G. Royer

Analytic expressions for the proximity energy, the fusion process and the α emission

Abstract The entrance and exit channels through quasimolecular shapes are compatible with the experimental data on fusion, light nucleus and α emissions when the proximity energy is taken into account. Analytic expressions allowing to determine rapidly this proximity energy are presented as well as formulas for the fusion barrier heights and radii and for the α emission barriers. Predictions for half-lives of exotic α emissions are proposed.

Light nucleus emission within a generalized liquid-drop model and quasimolecular shapes

The potential barrier governing the light-nucleus emission has been determined within a generalized liquid-drop model including the proximity effects between the light and daughter nuclei and adjusted to reproduce the experimental Q value. The partial decay half-lives have been calculated within the WKB barrier penetration probability, without introducing preformation factor. The agreement with the experimental data for the 14C, 20O, 23F, 24−26Ne, 28−30Mg and 32Si emission is good. Predictions for other possible decays are presented meeting two criteria: partial half-life ≤1030s and branching ratio relative to α emission ≥10−24. An analytic formula is proposed for the half-life of the light-nucleus decay.

CLUSTER RADIOACTIVITY AND VERY ASYMMETRIC FISSION THROUGH COMPACT AND CREVICED SHAPES

Abstract The decay of radioactive nuclei which emit heavy clusters such as C, O, Ne, Mg and Si has been studied in the fission valley which leads one spherical nucleus towards two spherical touching nuclei before crossing the barrier. Assuming volume conservation, the macroscopic deformation energy has been calculated within a generalized liquid-drop model taking into account the proximity effects between the cluster and the daughter nucleus. The microscopic corrections have been introduced empirically to reproduce the experimental Q values. The theoretical partial half-lives obtained within the WKB barrier penetration probability are in good agreement with the experimental data. The C, O, Ne, Mg and Si emission looks like a spontaneous fission through very asymmetric compact and creviced shapes formed at the early stage of the tunneling process.

On the formation and alpha decay of superheavy elements

The potential energy governing the entrance and α-decay channels for superheavy elements has been determined within a Generalized Liquid Drop Model including the proximity effects, the asymmetry, an accurate nuclear radius, an adjustment to reproduce the experimental Q value and within the asymmetric two-center shell model and the Strutinsky method. In cold fusion paths doublehump fusion barriers stand and incomplete fusion events may occur. Warm fusion reactions lead to one hump potential barriers and to very excited systems cooling down by neutron or even α-particle evaporation. α-decay half-lives of superheavy elements have been calculated and compared with the new available experimental data.  2002 Elsevier Science B.V. All rights reserved.

On the coefficients of the liquid drop model mass formulae and nuclear radii

The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and different powers of the relative neutron excess I = (N − Z)/A have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction Z 2 /A term or the charge exchange correction Z 4/3 /A 1/3 term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an |I| dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more e than an I 4 dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r0 of 1.22-1.23 fm.

Entrance channels and alpha decay half-lives of the heaviest elements

The barriers standing against the formation of superheavy elements and their con- secutivedecay have been determined in the quasimolecular shape path within a Generalized Liquid Drop Model including the proximity effects between nucleons in a neck, the mass and charge asymmetry, a precise nuclear radius and the shell effects given by the Droplet Model. For moderately asymmetric reactions double- hump potential barriers stand and fast fission of compact shapes in the outer well is possible. Very asymmetric reactions lead to one hump barriers which can be passed only with a high energy relatively to the superheavy element energy. Then, only the emission of several neutrons or anparticle can allow to reach an eventual ground state. For almost symmetric heavy-ion reactions, there is no more external well and the inner barrier is higher than the outer one. Predictions for partial � decay half-lives are given.

Asymmetric fission for 70,76Se and 90,94,98Mo via quasimolecular shapes and related formulas

Abstract The asymmetric fission has been described within quasimolecular shapes and a generalized liquid-drop model including the nuclear proximity energy. The fission barrier heights agree with the recent data obtained for 70,76 Se and 90,94,98 Mo. An analytical formula given the temperature-dependent fission barrier height as functions of the charges and masses of the parent nucleus and of one fragment is proposed. Another expression allows to obtain for a fixed fragment charge the associated most probable mass.

ANALYTIC DESCRIPTION OF THE FUSION AND FISSION PROCESSES THROUGH COMPACT QUASI-MOLECULAR SHAPES

Abstract Recent studies have shown that the characteristics of the entrance and exit channels through compact quasi-molecular shapes are compatible with the experimental data on fusion, fission and cluster radioactivity when the deformation energy is determined within a generalized liquid drop model. Analytic expressions allowing to calculate rapidly the main characteristics of this deformation path through necked shapes with quasi-spherical ends are presented now; namely formulas for the fusion and fission barrier heights, the fusion barrier radius, the symmetric fission barriers and the proximity energy.