Quasi-exact description of the γ-unstable shape phase transition

The equation of the [Formula: see text]-unstable Bohr Hamiltonian, with particular forms of the sextic potential in the [Formula: see text] shape variable, is exactly solved for a finite number of states. The shape of the quasi-exactly solvable potential is then defined by the number of exactly determined states. The effect of exact solvability order on the spectral characteristics of the model is closely investigated, especially, concerning the critical point of the phase transition from spherical to deformed shapes. The energy spectra and the [Formula: see text] transition probabilities, up to a scaling factor, depend only on a single-free parameter, while for the critical point, parameter-free results are available. Several numerical applications are done for nuclei undergoing a [Formula: see text]-unstable shape phase transition in order to identify critical nuclei based on the most suitable exact solvability order.

THE TRANSMUTATION METHOD AND SCHRÖDINGER EQUATION WITH PERTURBED EXACTLY SOLVABLE POTENTIAL

In this paper, it is proved the existence of a transmutation operator between two schrödinger equations with perturbed exactly solvable potential. An explicit formula for the solution of nucleus function by using Varsha and Jafari's method is also provided.

EXACTLY-SOLVABLE COUPLED-CHANNEL MODELS FROM SUPERSYMMETRIC QUANTUM MECHANICS

Starting from a system of N radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled N × N exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on N(N + 1)/2 unconstrained parameters and on one upper-bounded parameter, the factorization energy. For N = 2, previous results are reviewed, in particular regarding the number of bound states and resonances of the potential. A schematic inverse problem with one resonance is considered.