Analytical relationship for the cranking inertia

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.Comment: 12 pages, 4 figure

New island of cluster emitters

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

Two-dimensional nuclear inertia : analytical relationships

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

Liquid Drop Stability of a Superdeformed Prolate Semi-Spheroidal Atomic Cluster

Analytical relationships for the surface and curvature energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. By modifying the cluster shape from a spheroid to a semi-spheroid the most stable shape was changed from a sphere to a superdeformed prolate semi-spheroid (including the flat surface of the end cap). Potential energy surfaces vs. deformation and the number of atoms, N, illustrate this property independent of N.Comment: 5 pages, 3 figurex, revtex

Potential energy surfaces for cluster emitting nuclei

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.Comment: 10 pages, 21 figures, revtex

Deformed two center shell model

A highly specialized two-center shell model has been developed accounting for the splitting of a deformed parent nucleus into two ellipsoidaly deformed fragments. The potential is based on deformed oscillator wells in direct correspondance with the shape change of the nuclear system. For the first time a potential responsible for the necking part between the fragments is introduced on potential theory basis. As a direct consequence, spin-orbit {\bf ls} and {\bf l$^2$} operators are calculated as shape dependent. Level scheme evolution along the fission path for pairs of ellipsoidaly deformed fragments is calculated. The Strutinsky method yields the shell corrections for different mass asymmetries from the superheavy nucleus $^{306}$122 and $^{252}$Cf all along the splitting process.Comment: 32 pages, 8 figure

Cluster Radioactivity

Cluster radioactivity (spontaneous emission of heavy particles from nuclei) is presented from a theoretical point of view in good agreement with experimental results. After a brief historical account, we give details about the analytical super asymmetric fission (ASAF) model extensively used for predicting the half-lives of heavy and superheavy (Z ≥ 104) elements. For the already measured 26 cluster decays (from 14C to 32,34Si of parent nuclides with Z = 87-96) it is clear that cluster radioactivity is a rare phenomenon in the best case about 9 orders of magnitude weaker than the competing alpha decay. Then we show the theoretical possibility of a strong cluster decay compared to alpha decay for some superheavy nuclei with Z ≥ 122, e.g. 306122; 310-314122; 306-324124, and 311-323124