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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.

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.

This paper proposes an improved potential for the $\beta$-part of the collective Bohr Hamiltonian, namely, a Killingbeck plus Morse potential, while the $\gamma$-part is solved for a triaxial deformation close to $\gamma =30^{\circ }$. The Asymptotic Iteration Method is used, involving the Pekeris approximation, to calculate the energy eigenvalues and the eigenfunctions after an exact separation of the Bohr Hamiltonian into its variables is achieved. The results of these calculations are applied for energy spectra of the low-lying states and for corresponding $B(E2)$ quadrupole transition probabilities of the ${}^{192,194,196}Pt$ isotopes. Moreover, the results of the present solution are compared with those of the well-known $Z(5)$ and $esM$ models.

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 wobbling spectrum of ${}^{163}$Lu is described through a novel approach, starting from a triaxial rotor model within a semi-classical picture, and obtaining a new set of equations for all four rotational bands that have wobbling character. Redefining the band structure in the present model is done by adopting the concepts of Signature Partner Bands and Parity Partner Bands. Indeed, describing a wobbling spectrum in an even–odd nucleus through signature and parity quantum numbers is an inedited interpretation of the triaxial super-deformed bands.

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.

In this paper, we investigate the energy spectra, wave functions and the $B(E2)$ transition rates for ${}^{98–112}$Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the $\beta$-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in $\gamma$-part, with $\gamma$ fixed around $\frac{\pi }{6}$. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of $\alpha$, providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and $B(E2)$ transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.