Apr 6, 1992 - At first, particular temary fission valleys are selected starting from the viewpoint that the aim is always to search for a parametrization which ...
1. Phys. G: Nucl. Pan. Phys. IS (1992) 2015-2026. Printed in the UK
On nuclear ternary fission G Royer, F Haddad and J Mignen laboratoire de Physique NuclCaire, UA INZPUCNRS et Univenitt d e Nantes, 2 rue de la Houssiniere, 44072 Nantes Cedex 03, France Received I6 April 1992, in final form 22 July 1992 AbstrscL Prolate ternary fission and, to some extent, oblate ternary and cascade fission have been investigated within the liquid-drop model at finite temperature taking into account the nuclear proximity effects between the surfaces of the nascent fragments. In the whale m a s range, the potential barriers are higher in the oblate fission valley. Cascade fission is favoured for light nuclei while prolate fission becomes the most probable with increasing mass. The binary fission barriers are much lower than the ternary ones except for the superheavy nuclei for which lhey are comparable.
1. Introduction At low energies, the spontaneous fission of actinide isomers and the still pending question of the detection of superheavy elements have renewed interest in investigating the ternary fission mode (Moller and Nix 1976, Carjan el a/ 1986, Mignen and Royer 1987, Theobald et a/ 1989, Makarenko et a/ 1989 and Dai 1991). Experimentally, the upper limit for symmetric nuclear tripartition relative to binary fission is very much in question but seems to lie between (Muga er a/ and 1967, Schall et a/ 1987) except for very heavy systems formed in heavy-ion reactions (at low energies) where ternary fission is more frequent (Fleischer er a/ 1966). In contrast, very asymmetric tripartition with the emission of an oi particle occurs with a relative yield of 3 4 x The achievement of new accelerators in laboratories such as GANIL, GSI, MSU, Rxas AM, HMI and SATURNE has allowed heavy-ion reactions to be studied at intermediate energies (1&100 MeV U-]). In these experiments the incomplete fusion of the projectile with the targct leads to a very excited residue. Only a part of this excitation energy is thermalized while the other part permits the bot nuclear system to be used to investigate the different fragmentation channels (Peilert el a/ 1989, Friedman 1990, Lopez and Randrup 1990, Garcias er af 1991). Experimentally, the n-event probability decreases regularly with the number of fragments (Bowman et a/ 1991, Moretto er a/ 1991). Then, after binary fission and the evaporation mode, the ternary fission becomes the next step to novel modes of disassembly (Louvel et a/ 1992). In the present work the purpme is to determine the general macroscopic background of these exit channels which are very rarely taken at low energies and very poorly known at intermediate energies. At first, particular temary fission valleys are selected starting from the viewpoint that the aim is always to search for a parametrization which contains t h e least possible number of parameters but gives 0954-3899/m/122015+12~7.50 @ 1992 IOP Publishing Ltd
G Royer er a1
a reasonable approach to the equilibrium shapes. Then, the deformation energies in these different decay channels are compared. The potential energy was determined within the liquid-drop model taking into account both the temperature dependence and the nuclear proximity forces. Indeed, the ~ e n e r a trend l in recent studies (Hasse et a1 1983, Berger ef a1 1984, Heeg er a1 1989) of the fission process is to assume that binary and ternary fission occurs through more compact shapes than those previously expected. In such a case thc finite-range effects of the nuclear force in the crevices or between the surfaces are very important. Let us recall that the introduction of a proximity energy is also the only means by which to explain the fusion of incomingnuclei even when the Coulomb repulsion is very strong. The selected decay channels and the framework of the liquid-drop model energy are defined in sections 2 and 3. Comparisons between the different ternary and binary fission valleys are made in section 4, particularly for the saFe, IWEuand z4uPunuclei at T = 0 and 5 MeV Section 5 is devoted to the rotational energy that such nuclei can store while, in section 6, the translational kinetic energies of the fragments are given. The asymmetric ternary fission leading to the emission of a IzC nucleus is studied in section 7. Finally, in section 8, the profiles of these different potential barriers are compared for the ;y! superheavy nucleus.
2. Selected exit channels
The possibilities of fission into three nearly equal fragments are essentially two oblate and prolate direct modes and cascade or sequential fission, i.e. emission of a first fragment and the later separation of t h e remaining part into two equal nuclei. Within the liquid-drop model but without taking into account the nuclear proximity force efiecIs, Diehl and Greiner (1974) have found a preference for prolate over oblate saddle-point shapes. The question is to establish whether this conclusion is changed by the introduction of the temperature and proximity energy and by investigating the cascade fission. Asymmetric and symmetric prolate ternary fission is described within a two-parameter family of compact and creviced shapes leading the nucleus smoothly from an initial sphere to three aligned tangent and non-deformed fragments. ine two effective input parameters are tne ratio s between the neck radius ana tne elongation of the nascent fragments and the ratio @( 1) between the radius of the central fragment and that of the two other bigger spherical nuclei (see figure l(a)). The volume, surface and distance between the two halves of the system are given by analytical formulae (Mignen and Royer 1987, 1990). After the rupture of the necks, thc three fragments separate along thc common axis of fission. This path will later be labelled path a. The mass-symmetric oblate fission (path b) is roughly simulated from the contact point using an equilateral configuration (figure l(b)), the three equal spheres moving away in keeping with this spatial symmetry. In fact, this path b is a particular case Of a more general two-dimensional shape sequence: two equal spheres at the base of an isosceles triangle and a third eventually lightcr fragment at the apex (see figure l(b)). which minimizes i'ie iuini eneiD oii ;he ~ .~.. l T on, r path wiii refer io ihe associated two-dimensional potential surface, starting with three equal nuclei. Path d corresponds to the same picture but allows an initial mass asymmetry. On this deformation landscape, cascade fission is broadly reproduced in blocking rII(i.e. in