked target assembly was constructed by piling Al foils of appropriate thicknesses among eleven or twelve U30s plates. The last U,Os TABLE 1
Irradiation conditions and thicknesses of targets Target no.
Run 1 (ZV)
U308 fmg/cm*)
-&I WeV)
24.00 26.43 21.30 28.52 29.92 30.92 32.62 32.80 42.37 51.29 27.04
55.0*0.2 5O.lkO.2 44.9 10.2 40.1*0.2 35.0f0.2 29.9 kO.3 25.OhO.3 21.7 +0.4 18.2f0.5 15.7kO.5 13.1&0.6 none
1
2 3 4 5 6 I 8 9 10 11 12 “)
50.250.1 44.9kO.l 4O.OkO.l 35.lhO.l 30.1 hO.2 25.0+0.2 21.8*0.2 18.1 f0.2 15.9*0.3 13.0*0.5 none
Run 3
Run 2 u3os (mg/cm*) 61.47 55.94 55.34 54.24 45.61 52.33 62.08 61.76 64.05 65.57 64.74 68.44
(&‘) 55.01-0.2 49.9 +0.2 45.OkO.2 39.9kO.2 34.9f0.3 29.9 10.3 25.110.3 21.810.3 18.1 ho.4 15.5io.5 13.OhO.6 none
“) These targets were placed out of the proton range as the monitor for background
U&8 (mgicm’) 64.86 64.03 61.26 61.40 61.67 54.26 59.60 55.23 62.47 66.26 72.36 75.48 neutrons.
238u(P,
f)
179
plate was placed out of the incident-proton range for estimating the amount of the contribution from the neutron-induced fission. The proton energy at each target was calculated by following ref. I’). Details are shown in table 1. Irradiation was carried out with the 55 MeV proton beam from the INS synchrocyclotron of the University of Tokyo. The beam current was about 0.1 /IA throughout the experiment. The beam intensity was measured with an electronic integrator. After the irradiation, each target, sandwiched between two Al foils of thickness hydrochloric acid and nitric 6 mg/cm2, was dissolved in a mixture of concentrated acid containing the following carriers: 20 pg of cadmium, 12 pg of palladium, 50 pg each of molybdenum and tellurium, 0.1 PC of the 6 5Zn tracer, 10 c(g each of rubidium, cesium, strontium, barium, yttrium and rare earths from lanthanum to terbium. Fission products were then separated sequentially by an ion-exchange method 20). Alkalies, alkaline earths and rare earths were separated quantitatively. The recoveries of molybdenum, palladium, cadmium and tellurium, which were not quantitatively obtained, were determined by means of polarography. The recovery of zinc was determined by y-counting the 6 ‘Zn activity after the fission product 12Zn had decayed out. An aliquot or all of the solution containing a thus-isolated element was evaporated on Mylar film and covered with Scotch tape. .4ctivities of the fission products obtained were measured with end-window flow proportional counters for several half-lives. The observed decay curves were analyzed by non-linear least-squares fitting with an electronic computer. The resulting halflife values were reasonable 21) compared with the reported values. The radiochemical purity was also examined by y-ray spectroscopy with a 7.6 cm o x 7.6 cm NaI(T1) scintillator fed to a multichannel pulse-height analyzer. Thus identified and determined activities were “Zn, 86Rb, *‘Sr, ‘lY, “MO, ll%,gCd, 132~~, 136~ 140Ba, 141,‘44ce, 143pr, 147Nd, 148,149pm, 153Sm, ’ 5 6E~ and ’ 60* ’ 61Tb. In order to determine the counting efficiencies of the counters for these activities absolute measurements were carried out for all nucleides determined in this work, by means of the 47~8 counting and 47$--y coincidence counting measurements 22-24).
3. Results The observed yields of the fission products are listed in table 2. Among them, the values for 86Rb, 13’%s, ’ 48Pm and ’ 60Tb are independent yields, whereas the others are cumulative. In order to find the correction factor for converting an independent or a cumulative yield into the total chain yield, one needs to know the most probable charge, Z,, , for the mass number and the charge dispersion curve. Here, we introduce the following two assumptions: (i) The charge d’istri ‘b ution follows the systematics derived in ref. 25); that is, AZp =
0 y(jq-0.51-0.04) 0.3511-0.51
for lr]-0.51 5 0.04 for 0.04 6 Iv-O.51 5 0.085 for Iv-O.51 2 0.085,
(1)
0.82 kO.03 39.3 f1.8 42.9 kO.6 64 &3 58 60 &3 24 f3 37.2 *1.8 40.8 *1.7 35.8 kO.8 27.7 +1.6 18.8 *0.3 13.2 50.6 4.26 ho.09 1.94 60.13 0.478+0.019
TABLE 2
44.9
0.63810.019 38 12 41 -+2 72 *4 51 54 &3 30 52 42.1 il.1 38.5 Al.4 34.9 *0.8 28.3 h1.5 17.8 kO.4 12.9 10.7 4.03 50.07 1.84 kO.06 0.42 &0.02
50.1
0.72 10.05 37.8 +0.7 44.3 kO.8 69 16 55 57 *4 25 14 39.3 fl.0 40.0 +1.5 35.5 40.8 28.7 11.6 18.6 k1.2 13.0 11.9 4.25 *0.08 2.03 *0.07 0.456hO.017 44 ,3 24 &7 40 13 36 13 32 +2 26.4 +1.4 17 f2 12.1 *0.6 3.7 *0.3 1.75 kO.14 0.353*0.017
0.487&0.016 13.4 +0.5 38.1 *I.6 73 54 50
40.0
Cumulative yields of fission product nucleides (mb)
0.382&0.010 33.6 *to.7 42 13 72 $5 46 44 13 30 15 46 13 40.1 *1.5 37.0 +0.9 30.2 hl.6 18.4 ItI.2 12.5 f0.4 3.9 40.3 1.83 *0.07 0.34210.012
35.0
-CO.011 *2 +0.9 14 k-t3 +9 13 53 13 &2 12 k1.2 *0.3 ho.16 10.02
0.293 32 35.8 69 41 38 33 4.5 41 37 30 19 12.4 4.2 1.83 0.32
30.0
F 2 3 z
$
3
I-.._
The errors
13zTe lroBa ‘We ‘43Pr ‘%e 14’Nd 149Pm ‘%m r’=‘Eu 16’Tb
’ Wd
‘*Zn 8”Sr 91Y 9pMo l12Pd
Nucleide
‘-\
quoted
25.0
deviations
0.1971 0.007 29.3 f- 0.6 35 *2 64 rt3 33 28 12 36 *11 43 13 38.4 & 1.7 31 zk4 28.6 f 1.7 18 &2 12.0 f 0.6 3.8 & 0.2 I.75 i 0.15 0.25 & 0;02
are the standard
EP
(MeV) -y..,
among
the results
obtained
0.118*0.004 23.1 kl.2 28.2 hl.7 54 &3 26 20.7 11.3 26 19 37.0 +1.7 33.3 11.4 28.2 ho.6 24.8 51.4 15.1 hl.6 10.0 kO.6 3.1 f0.3 1.5 10.2 0.25 -+-0.03
21,8
18.1
by two or three
separate
0.069;1rO.O03 19.3 3r1.4 23.8 kl.6 43 &3 18 16.6 kO.9 29 &6 33.3 fl.9 29 f5 26.0 h1.9 21.9 rt1.6 13.2 h1.8 9.0 kO.5 2.7 1;0.2 1.06 &0.15 0.141 kO.013
TABLE 2 (continued)
bombardments.
0.0337+0.0010 12.8 hl.4 16.0 kl.8 24.8 k1.5 8.3 6.9 *0.5 17 -16 23 12 20 &2 16.7 kO.4 15.4 rtl.7 10.2 11.0 6.0 &to.7 1.8 10.2 0.73 f0.15 0.089 ~0.008
15.7
8.2 7.5 6.4 3.9 2.8 0.7 0.32 0.040
kl.1 fl.9 kl.5 kl.2 &OS LO.3 &0.07 f0.005
0.0108&0.0006 5.6 rt.l.1 6.8 kl.3 13.6 hO.8 3.5 2.3 10.2 8 xt3 10 &2
13.0
3
s
2
183
H. BABA
et al.
where AZ,, is the deviation of the most probable charge Z, from the unchanged charge distribution and q is the mass fraction given by
with the mass number of the product, A, and that of the compound nucleus, A,. The number of the post-scission neutrons, vpost, and the number of the pm-scission neutrons (plus neutrons emitted at the moment of scission}, v,,, are given by
vposl=
1‘0
for
A&88
l.O+O.l(A-88) 0
for for
78 $ A 5 88 A 6 78,
(3)
and II
W@
=
hi - -
j- g .
-([email protected]). c
(ii) The charge dispersion is described by a common Gaussian curve with 202 = 0.95 [refs. 26*“‘)I for all mass chains and energies. Therefore, the fractional independent yield, p,(Z, IQ, at excitation of Ex is given by
The resulting Z, values for the nucleide cumulative yields of which were obtained turned out to be far away from the observed charges except for a few cases. Consequently, no correction was necessary to convert the cumulative yield to the total chain yield. As exceptions, the yields of 14’Ba, 144Ce, rSGEu and 13’Te needed to be slightly corrected at high excitation energies. The correction factor for the independent yields amounted, on the contrary, to as large as a few orders of magnitude. The resulting total chain yields are presented in table 3.
4. Heavy-mass wing of the asymmetric mass distribution We shall postulate the two-mode-fission mechanism in the following discussion. Thorough discussion on the justification of the postulate shall be given in ref. 28)_ General& speaking, the total chain yield, Y(A*, E,), of the primary fragment mass A” at the excitation energy E, csuf be expressed by means of the fission cross section, c+(E,), and the fractional mass yield, p(A”, E,), as Y(A*, Q
= ~(&)P(A*, Q.
(6)
If one considers the ratio of the yields between two fragment masses produced in the
g : N
t' *
O’OE
~~~_____.
