Study of Bohr Mottelson Hamiltonian with minimal length effect for Woods-Saxon potential and its thermodynamic properties

Abstract

The Bohr Mottelson Hamiltonian with the variable of collective shape for the Woods-Saxon potential in the rigid deformed nucleus for = 0 and the X(3) model was investigated in the presence of the minimal length formalism. The Bohr Mottelson Hamiltonian was solved approximately by proposing a new wave function. The q-deformed hyperbolic potential concept such that the rigid deformed nucleus of the Bohr Mottelson equation in the minimal length formalism for Woods-Saxon potential was used, so that the equation was reduced to the form of Schrodinger-like equation with cotangent hyperbolic potential. The hypergeometric method was used to obtain the energy spectra equation and the unnormalized wave function of the system. The results showed that the energy spectra were affected by the quantum number, the minimal length parameter, and the atomic mass. The larger mass of the atom affected the energy spectra to decrease, the increase of the values of the minimal length affected the increase of the energy spectra of all atoms. The energy spectra were used to determine the thermodynamic properties including the partition function, mean energy, specific heat, free energy, and entropy of the quantum system with the help of the imaginary error function.

Simulasi Penyelesaian Tingkat Energi Sistem Molekul Dalam Pengaruh Potensial Kratzer Dengan Metode Parametrik Nikiforov-Uvarov

“…Schrodinger dengan potensial telah banyak dikaji di antaranya melibatkan potensial Coulomb (Karomah et al, 2021), Osilator Harmonik (Rusmini et al, 2022), Kratzer (Onyenegecha et al, 2021). Selain itu, potensial yang dikaji juga dapat berupa gabungan dari beberpa jenis potensial seperti Hulthen-Hellmann (Akpan et al, 2021), Potensial Quadratik Yukawa dan Eckart (Antia et al, 2020), Wood-Saxon (Suparmi et al, 2021), Hulthen-Non Sentral Posch Teller (Sunarmi et al, 2013) dan lain-lain. Semakin banyak potensial yang terlibat maka persamaan Schrodinger menjadi semakin rumit dan penyelesaian yang diperoleh dilakukan dengan metode aproksimasi.…”

Study of Klein Gordon Equation with Minimum Length Effect for Woods-Saxon Potetial using Nikiforov-Uvarov Functional Analysis

“…The elastic scattering between the nuclei provides great flexibility so as information about nuclear interactions can be obtained. The appropriate solution from the wave equation of this potential provides a conceptual understanding of the resonance and bound states of the interactions between nuclei (Suparmi et al, 2021). The average field perceived by the valence electrons in the Helium model can be described using the potential of Woods-Saxon (Dudek et al, 2004) The standard form of Woods-equation is as determined as…”

Thermodynamic properties and superstatistics analysis of particle in the non-relativistic system under the influence of trigonometric scarf potential using Dong proper quantization

“…The exactly solvable relativistic and non-relativistic quantum systems have become interesting research areas to many researchers because they reveal all the important information to study quantum models. Some techniques had been used to solve the Schrödinger-like equations using various potentials [1][2], for example, the asymptotic iteration method (AIM) [3], the Nikiforov-Uvarov (NU) method [4], the Hypergeometric method [5][6], and the Laplace transform method [7]. The algebraic techniques that are related to the inspection of the Hamiltonian of a quantum system as in the supersymmetric quantum mechanics (SUSY QM) which is developed by the idea of shape invariant potential [8] and close to the factorization method [9], the SWKB method [10], and other methods which formed on the proper and exact quantization rule [11].…”