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Correlation between fragment mass-distribution fine structure, charge distribution and nuclear structure for thermal-neutron-induced fission of 233U and 235U
I
2.J
I
Nuclear Physics A205 (1973) 348--362; (~) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprintor microfilmwithout writtenpermissionfrom the publisher
CORRELATION BETWEEN FRAGMENT MASS-DISTRIBUTION FINE STRUCTURE, CHARGE DISTRIBUTION AND NUCLEAR STRUCTURE FOR THERMAL-NEUTRON-INDUCED F I S S I O N O F 2aaU A N D 2aSU W. N. REISDORF *, J. P. UNIK and L. E. GLENDENIN Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 ~*
Received 20 December 1972
Abstract: Masses corresponding to observed fine-structure peaks in the fragment mass distributions for thermal-neutron-induced fission of 2aaU and 235U are shown to correspond to average measured masses for even-even nuclear charge splits. Evidence is presented that the yield enhancement for even-Z fragments is not restricted just to fission events with higher-thanaverage total kinetic energy. The anomalously high yield of fragments with mass 134 in 2aSU(n, f) as opposed to 233U(n, f) is tentatively correlated with rapidly changing nuclear structure properties as a function of the mass of the complementary light (Z : 40) fragments. I E
NUCLEAR FISSION 2aa.235U(n, f), E : th; measured fragment kinetic energies, (fragment) (fragment)-coin.; deduced fragment mass-total kinetic energy correlations.
1. Introduction F i n e structure has been previously observed 1 - 6 ) in fission-fragment mass distributions as a function of pre-neutron-emission mass .4 for t h e r m a l - n e u t r o n - i n d u c e d fission (n, f) of 233U, 235U, 239pu a n d s p o n t a n e o u s fission (sf) of 252Cf. There is general agreement that the fine structure observed in the mass distributions occurs at intervals of ~ 5 a m u (primarily for heavy-fragment masses A ~ 135, 140 a n d 145 and associated c o m p l e m e n t a r y light fragment masses), with the fine structure accentuated for fragments possessing low excitation energies. T h o m a s a n d V a n d e n b o s c h 7) have correlated the observed fine structure with structure in the calculated massenergy surface (as a f u n c t i o n of Z and N) for doubly even fragments. The nuclear pairing effect depresses the potential energy surfaces for f o r m a t i o n of doubly even fragments relative to odd-A a n d doubly odd fragments. Therefore, based o n simple energetic considerations, a preferential f o r m a t i o n of doubly even fragments may be expected in the fission of a doubly even nucleus at low excitation energies. The obLaboratoire R6n6 Bernas, Centre de Spectrom6trie Nucl6aire et de Spectrom6trie de Masse, 91 Orsay, France. ** Work performed under the auspices of the US Atomic Energy Commission. 348
233. 235 U THERMAL FISSION
349
served periodicity of ~ 5 amu can then be correlated 7) with the fact that the masses of the most stable nuclei for neighboring even-Z nuclei differ by ~ 5 amu. In a previous study 8) mass distributions as well as the distribution of nuclear charge between the two fragments (as deduced from K X-ray measurements) were obtained for thermal-neutron-induced fission of 233U, 235U, 239pu and spontaneous fission of 252Cf" In this paper the results obtained for the first two fissioning systems are used to investigate in detail (i) correlations between nuclear charge division and fine structure observed in fragment mass distributions, (ii) the dependence of the fine structure on the final excitation energies of the fragments, and (iii) the possible influence of single-particle effects on the fission process 9-11).
2. Experimental procedures and results Since the experimental and data analysis methods used have been previously described in detail s), only the more pertinent points will be given here. Enriched targets of 2aaU (75 pg/cm 2) and 235U (50 pg/cm 2) prepared by vacuum volatilization of the tetrafluorides onto nickel foils (90 pg/cm 2) were irradiated with a well-collimated beam of thermal neutrons (3 × 107 n" cm- z. sec- 1) at the Argonne CP-5 Research Reactor. The complementary fission fragments were detected in coincidence by two goldsurface-barrier silicon detectors. The two resultant pulse heights for each event were digitized and stored on magnetic tape for subsequent computer analysis. The preneutron-emission masses were calculated using the energy calibration method described by Schmitt et al. 1~), the conservation of mass and linear momentum in fission, and correction for prompt neutron-emission effects 13) as functions of mass and TKE. The fragment mass distributions for 233U(n, f) and 235U(n, f) (obtained from the analysis of 3.7 x 105 and 7.4 × 105 binary fission events, respectively) are shown in fig. 1. These mass distributions were not corrected for the experimental mass resolution of ~ 4 amu (FWHM), in order to illustrate the amount of fine structure directly observed. The observed distributions are relatively smooth and in excellent agreement with earlier work 14,15). It is apparent from fig. 1 that fine structure exists in the form of shoulders and smooth maxima in the peak-yield regions and that this structure is somewhat different in the two fissioning systems. In earlier studies t. z) the structure was shown to be more pronounced if a high-energy restriction is imposed on the kinetic energy of the light fragment, EL. This energy restriction, in effect, imposes a restriction on the total excitation energy of the fragments, E*. At infinite fragment separation, E*, is given as E* = BE*(AF, Z F ) - B E ( A n , ZH)--BE(AL, Z L ) - T K E .
(1)
Here, BE*(AF, ZF) represents the binding energy of the excited fissioning nucleus with m a s s A F and nuclear charge ZF; BE(AL, ZL) and BE(AH, ZH) represent the binding energies of the light and heavy complementary fragments, respectively,
350
W . N . RE1SDORF et al.
in their ground states. The total kinetic energy of the fragments, TKE, is given as TKE
E.,A~/.4.
=
= E.A~/aL.
(2)
From eqs. (1) and (2) it can be seen that the selection of those events for which the light-fragment kinetic energy EL is greater than the average EL will result in selection of events with lower than average excitation energies. Also, since the kinetic energy of the light fragments has previously been shown to be rather independent of the mass division in fission [with E L = 102.0-1-1.0 MeV f o r 233U(n, f) and E L = 101.4_+ 1.0 MeV for 235U(n, f)], the selection of light-fragment kinetic energies greater than the average value implies by eqs. (2) and (3) that ATKE and AE* are also rather constant for all mass divisions: AE*= E*-E*=
TKE-TKE
(3)
= -ATKE.
A demonstration of the fact that the available fragment excitation energies decrease rather uniformly for all mass divisions by selection of increasing values of E L is given in fig. 2a. Selecting values of EL = 112-113 M e ¥ for 2aSU(n, f) is seen to be equivalent to selecting those fission events for which the total kinetic energy release is 18 + 2 MeV greater than the average for each mass division, and consequently the average fragment excitation energies are reduced by this same amount. 106 I
LIGHT FRAGMENT MASS 96 86
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140 150 HEAVY FRAGMENT MASS
Fig. I. Fragment mass distributions for 233U(n, f) and 235U(n, f) measured by the double-energy method, uncorrected for experimental mass resolution a),
233, 235 U
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126
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Fig. 2. Energetics for 233U(n, f) a n d 235U(n, f). (a) Difference o f total f r a g m e n t kinetic energy release ( T K E ) relative to average values as a function o f f r a g m e n t m a s s for 235U(n, f) with lightf r a g m e n t kinetic energies restricted to EL = 112-113 MeV; (b) calculated m a x i m u m energy release ( Q - - T K E ) as a function o f f r a g m e n t m a s s for selected values o f EL.
Mass-yield curves (with the ordinate scale in absolute units of b/MeV • amu) obtained for selected values o f E L are shown in figs. 3 and 4for 235U(n, f) and 233U(n, f), respectively. By restricting the selection of E L to large values only a small fraction of the total data is used. For example, for E L m 104 MeV (near the average E L value of 101 MeV) the peak mass yields are g 3 b/MeV • amu as compared to m0.15 for E L ~ 112 MeV. The major experimental contribution to the widths of the observed fine-structure peaks in double-energy measurements as used here is the dispersion introduced in the fragment velocities by neutron emission (isotropic in the center of mass) and is proportional to the number of neutrons emitted by the fragments. For events associated with high T K E release (as in fig. 3d) the number of neutrons emitted is nearly zero, and hence the mass resolution is expected to be quite good, ~ 2 amu ( F W H M ) due to the intrinsic resolution of the detectors and slight energy loss in the tax get. For those mass distributions associated with lower TKE, larger numbers of neutrons are emitted, and consequently the experimental mass resolution is worse. This neutron contribution to the mass dispersion tends to mask fine-structure effects
352
W . N . RE1SDORF et aL LIGHT FRAGMENT MASS 86 106 96 86 23Su (n,f) ~ (b)EL = (a) EL = (1~-105) MeV i (108-109) MeV 1.5
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Fig. 3. The 2aSU(n, f) fragment mass distributions for selected light-fragment kinetic energies. Solid arrows indicate measured masses corresponding to even-Z charge divisions in fission a). Dotted arrows in (c) indicate masses predicted by the unchanged-charge-density (UCD) assumption.
