The sextic oscillator as a $\gamma$-independent potential

Abstract

The sextic oscillator is proposed as a two-parameter solvable $\gamma$-independent potential in the Bohr Hamiltonian. It is shown that closed analytical expressions can be derived for the energies and wavefunctions of the first few levels and for the strength of electric quadrupole transitions between them. Depending on the parameters this potential has a minimum at $\beta =0$ or at $\beta >0$, and might also have a local maximum before reaching its minimum. A comparison with the spectral properties of the infinite square well and the ${\beta }^4$ potential is presented, together with a brief analysis of the experimental spectrum and E2 transitions of the ${}^{134}$Ba nucleus.

15 pages, 5 figures; to appear in Phys. Rev. C

References in corpus (3)

• Analytically solvable potentials for $\gamma$-unstable nuclei
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing

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