SADDLE-TO-SCISSION LANDSCAPE IN FISSION : EXPERIMENTS AND THEORIES

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1 SADDLE-TO-SCISSION LANDSCAPE IN FISSION : EXPERIMENTS AND THEORIES M. Asghar, R. Hasse To cite this version: M. Asghar, R. Hasse. SADDLE-TO-SCISSION LANDSCAPE IN FISSION : EXPERI- MENTS AND THEORIES. Journal de Physique Colloques, 1984, 45 (C6), pp.c6-455-c < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1984 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque C6, suppl6ment au n06, Tome 45, juin 1984 page C6-455 SADDLE-TO-SCISSION LANDSCAPE IN FISSION : EXPERIMENTS AND THEORIES M. Asghar and R.W. Hasse* CEN and USTHB, B.P. 1017, Alger-Gare, Algeria *~nstitut Law-Langevin, 156 X, Grenoble Cedex, France Re'sum6 - On explore le paysage de l'6nergie potentielle du modzle de la goutte liquide (LDM) entre le point selle et le point scission. Le point sortie oh le col joignant les fragments naissants est encore 6pai~ dgfinit la configuration de scission ; ceci est confront6 aux resultats exp6rimentaux. On discute les donndes expdrimentales pour montrer que le paysage entre le point selle et le point scission est probablement plutdt plat et: non raide come prdvoit le LDM ordinaire. Abstract - The LDM saddle-to-scission potential energy landscape is investigated. The exit point, where the neck joining the nascent fragmentsis still rather thick, identifies the scission configuration ; this is confronted with different experimental evidence. Ex~erimental results are discussed to show that the saddle-to-scission landscape may be rather flat and not steep as the ordinary LDM predicts. Nuclear fission is a rather complex process, because it consists of a large-amplitude motion, where all the nucleons of the fissioning nucleus actively. Although much theoretical and experimental progress has been made over the past decade in understanding a part of the potential energy surface of a fissioning system, which shows different barriers and minima as a function of the stretching and necking-in deformation coordinates, we know little about the region from the outer barrier down to scission. For example, we do not even know whether the potential energy landscape in this region determined from the ordinary liquid drop model (LDM) represents nature or whether it lacks some significant ingredients. Obviousl) it is important to try to understand this landscape before going on to the dynamics of the process. 1.2 The potential energy landscape calculated with the LDM (which is limited to surface, surface asymmetry and Coulomb contributions) of Fig. 1 shows that, slightly beyond the barrier, the configuration of separated fragment shapes in the fusion vdlley becomes much lower in energy than the one of continuous shapes of the same elongation along the LDM valley, but also that there is a ridge separating these valleys, which acts as a barrier for the nucleus when necking-in and fissioning into two fragments. As the def ormation increases, however the height of the ridge decreases Fig. 1 - The LDM potential energy landscape for ~ in ~ terms of the {pcm,h) parameters. Article published online by EDP Sciences and available at

3 C6-456 JOURNAL DE PHYSIQUE and at a well defined value of deformation - called the exit point - not only it disappears, but the LDM valley ceases to exist and the system becomes unstable against scission At the exit point, the center of mass distance pm of the two halves of the nucleus is approximately where % is the radius of the fissioning nucleus. Pcm is practically independent of the fissibility parameter x. The radius d of -the neck at the exit point is rather thick, It is interesting to note that this value of d is comparable to the width of the tail of the density of a heavy nucleus. Beyond this point, the loss of saturation property of nuclear matter and a strong Coulomb repulsion between the two nascent fragments results in a strong necking-in force that should lead to a very fast rupture of the neck. Therefore, it is quite natural to identify the exit point as the physical scission configuration. The exit configuration is very compact and it exists for both symmetric and asymmetric modes of fission 121. Let us nowdiscuss the experimental evidences supporting the existence of the exit point and of the scission configuration Variation of the mean fission fragment kinetic energy <Ek> as a function of the fissioning nucleus. Since pcm at the exit point is almost independent of the fissibility parameter x and if the neck rupture is fast, then <Ek> should result mainly from Coulomb repulsion between the two halves of the nucleus with a center of mass distance pcm, <Ek> = k ZF / AF, (3) where k is a constant, and AF and ZF are the mass and charge of the fissioning nucleus. An empirical correlation of this type has been known for a long time 141. If we take ro = fm, then k = as compared to the empirical value of k = found by Viola /4/ from data on symmetric fission. This correlation indicates that at least a major part of <Ek> comes from Coulomb repulsion and the prescission energy should be quite small. 2. Dependence of <Ek> on excitation energy of the fissioning nucleus It is well known that <Ek> changes little and remains practically constant as a function of excitation energy of the fissioning nucleus 151. Most of the excitation energy is released as prompt neutrons. As discussed above, the exit point which determines <Ek>, results from the macroscopic (LDM) energetics of the fissioning nucleus. This property of the LDM parameters should be insensitive to the excitation energy of % MeV corresponding to a nuclear temperature T % 1-2 MeV 161. The variation of <E > with excitation energy seen experimentally can be k accounted for by the microscopic (single article) effects. 3. Width of alpha-particle angular distributions in ternary fission. At the exit point the configurations of the fissioning nuclei, say, from Th to 252~f are practically identical because the distance pcm changes only by about 3 %. Any phenomenon which scans this scission configuration should have similar properties for all the fissioning nuclei. Therefore, alpha-particles in ternary fission, which are believed to result from the sudden rupture of the neck joining the two nascent binary fragments /7,8/, should have similar distributions. The best existing results show that, indeed, the width B a, ~ (with respect to the light fission fragment L) is % 19' for both 235~ (nth,f) and 252Cf(s,f) 19,101. These results also confirm that the pre-scission energy is small : less than 9 MeV, for both systems - contrary to the non-viscid dynamical LDM calculation values of about 25 MeV and 40 HeeV for 235~