TABLE 1 Average pre-neutron fragment masses for various atomic numbers ") Zn
52 54 56 58
") Ref. 8). b) Associated errors I 0 . 3 amu.
Average pre-neutron fragment masses b) 23ZU(n, f)
zaSU(n, f)
133.7 138.6 143.5 148.3
134.6 139.7 144.8 149.8
233,235U T H E R M A L
FISSION
353
in the mass distributions for TKE values less than or near the average values bat allows the fine structure to be more easily observed for large values of TKE. Since an average energy of ~ 16 MeV/fission is released in the form of neutron emission for 2 3 5 U ( n , f ) (vx = 2.43 [ref. 16)], with an average energy of 6.5 MeV/neutron [re['. 17)]), it is concluded that for EL > 112 MeV the average number of neutrons emitted from the fragments is appreciably less than one, and that the post-neutron masses will be essentially identical to the pre-neutron masses.
94
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z 3 a U ( n , f) fragment mass distributions for selected light-fragment kinetic energies. Solid arrows indicate masses corresponding to even-Z charge divisions a). Dotted arrows in ( b ) indicate masses associated with even-Z charge splits observed for 23~Lr(n, f). F i g . 4. T h e
The correlation of the structure observed in fragment mass distributions with the previously determined charge division in fission 8) is shown in figs. 3 and 4. The average pre-neutron masses associated with even-even charge splits determined from the previous study 8) of charge division based on the measurement of characteristic K X-rays emitted by fragments of measured masses are indicated by solid arrows in figs. 3 and 4, and are also given in table 1. The excellent agreement between the average masses associated with even-Z charge splits and the masses associated with the finestructure peaks is a direct demonstration that the fine structure in fragment mass distributions is closely connected with even-even charge divisions in fission. As a demonstration of the sensitivity of this comparison, the dashed arrows in fig. 3 indicate the masses predicted by the "unchanged charge density" ( U C D ) assumption of nuclear charge division, i.e., the charge density (Z/A) of the fragments is the same as
354
W.N. REISDORF et al.
that of the fissioning nucleus. The experimentally measured charge distributions are generally displaced by ~0.5 charge units from the UCD assumption 8). The dashed arrows shown in fig. 4 for 233U(n, f) indicate the masses associated with even-even charge splits observed for 235U(n, f). Clearly the present correlation of the observed fine structure with even-even charge divisions is well within 0.5 charge units, and even small isotopic shifts can be observed. 3. Discussion
3.1. CORRELATION BETWEEN MASS-DISTRIBUTION FINE STRUCTURE AND CHARGE DISTRIBUTION IN NUCLEAR FISSION Some qualitative insight into the relative probabilities for the formation of fragments of various mass and charge in fission can be obtained on the basis of energy considerations. The calculated fragment excitation energies, E*(Z, A) = Q(Z, A ) - T K E ( A ) ,
(4)
for various fissioning conditions are shown in fig. 2b. For these calculations, the Qvalues were obtained from the work of Seeger and Perisho 18). The T K E values were those measured in this work by the double-energy method reduced by 2 MeV to partially compensate for the generally observed, and as yet unexplained, 4 MeV disagreement between T K E values measured by double-velocity and double-energy methods 19). The fragment excitation energies are always greatest for formation of doubly even nuclei as can be seen in fig. 2b by comparison of E* = (Q - TKE) values for doubly even nuclei with doubly odd nuclei in the case of 235U(n, f) with EL = 112-113 MeV. The energy surface for formation of odd-A nuclei (not shown) is a smoothly varying surface ~ 2.4 MeV lower than the surface for doubly even nuclei. On the basis of such calculations the formation of doubly even fragments is expected to become increasingly more probable relative to odd-A and doubly odd nuclei with decreasing excitation energy ( Q - T K E ) and consequently with increasing values of EL. For sufficiently large values of E L only doubly even fragments would be formed on the basis of these energy considerations. This is in qualitative agreement with the known experimental observations that with increasing values of E L the structure in fragment mass distributions becomes more pronounced and those mass divisions leading to formation of even-Z fragments are strongly enhanced. The vertical arrows shown in fig. 2b indicate the mass positions of the observed fine-structure peaks. These positions do not tend to coincide with the maxima of the excitation energy of doubly even nuclei. The simple criterion of maximum fragment excitation energy at infinite fragment separation is not expected to quantitatively explain mass-yield fine structure. The correlation between charge division and mass-distribution fine structure is more readily apparent through examination of charge division diagrams such as that given in fig. 5 for 2aSU(n, f). Plotted on this complementary charge and mass dia-
233, 235 U
THERMAL
FISSION
355
gram is the charge division line (KX) obtained by K X-ray measurements s). This line represents the experimentally measured average (more exactly the most probable) nuclear charge Zp for a given fragment mass. Instead of the most probable nuclear change (Zp), the quantity (Zp--ZucD)H, L has been chosen as ordinate where (ZucD)., L = ZFAH,LIAr. Individual nuclei are represented in this diagram by discrete points. For simplicity only points for doubly even nuclei are given. The lines labelled ZL/Zn connect points for fragments formed with the same nuclear charge but varying 2.(3
116
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LIGHT FRAGMENT MASS 96
86
76
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,,=t 0.~
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140 HEAVY FRAGMENT MASS
Fig. 5. Charge division d i a g r a m for 235U(n, f). Filled circles represent specific doubly even charge a n d m a s s splits. T h e diagonal lines represent constant charge splits ZL/ZH or c o n s t a n t n e u t r o n splits f o r NL = 50 a n d NH = 82. T h e line indicated K X represents the experimentally m e a s u r e d charge division s).
masses. Fragments formed with either 50 or 82 neutrons are joined by dashed lines. The probabilities for formation of fragments with given masses and nuclear charges depend strongly on the location of the individual nuclei relative to the charge division line since the pre-neutron charge (isobaric) dispersion is only ~ 1 charge unit (FWHM) for a given mass, and the pre-neutron isotopic dispersion (Zn/ZL constant) is only ~2.5 amu (FWHM) [ref. a)]. The locations of the fine-structure peaks seen in fig. 3 coincide with the mass values at which the corresponding constant charge lines for Z . --= 52, 54, 56 and 58 intersect the measured charge division line (KX) of fig. 5. In the vicinity of these even-charge intersections, the fragment yields are particularly large because these divisions are favoured by the even-even enhancement and the general smooth trend represented by the charge division line. For very high selected
356
W . N . REISDORF et al.
values of EL, and consequently TKE, there will be an enhancement of those nuclei lying close to the charge division line, and on the basis of the previously discussed energy considerations the yields of doubly even fragments near the charge division line will be enhanced relative to other nuclear types. In fact, with very high values of T K E this enhancement may become so large that the yields of other mass-charge divisions become almost negligible. In fig. 3d, the three peaks observed in the mass distribution are probably due to the enhanced formation of only a few specific nuclides with (AH, ZH) = (132,52), (140,54), (144,56) and (146,56), as indicated by circled points in fig. 5. The successful correlation of charge division with fine structure in mass distributions for high T K E values shows that the most probable charge splits for average fission events are identical with those which appear to be enhanced for very high T K E values as noted earlier s). The mechanisms which determine the most probable charge division for a given mass split are only weakly correlated with TKE. 3.2. THE E N H A N C E M E N T OF D O U B L Y - E V E N - F R A G M E N T YIELDS IN LOW-ENERGY FISSION
In subsect. 3.1 it was shown that there is an enhancement of the yields of doubly even fragments relative to other nuclear types for high values of T K E and correspondingly for low values of fragment excitation energies. However, the mass distributions for 235U(n, f) still exhibit fine structure for EL = 104-105 MeV (fig. 3a) corresponding to fragment excitation energies of ~ 2 0 MeV, an order of magnitude larger than typical pairing energies. Furthermore, such fine structure is even apparent in the gross mass distributions (shown in fig. 1) averaged over all T K E values. Therefore, one must conclude that the enhancement of even-Z fragments is not restricted to the rare high-TKE events but also occurs for a rather sizable proportion of the total events. From an analysis of the radiochemical independent yield data (prior to fl-decay) f o r 2 3 5 U ( n , f), Wahl et al. 20) have shown that appreciable enhancement exists for the primary formation of even-Z products relative to odd-Z products. In fact, the even-Z-odd-Z fluctuation in yield amounts to about +_20 % relative to a smooth or averaged Z-yield curve. An effect as large as this is, however, not as apparent in mass distributions obtained from double-energy measurements. In order to demonstrate the insensitivity of the mass distributions to large even-Z-odd-Z yield fluctuations, consider the following example. Assume that the fragment yields as a function of Z and A are given by
Y(Z, A, C) = Y(A)t(2na~)-t(1 + C ) e x p { - (Zp(A)-Z)2/2a~} 1,
(5)
where Y(A) is a structureless mass distribution (in this example the measured 235U(n,f) distribution with fine structure smoothed out) as illustrated by the dashed curve in fig. 6c. With C = 0, the expression in brackets is a normalized Gaussian charge distribution, with Zp(A) the most probable nuclear charge for a given mass A, and trz the charge dispersion. The parameter C is used here to approximate the odd-even-Z
233. 235 U T H E R M A L
357
FISSION
yield effect. For this example, it is assumed that C = 0 for odd-A fragments, -I-0.30 for doubly even fragments, and - 0 . 3 0 for doubly odd fragments, i.e. there is a 15 enhancement in the formation of even-Z fragments and 15 ~ decrease in formation of o d d - Z fragments relative to the average. The values of Zp(A) (shown as K X in fig. 5) and a z = 0.44 were obtained from K X-ray measurements a). The percentage mass-yield fluctuations which result with the inclusion of the measured charge distribution and the assumed odd-even-Z effect as given by eq. (5) are shown in fig. 6a.
