Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

Abstract

In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for γ−unstable nuclei as well as exactly separable rotational ones with γ ≈ 0. Some heavy nuclei with known β and γ bandheads have been fitted by using two parameters in the γ−unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.

Calculations of the decay transitions of the modified Pöschl–Teller potential model via Bohr Hamiltonian technique

“…Having found the expression of the total wave function, it leads to calculate the B(E2) transition rates [27]. The B(E2) transition rates from an initial to a final state are defined as [17,27] 2 ( 2) 5 ( 2; ) , 16 ( 2 1)…”

Electric quadrupole transitions of the Bohr Hamiltonian with Manning–Rosen potential

“…The normalization constants for the (n γ , K) = (0, 0) and (n γ , K) = (1, 2) states are found to be In the prolate axial rotor case the energy spectrum is obtained as [1] n,L = − 1 4…”

“…To determine the radial wave function one needs the parametrization [1] ξ n,L (β) = β −2 χ n,L (β), y = e −αβ , The radial wave functions are found to be f n,L (y) = N n,L 2 F 1 (−n, n + 2µ + 2ν n,L ; 1 + 2ν n,L ; y)…”

“…In Table ( 1) and Table (2) are given the values of the free parameters of the present problem, namely : the Manning-Rosen potential parameters β 0 and α and the harmonic oscillator potential parameter c for 34 γ-unstable and 38 axially symmetric prolate deformed nuclei respectively which are subject of the present study. These parameters have been already obtained in our previous work [1] by fitting the energy spectra to experimental data. We should notice here that such a fitting does not concern the transition probabilities.…”

Davydov–Chaban Hamiltonian with deformation-dependent mass term for γ= 30∘

“…The formulas for the energy levels as well as for the wave functions are obtained in closed analytical form by means of the asymptotic iteration method [22,23]. Thanks to its efficiency and easiness, we have already used this method to solve many similar problems [24,25,26,27,28,29,30]. On the basis of the obtained numerical results, by the present model, the staggering effect appearing in energy spectra of triaxial nuclei will also be treated by taking for example the nuclei 114 Pd and 192 Pt.…”