Narrow Results

This paper explores the Bohr Hamiltonian with a newly introduced generalized form of the sextic potential in the $\beta$-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 $\eta$. 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 $\beta$-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 ${}^{128}$Xe, ${}^{130}$Xe, ${}^{132}$Xe, ${}^{134}$Xe, ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei. Our model successfully reproduces experimental data of the isotopes under investigation, demonstrating good agreement in energy spectra and $B(E2)$ transition rates. Based on the significance of the parameter $\eta$, 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.

We determine the energy eigenvalues and eigenstates of the Bohr Hamiltonian for $\gamma$-rigid prolate nuclei with the Coulomb-like potential in minimal length formalism. We first show corresponding Hamiltonian of $\gamma$-rigid prolate nuclei then investigate the effects of minimal length parameter in energy levels and obtain the transition rates. Ordinary results are recovered for the vanishing minimal length parameter and for the clarity of our results, some instructive graphs have been prepared.

In this paper, the wave equation corresponding to the $\gamma$-rigid version of Bohr Hamiltonian for the modified Davidson potential is investigated in the position-dependent mass formalism. By solving the related differential equation, the wave function, energy spectra and transition rates are obtained. In order to evaluate our results, they are compared with experimental data through the standard error.

We analyze collective properties of the ^110-116Cd isotopes in the framework of the general Bohr Hamiltonian which is obtained from the ATDHFB theory with the Skyrme interaction. Calculated energies and B(E2) transition probabilities and experimental data are in good agreement.

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of ¹⁹²Pt, ¹⁹⁴Pt and ¹⁹⁶Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

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

In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis–Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.

This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis–Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.

Several typical triaxial models have been parallel addressed and applied to describe the energy values and $B(E2)$ transitional rates in the ground band and the $\gamma$ band for ${}^{192}$Os. It is shown that the different triaxial model presents different triaxial dynamics but each of them can only succeed to explain part of the spectral properties of this nucleus, which indicates that the triaxial shape of ${}^{192}$Os may be more complicated than that reflected by an ideal triaxial model. In addition, the staggering signature in experiments hints that $\gamma$-rigid triaxiality should be more or less involved in ${}^{192}$Os.

The properties of odd nuclei have been investigated within the collective model by assuming the system is composed of a single nucleon in the $j=3/2$ single particle orbit coupled to a $\gamma$-unstable even-core. The Davidson potential has been used in the corresponding Bohr Hamiltonian for the even core. The excitation energy spectrum and the electric quadrupole transition ratios have been obtained. The results have been used to predict the experimental data of the some selected odd isotopes.

In this paper, analytical solution of the Bohr model with Mie potential for even–even and odd–even nuclei are evaluated in the Bose alone symmetry $[E(5)-\mathrm{\text{Mie}}]$ and a new class of Bose–Fermi dynamical symmetry $[E(5)-\mathrm{\text{Mie}}\otimes U(4)]$, respectively. The excitation energy spectra as well as electromagnetic transition strengths, quadrupole moments and dipole moments are investigated near the critical point of shape phase transition between the spherical and deformed $\gamma$-unstable nuclei. To show our results are compatible with experiment, some examples are tested.

The Bohr Hamiltonian with four inverse power terms potential for the $\beta$-part and a harmonic oscillator for the $\gamma$-part is solved. The $\beta$-part has been solved using the biconfluent Heun equation. The total wave function and energy have been derived. The numerical results for energy triaxial nuclei spectra are compared with the experimental data, esM and esKM models known for ${}^{192,194,196}\mathrm{\text{Pt}}$ atomic nuclei. These results are in overall good agreement with the experimental data. After this, the corresponding $B(E2)$ transition rates have been calculated for each nuclei of Platinum.

In this paper, Bohr Hamiltonian is used to describe the behaviors of triaxial nuclei with screened Kratzer potential. The Nikivorov–Uvarov method is used to derive the energy spectrum and corresponding wave function. The electric quadruple transition ratios and energy spectrum of the ${}^{126}$Xe, ${}^{128}$Xe, ${}^{130}$Xe, ${}^{132}$Xe, ${}^{134}$Xe, ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt are calculated and compared with the experimental data. The results are in good agreement with experiment data.

The low-lying collective spectra for axially symmetric nuclei are described within the Bohr–Hamiltonian by considering deformation-dependent mass coefficients and Kratzer potential in $\beta$ part. The energy eigenvalues and the total wave function of the problem are obtained in compact forms by means of the asymptotic iteration method. The numerical calculations are carried out for energy spectra as well as electromagnetic transition probabilities, and compared with experimental data in both cases: within and without the deformation-dependent mass (DDM) formalism. We investigate the nuclear observables of four even-A nuclei ${}^{154}$Sm, ${}^{156}$Gd, ${}^{172}$Yb, ${}^{182}$W and two odd-A nuclei ${}^{173}$Yb, ${}^{163}$Dy. Moreover, we will show that the choice of the Kratzer potential minimizes the level spacings within the $\beta$ band, which are usually overestimated by Bohr–Hamiltonian with Davidson potential.