4 and 252~f,respectively. 4. Variance a: of the nuclear charge distribution in fission. The experimental results on 235~ (nth,f) show that the average value of the charge variance 0; is about 0.35 and it is constant and independent of the total deformationexcitation energy Etotal available to the fissioning nucleus in the range to 40 MeV This result was shown in Ref. 13 to be consistent with the zero point oscillation of a collective isovector giant dipole resonance of the composite system at the exit point. In this picture the charge mode is excited somewhere between saddle and exit and the fissioning nucleus moves down from saddle towards scission so slowly that the charge distribution wave function is able to adjust adiabatically to the instantaneous equilibrium value. At the exit point, however, the motion of the neck radius becomes suddenly so rapid (due to the process of rupture) that the charge wave function can no longer adjust adiabatically and a; undergoes a 'freezeout' at this point and remains constant thereafter. Since the scission configurations of different fissioning nuclei are practically identical, the variance 05 should be similar for all the fissioning systems ; this is confirmed by the recent results on 239~u(nth,f), where a$ has the same value / 141 as for 235~(nth,f). The constancy of 02 over a wide range of deformation-excitation energy shows that the heat-bath temperature T is quite low compared with the quantum energy hoz/2 of the charge mode. Furthermore, this result is incompatible with the semi-equilibrium model of Nijrenberg and questions its basic assumption of a thermodynamic equilibrium among the collective degrees of freedom excited in the fissioning nucleus between saddle and scission Since up to the exit point the neck joining the nascent fragments is so thick that it is quite likely that only the necessary minimum number of collective modes such as stretching (fission mode), necking-in, mass-asymmetry and charge modes, get excited between saddle and exit. The other modes such as bending, wriggling and twisting postulated by Nix and Swiatecki 1161 for two tangent spheriods may not have much chance to get excited up to the exit point and even beyond if the neck rupture is fast. Under this condition there may not be enough collective degrees of freedom to establish a thermodynamical equilibrium. The lack of thermodynamical equilibrium will also question the validity of Tcoll used in the Boltzmann factor e-v/tcoll by Wilkins et a in their static scission-point model. 5. Saddle-to-scission (exit) potential energy landscape and the cold fission phenomenon We give in Table I the saddle-to-scission energy difference Ess for a few representative nuclei. One notices that Ess increases quite rapidly with the ZF of the fissioning nucleus. Since the exit point is not a stationary point, it is not invariant under coordinate transformation. However, since the center of mass distance TABLE I Some quantities relevant for the scission energy. - Pissioning nucleus Neutron bind+= Energy (H,, (MeV) Tile scission energies were calculated with the Pauli-Ledergerber parameters Inner Barrier V, (MeV) Outer Barrier VB (MeV) Calculated seis- $ion - Energy relative to Ground state ESo (MeV) Scission energy relative to s~ddle ESS (me") f so + V~ 229 Th(nth.f) I ~(nth.~) P"(hth,f) ~m(nth,f) ~f(s,f)

5 C6-458 JOURNAL DE PHYSIQUE Heavy fragment moss [PHI Fig. 2 - The fragment mass distributions for ~ as a function of the heavy fragment mass for different light-fragment kinetic energy windows Heavy fragment mass [ph] Fig.3 - The fragment mass distributions for 232~, 233~ and 23% as a function of the heavy fragmentmass for different light-fragment kinetic- energy windows 1171.

