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Description
The sextic oscillator V(r) = Ar^2 + Br^4 +Cr^6 + D/r^2 offers a flexible shape that can be used in
the Bohr Hamiltonian to model transition between spherical and deformed shape phases in the
r=beta variable. The general form of the sextic oscillator is not solvable, however, the A, B and C
coefficients can be parametrized in terms of two independent parameters (a, b) such that the
problem reduces to a quasi-exactly (QES) form. This means that the lowest few energy eigenvalues
and the wave functions can be determined in closed form, and the B(E2) values can also be
calculated analytically [1,2]. The model has been applied to describe the transition between the
spherical and gamma-unstable shape phases [1,2] for even-even nuclei near the Z=50 shell closure,
and it has been shown that the two phases are separated by a parabola in the (a,b) phase space.
Later the model has been generalised to discuss further types of phase transitions too (see e.g. [3]).
Here we report on the extension of the model that allows the treatment of 22 energy levels instead
of the original 10, while all the calculations remain analytically solvable [4]. The model is applied to
the Ru, Pd, Pt and Os isotope chains, and the trajectory obtained in the (a,b) phase space is analysed
for each chain.
[1] G. Lévai and J. M. Arias, Phys. Rev. C 69 (2004) 014304.
[2] G. Lévai and J. M. Arias, Phys. Rev. C 81 (2010) 044304.
[3] R. Budaca et al. Ann. Phys. 375 (2016) 65.
[4] G. Lévai and J. M. Arias, J. Phys. G: Nucl. Part. Phys. 48 (2021) 085102