ZO’O + ZE’O 9I'O F Pg.1 E'O "F Z'P Z'I i P'ZI ZF 61 Z'f OE ET LE E'F IP ET LP 911 LS Ef 8E IP VT 69 L'O F 8'SE z+ ZE 110'0 f96Z.O
O’SE
ZIO’O FfpPC’O LO'0 F S8'1 c-0 ii- 07 P'O i S'ZI 2'1 F P'81 9'1 f S'OE 6'0 =F O’LE S’I ‘F I’OV Ei 6P I11 99 ET Ptr 9t SF ZL ET zv L’O i 9’EE 10’0 f 6.20
.._.
_II_
O’OP
LIO’O TSSE’O PI’0 f 9L’I E’O T L’E 9‘0 'f 1'21 IT Ll VT f L’9Z z’-F ZE E’F 9E C'F SP OZ'F 89 Ef w IS VT EL 9'1 3: I'8E 8'1 'f 6'1E L10'0 'F9os.o
-.__
6W
ZO’OTZP’O 9O'O'f98'1 LO'Oi LO? L’O’F 6'21 VO;c 6'LI 9'IF L'6Z 8'O'F 6'PE P'I'f S'8E E'IF t'IS L=F L6 f'f P5 ZS PT ZL zi IP Z+ 8C ZO'OTL9'0
1'0s
-____
ZO'O 'f9'b.o LO'0 7-SO'Z 80'0 ~6Z'P 6'1 F I'CI Z'I F L'81 L’I F L’OE 8’0 F S’SE 5'1 T E'OP E'I 'F 5'6P 8IF 011 ti'f LS 9s 9"f 69 8'0 F E'PP L'O 'F 0'8E SO'0 ‘f9L.O
-
O'SS
ZO'O ?66p'O El'0 5zo.z 60-O TOE'P 9'0 ?" E'fl E'O 3: 0.61 8'1 3: O'IE 8'0 F 0'9E L'I F O'IP ZT OS 9IT WI E"F 09 65 ES P9 9'0 =f 6'ZP 8'1 "F S'6E EO'O iL8'0
191 951 ES1 6PI LPI PPL EPI IPI OPI ZEI SIT 211 66 16 68 ZL
(MS, 1.
..
._._~~~
0.199+ 0.007 29.3 f 0.6 35 +2 64 It3 34 28 12 58 +18 44 *3 38.4 f 1.7 31 *4 28.9 & 1.7 18 h2 12.0 f 0.6 3.8 i 0.2 1.76 f 0.15 0.25 & 0.02
25.0
0.119~0.004 23.1 k1.2 28.2 kl.7 54 +3 26 20.7 +1.3 39 +14 37.4 h1.7 33.3 h1.4 28.2 f0.6 25.0 hl.4 15.1 rt1.6 10.0 kO.6 3.1 +0.3 1.5 10.2 0.25 ho.03
21.8
--.
____
18.1
0.070+0.003 19.3 f1.4 23.8 bl.6 43 +3 17.8 16.6 f0.9 40 &9 33.6 11.9 29 *5 26.0 f1.9 22.1 61.6 13.2 k1.8 9.0 *0.5 2.7 f0.2 1.06 f0.15 0.141 kO.013
TABLE 3 (continued)
0.034~0.001 12.8 11.4 16.0 11.8 24.8 *1.5 8.4 6.9 ho.5 22 18 24 +2 20 *2 16.7 kO.4 15.5 Al.7 10.2 11.0 6.0 kO.7 1.8 ho.2 0.73 hO.15 0.08910.008
15.3
The errors quoted are the standard deviations among the results obtained by two or three separate bombardments.
72 89 91 99 112 115 132 140 141 143 144 147 149 153 156 161
Mass number
‘%.
0.0109~0.0006 5.6 It1.1 6.8 11.3 13.6 50.8 3.6 2.3 *0.2 10 *4 11 52 8.2 I-tl.1 7.5 51.9 6.4 Al.5 3.9 *1.2 2.8 10.5 0.7 fkO.3 0.36 f0.07 0.037 30.005
13.0
? 2 3 >
F
3
=*u(P,
same mode
of fission,
the fission
185
f)
cross section
is cancelled
out:
It should be mentioned that the observed yields are connected to the secondary fragment mass and, therefore, they must be transformed to the primary fragment masses. Recent measurements of the prompt neutrons 29-32) at medium excitation have revealed that the fragment-mass dependence of the neutron number is very weak except for extremely light fragments. It foliows that the primary fragment masses, A: and AZ, in eq. (7) can be directly replaced by the secondary masses, A, and A,. The fine structure in the mass distribution, generally observed in the low-energy fission 33P34), disappears in the fission at medium excitation (cf. fig. 6). This is a great advantage of the energetic fission, in discussing the fundamental structure of the mass distribution. Let us assume that the mass distribution is decomposed into three Gaussian curves, according to the two-mode-fissiol~ mechallism. The two outer peaks represent the distribution of the light and heavy fragments in the asymmetric fission while the central peak is for the symmetric fission products. For two fragments belonging to the heavy-mass peak, eq. (7) is modified to the form: 3(A,+A,)
= QKlfA,,
(8)
with Q=
1 &42-4
Here, p(A, E,) is substituted
In WI
3 41 (9)
Y(A2
3 -&I
’
by
p(A, EJ = 1 exp - (A-AcJ2 CUC a ( J
I-
(10)
One, therefore, ought to find a straight line by plotting $(A r + A,) versus Q for various combination of A, and Al, for a fixed value of E,. The results of the analyses are depicted in fig. I ; the linear relationship was observed at eight energies ranging from 18 to 45 MeV excitation, whereas the situation became complicated at the highest three energies, 50, 55 and 60 MeV. We, therefore, conclude that the asymmetric mass distribution is Gaussian at least between 18 and 45 MeV excitation, and the contribution of the symmetric fission is negligible in the lowest mass chain used, e.g., 132 amu, up to 45 MeV. From the slope of the obtained straight line, we found the following relation between the width and the energy: & - 106 = 0.235(E, - 14.0),
(11)
as shown in fig. 2. The value of CIat the 14 MeV excitation corresponds to FWHM of 17.1 amu. We have collected the FWHM from available mass-distribution curves [refs. “* “-“)] in various &site systems. They are listed in table 4. The lowest
T_...____-_.~-
a/ *4’ 35 2 MeVT-
s 8+ d
Fig. 1. The linear presentation of the Gaussian mass distribution, eq. (8). The energy denoted near the right end of the solid line gives the excitation energy. For the highest three energies, the points to which the yield of the 132 mass chain is related are depicted with solid marks. The dotted lines there represent the likely mass distribution of the direct fission involved.
E, (MeV) Fig. 2. The energy dependence of the width parameter, cc, for the asymmetric mass-yield peak.
187
238U(P, f)
possible value of FWHM, 17.1 amu, of our Gaussian curves are obviously than those values in table 4. Mixing of fission occurring at various stages neutron-emission chain may partly be the reason for the higher value obtained
larger of the by the
TABLE 4 Widths
of the symmetric
and asymmetric
Reaction
(PWHM),,, (amu)
19’Au(c(, f) 204Pb(a, f) 206Pb(a, f) ‘04Bi(d, f) 226Ra(p,f)
*“‘Pb(a,
f)
226Ra(d,f) 232Th(n, f)
Z3ZTh(p, f) 233U(a, f) *38U(n, f) 238U(P, f) z40Pu(sp, f) 239Pu(a, f)
238Pu(a,
mass distributions, curves
f)
43 43 43 20 11 13.0 28.9 33.2 37.5 41.1 14.5 2.1 6-11 69 14.7 6.1 34.5 14.7 7.1 9.4 12.0 I 43.8 46.0 47.5 42.2
34 28 22 16 16 19 23 16 16 18 18 28
21
read from the constructed
(FWHM),,,, light
(amu)
distribution
Ref.
heavy
=) 3*) 38
)
=) -) 13 16
13 16
14
37 ) 53 ) 51 ) 51) 51 ) 51) =) 41
15 12 12.5
41 : 51 ) 41
14 14 14
14 14
35 ; =Y 42)
14
14
15
14
14
1
45 48 42 51
extrapolation. Further discussion on this question shall be however postponed until sect. 6. The intercept of the straight line in fig. 1 gives the peak position. The peak centre could be determined within +0.2 amu for all the energies. We found that the peak position was fixed at 136.0 amu for excitation up to 30 MeV, and then starts to shift towards the light-mass side as the energy increases. The stationary peak position may be connected with the observation that the edge of the heavy-mass peak lies at the same position for the fission of transuranium elements 33, 34).
188
H. BABA et al.
5. Centre of the light-fragment
peak
In the region of the light-mass peak, sufficient numbers of the total chain yields are not available for carrying out the same type of the analysis as for the heavy-mass peak. Therefore, we combine the yield, Y(A,, &), of a mass chain A, in the Iightmass region with that of a mass chain A, in the heavy-mass region. Then, we have the following relation:
Kere, we already know the values of Ati,* and cr,. Equating aL to aH, one can caiculate A,_, o, which should be the same for different masses of AL and AH. The approximation that aL = ti,., may be allowed because the number of the post-scission neutrons is reported to be very small in any respect29-32). 110 -, ,
loo-
_I_ Im_.--)
_,-,.
Ex = 501 t&V
go-
1
451hw
90 q1oQz_
._._ ___~_..
goIOOL_..
_.---,-.----.
hw
_L,-..-,_*_.~
__..,
_I_.*_
352t.W
90100”
_._ ___.
401
1
go-
‘-,-,_‘_‘_,_,-.-.--~302 Mev
tGor._y._.__
._,. _-.._
.._..
, L_-_--.I__
_,_-___,-
-.-
27OM2V
90-
~or_i_~.~._...-.-.-_-,_.___,~
90” 100r_,____90-
130
233
MoV
m_,m,_*.‘_*
-,--
209hw
140 150 HEAVY FRAGMENT MASS
Fig, 3. Det~r~nation
160
of the light-fragment-yield
peak.