%, O vA !
~ AH//ALI 134/102 I +20 +10 O3 Z 0
~_. I-
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/ h ~3
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+10
52/40
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HEAVY FRAGMENT MASS AH Fig. 6. E v e n - Z f r a g m e n t e n h a n c e m e n t in 23SU(n, f). In (a) are s h o w n the percentage m a s s yield fluctuations as a function o f f r a g m e n t m a s s a s s u m i n g ÷ 3 0 ~ e n h a n c e m e n t for doubly even f r a g m e n t s , 0% for odd-A f r a g m e n t s a n d - - 3 0 ~ for doubly odd fragments. In (b) the fluctuations s h o w n in (a) are dispersed with a m a s s resolution o f 2.0 a m u ( F W H M ) . T h e dashed curve o f (c) represents an a s s u m e d s m o o t h mass distribution. T h e solid curve o f (c) represents the m a s s yield fluctuations o f (b) c o m b i n e d with the a s s u m e d s m o o t h m a s s distribution. T h e dot-dashed curve in (c) is the experimentally m e a s u r e d m a s s distribution obtained by double time-of-flight meas u r e m e n t s 3) with a m a s s resolution o f ~ 2 a m u ( F W H M ) .
Fig. 6b illustrates the percentage fluctuations which are obtained when the curve shown in fig. 6a is dispersed with an experimental mass resolution of ~ 2 amu ( F W H M ) . This mass resolution is typical of that expected for high-resolution timeof-flight methods for fragment-mass determinations. The resultant calculated mass distribution dispersed with a 2 amu ( F W H M ) experimental mass resolution is shown
358
W.N. RE1SDORF et al.
as a solid curve in fig. 6c. Dispersion with a mass resolution of ~ 4 amu inherent in double-energy measurements as used in this work, yields a calculated mass distribution with less structure than in fig. 6c and very similar to the measured mass distribution shown in fig. 1. Even with such large fluctuations (_+ 15 %) in the even-Zodd-Z fragment yields, it is seen that (i) the structure in the mass distributions Y(Z, A, C) is substantially less; (ii) the fluctuation observed in the calculated "timeof-flight" mass distribution amounts to ~ 7 % and is quite consistent with experimental results 3) shown as the dot-dashed curve in fig. 6c; (iii) very little structure is expected in the gross '°double-energy" mass distribution, again consistent with experiment (see fig. 1); and (iv) all calculated mass distributions exhibit the familiar 5 amu periodicity. From these calculations, one can conclude that the fine structure observed in fission-fragment mass distributions can be attributed to a substantial enhancement of even-Z fragments consistent with the ___20% Z-yield fluctuations found in radiochemical work 2o). The influence of pairing correlations during the fission process, manifested experimentally as an enhancement of even-Z fragments, seems reasonable if the fission process is quasi-adiabatic. At the saddlepoint, the available energy for intrinsic excitation in the two cases studied here is rather low and we have at the initial stage of descent to the scission point a configuration with a very small probability that a nucleon pair is broken. If the pair breaking interactions are weak, and the descent to scission point is fast compared to a typical relaxation time for these interactions, many nucleon pairs are expected to survive the fission process unbroken. Similar arguments have been made in the literature to justify the assumption of the approximate conservation of the quantum number K (projection of the angular momentum on the nuclear symmetry axis) during fission. In fact, a correlation between conservation of pairing and conservation of the K quantum number might be expected since the Coriolis interaction which mixe~ states with different K will appear when unpaired nucleons are formed. 3.3. INFLUENCE OF LOCALIZED NUCLEAR STRUCTURE EFFECTS ON FRAGMENT MASS DISTRIBUTIONS The major characteristics of thermal-neutron-induced fission of 233U and 235U are quite similar. The average TKE values as a function of fragment mass differ generally by only 0.5-1.0 MeV. The gross mass distributions as seen in fig. 1 are also similar. The neutron multiplicities as a function of fragment mass have the same general saw-tooth shapes 13), and the total numbers of neutrons emitted from each fissioning system are the same within 0.1 neutrons indicating that the total energy release is the same within 1-2 MeV for both cases. It is therefore striking that the mass distributions differ considerably for E L > 108 MeV, as can be seen by comparison of fig. 3 with fig. 4. It is difficult at this time to compare in detail the mass distributions for both fissioning systems at the same fragment excitation energy E*, since the accuracy of computed Q-values is probably of the order of 1-2 MeV, and
233'z35U THERMAL FISSION
359
the uncertainties in the measured T K E values are of the same order. However, for a given charge split in fission, E* values calculated for 233U(n, f) are generally found to be ~ 1 MeV greater than for 235U(n, f). Therefore E L values for 235U(n, f) ~ 1 MeV less than for 233U(n, f) should be used to compare the mass distributions shown in figs. 3 and 4 for the two fissioning systems at the same fragment excitation energies. Since the thermal-neutron fission cross sections for both systems are the same within / 10 o~o, the yields are given in figs. 3 and 4 in terms of (b/MeV. ainu) to relate not only the relative yields but also the absolute yields of fragments for a given EL value for both fissioning systems. By comparison of the 235U(n, f) mass distributions of fig. 3 for E L values ~ 1 MeV less than the 133U(n, f) distributions of fig. 4, the yields in the vicinities of A ~ 140 and ~ 145 are seen to be approximately the same for both fissioning systems, whereas the yield at A ~ 134 for E L > 110 MeV is enhanced by at least a factor of 2 for 235U(n, f) relative to 233U(n, f). This relative enhancement has also been observed radiochemically in the post-neutron mass distributions [ref. 21)]. The cumulative yield for A = 134 for 235U(n, f) has been measured to be 7.92 ~o, whereas the yields of neighboring masses are ~ 6.5 %. No such enhancement of the yield at A = 134 has been observed radiochemically for 133U(n, f); the yields for A = 133-136 range from 5.96 to 6.09 ~ . The strong enhancement of fragments with mass 134 occurring in Z35U(n, f) but not in 233U(11, f) may be attributed to a localized nuclear structure effect which gives rise to such an enhancement in the fission act itself prior to neutron emission from the fragments. The charge division diagram of fig. 5 shows that the mo3t probable fragments formed at mass split 102/134 for 235U(n, f) will be l°ZZr and 134Te. Radiochemical results show that 134Te, with an independent fractional yield of 86 ~o, is the most prominent species initially formed for post-neutron emission mass 134. Examination of the charge division measured 8) for 233U(n, f) indicates the most probable fragments in this case will be ~°°Zr and 134Te. Since the mass divisions for both fissioning systems contain the same heavy fragment 134Te, the differences in the probabilities of forming these mass divisions may be due to differences in the properties of the light fragments, ~°°Zr for 233U(n, f) and ~°2Zr for 235U(n, f). Rapid changes in nuclear structure properties with isotopic mass are well known for Sm and Gd nuclei in the region N = 88 to 92 and are associated with a relatively sudden onset of a stable nuclear deformation as the neutron number increase3. Such a phase transition gives rise to a large numbers of changes in the static and dynamic properties of nuclei in this region such as the increase in two-neutron separation energies, increase of static quadrupole moments, change from a soft-vibrator to a rigid-rotator band structure, increased B(E2)values, changes in giant-dipole-resonance peak structure 2z), variations in the L --- 0 transfer strengths in (t, p) and (p, t) reactions 23-26), etc. Although not entirely conclusive, there is information currently available suggesting that such a phase transition may also occur between 98Zr and 102Zr" From the fission-fragment y-ray studies of Cheifitz et al. 2~), the ratio of the energy of the first 4 + excited state to the first 2 + excited state for 100Zr is 2.65 whereas
360
W.N.
