https://doi.org/10.1140/epja/i2014-14087-8
Regular Article - Theoretical Physics
Quartic oscillator potential in the γ-rigid regime of the collective geometrical model
Horia Hulubei National Institute of Physics and Nuclear Engineering, RO-077125, Bucharest-Magurele, Romania
* e-mail: rbudaca@theory.nipne.ro
Received:
5
November
2013
Revised:
26
March
2014
Accepted:
22
April
2014
Published online:
20
May
2014
A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β 2 models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.
© SIF, Springer-Verlag Berlin Heidelberg, 2014
