Abstract
The Bohr-Mottelson Hamiltonian is amended with a potential which depends on both β and γ deformation variables and which allows us to separate the β variable from the other variables. The equation for the β variable is quasi-exactly solved for a sextic oscillator with centrifugal barrier potential. Concerning the γ equation, its solutions are the angular spheroidal and Mathieu functions for X(5) type and triaxial nuclei, respectively. The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) and the Sextic and Mathieu Approach (SMA). SSA and SMA was successfully applied for several nuclei, details being presented below.
Highlights
A great interest in solving the eigenvalue problem of the Bohr-Mottelson Hamiltonian [1] having a potential which depends on both β and γ variables appeared when nuclei being close to the critical points of some shape phase transition were very well described by analytically solvable equations
We present new interesting solutions for the Hamiltonian [1], namely, Sextic and Mathieu Approach (SMA) [6,7,8] and Sextic and Spheroidal Approach (SSA) [9], respectively
The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) [9] and the Sextic and Mathieu Approach (SMA) [6,7,8], respectively
Summary
A great interest in solving the eigenvalue problem of the Bohr-Mottelson Hamiltonian [1] having a potential which depends on both β and γ variables appeared when nuclei being close to the critical points of some shape phase transition were very well described by analytically solvable equations. SMA represents a realistic tool for the description of triaxial nuclei having axial deformations close to π/6, while SSA works very well for X(5) type and axial nuclei. By performing a second order expansion of the rotational term around γ0 = 0 and γ0 = π/6 for X(5) type nuclei and triaxial nuclei respectively, and averaging the resulting terms with specific Wigner functions, a complete separation is achieved [6, 9]:. The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) [9] and the Sextic and Mathieu Approach (SMA) [6,7,8], respectively
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