The sextic oscillator as a $γ$-independent potential

Details The sextic oscillator as a $γ$-independent potential The sextic oscillator as a $γ$-independent potential

2003-11-20

arxiv.org/abs/nucl-th/0311069v1

Phys.Rev. C69 (2004) 014304

Physics

Nuclear Physics

Nuclear Theory

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

Scientific paper

10.1103/PhysRevC.69.014304

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.

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