RE1SDORF
e t al.
the ratio is 3.15 for 102Zr" This ratio is commonly used as an indication of regions of stable deformation or of nuclei behaving as rigid rotors. For a rigid rotator this ratio would be expected to be 3.33 and in the rare-earth region of nuclei with known stable deformations this ratio has been found to be generally around 3.25. In the reaction 96Zr(t, p)98Zr no excited level below 1 MeV was observed 28) indicating that 98Zr is a relatively stiff quasi-spherical nucleus. Therefore there is evidence that for N = 58, 60, 62 the Zr isotopes undergo a rapid phase transition in many ways similar to the Sm and Gd isotopes for N = 88, 90, 92. 16 I'-~A / [,~~
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.\. ~"
i
I B8
I
I 92
I
Fig. 7. T w o - n e u t r o n s e p a r a t i o n e n e r g i e s for Z r , S m a n d G d .
The possible existence of a phase transition can become important for high-TKE fission events. The variation of the binding energies of nuclei with isotopic mass will experience a break from their normal trend in phase transition regions, as is illustrated in fig. 7. Plotted on the right-hand side of the figure are the two-neutron separation energies B2n for doubly even Sm and Gd isotopes 29). From N = 88 to 92, B2, does not decrease as expected from extrapolation of the data for isotopes with smaller neutron numbers (dashed line). As a result, the binding energy of 154Sm92 exceeds the extrapolated binding energy by at least 1.5 MeV, an amount comparable to the pairing energy. This gain in binding strength is associated with the rearrangement of the single-particle orbits accommodating to the increasingly stable and large deformation of the nucleus as the neutron number increases by just a few units. A similar plot is presented for Zr isotopes on the left-hand side of fig. 7. Two-neutron separation energies are known experimentally for Zr isotopes (solid points in fig. 7) up to N = 58 [ref. 29)]. A general linear trend which might be used to extrapolate up to N = 60 and 62 is represented by the dashed line. In the case of an abrupt transition from a stiff spherical to a stiff deformed nucleus, the analogy with the Sm and Gd isotopes suggests an extrapolation shown in fig. 7 as a dot-dashed line, which
233,235U THERMAL FISSION
36l
implies again that the binding energies and consequently the values ( Q - T K E ) in fission undergo a break from the normal trend. For the specific cases presented here 236U fissioning into (134Te, l°2Zr) would be expected to have a larger available excitation energy at the scission point (in excess of 1 to 2 MeV) compared to 234U fissioning into (134Te, l°°Zr) for comparable T K E values. Therefore, for very high T K E values the yield of heavy fragments with mass 134 would be expected to be greater f o r 2 3 5 U ( n , f ) than for 233U(n, f ) , as is o b s e r v e d . The interpretation given above implies that the shell structures of the fragments in or near their ground-st~tte deformations are important in fission. For high-TKE events this can be understood in terms of the following semiquantitative considerations. The influence of the ground-state shell structure of fragments formed in fission may be important if the available deformation energy at the scission point ( Q - ~ [ K E ) is smaller than the sum of the shell correction energies 30) of the nascent fragments. According to Rubchenya 3t) the shell correction to the liquid-drop energy for x34Te is -~ - 5 MeV by analogy with stiff deformed nuclei in the rare-earth and actinide regions 32, 33). The shell energy minus the zero-point energy of ~ 1 MeV roughly represents the amount of energy (in addition to the liquid-drop deformation energy) which has to be available to deform the fragments by amounts f l - f l o ~ 0.3, the approximate half-period of the shell correction modulations to the liquid-drop energy 30). The maximum total available deformation energy (cold fragments) in 235U(n, f) at A H = 134 is about l0 MeV for E L = 112 MeV (fig. 2b) and is smaller than the sum of the shell energies for the stiff complementary fragments 134Te and 102Zr" If the excitation energy is divided in such a way that both are not deformed appreciably beyond their ground-state minima, events with comparatively low deformation of both fragments and consequently high T K E will be observed. For 233U(n, f) the l°°Zr fragment is a soft transition nucleus, and one expects in a static description that most of the available deformation energy will be transferred to this softer nucleus 34) giving rise to fairly strong elongation of this nucleus and decreasing considerably the probability of very high-TKE events. As a conclusion, fragment mass-yield fine structure correlated with high total kinetic energy release may be closely connected with low-energy nuclear structure properties such as the ground-state deformation shell energies. It should be interesting to test the ideas presented here by studying in a similar way other fissioning systems. References 1) W. M. Gibson, T. D. Thomas and G. L. Miller, Phys. Rev. Lett. 7 (1961) 65 2) T. D. Thomas, W. M. Gibson and G. J. Stafford, Physics and chemistry of fission (IAEA, Vienna, 1965) p. 467 3) J. C. D. Milton and J. S. Fraser, Can. J. Phys. 40 (1962) 1626 4) J. S. Fraser, J. C. D. Milton, H. R. Bowman and S. G. Thompson, Can. J. Phys. 41 (1963) 2080 5} J. S. Fraser and J. C. D. Milton, Ann. Rev. Nucl. Sci. 16 (1966) 379 6) I. A. Baranov, A. N. Protopopov and B. M. Shiryaev, Yad. Fiz. 10 (1969) 1149 ,rtrans.: Soy. J. Nucl. Phys. 10 (1970) 654]
362
W . N . REISDORF et aL
7) T. D. Thomas and R. Vandenbosch, Phys. Rev. 133 (1964) B976 8) W. Reisdorf, J. P. Unik, H. C. Griffin and L. E. Glendenin, Nucl. Phys. A177 (1971) 337 9) M Bolsterli, F. O. Fiset and J. R. Nix, Physics and chemistry of fission (IAEA, Vienna, 1969) p. 183 10) P. M611er and S. G. Nilsson, Phys. Lett. 31B (1970) 283 11) U. Mosel and D. Scharnweber, Phys. Lett. 32B (1970) 229 12) H. W. Schmitt, W. E. Kiker and C. W. Williams, Phys. Rev. 137 (1965) B837 13) J. C. D. Milton and J. S. Fraser, Physics and chemistry of fission (IAEA, Vienna, 1965) p. 531 14) H. W. Schmitt, J. H. Neiler and F. J. Walter, Phys. Rev. 141 (1966) 894 15) F. Pleasonton, Phys. Rev. 174 (1968) 1500 16) J. Terrell, Phys. Rev. 127 (1962) 880 17) H. R. Bowman, J. C. D. Milton, S. G. Thompson and W. J. Swiatecki, Phys. Rev. 129 (1963) 2133 18) P. A. Seeger and R. C. Perisho, Los Alamos Scientific Laboratory report LA-3751 (1967) 19) J. P. Unik and J. E. Gindler, Argonne National Laboratory report ANL-7748 (1971) 20) A. C. Wahl, A. E. Norris, R. A. Rouse and J. C. Williams, Physics and chemistry of fission (IAEA, Vienna, 1969) p. 813 21) M. E. Meek ano B. F. Rider, General Electric reports APED-5352 (1967) and APED-5398 (1968) 22) S. F. Semenko, O. V. Vasilijev and V. A. Semenov, Phys. Lett. 31B (1970) 429 23) .1. H. Bjerregaard, O. Hansen, O. Nathan and S. Hinds, Nucl. Phys. 86 (1966) 145 24) J. R. Maxwell, G. M. Reynolds and N. M. Hintz, Phys. Rev. 151 (1966) 1000 25) W. McLatchie, J. E. Kitching and W. Darrey, Phys. Lett. 30B (1969) 529 26) P. Debenham and N'. M. Hintz, Phys. Rev. Lett. 25 (1970) 44 27) E. Cheifetz, R. C. Jared, S. G. Thompson and J. B. Wilhelmy, Phys. Rev. Lett. 25 (1970) 38 28) A. G. Blair, J. G. Beery and E. R. Flynn, Phys. Rev. Lett. 22 (1969) 470 29) A. H. Wapstra and B. N. Gove, Nucl. Data Tables 9 (1971) 303 30) V. M. Strutinsky, Nucl. Phys. A95 (1967) 420; A122 (1968) 1 31) V. A. Rubchenya, Sov. J. N.ucl. Phys. 9 (1969) 697 32) S. G. N'ilsson et aL, Nucl. Phys. A131 (1969) 1 33) W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81 (1966) 1 34) R. Vandenbosch, Nucl. Phys. 46 (1963) 129
2.J
I
Nuclear Physics A205 (1973) 348--362; (~) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprintor microfilmwithout writtenpermissionfrom the publisher
CORRELATION BETWEEN FRAGMENT MASS-DISTRIBUTION FINE STRUCTURE, CHARGE DISTRIBUTION AND NUCLEAR STRUCTURE FOR THERMAL-NEUTRON-INDUCED F I S S I O N O F 2aaU A N D 2aSU W. N. REISDORF *, J. P. UNIK and L. E. GLENDENIN Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 ~*
Received 20 December 1972
Abstract: Masses corresponding to observed fine-structure peaks in the fragment mass distributions for thermal-neutron-induced fission of 2aaU and 235U are shown to correspond to average measured masses for even-even nuclear charge splits. Evidence is presented that the yield enhancement for even-Z fragments is not restricted just to fission events with higher-thanaverage total kinetic energy. The anomalously high yield of fragments with mass 134 in 2aSU(n, f) as opposed to 233U(n, f) is tentatively correlated with rapidly changing nuclear structure properties as a function of the mass of the complementary light (Z : 40) fragments. I E
NUCLEAR FISSION 2aa.235U(n, f), E : th; measured fragment kinetic energies, (fragment) (fragment)-coin.; deduced fragment mass-total kinetic energy correlations.