-TJ(p,
f)
189
Fairly well constant values were obtained for the nine energies + between 18 and 50 MeV, as shown in fig. 3, so that AL,O were determined with high precision. The resulting peak positions, AH,O and ALSO, and also the centre of the whole mass distribution, A, = +(AH,O +AL,O) are displayed versus excitation energy in fig. 4. Up to 30 MeV excitation, the light-mass peak is found to shift toward the lighter-
0
0 0
130-
2 120.z! B
0
cantra
of
maaS dlstrlhullon @oeeeo eaAA
!i 2
llO-
0
20
40
GO
E, (Mei’)
Fig. 4. The determined peak positions of the light- and heavy-fragment-yield curves and the resulting centre of the mass distribution. Triangles represent the mass-distribution centre deduced from the neutron systematics, eqs. (3) and (4).
mass side, due to the increase of the pre-fission neutrons per fission. Meanwhile, the heavy-mass peak is fixed at 136 amu. When the excitation energy exceeds 30 MeV, the hindering factor against the shift of the heavy-mass peak, AH,O, is removed and the An, o begins to decrease so rapidly that the A,, o inverts from decrease to increase. One can obtain the total number of neutrons from the difference between twice A, and the mass of the compound nucleus. On the other hand, we have introduced the neutron systematics, eqs. (3) and (4), in the charge-distribution correction. The centre of the observed mass distribution, A,, is given by
4, =
!&k-~pre>-1-
(13)
Here, the last term in the right, 1, arises from vpost given by the first of eqs. (3). The value of A,,, thus deduced is also displayed in fig. 4. One may notice that the agreement between the values of A, from two different sources is satisfactory. This is more t The result obtained on the 50 MeV data is included in figs. 2 and 3 since it is still meaningful even at that energy, as shown in sect. 7.
H. BABA et al.
190
clearly visualized in fig. 5, in the form of the total number of the neutrons emitted per fission. The Leachman’s systematics 44) is also added in the figure. As was stated in sect. 3, most cumulative yields were practically the total chain yields as they were. It follows that there was not much freedom in the choice of the neutron systematics because the centre of reflection in the mass-yield curve had been lo-
I
1
,
/
,
,
l
8.
f
060 . Q
6-
68 0,
,a* l
e*+ +
o+ + 0
4-
Obserbed
.
+2++
+
Z2 J’“~+-&-‘90
2-
I OO
I 20
I
I
I
I 60
E, (Me:: Fig. 5. The total numbers of the neutron emitted per fission, obtained from three different sources of information.
tightly fixed. One sees, in fig. 6, that the introdu~d neutron systematics, given by eqs. (3) and (4), determines the reflection centre very well. Now, we have found that the total number of the emitted neutrons, obtained as a result of the analysis, is almost the same as that introduced at the beginning. This implies that we have successfully constructed a self-consistent systematics governing the charge and mass distributions and the number of emitted neutrons.
6. Off-Gaussian structure of either peak in the asymmetric region and the symmetric mass distribution By making use of the information we have extracted on the mass-yield curve, we can reproduce the mass-distribution curve in the asymmetric region; namely, the width of the Gaussian curve is calculated by eq. (1 I), the peak position is read from fig. 4, and the peak height is normalized to the observed yields. The resulting curves are represented by the dotted line in fig. 6. The observed yields are found to fit very well to the thus-drawn Gaussian curves in the mass region heavier than 131 amu and in the corresponding light-mass wing.
2YJ(p,
f)
191
.
9 13 e 15 o this work A
1
0.01
o-3. I
I
GO
80
100
FRAGMENT
120
140
160
MASS
Fig. 6. The secondary mass-yield curves. The dotted line gives the sum of the two Gaussian curves fitted to the observed yields in far-asymmetric-mass regions. The dashed lines represent the resulting mass-distribution curves both for the symmetric and asymmetric modes of fission: the sum of the three dashed curves equals the gross mass-yield curve drawn with the solid line.
calcd. Ba = 5.7 MeV as= G 7MeV a = 27MeV‘’ tiw = 0.5MeV
0
r
I
I
20 EXCITATION
f
!
I
I
40 60 ENERGY(MoV)
Fig. 7. The observed trough-to-peak ratios in the fission of 238U with protons. The solid line is the result of the calculation by means of eq. (6) of ref. zs).
From the peak height of the mass-yield curve and the bottom of the valley, we obtain the trough-to-peak ratio. They are plotted versus excitation energy in fig. 7, together with the reported trough-to-peak ratios 4V9S13*1 “). They all are found fairly well consistent with one another. The dotted line in fig. 6 suggests that one must admit the existence of asymmetric fission in an appropriate proportion even at the very symmetric mass division. The observed fragment-kinetic-energy distribution 45-48) and the charge distribution “), however, strongly indicate the non-existence of the asymmetric mode of fission in the
H. BABA
192
et al.
symmetric mass region. Therefore, our Gaussian mass-distribution curve must be depressed in the near-symmetric side. This type of distortion of the asymmetric mass distribution peak is consistent with the asymmetric peak shape of the massyield curve in the low-energy fission of transuranium elements 34*4g), in which the slope of the inner wall is much steeper than that of the outer wall. In sect. 4, we have obtained considerably larger value, for the smallest possible FWHM of the Gaussian curve, than the observed FWHM from various mass distribution curves. Then, we ascribed the reason partly to mixing of multiple chance fission. Now, we can also interpret the discrepancy in terms of the distortion of the peak from the Gaussian shape. Suppose one accepts that the contribution of asymmetric fission is negligible in the trough region. Then, the trough-to-peak ratio presented in fig. 7 can be directly subjected to the analysis explained in ref. ““) [cf. fig. 3a of ref. ‘s)]. According to the results obtained, the following relation was confirmed to hold between the trough-topeak ratio, Rfjp, and the cross section ratio, cr,/cr,:
On the other hand, half the trough-to-peak
ratio is given by
where CC,is the width parameter for the symmetric mass distribution and S is the apparent asymmetric fission cross section, deviating from the real cross section u, because of the distortion of the peak shape. The total chain yield, Y(A, E;), should now be described as S(E >
(16)
instead of eq. (6). If we introduce the simple approximation of the substitution of the sudden cut-off of the Gaussian curve at mass AG for the distortion, the apparent cross section S is expressed
as =qE
) I
2dEJ
(17)
1+erf’
in terms of the real cross section g= and the error function,
erf(Z),
with
(18) By making
use of eqs. (14), (15) and (17), one obtains Ja,
= +(l +erf (Z)>JE.
(19)
z3*u(P,
The residue in the subtraction from the whole outline should
193
f)
of the thus-constructed Gaussian mass distribution in turn constitute the inner slope of the asymmetric TABLE 5
The resulting
18.2 20.9 23.3 27.0 30.2 35.2 40.1 45.1
0.21 0.46 0.71 0.82 0.94 1.09 1.21 1.31
0.018 0.055 0.13 0.19 0.25 0.36 0.41 0.43
fission
cross sections
0.23 0.52 0.85 1.01 1.19 1.45 1.63 1.74
0.22 0.51 0.84 1.01 1.21 1.45 1.63 1.76
0.086 0.12 0.19 0.23 0.27 0.33 0.34 0.33
0.077 0.13 0.18 0.23 0.28 0.33 0.33 0.31
The fourth column gives the sum of 6. and CT$,the second and the third columns, while the fifth column shows half the integrated area under the gross mass-yield curve. The sixth column gives the crosssection ratio of the symmetric to asymmetric mode of fission, which should be equal to half the trough-to-peak ratio, &R,in the last column.
distribution; now, the area of the asymmetric peak must satisfy the requirement, eq. (14). Construction of the self-consistent mass distribution, therefore, depends on the appropriate choice of the parameter 2. Consistent results could be obtained by a simple assumption: Ao = A,+6. The resulting symmetric and asymmetric peaks are displayed and the obtained cross sections are summarized in table 5.
PO) with dash lines in fig. 6,
7. Fission following direct processes So far we have excluded the data for the highest three energies, 50, 55 and 60 MeV excitation, or more reasonably the incident proton energies of 45, 50 and 55 MeV, because of their anomaly (cf. fig. 1). As is obviously seen in fig. 9, the yield of the 132 mass chain is abnormally high for these three energies. This is the result of the overcorrection for the charge distribution regarding the yield of ‘32Te, because of the invalidity of the systematics, eqs. (1) to (4), in that energy range ‘“). Let us, therefore, use the interpolated value in the mass-yield curve for the yield of the 132 mass chain, instead. The points with which the interpolated value of the 132 mass yield is concerned are displayed with solid marks for the three energies in fig. 1. From the figures, we can conclude that the anomaly is not of a superficial character evoked merely by the superposition of the symmetric mass distribution on the lowermass side of the asymmetric mass distribution. If the anomaly is caused by the inflow
I94
H. BABA
et al.
