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The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the 240 Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.
Potential energy surfaces are calculated by using the most advanced asymmetric two-center shell model allowing to obtain shell and pairing corrections which are added to the Yukawa-plus-exponential model deformation energy. Shell effects are of crucial importance for experimental observation of spontaneous disintegration by heavy ion emission. Results for 222Ra, 232U, 236Pu and 242Cm illustrate the main ideas and show for the first time for a cluster emitter a potential barrier obtained by using the macroscopic-microscopic method.
Complex fission phenomena
(2004)
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to binary, ternary, and quaternary fission are outlined.
A new region of proton-rich parent nuclei decaying by spontaneous cluster emission with a measurable branching ratio relative to alpha decay is predicted within the analytical superasymmetric fission model. After a brief presentation of the model and of the seven mass tables used to calculate the released energy, the obtained results are discussed. Measurable half-lives and branching ratios are estimated for 12C, 16O, 28Si, and other cluster radioactivities of some nuclides having proton and neutron numbers in the range Z=56–64 and N=58–72. Such nuclei far from stability could be produced in reactions induced by radioactive beams.
The components of the nuclear inertia tensor, functions of the separation distance R and of the radius of the light fragment R2, BRR(R,R2), BRR2(R,R2), and BR2R2(R,R2) are calculated within the Werner-Wheeler approximation, by using the parametrization of two intersected symmetric or asymmetric spheres. Analytical relationships are derived. When projected to a path R2=R2(R), the reduced mass is obtained at the touching point. The two one-dimensional parametrizations with R2=const, and the volume V2=const previously studied, are found to be particular cases of the present more general approach. Illustrations for the cold fission, cluster radioactivity, and α decay of 252Cf are given.