1. Introduction F i n e structure has been previously observed 1 - 6 ) in fission-fragment mass distributions as a function of pre-neutron-emission mass .4 for t h e r m a l - n e u t r o n - i n d u c e d fission (n, f) of 233U, 235U, 239pu a n d s p o n t a n e o u s fission (sf) of 252Cf. There is general agreement that the fine structure observed in the mass distributions occurs at intervals of ~ 5 a m u (primarily for heavy-fragment masses A ~ 135, 140 a n d 145 and associated c o m p l e m e n t a r y light fragment masses), with the fine structure accentuated for fragments possessing low excitation energies. T h o m a s a n d V a n d e n b o s c h 7) have correlated the observed fine structure with structure in the calculated massenergy surface (as a f u n c t i o n of Z and N) for doubly even fragments. The nuclear pairing effect depresses the potential energy surfaces for f o r m a t i o n of doubly even fragments relative to odd-A a n d doubly odd fragments. Therefore, based o n simple energetic considerations, a preferential f o r m a t i o n of doubly even fragments may be expected in the fission of a doubly even nucleus at low excitation energies. The obLaboratoire R6n6 Bernas, Centre de Spectrom6trie Nucl6aire et de Spectrom6trie de Masse, 91 Orsay, France. ** Work performed under the auspices of the US Atomic Energy Commission. 348
233. 235 U THERMAL FISSION
349
served periodicity of ~ 5 amu can then be correlated 7) with the fact that the masses of the most stable nuclei for neighboring even-Z nuclei differ by ~ 5 amu. In a previous study 8) mass distributions as well as the distribution of nuclear charge between the two fragments (as deduced from K X-ray measurements) were obtained for thermal-neutron-induced fission of 233U, 235U, 239pu and spontaneous fission of 252Cf" In this paper the results obtained for the first two fissioning systems are used to investigate in detail (i) correlations between nuclear charge division and fine structure observed in fragment mass distributions, (ii) the dependence of the fine structure on the final excitation energies of the fragments, and (iii) the possible influence of single-particle effects on the fission process 9-11).
2. Experimental procedures and results Since the experimental and data analysis methods used have been previously described in detail s), only the more pertinent points will be given here. Enriched targets of 2aaU (75 pg/cm 2) and 235U (50 pg/cm 2) prepared by vacuum volatilization of the tetrafluorides onto nickel foils (90 pg/cm 2) were irradiated with a well-collimated beam of thermal neutrons (3 × 107 n" cm- z. sec- 1) at the Argonne CP-5 Research Reactor. The complementary fission fragments were detected in coincidence by two goldsurface-barrier silicon detectors. The two resultant pulse heights for each event were digitized and stored on magnetic tape for subsequent computer analysis. The preneutron-emission masses were calculated using the energy calibration method described by Schmitt et al. 1~), the conservation of mass and linear momentum in fission, and correction for prompt neutron-emission effects 13) as functions of mass and TKE. The fragment mass distributions for 233U(n, f) and 235U(n, f) (obtained from the analysis of 3.7 x 105 and 7.4 × 105 binary fission events, respectively) are shown in fig. 1. These mass distributions were not corrected for the experimental mass resolution of ~ 4 amu (FWHM), in order to illustrate the amount of fine structure directly observed. The observed distributions are relatively smooth and in excellent agreement with earlier work 14,15). It is apparent from fig. 1 that fine structure exists in the form of shoulders and smooth maxima in the peak-yield regions and that this structure is somewhat different in the two fissioning systems. In earlier studies t. z) the structure was shown to be more pronounced if a high-energy restriction is imposed on the kinetic energy of the light fragment, EL. This energy restriction, in effect, imposes a restriction on the total excitation energy of the fragments, E*. At infinite fragment separation, E*, is given as E* = BE*(AF, Z F ) - B E ( A n , ZH)--BE(AL, Z L ) - T K E .
(1)
Here, BE*(AF, ZF) represents the binding energy of the excited fissioning nucleus with m a s s A F and nuclear charge ZF; BE(AL, ZL) and BE(AH, ZH) represent the binding energies of the light and heavy complementary fragments, respectively,
350
W . N . RE1SDORF et al.
in their ground states. The total kinetic energy of the fragments, TKE, is given as TKE
E.,A~/.4.
=
= E.A~/aL.
(2)
From eqs. (1) and (2) it can be seen that the selection of those events for which the light-fragment kinetic energy EL is greater than the average EL will result in selection of events with lower than average excitation energies. Also, since the kinetic energy of the light fragments has previously been shown to be rather independent of the mass division in fission [with E L = 102.0-1-1.0 MeV f o r 233U(n, f) and E L = 101.4_+ 1.0 MeV for 235U(n, f)], the selection of light-fragment kinetic energies greater than the average value implies by eqs. (2) and (3) that ATKE and AE* are also rather constant for all mass divisions: AE*= E*-E*=
TKE-TKE
(3)
= -ATKE.
A demonstration of the fact that the available fragment excitation energies decrease rather uniformly for all mass divisions by selection of increasing values of E L is given in fig. 2a. Selecting values of EL = 112-113 M e ¥ for 2aSU(n, f) is seen to be equivalent to selecting those fission events for which the total kinetic energy release is 18 + 2 MeV greater than the average for each mass division, and consequently the average fragment excitation energies are reduced by this same amount. 106 I
LIGHT FRAGMENT MASS 96 86
I
I
I
++ +++ 6-
/
j
~
i
I
[
zt,SUln,f) + 233U(n,f)
--
+
N4 a _J
:'- 3
2
I
130
140 150 HEAVY FRAGMENT MASS
Fig. I. Fragment mass distributions for 233U(n, f) and 235U(n, f) measured by the double-energy method, uncorrected for experimental mass resolution a),
233, 235 U
130
126
p
i
154 I
/
THERMAL
FISSION
HEAVY FRAGMENT MASS 158 142 146 I
I
j
n
J
351
t
150 j
154
~
I
(o) 235U (n,f) EL=(II2-113) MeV
~o
P
t -------o----
i ---o---
I
d
F
EL= 112-115 I12-I13 I I0-III 112-113
]
I
[
I
I
4
i
I
ee nuclei] oo 1 23"5U(n'f) ee ee 233U(n, f)
~
I
(b)
.-f ]o L LO v (21
5b
126
130
134
138 142 146 HEAVY FRAGMENT MASS
150
154
Fig. 2. Energetics for 233U(n, f) a n d 235U(n, f). (a) Difference o f total f r a g m e n t kinetic energy release ( T K E ) relative to average values as a function o f f r a g m e n t m a s s for 235U(n, f) with lightf r a g m e n t kinetic energies restricted to EL = 112-113 MeV; (b) calculated m a x i m u m energy release ( Q - - T K E ) as a function o f f r a g m e n t m a s s for selected values o f EL.
Mass-yield curves (with the ordinate scale in absolute units of b/MeV • amu) obtained for selected values o f E L are shown in figs. 3 and 4for 235U(n, f) and 233U(n, f), respectively. By restricting the selection of E L to large values only a small fraction of the total data is used. For example, for E L m 104 MeV (near the average E L value of 101 MeV) the peak mass yields are g 3 b/MeV • amu as compared to m0.15 for E L ~ 112 MeV. The major experimental contribution to the widths of the observed fine-structure peaks in double-energy measurements as used here is the dispersion introduced in the fragment velocities by neutron emission (isotropic in the center of mass) and is proportional to the number of neutrons emitted by the fragments. For events associated with high T K E release (as in fig. 3d) the number of neutrons emitted is nearly zero, and hence the mass resolution is expected to be quite good, ~ 2 amu ( F W H M ) due to the intrinsic resolution of the detectors and slight energy loss in the tax get. For those mass distributions associated with lower TKE, larger numbers of neutrons are emitted, and consequently the experimental mass resolution is worse. This neutron contribution to the mass dispersion tends to mask fine-structure effects
352
W . N . RE1SDORF et aL LIGHT FRAGMENT MASS 86 106 96 86 23Su (n,f) ~ (b)EL = (a) EL = (1~-105) MeV i (108-109) MeV 1.5
106
96
1.0
/
!
I
3,5
/ I
~
0 0.75
0 (el EL=(IIO-III) MeV
•tl
l
l
I
(d) EI= (112-115) MeV
11
,,Q
C.15
b 0.50
C.IO
11
0.25 C.O5
] I
~
130
I
140
i
"
0
/~
'
150 150 140 HEAVY FRAGMENT MASS
150
Fig. 3. The 2aSU(n, f) fragment mass distributions for selected light-fragment kinetic energies. Solid arrows indicate measured masses corresponding to even-Z charge divisions in fission a). Dotted arrows in (c) indicate masses predicted by the unchanged-charge-density (UCD) assumption.