of the symmetric mode of fission into, say, the 132 mass chain while the Gaussian distribution following eq. (11) and fig. 4 still exists, one should observe a straight line, from which only the solid marks deviate to the right. The disappearance of the systematics above 45 MeV reminds us that the violation of the systematics of the charge distribution has begun about the same energy ‘“)_ The most naturally expected cause is the mixing of direct fission. We shall attempt to find the analyzing method of the mass distribution when direct fission is mixing. Let us denote the asymmetric direct fission cross section by a,,, and the cross section for the asymmetric fission via the compound nucleus formation by o,,,. The total chain yield for the asymmetric fission is now described as
where S, and S, are the apparent fission cross sections, respectively corresponding to d B,c and c*,~, as functions of the incident energy Ep, and pd is the mass distribution function for the direct fission at the effective excitation energy Ed. Here, we have taken into account the effect of the distortion of each distribution function from the full Gaussian curve. For the combination of mass chains, A, and AZ, we obtain
(22) where A
Y
=
‘CA,3 E,7) ___.____ _ Y(A, Ep) 1641s Ed ~(4 4) 9
9
and
One, therefore, should obtain a straight line through the origin when plotting dy versus A,, if one knows the two distribution functions, p and pd. As for the mechanism of direct fission, one may recall the following two types; direct fission in the literal sense as found in the extremely high-energy region 50) and the usual type of fission through saddle-point deformation of the residual nucleus formed by the direct process. Considering our energy range, it would be reasonable to postulate the latter mechanism. Then, the difference between the via-compound fission and the direct fission is mainly in the magnitude of the available energy. Hence, we assume that p follows the systematics given by eq. (1 I), which are depicted with solid lines in fig. 1, andp, is considered to be replaced byp at E, = Ed. With this postulate, our concern is now to find the most likely value of Ed satisfying eq. (22). Quite satisfactory results were obtained when we chose 31, 34 and 37 MeV as Ed, respectively for the incident energy of 45,SO and 55 MeV. The results are shown in fig. 8. Considering that eq. (22) requires high precision for the observed yield values, the agreement is rather remarkable. The anomaly of the yield of the 161 mass chain,
z38u(P,
displayed
with triangles
195
f)
in fig. 8, may be ascribed
to the warp in p from the Gaussian
curve in the region far off the centre. From the slopes of the straight lines in fig. 8, S, is read out to be 0.25,0.80 and 1.10 b for the incident proton energies, EP = 45, 50 and 55 MeV, respectively. With these values of S,, the S, values are found to be 1.62,0.88 and 0.51 b in the above order of
-1
cl
1
-1
0
1
-1
0
1
7.
4
Fig. 8. The linear presentation of the contribution of the direct fission. In order to show the offGaussian character of the yreld of the heaviest mass chain of 161 amu, the points to which it is related are distinguishedly depicted with triangles.
80
120 140 100 FRAGMENT MASS
160
Fig. 9. Analysis of the mass-yield curve obtained in the three proton energies, 45, 50 and 55 MeV. The asymmetric-mass region was decomposed into two Gaussian curves, one for the via-compound fission and the other for direct fission, according to the results of fig. 8. The dotted lines represent the two Gaussian curves, while the dashed line gives the sum of them. The solid line, the whole mass distribution, was drawn through the observed yields.
H. BABA et al.
196
the energy. The resulting mass-yield curves in the asymmetric region are drawn with dotted lmes for the non-direct and direct fission and the sum of the two in fig. 9. The light-mass wing of the whole mass-yield curve was found to be the perfect mirror image of the heavy-mass wing as shown in fig. 9. That is, the centre of reflection for the direct fission lies at the same position as that for the via-compound fission, though it is not necessarily expected. In order to obtain the true cross sections, (T~,~and o,,,, we claim that the relations through eqs. (17) and (20) hold also in this case. The resulting values of c*,~ and u~,~ are given in the third and fifth columns of table 6, while the total fission cross section, as half the area under the solid line in fig. 9, is given in the last column of the table. We shall not attempt further analysis of the near-symmetric part of the massyield curve since there are a number of unknown factors involved. TABLE 6
The through-compound
Incident energy
fission cross section, CT,,,, the direct fission cross section, Ga,d, in the asymmetric mode, and the totai fission cross section, n,
(2”)
0a.s (b)
EP
( MeV) 45 50 55
50 55 60
1.30 0.65 0.33
31 34 37
0.24 0.16 1.05
1.90 1.87 1.88
The two-mode-fission mechanism was found to work quite satisfactorily on the observed mass-yield curve for the proton-induced fission of 238U at least up to 45 MeV excitation. The mass-yield curve was decomposed into three Gaussian curves, though the outer two curves had to be distorted on the near-symmetric side. The centre of the hevay-mass peak was found to be fixed at 136 amu up to 30 MeV and start to shift towards the lighter-mass side above 30 MeV. The energy dependence was found for the width of the Gaussian curve. An anomaly was found in the mass-yield curve above 45 MeV excitation or at the incident energy more than 40 MeV. The anomaly was then shown to be explained in terms of the mixing of the ordinary type of fission following direct process. The difference of the direct fission from the via-compound fission was seen to give rise merely to the difference in the effective excitation energy. The effective energy involved in the direct fission was about 60 % of the full excitation energy. Although we have obtained great success by decomposing the mass-yield curve into a number of the Gaussian curves, there remain some doubts about the general validity of the iitting. For example, for the same proton-induced fission of 238U at lower
197
---
ret
1
0
2
al
3 5
10
0
6
0
7
.
8
.
3
.
11
-
12
-.-
13
A
15
8
16
100
1000
Q(MeV)
Fig. 10. Observed values of the total fission cross section.
energies, the mass distribution peak is reported to have steeper slope in the far-asymmetric side than the near-symmetric side “). This is the opposite trend against the observation on the thermal-neutron-induced or spontaneous fission and the present work. Further investigation is needed on this question. The total fission cross section was estimated by integrating half the area under the solid line constructed in fig. 6 or 9. The resulting cross section values are displayed in fig. 10, together with the reported values.
References 1) H. G. Hicks and R. S. Gilbert, Phys. Rev. 100 (1955) 1286 2) 3) 4) 5) 6) 7) 8) 9) 10)
G. H. McCormic and B. L. Cohen, Phys. Rev. 96 (1954) 722 G. N. Harding, AERE report no. AERE N/R 1438 (1954) W. H. Jones, A. Timnick, J. H. Paehler and T. H. Handley, Phys. Rev. 99 (1955) 184 H. M. Steiner and J. A. Jungerman, Phys. Rev. 101 (1956) 807 A. Kjelberg and A. C. Pappas, Nucl. Phys. 1 (1956) 322 N. S. Ivanova, ZhETF (USSR) 31 (1956) 413; JETP (Sov. Phys.) 4 (1957) 365 A. K. Lavrukhina and L. D. Krasavina, J. Nucl. Energ. II, 5 (1957) 236 P. C. Stevenson, H. G. Hicks, W. E. Nervik and D. R. Nethaway, Phys. Rev. 111 (1958) 886 J. P. Butler, B. J. Bowles and F. Brown, Proc. Second Int. Conf. on the peaceful uses of atomic energy, Geneva (1958) paper P/6 11) C. B. Fulmer, Phys. Rev. 116 (1959) 418 12) G. R. Choppin, J. R. Meriwether and J. D. Fox, Phys. Rev. 131 (1963) 2149 13) G. L. Bate and J. R. Huizenga, Phys. Rev. 133 (1964) B1471
198 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34)
35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51)
H. BABA er ni. E. Hagebo, A. C. Pappas and P. Aagaard, J. Inorg. Nucl. Chem. 26 (1964) 1639 G. R. Choppin and E. F. Meyer, Jr., J. Inorg. Nucl. Chem. 28 (1966) 1509 A. C. Pappas and E. Hagebo, J. Inorg. Nucl. Chem. 28 (1966) 1769 G. P. Ford, Phys. Rev. 118 (1960) 1261 T. Suzuki, S. Baba, H. Umezawa and H. Amano, Nucl. Ins&. 87 (1970) 311 W. P. Trower, Univ. of Calif. Radiation Lab. report no. UCRL-11647 Rev. (1966) unpublished H. Natsume, H. Umezawa, T. Suzuki, F. Tchikawa, T. Sato, S. Baba and H. Amano, J. Radioanal. Chem. 7 (1971) 1.59 S. Baba, H. Baba and H. Natsume, J. Inorg. Nucl. Chem. 33 (1971) 589 H. Baba, S. Baba, T, Suzuki, 1. Ishikawa and H. Umezawa, Int. J. Appl. Radiat. Isotopes 21 (1970) 607 H. Baba, H. Umezawa, S. Baba and 1. Ishikawa, Int. J. Appl. Radiat. Isotopes 22 (1971) 141 M. J. Cabell, J. Inorg. Nucl. Chem. 21 (1961) 1 H. Umezawa, S. Baba and H. Baba, Nucl. Phys. A160 (1971) 65 J. A. McHugh and M. C. Michel, Phys. Rev. 172 (1968) 1160 H. Umezawa, J. Inorg. Nucl. Chem. 33 (1971) 2731 H. Baba and S. Baba, Nucl. Phys., Al75 (1971) 199 H. C. Britt and S. L. Whetstone, Jr., Phys. Rev. 133 (1964) B603 S. C. Burnett, R. L. Ferguson, F. Plasil and H. W. Schmitt, Phys. Rev. Lett. 21 (1968) 1350 E. Cheifetz and Z. Fraenkel, Phys. Rev. Lett. 21 (1968) 36 C. J. Bishop, R. Vandenbosch, R. Aley, R. W. Shaw, Jr. and 1. Halpern, Nud. Phys. A150 (1970) 129 1. Halpern, Ann. Rev. Nucl. Sci. 9 (1959) 245 E. K. Hyde, report UCRL-9036 Rev. (1962) unpublished; E. K. Hyde, Fission phenomena, The nuclear properties of the heavy elements, vol. III (Prentice-Hall, Englewood Cliffs, New Jersey, 1964) H. A. Tewes and R. A. James, Phys. Rev. 88 (1952) 860 R. A. Glass, R. J. Carr, J. W. Cobble and G. T. Seaborg, Phys. Rev. 104 (1956) 434 R. C. Jensen and A. W. Fairhall, Phys. Rev. 109 (1958) 942 R. C. Jensen and A. W. Fairhall, Phys. Rev. 118 (1960) 771 L. J. Colby, Jr., M. L. Shoaf and J. W. Cobble, Phys. Rev. 121 (1961) 1415 J. B. Laidler and F. Brown, J. Inorg. Nucl. Chem. 24 (1962) 1485 S. J. Lyle, Ci. R. Martin and J. E. Whitley, Radiochim. Acta 3 (1964) 80 R. H. James, G. R. Martin and D. J. Siivester, Radiochim. Acta 3 (1964) 76 E. Konecny and H. W. Schmitt, Phys. Rev. 172 (1968) 1213 R. B. Leachman, Proc. Second Int. Conf. on the peaceful uses ofatomic energy, Geneva (1958) paper P/2467 B. A. Bochagov. A. P. Komar and G. E. Solyakin, ZhETF (USSR) 38 (1960) 1374; JETP (Sov. Phys.) 11 (1960) 990 B. A. Bochagov, A. P. Komar, G. E. Soiyakin and V. I. Fadeev, Atom. Energ. 11 (1961) 540 S. S. Kapoor, D. M. Nadkarni, R. Ramanna and P. N. Rama Rao, Phys. Rev. 137 (1965) B511 T. D. Thomas, W. M. Gibson and G. J. Safford, Proc. Symp. on physics and chemistry of fission, Safzburg (1965) paper SM-60/36 T. T. Sugihara, P. J. Drevinsky, E. J. Troianello and J. M. Alexander, Phys. Rev. 108 (1957) 1264 G. Friedlander, L. Friedman, B. Gordon and L. Yaffe, Phys. Rev. 129 (1963) 1809 E. F. Neuzil, J. Inorg. Nucl. Chem. 28 (1966) 1519
2.J
I
Nuclear Physics Al75 (1971) 177-198; Not to be reproduced
MASS DISTRIBUTION
by photoprint
@ North-Holland
or microfilm without
Publishing
written permission
Co., Amsterdam from the publisher
AND THE TOTAL FISSION CROSS SECTION
IN THE FISSION OF =*U WITH PROTONS OF ENERGIES
RANGING BETWEEN
S. BABA, H. UMEZAWA Japan Atomic
Energy
Research
Institute,
13 AND 55 MeV
and H. BABA
Tokai-mura,
Naka-gun,
Zbaraki-ken,
Japan
Received 2 June 1971 Abstract: The fission of 238U with protons of energy ranging from 13 to 55 MeV was studied radiochemically. The mass-yield curve was obtained for each of the eleven incident energies, and an analysis was performed, based on the two-mode-fission mechanism. The observed total chain yields were reasonably reproduced by the combination of the three Gaussian curves with partial distortions. The deduced number of neutrons emitted in the fission was found to agree well with the postulated value in the study of the charge distribution systematics. For the three highest incident energies, the formation of the fissile nuclei through a direct process was shown to occur and the analyzing method was discussed. The peak-to-trough ratio and the total fission cross section were obtained from thus-established mass distribution curves. E
NUCLEAR
FISSION 2J8U(p, f), E = 13-55 MeV; measured fission product yields; deduced mass distribution, or, prompt n’s.
