Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei

Abstract

In this paper, we solve the eigenvalues and eigenvectors problem with Bohr collective Hamiltonian for triaxial nuclei. The β-part of the collective potential is taken to be equal to Hulthén potential while the γ-part is defined by a new generalized potential obtained from a ring shaped one. Analytical expressions for spectra and wave functions are derived by means of a recent version of the asymptotic iteration method and the usual approximations. The calculated energies and B(E2) transition rates are compared with experimental data and the available theoretical results in the literature.

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

“…(11) are evaluated. This equation depends on three parameters, the screening parameter in the potential and the rig-shape parameters c and s of the potential [17]. To obtain the potential parameters for each nuclei, we need to evaluate the root mean square (rms) deviation between the experimental data and the theoretical ones by means of the equation [28].…”

“…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)…”

“…In all these cases, dynamical symmetries are related to exactly solvable problems and also produce results for observables in explicit analytic form. Recently, with the aim of describing appropriately shape phase transitions in atomic nuclei, some authors have devoted to construct analytical solutions of the Schrodinger equation associated with the Bohr Hamiltonian using various potential models [12][13][14][15][16][17][18].…”

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

“…The asymptotic iteration method [22] is proposed to solve the second-order homogeneous differential equation of the form y = λ 0 (x)y + s 0 (x)y (45) where the variables λ 0 and s 0 are sufficiently differentiable. The differential equation (45) has a general solution [22] y…”

Davydov–Chaban Hamiltonian in presence of time-dependent potential

“…For example, Chabab et al consider Hulthén potential for β-part of collective potential while for the γ -part defined a new generalized potential obtained from a ring shaped one [12] as well as an interesting numerical results they mentioned in their paper. D. Bonatsos et al used Davidson potential to describe ground state bands of the E(5) and X(5) critical symmetries [13], or they derived in another paper an expression for a system in which the mass has a dependency to the nuclear deformation [14].…”