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An analytical solution for the Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable $beta$ and $gamma$ fixed to $30^{circ}$, is proposed. The model is conventionally called Z(4)-Sextic. For the considered potential shapes the solution is exact for the ground and $beta$ bands, while for the $gamma$ band an approximation is adopted. Due to the scaling property of the problem the energy and $B(E2)$ transition ratios depend on a single parameter apart from an integer number which limits the number of allowed states. For certain constraints imposed on the free parameter, which lead to simpler special potentials, the energy and $B(E2)$ transition ratios are parameter independent. The energy spectra of the ground and first $beta$ and $gamma$ bands as well as the corresponding $B(E2)$ transitions, determined with Z(4)-Sextic, are studied as function of the free parameter and presented in detail for the special cases. Numerical applications are done for the $^{128,130,132}$Xe and $^{192,194,196}$Pt isotopes, revealing a qualitative agreement with experiment and a phase transition in Xe isotopes.
We deal with the Hamiltonian hierarchy problem of the Hulth{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorpora
We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the variational col
We found an analytical solution for the neutrino mass matrix in the most general case of the Zee model. Using the recent data on the neutrino parameters besides generating neutrino masses at 1-loop level we fit also the masses of the charged leptons
In this paper we find analytical solutions for the scalar and gauge fields in the Freedman-Robertson-Walker multiply warped braneworld scenario. With this we find the precise mass spectra for these fields. We compare these spectra with that previously found in the literature for the static case.
Based on ab initio calculation, we propose a new structure for the fundamental excitation of the reconstructed 30$^circ$ partial dislocation in silicon. This soliton has a rare structure involving a five-fold coordinated atom near the dislocation cor