Bohr Hamiltonian with trigonometric Pöschl-Teller potential in \( \gamma\)-unstable and \( \gamma\)-stable pictures
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In this paper, we present an analytical solution for the Bohr Hamiltonian with the trigonometric Pöschl-Teller (PT) potential in the cases of \( \gamma\)-unstable nuclei and \( \gamma\)-stable axially symmetric prolate deformed ones with \( \gamma \approx 0\). The energy spectra and corresponding wave functions are derived by means of the asymptotic iteration method. In addition, B(E2) transition rates are calculated and compared with experimental data. Overall good agreement is obtained for inter and intra-band transitions within ground-state and \( \beta\) bands. Our numerical results, particularly for transition rates are much closer to experimental ones in comparison with those obtained by Davidson and Kratzer potentials which are widely used in the litterature.
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