TABLE 1 Average pre-neutron fragment masses for various atomic numbers ") Zn
52 54 56 58
") Ref. 8). b) Associated errors I 0 . 3 amu.
Average pre-neutron fragment masses b) 23ZU(n, f)
zaSU(n, f)
133.7 138.6 143.5 148.3
134.6 139.7 144.8 149.8
233,235U T H E R M A L
FISSION
353
in the mass distributions for TKE values less than or near the average values bat allows the fine structure to be more easily observed for large values of TKE. Since an average energy of ~ 16 MeV/fission is released in the form of neutron emission for 2 3 5 U ( n , f ) (vx = 2.43 [ref. 16)], with an average energy of 6.5 MeV/neutron [re['. 17)]), it is concluded that for EL > 112 MeV the average number of neutrons emitted from the fragments is appreciably less than one, and that the post-neutron masses will be essentially identical to the pre-neutron masses.
94
104
,
d
LIGHT FRAGMENT MASS 104 84 i
,233Uf.,, n, f),
94 t
J
~
EL=(I I0-111)MeV
T
84 I
r
EL=(IIZ-ll3) MeV
(a) 0.15 0.50 >
0.I0
E b 0.25
I 130
/, 140
,
130 140 HEAVY FRAGMENTMASS
150
,
/'-% 150
z 3 a U ( n , f) fragment mass distributions for selected light-fragment kinetic energies. Solid arrows indicate masses corresponding to even-Z charge divisions a). Dotted arrows in ( b ) indicate masses associated with even-Z charge splits observed for 23~Lr(n, f). F i g . 4. T h e
The correlation of the structure observed in fragment mass distributions with the previously determined charge division in fission 8) is shown in figs. 3 and 4. The average pre-neutron masses associated with even-even charge splits determined from the previous study 8) of charge division based on the measurement of characteristic K X-rays emitted by fragments of measured masses are indicated by solid arrows in figs. 3 and 4, and are also given in table 1. The excellent agreement between the average masses associated with even-Z charge splits and the masses associated with the finestructure peaks is a direct demonstration that the fine structure in fragment mass distributions is closely connected with even-even charge divisions in fission. As a demonstration of the sensitivity of this comparison, the dashed arrows in fig. 3 indicate the masses predicted by the "unchanged charge density" ( U C D ) assumption of nuclear charge division, i.e., the charge density (Z/A) of the fragments is the same as
354
W.N. REISDORF et al.
that of the fissioning nucleus. The experimentally measured charge distributions are generally displaced by ~0.5 charge units from the UCD assumption 8). The dashed arrows shown in fig. 4 for 233U(n, f) indicate the masses associated with even-even charge splits observed for 235U(n, f). Clearly the present correlation of the observed fine structure with even-even charge divisions is well within 0.5 charge units, and even small isotopic shifts can be observed. 3. Discussion
3.1. CORRELATION BETWEEN MASS-DISTRIBUTION FINE STRUCTURE AND CHARGE DISTRIBUTION IN NUCLEAR FISSION Some qualitative insight into the relative probabilities for the formation of fragments of various mass and charge in fission can be obtained on the basis of energy considerations. The calculated fragment excitation energies, E*(Z, A) = Q(Z, A ) - T K E ( A ) ,
(4)
for various fissioning conditions are shown in fig. 2b. For these calculations, the Qvalues were obtained from the work of Seeger and Perisho 18). The T K E values were those measured in this work by the double-energy method reduced by 2 MeV to partially compensate for the generally observed, and as yet unexplained, 4 MeV disagreement between T K E values measured by double-velocity and double-energy methods 19). The fragment excitation energies are always greatest for formation of doubly even nuclei as can be seen in fig. 2b by comparison of E* = (Q - TKE) values for doubly even nuclei with doubly odd nuclei in the case of 235U(n, f) with EL = 112-113 MeV. The energy surface for formation of odd-A nuclei (not shown) is a smoothly varying surface ~ 2.4 MeV lower than the surface for doubly even nuclei. On the basis of such calculations the formation of doubly even fragments is expected to become increasingly more probable relative to odd-A and doubly odd nuclei with decreasing excitation energy ( Q - T K E ) and consequently with increasing values of EL. For sufficiently large values of E L only doubly even fragments would be formed on the basis of these energy considerations. This is in qualitative agreement with the known experimental observations that with increasing values of E L the structure in fragment mass distributions becomes more pronounced and those mass divisions leading to formation of even-Z fragments are strongly enhanced. The vertical arrows shown in fig. 2b indicate the mass positions of the observed fine-structure peaks. These positions do not tend to coincide with the maxima of the excitation energy of doubly even nuclei. The simple criterion of maximum fragment excitation energy at infinite fragment separation is not expected to quantitatively explain mass-yield fine structure. The correlation between charge division and mass-distribution fine structure is more readily apparent through examination of charge division diagrams such as that given in fig. 5 for 2aSU(n, f). Plotted on this complementary charge and mass dia-
233, 235 U
THERMAL
FISSION
355
gram is the charge division line (KX) obtained by K X-ray measurements s). This line represents the experimentally measured average (more exactly the most probable) nuclear charge Zp for a given fragment mass. Instead of the most probable nuclear change (Zp), the quantity (Zp--ZucD)H, L has been chosen as ordinate where (ZucD)., L = ZFAH,LIAr. Individual nuclei are represented in this diagram by discrete points. For simplicity only points for doubly even nuclei are given. The lines labelled ZL/Zn connect points for fragments formed with the same nuclear charge but varying 2.(3
116
106
LIGHT FRAGMENT MASS 96
86
76
150
160
1.5
I.C ~
'~"
,,=t 0.~
m
-F
0
N
-0.5
-1.0
- I .5
120
l_ 3O
140 HEAVY FRAGMENT MASS
Fig. 5. Charge division d i a g r a m for 235U(n, f). Filled circles represent specific doubly even charge a n d m a s s splits. T h e diagonal lines represent constant charge splits ZL/ZH or c o n s t a n t n e u t r o n splits f o r NL = 50 a n d NH = 82. T h e line indicated K X represents the experimentally m e a s u r e d charge division s).
masses. Fragments formed with either 50 or 82 neutrons are joined by dashed lines. The probabilities for formation of fragments with given masses and nuclear charges depend strongly on the location of the individual nuclei relative to the charge division line since the pre-neutron charge (isobaric) dispersion is only ~ 1 charge unit (FWHM) for a given mass, and the pre-neutron isotopic dispersion (Zn/ZL constant) is only ~2.5 amu (FWHM) [ref. a)]. The locations of the fine-structure peaks seen in fig. 3 coincide with the mass values at which the corresponding constant charge lines for Z . --= 52, 54, 56 and 58 intersect the measured charge division line (KX) of fig. 5. In the vicinity of these even-charge intersections, the fragment yields are particularly large because these divisions are favoured by the even-even enhancement and the general smooth trend represented by the charge division line. For very high selected
356
W . N . REISDORF et al.
values of EL, and consequently TKE, there will be an enhancement of those nuclei lying close to the charge division line, and on the basis of the previously discussed energy considerations the yields of doubly even fragments near the charge division line will be enhanced relative to other nuclear types. In fact, with very high values of T K E this enhancement may become so large that the yields of other mass-charge divisions become almost negligible. In fig. 3d, the three peaks observed in the mass distribution are probably due to the enhanced formation of only a few specific nuclides with (AH, ZH) = (132,52), (140,54), (144,56) and (146,56), as indicated by circled points in fig. 5. The successful correlation of charge division with fine structure in mass distributions for high T K E values shows that the most probable charge splits for average fission events are identical with those which appear to be enhanced for very high T K E values as noted earlier s). The mechanisms which determine the most probable charge division for a given mass split are only weakly correlated with TKE. 3.2. THE E N H A N C E M E N T OF D O U B L Y - E V E N - F R A G M E N T YIELDS IN LOW-ENERGY FISSION
In subsect. 3.1 it was shown that there is an enhancement of the yields of doubly even fragments relative to other nuclear types for high values of T K E and correspondingly for low values of fragment excitation energies. However, the mass distributions for 235U(n, f) still exhibit fine structure for EL = 104-105 MeV (fig. 3a) corresponding to fragment excitation energies of ~ 2 0 MeV, an order of magnitude larger than typical pairing energies. Furthermore, such fine structure is even apparent in the gross mass distributions (shown in fig. 1) averaged over all T K E values. Therefore, one must conclude that the enhancement of even-Z fragments is not restricted to the rare high-TKE events but also occurs for a rather sizable proportion of the total events. From an analysis of the radiochemical independent yield data (prior to fl-decay) f o r 2 3 5 U ( n , f), Wahl et al. 20) have shown that appreciable enhancement exists for the primary formation of even-Z products relative to odd-Z products. In fact, the even-Z-odd-Z fluctuation in yield amounts to about +_20 % relative to a smooth or averaged Z-yield curve. An effect as large as this is, however, not as apparent in mass distributions obtained from double-energy measurements. In order to demonstrate the insensitivity of the mass distributions to large even-Z-odd-Z yield fluctuations, consider the following example. Assume that the fragment yields as a function of Z and A are given by
Y(Z, A, C) = Y(A)t(2na~)-t(1 + C ) e x p { - (Zp(A)-Z)2/2a~} 1,
(5)
where Y(A) is a structureless mass distribution (in this example the measured 235U(n,f) distribution with fine structure smoothed out) as illustrated by the dashed curve in fig. 6c. With C = 0, the expression in brackets is a normalized Gaussian charge distribution, with Zp(A) the most probable nuclear charge for a given mass A, and trz the charge dispersion. The parameter C is used here to approximate the odd-even-Z
233. 235 U T H E R M A L
357
FISSION
yield effect. For this example, it is assumed that C = 0 for odd-A fragments, -I-0.30 for doubly even fragments, and - 0 . 3 0 for doubly odd fragments, i.e. there is a 15 enhancement in the formation of even-Z fragments and 15 ~ decrease in formation of o d d - Z fragments relative to the average. The values of Zp(A) (shown as K X in fig. 5) and a z = 0.44 were obtained from K X-ray measurements a). The percentage mass-yield fluctuations which result with the inclusion of the measured charge distribution and the assumed odd-even-Z effect as given by eq. (5) are shown in fig. 6a.