1. Introduction of the mass distriMany studies have been reported r-16) on the measurement bution and of the fission cross section in the 238U fission induced by protons with energies less than 20 MeV. Jn this energy region, the 238U fission is known to take place in both asymmetric and symmetric fission modes with comparable probabilities. Jones et al. have observed “) that the probability of asymmetric fission relative to that of symmetric fission decreases with increasing proton energy. The peak-to-trough ratio in the mass distribution is studied in detail by Butler et al. lo) and by Choppin et al. 12), as function of the proton energy, E,. They both find a prominent discontinuity in the peak-to-trough ratio at Ep z 7 MeV. The discontinuity has then been understood in relation to the threshold for the 238U(p, nf) reaction: intrusion of the 238U(p, nf) reaction causes decrease of the average excitation energy to be spent for fission, and consequently results in increase of the fission asymmetry. Ford has introduced an analyzing method “) of the mass distribution curve by means of the vector representations of the asymmetric and the symmetric mass distribution. He postulates that any mass distribution must be represented by the linear combination of the above two normal vectors, if the fission follows the two177
178
H. BABA et al.
mode-fission mechanism. Choppin et al. have applied ’ “) the method to the massyield curve of the 238U fission with protons of energies below 12 MeV. The limitation of this analyzing method lies in the fact that the basic two vectors must be fixed while energy changes. Therefore, it can not be applied for a wide range of the energy. For very high proton energies, the mass-yield curve and the fission excitation function have been studied by Lavrukhina et al. ‘), by Stevenson et al. “) and by Hagebo et al. 14). Th eir results indicate that the trough in the mass distribution disappears above about 100 MeV excitation, and the fission cross section remains constant above 30 MeV. Available data of the mass distribution and the fission cross section are rather scarce for the proton-induced fission of 238U in the energy range between 20 to 100 MeV. In this work, we, therefore, intended to supply those data in this energy region, connecting the low- and high-energy data. We expect in the present work to observe the continuous transition from the asymmetric fission at low excitation to the equivalent mixing of the symmetric fission into the asymmetric fission at high excitation. The energy dependence of each mass distribution and of the number of the prefission neutrons are also the object of our interest. 2. Experimental The uranium targets were prepared by sedimenting the purified U30, powder, suspended in liquid paraffin, onto the Al backing foil by means of the centrifugal force ‘*). Slightly depleted uranium (99.3 % of 238U and 0.68 % of 235U) was used. With this technique, targets ranging from 20 to 60 mg/cm’ in thickness were obtained with sufficient uniformity. Each stacked target assembly was constructed by piling Al foils of appropriate thicknesses among eleven or twelve U30s plates. The last U,Os TABLE 1
Irradiation conditions and thicknesses of targets Target no.
Run 1 (ZV)
U308 fmg/cm*)
-&I WeV)
24.00 26.43 21.30 28.52 29.92 30.92 32.62 32.80 42.37 51.29 27.04
55.0*0.2 5O.lkO.2 44.9 10.2 40.1*0.2 35.0f0.2 29.9 kO.3 25.OhO.3 21.7 +0.4 18.2f0.5 15.7kO.5 13.1&0.6 none
1
2 3 4 5 6 I 8 9 10 11 12 “)
50.250.1 44.9kO.l 4O.OkO.l 35.lhO.l 30.1 hO.2 25.0+0.2 21.8*0.2 18.1 f0.2 15.9*0.3 13.0*0.5 none
Run 3
Run 2 u3os (mg/cm*) 61.47 55.94 55.34 54.24 45.61 52.33 62.08 61.76 64.05 65.57 64.74 68.44
(&‘) 55.01-0.2 49.9 +0.2 45.OkO.2 39.9kO.2 34.9f0.3 29.9 10.3 25.110.3 21.810.3 18.1 ho.4 15.5io.5 13.OhO.6 none
“) These targets were placed out of the proton range as the monitor for background
U&8 (mgicm’) 64.86 64.03 61.26 61.40 61.67 54.26 59.60 55.23 62.47 66.26 72.36 75.48 neutrons.
238u(P,
f)
179
plate was placed out of the incident-proton range for estimating the amount of the contribution from the neutron-induced fission. The proton energy at each target was calculated by following ref. I’). Details are shown in table 1. Irradiation was carried out with the 55 MeV proton beam from the INS synchrocyclotron of the University of Tokyo. The beam current was about 0.1 /IA throughout the experiment. The beam intensity was measured with an electronic integrator. After the irradiation, each target, sandwiched between two Al foils of thickness hydrochloric acid and nitric 6 mg/cm2, was dissolved in a mixture of concentrated acid containing the following carriers: 20 pg of cadmium, 12 pg of palladium, 50 pg each of molybdenum and tellurium, 0.1 PC of the 6 5Zn tracer, 10 c(g each of rubidium, cesium, strontium, barium, yttrium and rare earths from lanthanum to terbium. Fission products were then separated sequentially by an ion-exchange method 20). Alkalies, alkaline earths and rare earths were separated quantitatively. The recoveries of molybdenum, palladium, cadmium and tellurium, which were not quantitatively obtained, were determined by means of polarography. The recovery of zinc was determined by y-counting the 6 ‘Zn activity after the fission product 12Zn had decayed out. An aliquot or all of the solution containing a thus-isolated element was evaporated on Mylar film and covered with Scotch tape. .4ctivities of the fission products obtained were measured with end-window flow proportional counters for several half-lives. The observed decay curves were analyzed by non-linear least-squares fitting with an electronic computer. The resulting halflife values were reasonable 21) compared with the reported values. The radiochemical purity was also examined by y-ray spectroscopy with a 7.6 cm o x 7.6 cm NaI(T1) scintillator fed to a multichannel pulse-height analyzer. Thus identified and determined activities were “Zn, 86Rb, *‘Sr, ‘lY, “MO, ll%,gCd, 132~~, 136~ 140Ba, 141,‘44ce, 143pr, 147Nd, 148,149pm, 153Sm, ’ 5 6E~ and ’ 60* ’ 61Tb. In order to determine the counting efficiencies of the counters for these activities absolute measurements were carried out for all nucleides determined in this work, by means of the 47~8 counting and 47$--y coincidence counting measurements 22-24).
