Hyperbolic tangent form of sextic potential in Bohr Hamiltonian: Analytical approach via extended Nikiforov–Uvarov and Heun equations

This paper explores the Bohr Hamiltonian with a newly introduced generalized form of the sextic potential in the [Formula: see text]-part of the nuclear potential. The generalized sextic potential proposed in this research is based on hyperbolic functions and is characterized by parameters a, b, c, d, and [Formula: see text]. It is quite versatile and reduces to several well-known potential models of physical interest, making it particularly rich for nuclear structure studies. We employed the extended Nikiforov–Uvarov method and confluent Heun equation to obtain analytical solutions of the [Formula: see text]-part of the Schrödinger equation for the Bohr Hamiltonian, with the Greene–Aldrich approximation scheme applied to the centrifugal barrier term. The results of calculations are employed to study the energy spectra and electric quadrupole transition rates of [Formula: see text]Xe, [Formula: see text]Xe, [Formula: see text]Xe, [Formula: see text]Xe, [Formula: see text]Pt, [Formula: see text]Pt and [Formula: see text]Pt atomic nuclei. Our model successfully reproduces experimental data of the isotopes under investigation, demonstrating good agreement in energy spectra and [Formula: see text] transition rates. Based on the significance of the parameter [Formula: see text], the generalized sextic potential provides a valuable tool for studying various unexplored potential models and transitions in nuclear structure, with potential applications in identifying new states of triaxial nuclei.