%, O vA !
~ AH//ALI 134/102 I +20 +10 O3 Z 0
~_. I-
o
0 -I0
/ h ~3
-20
;
+10
52/40
ZH/ZL
I ~ 140/96 144/92
54/58
[
150,/86 |
56/36 5 8 / 3 4
(a)
(b)
i
=
-I0
.r,.
I
A
7
/
le)
\..,
.-I bJ :>,R
(~ CO <{
130
140
150
160
HEAVY FRAGMENT MASS AH Fig. 6. E v e n - Z f r a g m e n t e n h a n c e m e n t in 23SU(n, f). In (a) are s h o w n the percentage m a s s yield fluctuations as a function o f f r a g m e n t m a s s a s s u m i n g ÷ 3 0 ~ e n h a n c e m e n t for doubly even f r a g m e n t s , 0% for odd-A f r a g m e n t s a n d - - 3 0 ~ for doubly odd fragments. In (b) the fluctuations s h o w n in (a) are dispersed with a m a s s resolution o f 2.0 a m u ( F W H M ) . T h e dashed curve o f (c) represents an a s s u m e d s m o o t h mass distribution. T h e solid curve o f (c) represents the m a s s yield fluctuations o f (b) c o m b i n e d with the a s s u m e d s m o o t h m a s s distribution. T h e dot-dashed curve in (c) is the experimentally m e a s u r e d m a s s distribution obtained by double time-of-flight meas u r e m e n t s 3) with a m a s s resolution o f ~ 2 a m u ( F W H M ) .
Fig. 6b illustrates the percentage fluctuations which are obtained when the curve shown in fig. 6a is dispersed with an experimental mass resolution of ~ 2 amu ( F W H M ) . This mass resolution is typical of that expected for high-resolution timeof-flight methods for fragment-mass determinations. The resultant calculated mass distribution dispersed with a 2 amu ( F W H M ) experimental mass resolution is shown
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as a solid curve in fig. 6c. Dispersion with a mass resolution of ~ 4 amu inherent in double-energy measurements as used in this work, yields a calculated mass distribution with less structure than in fig. 6c and very similar to the measured mass distribution shown in fig. 1. Even with such large fluctuations (_+ 15 %) in the even-Zodd-Z fragment yields, it is seen that (i) the structure in the mass distributions Y(Z, A, C) is substantially less; (ii) the fluctuation observed in the calculated "timeof-flight" mass distribution amounts to ~ 7 % and is quite consistent with experimental results 3) shown as the dot-dashed curve in fig. 6c; (iii) very little structure is expected in the gross '°double-energy" mass distribution, again consistent with experiment (see fig. 1); and (iv) all calculated mass distributions exhibit the familiar 5 amu periodicity. From these calculations, one can conclude that the fine structure observed in fission-fragment mass distributions can be attributed to a substantial enhancement of even-Z fragments consistent with the ___20% Z-yield fluctuations found in radiochemical work 2o). The influence of pairing correlations during the fission process, manifested experimentally as an enhancement of even-Z fragments, seems reasonable if the fission process is quasi-adiabatic. At the saddlepoint, the available energy for intrinsic excitation in the two cases studied here is rather low and we have at the initial stage of descent to the scission point a configuration with a very small probability that a nucleon pair is broken. If the pair breaking interactions are weak, and the descent to scission point is fast compared to a typical relaxation time for these interactions, many nucleon pairs are expected to survive the fission process unbroken. Similar arguments have been made in the literature to justify the assumption of the approximate conservation of the quantum number K (projection of the angular momentum on the nuclear symmetry axis) during fission. In fact, a correlation between conservation of pairing and conservation of the K quantum number might be expected since the Coriolis interaction which mixe~ states with different K will appear when unpaired nucleons are formed. 3.3. INFLUENCE OF LOCALIZED NUCLEAR STRUCTURE EFFECTS ON FRAGMENT MASS DISTRIBUTIONS The major characteristics of thermal-neutron-induced fission of 233U and 235U are quite similar. The average TKE values as a function of fragment mass differ generally by only 0.5-1.0 MeV. The gross mass distributions as seen in fig. 1 are also similar. The neutron multiplicities as a function of fragment mass have the same general saw-tooth shapes 13), and the total numbers of neutrons emitted from each fissioning system are the same within 0.1 neutrons indicating that the total energy release is the same within 1-2 MeV for both cases. It is therefore striking that the mass distributions differ considerably for E L > 108 MeV, as can be seen by comparison of fig. 3 with fig. 4. It is difficult at this time to compare in detail the mass distributions for both fissioning systems at the same fragment excitation energy E*, since the accuracy of computed Q-values is probably of the order of 1-2 MeV, and
233'z35U THERMAL FISSION
359
the uncertainties in the measured T K E values are of the same order. However, for a given charge split in fission, E* values calculated for 233U(n, f) are generally found to be ~ 1 MeV greater than for 235U(n, f). Therefore E L values for 235U(n, f) ~ 1 MeV less than for 233U(n, f) should be used to compare the mass distributions shown in figs. 3 and 4 for the two fissioning systems at the same fragment excitation energies. Since the thermal-neutron fission cross sections for both systems are the same within / 10 o~o, the yields are given in figs. 3 and 4 in terms of (b/MeV. ainu) to relate not only the relative yields but also the absolute yields of fragments for a given EL value for both fissioning systems. By comparison of the 235U(n, f) mass distributions of fig. 3 for E L values ~ 1 MeV less than the 133U(n, f) distributions of fig. 4, the yields in the vicinities of A ~ 140 and ~ 145 are seen to be approximately the same for both fissioning systems, whereas the yield at A ~ 134 for E L > 110 MeV is enhanced by at least a factor of 2 for 235U(n, f) relative to 233U(n, f). This relative enhancement has also been observed radiochemically in the post-neutron mass distributions [ref. 21)]. The cumulative yield for A = 134 for 235U(n, f) has been measured to be 7.92 ~o, whereas the yields of neighboring masses are ~ 6.5 %. No such enhancement of the yield at A = 134 has been observed radiochemically for 133U(n, f); the yields for A = 133-136 range from 5.96 to 6.09 ~ . The strong enhancement of fragments with mass 134 occurring in Z35U(n, f) but not in 233U(11, f) may be attributed to a localized nuclear structure effect which gives rise to such an enhancement in the fission act itself prior to neutron emission from the fragments. The charge division diagram of fig. 5 shows that the mo3t probable fragments formed at mass split 102/134 for 235U(n, f) will be l°ZZr and 134Te. Radiochemical results show that 134Te, with an independent fractional yield of 86 ~o, is the most prominent species initially formed for post-neutron emission mass 134. Examination of the charge division measured 8) for 233U(n, f) indicates the most probable fragments in this case will be ~°°Zr and 134Te. Since the mass divisions for both fissioning systems contain the same heavy fragment 134Te, the differences in the probabilities of forming these mass divisions may be due to differences in the properties of the light fragments, ~°°Zr for 233U(n, f) and ~°2Zr for 235U(n, f). Rapid changes in nuclear structure properties with isotopic mass are well known for Sm and Gd nuclei in the region N = 88 to 92 and are associated with a relatively sudden onset of a stable nuclear deformation as the neutron number increase3. Such a phase transition gives rise to a large numbers of changes in the static and dynamic properties of nuclei in this region such as the increase in two-neutron separation energies, increase of static quadrupole moments, change from a soft-vibrator to a rigid-rotator band structure, increased B(E2)values, changes in giant-dipole-resonance peak structure 2z), variations in the L --- 0 transfer strengths in (t, p) and (p, t) reactions 23-26), etc. Although not entirely conclusive, there is information currently available suggesting that such a phase transition may also occur between 98Zr and 102Zr" From the fission-fragment y-ray studies of Cheifitz et al. 2~), the ratio of the energy of the first 4 + excited state to the first 2 + excited state for 100Zr is 2.65 whereas
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RE1SDORF
e t al.