6 Pcm is a natural dynamical variable, it should minimize the non-diagonal elements of the inertial tensor and the dynamics of the fission process may be determined mostly by the potential energy 1/21. In the following discussion, we take this to be true. In Figures 2 and 3, we show the experimental data on mass distributions for the thermal-neutron induced fission of 229Th, 232~, 233~ and 235~ as a function bf the light fragment kinetic energy window 1/71 EL. These results show the existence of fission events whose kinetic energies Ek,max approach their specific Q-values within an experimental uncertainty of 2-3 MeV. This is particularly true for events with heavy fragment masses MH around 144 for 229~h and 232~ and & around 134 for 23% and 235~, and 238~~, and ~ ~ (ref ~ ~./18/)not shown here. In Fig, 4,.we show the results of Si narbieux et a1 I191 of EkImaX (MH) for 293JJ and compared with the corresponding Q(t4~) values. These data were obtained with a relatively simple and purely electronic method that helped to separate the fragments mass by mass in the high fragment kinetic energy region One notices here, too, that the Ek of fission events with MH around 114 reach the highest possible Q-values. Let us consider the MH/ML = fragmentation of 235~ (nth,f). If the prescission energy Epre is small as discussed above and if one therefore can assume that the fragment kinetic energy -- results from Coulomb repulsion only, then 190t 2 E~ = E = F Z1Z2 e Ip,,, (4) where F is the form factor, and Z1 and 22 are the nuclear charges of the fragments. We can trace the locus of the fusion valley (fragments separated) as a function of Ek for this fragmentation. This is shown schematically in Fig. 5 along with the LDM valley and the double humped-barrier for 236~. One knows that the LDM predicts only symmetric fission, but in reality the asymmetric mode is the dominant mode in the actinide region. Furthermore, a large variety of data on fission obser-- vables suggest strongly that the poten-. tial energy of the fissioning nucleus plays a decisive role in determining their probabilities. Hence one can assume that the total potential energy, i.e. LDM plus microscopic effects, should be lower than the LDM valley energy alone. For the asymmetric mode of fission this has been shown by Mustafa et a1 /21/ to be the case. As a1 rule, each MH/ML fragmentation has a potential energy surface. However, we limit ourselves to the LDM valley. As discussed before (point l), the mean - hence, the most probable fission for a given M ~ / M - ~ occurs at the exit point, where the barrier between the two valleys disappears. In this picture, 23s~(t~.n,f) \ 1 v.,., HEAVY MASS (a.m.u.1 Fig. 4 - Ek,max plotted against the heavy fragment mass (solid line). The dashed line joins the highest possible Q-values, whereas the dotted line joins the second highest Q:values / 191. Fig. 5 - The separated fragment shapes in the fusion valley for MH/~L= and the double-humped barrier along with the LDM valley. The elongation coordinate is the center of mass distance p cm' I

7 C6-460 JOURNAL DE PHYSIQUE the fission events with Ek higher than <Ek> result from a penetration (when neckingin) through the barrier between the two valleys 1221 ; this can happen as long as the fusion valley is lower than the LDM valley. However, as Ek increases, pcm decreases and the difference between the two valleys decreases and for Ek = E ~,A (Fig. 5), the two valleys have the same energy. For Ek -t Q and for pcm % 14.5 fm, one notices in Fig. 5 that the fusion valley is AE % 10 MeV higher than the LDM valley and yet the nucleus fissions. Even by the uncertainty relation the nucleus could borrow this energy only during At % 6.6 x sec to fission, much shorter than a nucleonic time in a nucleus. AE is even higher for heavier nuclei like 239~~. One can invoke an involved solution to this problem However, the simplest solution may be to consider that the potential energy surface in this region is rather flat (the points B and C are close to each other) and not steep as predicted by the ordinary LDM. Hence, the LDM, as used generally, lacks some essential ingredients. The recent results of constrained HFB calculations of Berger et al./23/ show a relatively flat energy surface in this region - substantiating this conjecture. Furthermore, when the curvature and the incompressibility terms are added to the LDM, the landscape becomes flatter similar to the HFB result 124,251. However, the barrier also becomes much higher than the experimental value. It is argued that the zero point energies on top of this landscape should take care of the increase in the barrier height. This point is presently under investigation. Pertinent to this context is the calculation of Brack at al.1261 with a realistic SKMX-force using an extended Thomas-Fermi (ETF) formalism. The SKMX is normalised to the LDM barrier of 240~~. Their landscape beyond the saddle point is quite similar to the LDM. Hence it would seem that the energy of the barrier determines the shape of the landscape. With such a flat landscape in mind, Ess freed from saddle to scission should be much less than given in Table 1. Ess may be divided into different partsas where Ecoll represents the part going into collective modes other than deformation, and E? ~ into intrinsic excitation. We take Epre % 0. Since, as discussed above, probably only the minimum number of collective modes get excited, a few MeV may be taken up by them. The remaining energy freed will end up as E?~. One can get some idea of E F from ~ the odd-even effect on charge 21- yields. The amplitude of this odd-even effect jvh+z 20- suggests that E? ~ should be smaller than about , MeV because some pairs may be bro- IO- -: ken during the rapid neck rupture These results seem to indicate that there is not much 61s- - energy freed and available to go into E& via EIO- qp-excitations. However, one expects EA, to go 3 up with the fissility parameter. This may ex- \O:; *,." - plain the rapid decrease of odd-even effects r l 5-0 from about 40 % for 229~h(nth,f) down to about - 12 % for /14,30,31/ 239~u(n~~,~). 05-2s." >.7 %lo- The relative flatness of the landscape, the presence of only a restricted number of collec- : tive modes and a low Em may also explain the z ID- conservation of the K-quantum number, the proalic - jection of the total angular momentum J on the 2rr~u - o- l - nuclear symmetry axis as evidenced by the frag ment angular distribution in low energy fission 11) The fission fragment anisotropies of Fig. 6 show a systematic change in the character of angular distributions, when going from I 00 LO 29 lighter to heavier nuclei. The anisotropy NEUTRON ENERGY (MeV) varies strongly with energy for the lighter elements, but becomes rather structureless for Fig. 6 - Fission-fragment anisotro- the heavier elements. This was thought to be pies for neutron-induced fission in due to the systematic trend for the outer some actinides 1321.

