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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 explore, respectively, from the viewpoints of a locally inertial observer and a coaccelerated observer, the transition rates of a two-atom system in the symmetric or antisymmetric entangled state, $|{\psi }_{+}〉$ or $|{\psi }_{-}〉$, and coupled to the electromagnetic fields. The interatomic separation is assumed to be constant and perpendicular to the acceleration; the fields to which the atoms are coupled are assumed to be in the vacuum state in the locally inertial frame and in a thermal state in the coaccelerated frame. We find that, in the viewpoints of the two observers, both the downward transition $|{\psi }_{\pm }〉\to |g_A{g}_B〉$ and the upward transition $|{\psi }_{\pm }〉\to |e_A{e}_B〉$ can take place, where $|g_A{g}_B〉$ and $|e_A{e}_B〉$ denote two eigenstates of the two-atom system with both atoms in their ground states and excited states, respectively. With an appropriate choice of the orientations of the atomic dipole moments, coherent radiation can happen for a system in acceleration but not for one in inertial motion. By comparing the transition rates viewed by the two observers, we show that the transition rates of the accelerated two-atom system viewed by a locally inertial observer can only be recovered in the coaccelerated frame by assuming a thermal bath at the Fulling–Davies–Unruh temperature. The effects of these collective transitions on the evolution of energy of the two-atom system are also analyzed.

In a SO(3,1)×U(1) framework, we analytically derive the first-order approximating solutions to the system of Klein–Gordon–Maxwell–Einstein equations describing a minimally coupled charged boson field to a spherically symmetric spacetime. Within a perturbative approach, we analyze the feedback of gravity and electric field on the charged scalar source and we get the coherent source-field regeneration rate. It turns out that we are dealing with an extremely short time-constant which is confirming the other authors' conclusion that intense gravitational bursts are accompanying the boson star formation.

A brief survey of results of studies of nuclear chirality in the mass 80 and 190 region at iThemba LABS is given, before looking at the case of ¹⁰⁶Ag in detail. Here, the crossing of a pair of candidate chiral bands is re-interpreted as the crossing of a prolate band by an aligned four-quasiparticle band.

We determine the energy spectrum and wave function for the Bohr–Mottelson Hamiltonian on $\gamma$-rigid regime separately with the harmonic and Coulomb energy-dependent potentials. We study the effect of potential parameters on the energy levels and probability density distribution. The transition rates are determined in each case.

In this work, we investigate the $\gamma$-rigid version of Bohr–Hamiltonian for the modified Davidson potential. Since the corresponding wave equation cannot be solved analytically, we apply the variational method. The related wave function, energy spectra and transition rates are determined. In order to evaluate our results, we fit the formula for the energy spectra to the available experimental data for some nuclei and compare the obtained standard error with the corresponding one in other similar work. Moreover, we study the collective behavior of these nuclei through the evolution of two quantities $E(2_1)$ and $\frac{E(4_1)}{E(2_1)}$ in terms of number of valence nucleons.

The present work is aimed at considering the recent forms of Bohr Hamiltonian, which are namely the hybrid model and the model combining the X(3) and E(5) symmetries, in the presence of the $\beta$-dependent Morse potential. The energy spectra and the transition rates of each model have been obtained. Some nuclei, the isotopes of Ru, Pd, Xe and ${}^{134}$Ba, have been fitted by using the three-parameter solution of the combined Hamiltonian with the Morse potential. Also, a few nuclei have been fitted by using the four-parameter solution of the hybrid model. In order to evaluate our results, in addition to reporting the root mean square (rms), we compare our data for each nucleus with the corresponding results of other references.

A brief survey of results of studies of nuclear chirality in the mass 80 and 190 region at iThemba LABS is given, before looking at the case of ¹⁰⁶Ag in detail. Here, the crossing of a pair of candidate chiral bands is re-interpreted as the crossing of a prolate band by an aligned four-quasiparticle band.