the ratio is 3.15 for 102Zr" This ratio is commonly used as an indication of regions of stable deformation or of nuclei behaving as rigid rotors. For a rigid rotator this ratio would be expected to be 3.33 and in the rare-earth region of nuclei with known stable deformations this ratio has been found to be generally around 3.25. In the reaction 96Zr(t, p)98Zr no excited level below 1 MeV was observed 28) indicating that 98Zr is a relatively stiff quasi-spherical nucleus. Therefore there is evidence that for N = 58, 60, 62 the Zr isotopes undergo a rapid phase transition in many ways similar to the Sm and Gd isotopes for N = 88, 90, 92. 16 I'-~A / [,~~
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Fig. 7. T w o - n e u t r o n s e p a r a t i o n e n e r g i e s for Z r , S m a n d G d .
The possible existence of a phase transition can become important for high-TKE fission events. The variation of the binding energies of nuclei with isotopic mass will experience a break from their normal trend in phase transition regions, as is illustrated in fig. 7. Plotted on the right-hand side of the figure are the two-neutron separation energies B2n for doubly even Sm and Gd isotopes 29). From N = 88 to 92, B2, does not decrease as expected from extrapolation of the data for isotopes with smaller neutron numbers (dashed line). As a result, the binding energy of 154Sm92 exceeds the extrapolated binding energy by at least 1.5 MeV, an amount comparable to the pairing energy. This gain in binding strength is associated with the rearrangement of the single-particle orbits accommodating to the increasingly stable and large deformation of the nucleus as the neutron number increases by just a few units. A similar plot is presented for Zr isotopes on the left-hand side of fig. 7. Two-neutron separation energies are known experimentally for Zr isotopes (solid points in fig. 7) up to N = 58 [ref. 29)]. A general linear trend which might be used to extrapolate up to N = 60 and 62 is represented by the dashed line. In the case of an abrupt transition from a stiff spherical to a stiff deformed nucleus, the analogy with the Sm and Gd isotopes suggests an extrapolation shown in fig. 7 as a dot-dashed line, which
233,235U THERMAL FISSION
36l
implies again that the binding energies and consequently the values ( Q - T K E ) in fission undergo a break from the normal trend. For the specific cases presented here 236U fissioning into (134Te, l°2Zr) would be expected to have a larger available excitation energy at the scission point (in excess of 1 to 2 MeV) compared to 234U fissioning into (134Te, l°°Zr) for comparable T K E values. Therefore, for very high T K E values the yield of heavy fragments with mass 134 would be expected to be greater f o r 2 3 5 U ( n , f ) than for 233U(n, f ) , as is o b s e r v e d . The interpretation given above implies that the shell structures of the fragments in or near their ground-st~tte deformations are important in fission. For high-TKE events this can be understood in terms of the following semiquantitative considerations. The influence of the ground-state shell structure of fragments formed in fission may be important if the available deformation energy at the scission point ( Q - ~ [ K E ) is smaller than the sum of the shell correction energies 30) of the nascent fragments. According to Rubchenya 3t) the shell correction to the liquid-drop energy for x34Te is -~ - 5 MeV by analogy with stiff deformed nuclei in the rare-earth and actinide regions 32, 33). The shell energy minus the zero-point energy of ~ 1 MeV roughly represents the amount of energy (in addition to the liquid-drop deformation energy) which has to be available to deform the fragments by amounts f l - f l o ~ 0.3, the approximate half-period of the shell correction modulations to the liquid-drop energy 30). The maximum total available deformation energy (cold fragments) in 235U(n, f) at A H = 134 is about l0 MeV for E L = 112 MeV (fig. 2b) and is smaller than the sum of the shell energies for the stiff complementary fragments 134Te and 102Zr" If the excitation energy is divided in such a way that both are not deformed appreciably beyond their ground-state minima, events with comparatively low deformation of both fragments and consequently high T K E will be observed. For 233U(n, f) the l°°Zr fragment is a soft transition nucleus, and one expects in a static description that most of the available deformation energy will be transferred to this softer nucleus 34) giving rise to fairly strong elongation of this nucleus and decreasing considerably the probability of very high-TKE events. As a conclusion, fragment mass-yield fine structure correlated with high total kinetic energy release may be closely connected with low-energy nuclear structure properties such as the ground-state deformation shell energies. It should be interesting to test the ideas presented here by studying in a similar way other fissioning systems. References 1) W. M. Gibson, T. D. Thomas and G. L. Miller, Phys. Rev. Lett. 7 (1961) 65 2) T. D. Thomas, W. M. Gibson and G. J. Stafford, Physics and chemistry of fission (IAEA, Vienna, 1965) p. 467 3) J. C. D. Milton and J. S. Fraser, Can. J. Phys. 40 (1962) 1626 4) J. S. Fraser, J. C. D. Milton, H. R. Bowman and S. G. Thompson, Can. J. Phys. 41 (1963) 2080 5} J. S. Fraser and J. C. D. Milton, Ann. Rev. Nucl. Sci. 16 (1966) 379 6) I. A. Baranov, A. N. Protopopov and B. M. Shiryaev, Yad. Fiz. 10 (1969) 1149 ,rtrans.: Soy. J. Nucl. Phys. 10 (1970) 654]
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7) T. D. Thomas and R. Vandenbosch, Phys. Rev. 133 (1964) B976 8) W. Reisdorf, J. P. Unik, H. C. Griffin and L. E. Glendenin, Nucl. Phys. A177 (1971) 337 9) M Bolsterli, F. O. Fiset and J. R. Nix, Physics and chemistry of fission (IAEA, Vienna, 1969) p. 183 10) P. M611er and S. G. Nilsson, Phys. Lett. 31B (1970) 283 11) U. Mosel and D. Scharnweber, Phys. Lett. 32B (1970) 229 12) H. W. Schmitt, W. E. Kiker and C. W. Williams, Phys. Rev. 137 (1965) B837 13) J. C. D. Milton and J. S. Fraser, Physics and chemistry of fission (IAEA, Vienna, 1965) p. 531 14) H. W. Schmitt, J. H. Neiler and F. J. Walter, Phys. Rev. 141 (1966) 894 15) F. Pleasonton, Phys. Rev. 174 (1968) 1500 16) J. Terrell, Phys. Rev. 127 (1962) 880 17) H. R. Bowman, J. C. D. Milton, S. G. Thompson and W. J. Swiatecki, Phys. Rev. 129 (1963) 2133 18) P. A. Seeger and R. C. Perisho, Los Alamos Scientific Laboratory report LA-3751 (1967) 19) J. P. Unik and J. E. Gindler, Argonne National Laboratory report ANL-7748 (1971) 20) A. C. Wahl, A. E. Norris, R. A. Rouse and J. C. Williams, Physics and chemistry of fission (IAEA, Vienna, 1969) p. 813 21) M. E. Meek ano B. F. Rider, General Electric reports APED-5352 (1967) and APED-5398 (1968) 22) S. F. Semenko, O. V. Vasilijev and V. A. Semenov, Phys. Lett. 31B (1970) 429 23) .1. H. Bjerregaard, O. Hansen, O. Nathan and S. Hinds, Nucl. Phys. 86 (1966) 145 24) J. R. Maxwell, G. M. Reynolds and N. M. Hintz, Phys. Rev. 151 (1966) 1000 25) W. McLatchie, J. E. Kitching and W. Darrey, Phys. Lett. 30B (1969) 529 26) P. Debenham and N'. M. Hintz, Phys. Rev. Lett. 25 (1970) 44 27) E. Cheifetz, R. C. Jared, S. G. Thompson and J. B. Wilhelmy, Phys. Rev. Lett. 25 (1970) 38 28) A. G. Blair, J. G. Beery and E. R. Flynn, Phys. Rev. Lett. 22 (1969) 470 29) A. H. Wapstra and B. N. Gove, Nucl. Data Tables 9 (1971) 303 30) V. M. Strutinsky, Nucl. Phys. A95 (1967) 420; A122 (1968) 1 31) V. A. Rubchenya, Sov. J. N.ucl. Phys. 9 (1969) 697 32) S. G. N'ilsson et aL, Nucl. Phys. A131 (1969) 1 33) W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81 (1966) 1 34) R. Vandenbosch, Nucl. Phys. 46 (1963) 129