In this work, Bohr Hamiltonian is used to explain the behavior of triaxial nuclei. A new potential, called Morse plus screened Kratzer potential, has been developed for the $\beta$-part with $\gamma$ fixed at $\frac{\pi }{6}$. The Extended Nikiforov–Uvarov method involving Confluent Heun functions is used to derive the wave function and energy expression. The electric quadrupole transition rates and energy spectrum of platinum ${}^{192,194,196}\mathrm{\text{Pt}}$ are determined and compared with the experimental data and some theoretical results.

In this paper, we look for a novel analytical solution of the Conformable Fractional Bohr Hamiltonian in the presence of a four inverse power terms potential in $\beta$-part of the collective nuclear potential. The new expression for the wave functions and energy spectra is obtained using the conformable fractional extended Nikiforov–Uvarov method. The effect of the conformable fractional formulation is studied on root mean square deviation, and normalized fractional eigen energies of ground state band, $\gamma$-band and $\beta$-band of ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei. The $B(E2)$ transition rates are calculated within the fractional domain. We compare our results with the experimental data, the classical Bohr Hamiltonian model with four inverse power terms potential, and other relevant theoretical works. We discuss on how the fractional parameter $\alpha$ acts on the spectra of triaxial nuclei. The results provided by our new approach are found to be in good agreement with the experimental data and improved compared to previous works.

In this paper, we look for a novel analytical solution of the Bohr Hamiltonian in the presence of the Hulthen plus screened Kratzer potential in $\beta$-part of the collective nuclear potential. The new expression for the energy spectra is obtained using the method of super symmetric quantum mechanics. The effect of the Hulthen plus screened Kratzer potential is studied on root mean square deviation, and normalized eigen energies of ground state band, $\gamma$-band and $\beta$-band of ¹⁹²Pt, ¹⁹⁴Pt and ¹⁹⁶Pt atomic nuclei. The $B(E2)$ transition rates are calculated for the latter potential. Furthermore, our results are compared with experimental data, and other relevant theoretical works. We discuss on how the combination of these two potentials makes it possible to improve the results of energy spectra and quadrupole transitions of triaxial nuclei. We discuss the quantitative and qualitative descriptions concerning the structure of the nucleus using some indicators such as root mean square and staggering of the $\gamma$-band. The results provided by our model are found to be in good agreement with experimental data and improved in comparison with previous works.

In this work, we study the collective Bohr Hamiltonian of triaxial nuclei within deformation-dependent mass formalism (DDM) using the new Anharmonic potential. The Schrödinger equation with Bohr Hamiltonian is separated into two parts and the $\beta$-part is solved by mean of Nikiforov–Uvarov method to obtain the energy spectra. The $\gamma$-part is defined by a ring shape potential and solved with the same method. The energies and the $B(E2)$ transition rates for nuclide ${}^{192,194,196}$Pt are calculated and compared with the experimental data and with some others models in the same formalism.

In this work, we obtain new solutions of the Bohr Hamiltonian model appropriate for triaxial nuclei, with screened Kratzer potential in the framework of conformable fractional derivative. The analytical solutions for energy spectra are obtained using the conformable fractional Nikiforov–Uvarov method. We discuss the link between the present model and other relevant related models such as Z(5) model, classical screened Kratzer model and conformable fractional Kratzer model. The effect of the fractional-order parameter is investigated on the variations of the interaction potential. The normalized eigen-energies are calculated as well as normalized B(E2) transitions probabilities at different values of the fractional-order parameter. Our results reproduced well the experimental data for ${}^{126}$Xe, ${}^{128}$Xe, ${}^{130}$Xe, ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei, and are found to be improved in comparison with other related theoretical models.

Bohr Hamiltonian with inversely quadratic Yukawa plus screened Kratzer potential for the $\beta$-part and a harmonic oscillator for the $\gamma$-part is investigated. The expressions of energies and wave functions are obtained using the parametric Nikiforov–Uvarov method. The obtained results are used to evaluate the normalized eigen energies, the root mean square deviation and $B(E2)$ transition rates of ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei. The numerical results of our model are compared to those of other relevant theoretical models and experimental data. Furthermore, to test the sensitive signature of triaxiality, we used some indicators such as the staggering effect in the $\gamma$-band. It appears that the results provided by our calculations are in accordance with experimental values and improved in comparison with previous models.