3. Results The observed yields of the fission products are listed in table 2. Among them, the values for 86Rb, 13’%s, ’ 48Pm and ’ 60Tb are independent yields, whereas the others are cumulative. In order to find the correction factor for converting an independent or a cumulative yield into the total chain yield, one needs to know the most probable charge, Z,, , for the mass number and the charge dispersion curve. Here, we introduce the following two assumptions: (i) The charge d’istri ‘b ution follows the systematics derived in ref. 25); that is, AZp =
0 y(jq-0.51-0.04) 0.3511-0.51
for lr]-0.51 5 0.04 for 0.04 6 Iv-O.51 5 0.085 for Iv-O.51 2 0.085,
(1)
0.82 kO.03 39.3 f1.8 42.9 kO.6 64 &3 58 60 &3 24 f3 37.2 *1.8 40.8 *1.7 35.8 kO.8 27.7 +1.6 18.8 *0.3 13.2 50.6 4.26 ho.09 1.94 60.13 0.478+0.019
TABLE 2
44.9
0.63810.019 38 12 41 -+2 72 *4 51 54 &3 30 52 42.1 il.1 38.5 Al.4 34.9 *0.8 28.3 h1.5 17.8 kO.4 12.9 10.7 4.03 50.07 1.84 kO.06 0.42 &0.02
50.1
0.72 10.05 37.8 +0.7 44.3 kO.8 69 16 55 57 *4 25 14 39.3 fl.0 40.0 +1.5 35.5 40.8 28.7 11.6 18.6 k1.2 13.0 11.9 4.25 *0.08 2.03 *0.07 0.456hO.017 44 ,3 24 &7 40 13 36 13 32 +2 26.4 +1.4 17 f2 12.1 *0.6 3.7 *0.3 1.75 kO.14 0.353*0.017
0.487&0.016 13.4 +0.5 38.1 *I.6 73 54 50
40.0
Cumulative yields of fission product nucleides (mb)
0.382&0.010 33.6 *to.7 42 13 72 $5 46 44 13 30 15 46 13 40.1 *1.5 37.0 +0.9 30.2 hl.6 18.4 ItI.2 12.5 f0.4 3.9 40.3 1.83 *0.07 0.34210.012
35.0
-CO.011 *2 +0.9 14 k-t3 +9 13 53 13 &2 12 k1.2 *0.3 ho.16 10.02
0.293 32 35.8 69 41 38 33 4.5 41 37 30 19 12.4 4.2 1.83 0.32
30.0
F 2 3 z
$
3
I-.._
The errors
13zTe lroBa ‘We ‘43Pr ‘%e 14’Nd 149Pm ‘%m r’=‘Eu 16’Tb
’ Wd
‘*Zn 8”Sr 91Y 9pMo l12Pd
Nucleide
‘-\
quoted
25.0
deviations
0.1971 0.007 29.3 f- 0.6 35 *2 64 rt3 33 28 12 36 *11 43 13 38.4 & 1.7 31 zk4 28.6 f 1.7 18 &2 12.0 f 0.6 3.8 & 0.2 I.75 i 0.15 0.25 & 0;02
are the standard
EP
(MeV) -y..,
among
the results
obtained
0.118*0.004 23.1 kl.2 28.2 hl.7 54 &3 26 20.7 11.3 26 19 37.0 +1.7 33.3 11.4 28.2 ho.6 24.8 51.4 15.1 hl.6 10.0 kO.6 3.1 f0.3 1.5 10.2 0.25 -+-0.03
21,8
18.1
by two or three
separate
0.069;1rO.O03 19.3 3r1.4 23.8 kl.6 43 &3 18 16.6 kO.9 29 &6 33.3 fl.9 29 f5 26.0 h1.9 21.9 rt1.6 13.2 h1.8 9.0 kO.5 2.7 1;0.2 1.06 &0.15 0.141 kO.013
TABLE 2 (continued)
bombardments.
0.0337+0.0010 12.8 hl.4 16.0 kl.8 24.8 k1.5 8.3 6.9 *0.5 17 -16 23 12 20 &2 16.7 kO.4 15.4 rtl.7 10.2 11.0 6.0 &to.7 1.8 10.2 0.73 f0.15 0.089 ~0.008
15.7
8.2 7.5 6.4 3.9 2.8 0.7 0.32 0.040
kl.1 fl.9 kl.5 kl.2 &OS LO.3 &0.07 f0.005
0.0108&0.0006 5.6 rt.l.1 6.8 kl.3 13.6 hO.8 3.5 2.3 10.2 8 xt3 10 &2
13.0
3
s
2
183
H. BABA
et al.
where AZ,, is the deviation of the most probable charge Z, from the unchanged charge distribution and q is the mass fraction given by
with the mass number of the product, A, and that of the compound nucleus, A,. The number of the post-scission neutrons, vpost, and the number of the pm-scission neutrons (plus neutrons emitted at the moment of scission}, v,,, are given by
vposl=
1‘0
for
A&88
l.O+O.l(A-88) 0
for for
78 $ A 5 88 A 6 78,
(3)
and II
W@
=
hi - -
j- g .
-([email protected]). c
(ii) The charge dispersion is described by a common Gaussian curve with 202 = 0.95 [refs. 26*“‘)I for all mass chains and energies. Therefore, the fractional independent yield, p,(Z, IQ, at excitation of Ex is given by
The resulting Z, values for the nucleide cumulative yields of which were obtained turned out to be far away from the observed charges except for a few cases. Consequently, no correction was necessary to convert the cumulative yield to the total chain yield. As exceptions, the yields of 14’Ba, 144Ce, rSGEu and 13’Te needed to be slightly corrected at high excitation energies. The correction factor for the independent yields amounted, on the contrary, to as large as a few orders of magnitude. The resulting total chain yields are presented in table 3.
4. Heavy-mass wing of the asymmetric mass distribution We shall postulate the two-mode-fission mechanism in the following discussion. Thorough discussion on the justification of the postulate shall be given in ref. 28)_ General& speaking, the total chain yield, Y(A*, E,), of the primary fragment mass A” at the excitation energy E, csuf be expressed by means of the fission cross section, c+(E,), and the fractional mass yield, p(A”, E,), as Y(A*, Q
= ~(&)P(A*, Q.
(6)
If one considers the ratio of the yields between two fragment masses produced in the
g : N
t' *
O’OE
~~~_____.
ZO’O + ZE’O 9I'O F Pg.1 E'O "F Z'P Z'I i P'ZI ZF 61 Z'f OE ET LE E'F IP ET LP 911 LS Ef 8E IP VT 69 L'O F 8'SE z+ ZE 110'0 f96Z.O
O’SE
ZIO’O FfpPC’O LO'0 F S8'1 c-0 ii- 07 P'O i S'ZI 2'1 F P'81 9'1 f S'OE 6'0 =F O’LE S’I ‘F I’OV Ei 6P I11 99 ET Ptr 9t SF ZL ET zv L’O i 9’EE 10’0 f 6.20
.._.
_II_
O’OP
LIO’O TSSE’O PI’0 f 9L’I E’O T L’E 9‘0 'f 1'21 IT Ll VT f L’9Z z’-F ZE E’F 9E C'F SP OZ'F 89 Ef w IS VT EL 9'1 3: I'8E 8'1 'f 6'1E L10'0 'F9os.o
-.__
6W
ZO’OTZP’O 9O'O'f98'1 LO'Oi LO? L’O’F 6'21 VO;c 6'LI 9'IF L'6Z 8'O'F 6'PE P'I'f S'8E E'IF t'IS L=F L6 f'f P5 ZS PT ZL zi IP Z+ 8C ZO'OTL9'0
1'0s
-____
ZO'O 'f9'b.o LO'0 7-SO'Z 80'0 ~6Z'P 6'1 F I'CI Z'I F L'81 L’I F L’OE 8’0 F S’SE 5'1 T E'OP E'I 'F 5'6P 8IF 011 ti'f LS 9s 9"f 69 8'0 F E'PP L'O 'F 0'8E SO'0 ‘f9L.O
-
O'SS
ZO'O ?66p'O El'0 5zo.z 60-O TOE'P 9'0 ?" E'fl E'O 3: 0.61 8'1 3: O'IE 8'0 F 0'9E L'I F O'IP ZT OS 9IT WI E"F 09 65 ES P9 9'0 =f 6'ZP 8'1 "F S'6E EO'O iL8'0
191 951 ES1 6PI LPI PPL EPI IPI OPI ZEI SIT 211 66 16 68 ZL
(MS, 1.
..
._._~~~
0.199+ 0.007 29.3 f 0.6 35 +2 64 It3 34 28 12 58 +18 44 *3 38.4 f 1.7 31 *4 28.9 & 1.7 18 h2 12.0 f 0.6 3.8 i 0.2 1.76 f 0.15 0.25 & 0.02
25.0
0.119~0.004 23.1 k1.2 28.2 kl.7 54 +3 26 20.7 +1.3 39 +14 37.4 h1.7 33.3 h1.4 28.2 f0.6 25.0 hl.4 15.1 rt1.6 10.0 kO.6 3.1 +0.3 1.5 10.2 0.25 ho.03
21.8
--.
____
18.1
0.070+0.003 19.3 f1.4 23.8 bl.6 43 +3 17.8 16.6 f0.9 40 &9 33.6 11.9 29 *5 26.0 f1.9 22.1 61.6 13.2 k1.8 9.0 *0.5 2.7 f0.2 1.06 f0.15 0.141 kO.013
TABLE 3 (continued)
0.034~0.001 12.8 11.4 16.0 11.8 24.8 *1.5 8.4 6.9 ho.5 22 18 24 +2 20 *2 16.7 kO.4 15.5 Al.7 10.2 11.0 6.0 kO.7 1.8 ho.2 0.73 hO.15 0.08910.008
15.3
The errors quoted are the standard deviations among the results obtained by two or three separate bombardments.
72 89 91 99 112 115 132 140 141 143 144 147 149 153 156 161
Mass number
‘%.
