Accurate Exponential Representations for the Ground State Wave Functions of the Collinear Two-Electron Atomic Systems

In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant S-state. It is worth noting that the considered states include the well-known states of the electron–nucleus and electron–electron coalescences as a particular case. The simplicity and compactness imply that the considered wave functions represent linear combinations of a few single exponentials. We have calculated such model wave functions for the ground state of helium and the two-electron ions with nucleus charge 1≤Z≤5. The parameters and the accompanying characteristics of these functions are presented in tables for number of exponential from 3 to 6. The accuracy of the resulting wave functions are confirmed graphically. The specific properties of the relevant codes by Wolfram Mathematica are discussed. An example of application of the compact wave functions under consideration is reported.

CLUSTER SHELL MODEL WAVE FUNCTION: STRUCTURE OF 6LI NUCLEUS

In this paper cluster model wave function for 6Li using Shell Model with definite parity and angular momentum is written along with cluster co-ordinates, which are relative to the center-of-mass of various clusters and involve with parameters. These parameters can be adjusted to some extent to obtain predictions close to experimental properties. The cluster model wave function is written along with resonating group method (RGM) and the Complex Generator Coordinate Technique (CGCT). The Complex Generator Coordinate Technique allows the transformation of the cluster model wave function written in terms of cluster co-ordinates into anti-symmetrized product of single particle wave function. This wave function is written in terms of single particle co-ordinates, the center-of-mass co-ordinates, parameter coordinates and generator coordinates.

Magic numbers for shape coexistence

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82…) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70,…) emerge at deformations around ε=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy–SU(3) scheme.