8 barrier to change from an energy higher than the inner barrier for the lighter elements to an energy lower than the inner barrier for the heavier elements. The lack of structure in the anisotropy for the heavier elements has been explained on the assumption that the K values are not conserved during the passage through the second minimum. It was assumed that the time of passage through the region of the second minimum is sufficiently long so that the memory of K-values at the first barrier is lost and reestablished at the second barrier. When the second barrier is lower than the first one, a quasi-statistical distribution of K-values may prevail resulting in a structureless anisotropy. However, we have just seen above that the amplitude of odd-even effects decreases rapidly as one goes from the lighter elements to the heavier ones and it has been shown that pairs are not broken at the second barrier tie think, therefore, that a large part of the alignment of the fissioning nucleus - hence, of K - is destroyed during the saddle-to-scission descent where pairs are broken and quasi-particles are excited. However, it should be noted that this saddle-to-scission landscape does not seem to be able to explain the fragment energy distribution which, for a given MH/ML ratio, is about Gaussian in shape 117,221. As discussed above, the upper half of the Gaussian, Ek><Ek>, results from a penetration through the barrier between the two valleys and as Ek goes up, the pcm decreases and the barrier height increases resulting in a decreased probability of fission. The production probability for low energy events, Ek < <Ek>, is rather similar yet there is no barrier present in this case. Furthermore, one has to look into as to how the relative flatness of the potential landscape beyond the second barrier may influence the ground state spontaneous fission half-lives. Acknowledgements One of us (R.W.H.) is indebted to the members of the Commissariat aux Energies Nouvelles, Algiers, for the warm hospitality extended to him. References 1. STRUTINSKY V.M., LYASHCHENKO N.Y. and POPOV N.A., Nucl. Phys. 6 (1963) BRACK M., DAMGAARD J., JENSEN A.S., PAUL1 H.C., STRUTINSKY V.M., and WONG C.Y., Rev. Mod. Phys. 3 (1972) ASGHAR M. and RAMAMURTHY V.S., ILL Report (1981) Nr. SP VIOLA V., Nuclear Data 1 (1976) VANDENBOSCH R. and HUIZENGA J.R., 'Nuclear Fission', Academic Press (1973) 6. HASSE R.W. and STOCKER W., Phys. Lett. 44B (1973) FULLER R.W., Phys. Rev. 126 (1962) HALPERN I., Proc. 1st Symp. on Physics and Chemistry of Fission, Salzburg, 1965, Vol. 2 (IAEA Vienna, 1965) p FLUSS M.J., KAUFMAN S.B., STEINBERG E.P. and WILKINS B.D., Phys. Rev. Cz (1971) 11'2 10. LL2 GUET C., SIGNARBIEUX C., PERRIN P., NIFENECKER H., ASGHAR M., LEROUX B., Nucl. Phys. A 9 (1979) 1 CAT TUCOLI F. and 11. NIX J.R., Nucl. Phys. A 130 (1969) CLERC H.G., LANG W., WOHLFARTH H., SCHRADER H. and SCHMIDT K.H., Proc. 4th Symp. on Physics and Chemistry of Fission, Jiilich 1979 (IAEA, Vienna) p. 65 ; LANG W., CLERC H.G., WOHLFARTH H., SCHRADER H. and SCHMIDT K.H., Nucl. Phys. A 345 (1980) ASGHAR M., Z. Phys. A 296 (1980) SCHMITT C., GUESSOUS A., BOCQUET J.P., CLERC H.G., BRISSOT R., ENGELHARDT D., FAUST H.R., GONNENWEIN F., MUTTERER M., NIFENECKER H., PANNICKE J., RISTORI Ch. and THEOBALD J.P., preprint, 1984

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