0.0109~0.0006 5.6 It1.1 6.8 11.3 13.6 50.8 3.6 2.3 *0.2 10 *4 11 52 8.2 I-tl.1 7.5 51.9 6.4 Al.5 3.9 *1.2 2.8 10.5 0.7 fkO.3 0.36 f0.07 0.037 30.005
13.0
? 2 3 >
F
3
=*u(P,
same mode
of fission,
the fission
185
f)
cross section
is cancelled
out:
It should be mentioned that the observed yields are connected to the secondary fragment mass and, therefore, they must be transformed to the primary fragment masses. Recent measurements of the prompt neutrons 29-32) at medium excitation have revealed that the fragment-mass dependence of the neutron number is very weak except for extremely light fragments. It foliows that the primary fragment masses, A: and AZ, in eq. (7) can be directly replaced by the secondary masses, A, and A,. The fine structure in the mass distribution, generally observed in the low-energy fission 33P34), disappears in the fission at medium excitation (cf. fig. 6). This is a great advantage of the energetic fission, in discussing the fundamental structure of the mass distribution. Let us assume that the mass distribution is decomposed into three Gaussian curves, according to the two-mode-fissiol~ mechallism. The two outer peaks represent the distribution of the light and heavy fragments in the asymmetric fission while the central peak is for the symmetric fission products. For two fragments belonging to the heavy-mass peak, eq. (7) is modified to the form: 3(A,+A,)
= QKlfA,,
(8)
with Q=
1 &42-4
Here, p(A, E,) is substituted
In WI
3 41 (9)
Y(A2
3 -&I
’
by
p(A, EJ = 1 exp - (A-AcJ2 CUC a ( J
I-
(10)
One, therefore, ought to find a straight line by plotting $(A r + A,) versus Q for various combination of A, and Al, for a fixed value of E,. The results of the analyses are depicted in fig. I ; the linear relationship was observed at eight energies ranging from 18 to 45 MeV excitation, whereas the situation became complicated at the highest three energies, 50, 55 and 60 MeV. We, therefore, conclude that the asymmetric mass distribution is Gaussian at least between 18 and 45 MeV excitation, and the contribution of the symmetric fission is negligible in the lowest mass chain used, e.g., 132 amu, up to 45 MeV. From the slope of the obtained straight line, we found the following relation between the width and the energy: & - 106 = 0.235(E, - 14.0),
(11)
as shown in fig. 2. The value of CIat the 14 MeV excitation corresponds to FWHM of 17.1 amu. We have collected the FWHM from available mass-distribution curves [refs. “* “-“)] in various &site systems. They are listed in table 4. The lowest
T_...____-_.~-
a/ *4’ 35 2 MeVT-
s 8+ d
Fig. 1. The linear presentation of the Gaussian mass distribution, eq. (8). The energy denoted near the right end of the solid line gives the excitation energy. For the highest three energies, the points to which the yield of the 132 mass chain is related are depicted with solid marks. The dotted lines there represent the likely mass distribution of the direct fission involved.
E, (MeV) Fig. 2. The energy dependence of the width parameter, cc, for the asymmetric mass-yield peak.
187
238U(P, f)
possible value of FWHM, 17.1 amu, of our Gaussian curves are obviously than those values in table 4. Mixing of fission occurring at various stages neutron-emission chain may partly be the reason for the higher value obtained
larger of the by the
TABLE 4 Widths
of the symmetric
and asymmetric
Reaction
(PWHM),,, (amu)
19’Au(c(, f) 204Pb(a, f) 206Pb(a, f) ‘04Bi(d, f) 226Ra(p,f)
*“‘Pb(a,
f)
226Ra(d,f) 232Th(n, f)
Z3ZTh(p, f) 233U(a, f) *38U(n, f) 238U(P, f) z40Pu(sp, f) 239Pu(a, f)
238Pu(a,
mass distributions, curves
f)
43 43 43 20 11 13.0 28.9 33.2 37.5 41.1 14.5 2.1 6-11 69 14.7 6.1 34.5 14.7 7.1 9.4 12.0 I 43.8 46.0 47.5 42.2
34 28 22 16 16 19 23 16 16 18 18 28
21
read from the constructed
(FWHM),,,, light
(amu)
distribution
Ref.
heavy
=) 3*) 38
)
=) -) 13 16
13 16
14
37 ) 53 ) 51 ) 51) 51 ) 51) =) 41
15 12 12.5
41 : 51 ) 41
14 14 14
14 14
35 ; =Y 42)
14
14
15
14
14
1
45 48 42 51
extrapolation. Further discussion on this question shall be however postponed until sect. 6. The intercept of the straight line in fig. 1 gives the peak position. The peak centre could be determined within +0.2 amu for all the energies. We found that the peak position was fixed at 136.0 amu for excitation up to 30 MeV, and then starts to shift towards the light-mass side as the energy increases. The stationary peak position may be connected with the observation that the edge of the heavy-mass peak lies at the same position for the fission of transuranium elements 33, 34).
188
H. BABA et al.
5. Centre of the light-fragment
peak
In the region of the light-mass peak, sufficient numbers of the total chain yields are not available for carrying out the same type of the analysis as for the heavy-mass peak. Therefore, we combine the yield, Y(A,, &), of a mass chain A, in the Iightmass region with that of a mass chain A, in the heavy-mass region. Then, we have the following relation:
Kere, we already know the values of Ati,* and cr,. Equating aL to aH, one can caiculate A,_, o, which should be the same for different masses of AL and AH. The approximation that aL = ti,., may be allowed because the number of the post-scission neutrons is reported to be very small in any respect29-32). 110 -, ,
loo-
_I_ Im_.--)
_,-,.
Ex = 501 t&V
go-
1
451hw
90 q1oQz_
._._ ___~_..
goIOOL_..
_.---,-.----.
hw
_L,-..-,_*_.~
__..,
_I_.*_
352t.W
90100”
_._ ___.
401
1
go-
‘-,-,_‘_‘_,_,-.-.--~302 Mev
tGor._y._.__
._,. _-.._
.._..
, L_-_--.I__
_,_-___,-
-.-
27OM2V
90-
~or_i_~.~._...-.-.-_-,_.___,~
90” 100r_,____90-
130
233
MoV
m_,m,_*.‘_*
-,--
209hw
140 150 HEAVY FRAGMENT MASS
Fig, 3. Det~r~nation
160
of the light-fragment-yield
peak.
-TJ(p,
f)
189
Fairly well constant values were obtained for the nine energies + between 18 and 50 MeV, as shown in fig. 3, so that AL,O were determined with high precision. The resulting peak positions, AH,O and ALSO, and also the centre of the whole mass distribution, A, = +(AH,O +AL,O) are displayed versus excitation energy in fig. 4. Up to 30 MeV excitation, the light-mass peak is found to shift toward the lighter-
0
0 0
130-
2 120.z! B
0
cantra
of
maaS dlstrlhullon @oeeeo eaAA
!i 2
llO-
0
20
40
GO
E, (Mei’)
Fig. 4. The determined peak positions of the light- and heavy-fragment-yield curves and the resulting centre of the mass distribution. Triangles represent the mass-distribution centre deduced from the neutron systematics, eqs. (3) and (4).
mass side, due to the increase of the pre-fission neutrons per fission. Meanwhile, the heavy-mass peak is fixed at 136 amu. When the excitation energy exceeds 30 MeV, the hindering factor against the shift of the heavy-mass peak, AH,O, is removed and the An, o begins to decrease so rapidly that the A,, o inverts from decrease to increase. One can obtain the total number of neutrons from the difference between twice A, and the mass of the compound nucleus. On the other hand, we have introduced the neutron systematics, eqs. (3) and (4), in the charge-distribution correction. The centre of the observed mass distribution, A,, is given by
4, =
!&k-~pre>-1-
(13)
Here, the last term in the right, 1, arises from vpost given by the first of eqs. (3). The value of A,,, thus deduced is also displayed in fig. 4. One may notice that the agreement between the values of A, from two different sources is satisfactory. This is more t The result obtained on the 50 MeV data is included in figs. 2 and 3 since it is still meaningful even at that energy, as shown in sect. 7.
H. BABA et al.
190
clearly visualized in fig. 5, in the form of the total number of the neutrons emitted per fission. The Leachman’s systematics 44) is also added in the figure. As was stated in sect. 3, most cumulative yields were practically the total chain yields as they were. It follows that there was not much freedom in the choice of the neutron systematics because the centre of reflection in the mass-yield curve had been lo-
I
1
,
/
,
,
l
8.
f
060 . Q
6-
68 0,
,a* l
e*+ +
o+ + 0
4-
Obserbed
.
+2++
+
Z2 J’“~+-&-‘90
2-
I OO
I 20
I
I
I
I 60
E, (Me:: Fig. 5. The total numbers of the neutron emitted per fission, obtained from three different sources of information.
tightly fixed. One sees, in fig. 6, that the introdu~d neutron systematics, given by eqs. (3) and (4), determines the reflection centre very well. Now, we have found that the total number of the emitted neutrons, obtained as a result of the analysis, is almost the same as that introduced at the beginning. This implies that we have successfully constructed a self-consistent systematics governing the charge and mass distributions and the number of emitted neutrons.
6. Off-Gaussian structure of either peak in the asymmetric region and the symmetric mass distribution By making use of the information we have extracted on the mass-yield curve, we can reproduce the mass-distribution curve in the asymmetric region; namely, the width of the Gaussian curve is calculated by eq. (1 I), the peak position is read from fig. 4, and the peak height is normalized to the observed yields. The resulting curves are represented by the dotted line in fig. 6. The observed yields are found to fit very well to the thus-drawn Gaussian curves in the mass region heavier than 131 amu and in the corresponding light-mass wing.
2YJ(p,
f)
191
.
9 13 e 15 o this work A
1
0.01
o-3. I
I
GO
80
100
FRAGMENT
120
140
160
MASS
Fig. 6. The secondary mass-yield curves. The dotted line gives the sum of the two Gaussian curves fitted to the observed yields in far-asymmetric-mass regions. The dashed lines represent the resulting mass-distribution curves both for the symmetric and asymmetric modes of fission: the sum of the three dashed curves equals the gross mass-yield curve drawn with the solid line.
calcd. Ba = 5.7 MeV as= G 7MeV a = 27MeV‘’ tiw = 0.5MeV
0
r
I
I
20 EXCITATION
f
!
I
I
40 60 ENERGY(MoV)
Fig. 7. The observed trough-to-peak ratios in the fission of 238U with protons. The solid line is the result of the calculation by means of eq. (6) of ref. zs).
From the peak height of the mass-yield curve and the bottom of the valley, we obtain the trough-to-peak ratio. They are plotted versus excitation energy in fig. 7, together with the reported trough-to-peak ratios 4V9S13*1 “). They all are found fairly well consistent with one another. The dotted line in fig. 6 suggests that one must admit the existence of asymmetric fission in an appropriate proportion even at the very symmetric mass division. The observed fragment-kinetic-energy distribution 45-48) and the charge distribution “), however, strongly indicate the non-existence of the asymmetric mode of fission in the
H. BABA
192
et al.
symmetric mass region. Therefore, our Gaussian mass-distribution curve must be depressed in the near-symmetric side. This type of distortion of the asymmetric mass distribution peak is consistent with the asymmetric peak shape of the massyield curve in the low-energy fission of transuranium elements 34*4g), in which the slope of the inner wall is much steeper than that of the outer wall. In sect. 4, we have obtained considerably larger value, for the smallest possible FWHM of the Gaussian curve, than the observed FWHM from various mass distribution curves. Then, we ascribed the reason partly to mixing of multiple chance fission. Now, we can also interpret the discrepancy in terms of the distortion of the peak from the Gaussian shape. Suppose one accepts that the contribution of asymmetric fission is negligible in the trough region. Then, the trough-to-peak ratio presented in fig. 7 can be directly subjected to the analysis explained in ref. ““) [cf. fig. 3a of ref. ‘s)]. According to the results obtained, the following relation was confirmed to hold between the trough-topeak ratio, Rfjp, and the cross section ratio, cr,/cr,:
On the other hand, half the trough-to-peak
ratio is given by
where CC,is the width parameter for the symmetric mass distribution and S is the apparent asymmetric fission cross section, deviating from the real cross section u, because of the distortion of the peak shape. The total chain yield, Y(A, E;), should now be described as S(E >
(16)
instead of eq. (6). If we introduce the simple approximation of the substitution of the sudden cut-off of the Gaussian curve at mass AG for the distortion, the apparent cross section S is expressed
as =qE
) I
2dEJ
(17)
1+erf’
in terms of the real cross section g= and the error function,
erf(Z),
with
(18) By making
use of eqs. (14), (15) and (17), one obtains Ja,
= +(l +erf (Z)>JE.
(19)
z3*u(P,
The residue in the subtraction from the whole outline should
193
f)
of the thus-constructed Gaussian mass distribution in turn constitute the inner slope of the asymmetric TABLE 5
The resulting
18.2 20.9 23.3 27.0 30.2 35.2 40.1 45.1
0.21 0.46 0.71 0.82 0.94 1.09 1.21 1.31
0.018 0.055 0.13 0.19 0.25 0.36 0.41 0.43
fission
cross sections
0.23 0.52 0.85 1.01 1.19 1.45 1.63 1.74
0.22 0.51 0.84 1.01 1.21 1.45 1.63 1.76
0.086 0.12 0.19 0.23 0.27 0.33 0.34 0.33
0.077 0.13 0.18 0.23 0.28 0.33 0.33 0.31
The fourth column gives the sum of 6. and CT$,the second and the third columns, while the fifth column shows half the integrated area under the gross mass-yield curve. The sixth column gives the crosssection ratio of the symmetric to asymmetric mode of fission, which should be equal to half the trough-to-peak ratio, &R,in the last column.
distribution; now, the area of the asymmetric peak must satisfy the requirement, eq. (14). Construction of the self-consistent mass distribution, therefore, depends on the appropriate choice of the parameter 2. Consistent results could be obtained by a simple assumption: Ao = A,+6. The resulting symmetric and asymmetric peaks are displayed and the obtained cross sections are summarized in table 5.
PO) with dash lines in fig. 6,
7. Fission following direct processes So far we have excluded the data for the highest three energies, 50, 55 and 60 MeV excitation, or more reasonably the incident proton energies of 45, 50 and 55 MeV, because of their anomaly (cf. fig. 1). As is obviously seen in fig. 9, the yield of the 132 mass chain is abnormally high for these three energies. This is the result of the overcorrection for the charge distribution regarding the yield of ‘32Te, because of the invalidity of the systematics, eqs. (1) to (4), in that energy range ‘“). Let us, therefore, use the interpolated value in the mass-yield curve for the yield of the 132 mass chain, instead. The points with which the interpolated value of the 132 mass yield is concerned are displayed with solid marks for the three energies in fig. 1. From the figures, we can conclude that the anomaly is not of a superficial character evoked merely by the superposition of the symmetric mass distribution on the lowermass side of the asymmetric mass distribution. If the anomaly is caused by the inflow
I94
H. BABA
et al.
of the symmetric mode of fission into, say, the 132 mass chain while the Gaussian distribution following eq. (11) and fig. 4 still exists, one should observe a straight line, from which only the solid marks deviate to the right. The disappearance of the systematics above 45 MeV reminds us that the violation of the systematics of the charge distribution has begun about the same energy ‘“)_ The most naturally expected cause is the mixing of direct fission. We shall attempt to find the analyzing method of the mass distribution when direct fission is mixing. Let us denote the asymmetric direct fission cross section by a,,, and the cross section for the asymmetric fission via the compound nucleus formation by o,,,. The total chain yield for the asymmetric fission is now described as
where S, and S, are the apparent fission cross sections, respectively corresponding to d B,c and c*,~, as functions of the incident energy Ep, and pd is the mass distribution function for the direct fission at the effective excitation energy Ed. Here, we have taken into account the effect of the distortion of each distribution function from the full Gaussian curve. For the combination of mass chains, A, and AZ, we obtain
(22) where A
Y
=
‘CA,3 E,7) ___.____ _ Y(A, Ep) 1641s Ed ~(4 4) 9
9
and
One, therefore, should obtain a straight line through the origin when plotting dy versus A,, if one knows the two distribution functions, p and pd. As for the mechanism of direct fission, one may recall the following two types; direct fission in the literal sense as found in the extremely high-energy region 50) and the usual type of fission through saddle-point deformation of the residual nucleus formed by the direct process. Considering our energy range, it would be reasonable to postulate the latter mechanism. Then, the difference between the via-compound fission and the direct fission is mainly in the magnitude of the available energy. Hence, we assume that p follows the systematics given by eq. (1 I), which are depicted with solid lines in fig. 1, andp, is considered to be replaced byp at E, = Ed. With this postulate, our concern is now to find the most likely value of Ed satisfying eq. (22). Quite satisfactory results were obtained when we chose 31, 34 and 37 MeV as Ed, respectively for the incident energy of 45,SO and 55 MeV. The results are shown in fig. 8. Considering that eq. (22) requires high precision for the observed yield values, the agreement is rather remarkable. The anomaly of the yield of the 161 mass chain,
z38u(P,
displayed
with triangles
195
f)
in fig. 8, may be ascribed
to the warp in p from the Gaussian
curve in the region far off the centre. From the slopes of the straight lines in fig. 8, S, is read out to be 0.25,0.80 and 1.10 b for the incident proton energies, EP = 45, 50 and 55 MeV, respectively. With these values of S,, the S, values are found to be 1.62,0.88 and 0.51 b in the above order of
-1
cl
1
-1
0
1
-1
0
1
7.
4
Fig. 8. The linear presentation of the contribution of the direct fission. In order to show the offGaussian character of the yreld of the heaviest mass chain of 161 amu, the points to which it is related are distinguishedly depicted with triangles.
80
120 140 100 FRAGMENT MASS
160
Fig. 9. Analysis of the mass-yield curve obtained in the three proton energies, 45, 50 and 55 MeV. The asymmetric-mass region was decomposed into two Gaussian curves, one for the via-compound fission and the other for direct fission, according to the results of fig. 8. The dotted lines represent the two Gaussian curves, while the dashed line gives the sum of them. The solid line, the whole mass distribution, was drawn through the observed yields.
H. BABA et al.
196
the energy. The resulting mass-yield curves in the asymmetric region are drawn with dotted lmes for the non-direct and direct fission and the sum of the two in fig. 9. The light-mass wing of the whole mass-yield curve was found to be the perfect mirror image of the heavy-mass wing as shown in fig. 9. That is, the centre of reflection for the direct fission lies at the same position as that for the via-compound fission, though it is not necessarily expected. In order to obtain the true cross sections, (T~,~and o,,,, we claim that the relations through eqs. (17) and (20) hold also in this case. The resulting values of c*,~ and u~,~ are given in the third and fifth columns of table 6, while the total fission cross section, as half the area under the solid line in fig. 9, is given in the last column of the table. We shall not attempt further analysis of the near-symmetric part of the massyield curve since there are a number of unknown factors involved. TABLE 6
The through-compound
Incident energy
fission cross section, CT,,,, the direct fission cross section, Ga,d, in the asymmetric mode, and the totai fission cross section, n,
(2”)
0a.s (b)
EP
( MeV) 45 50 55
50 55 60
1.30 0.65 0.33
31 34 37
0.24 0.16 1.05
1.90 1.87 1.88
The two-mode-fission mechanism was found to work quite satisfactorily on the observed mass-yield curve for the proton-induced fission of 238U at least up to 45 MeV excitation. The mass-yield curve was decomposed into three Gaussian curves, though the outer two curves had to be distorted on the near-symmetric side. The centre of the hevay-mass peak was found to be fixed at 136 amu up to 30 MeV and start to shift towards the lighter-mass side above 30 MeV. The energy dependence was found for the width of the Gaussian curve. An anomaly was found in the mass-yield curve above 45 MeV excitation or at the incident energy more than 40 MeV. The anomaly was then shown to be explained in terms of the mixing of the ordinary type of fission following direct process. The difference of the direct fission from the via-compound fission was seen to give rise merely to the difference in the effective excitation energy. The effective energy involved in the direct fission was about 60 % of the full excitation energy. Although we have obtained great success by decomposing the mass-yield curve into a number of the Gaussian curves, there remain some doubts about the general validity of the iitting. For example, for the same proton-induced fission of 238U at lower
197
---
ret
1
0
2
al
3 5
10
0
6
0
7
.
8
.
3
.
11
-
12
-.-
13
A
15
8
16
100
1000
Q(MeV)
Fig. 10. Observed values of the total fission cross section.
energies, the mass distribution peak is reported to have steeper slope in the far-asymmetric side than the near-symmetric side “). This is the opposite trend against the observation on the thermal-neutron-induced or spontaneous fission and the present work. Further investigation is needed on this question. The total fission cross section was estimated by integrating half the area under the solid line constructed in fig. 6 or 9. The resulting cross section values are displayed in fig. 10, together with the reported values.
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