Anharmonicity of the excited octupole band in actinides using supersymmetric quantum mechanics

Abstract

Background: Low-lying octupole collective excitations play an important role in the description of the structure of nuclei in the actinide region. Ground state alternating parity rotational bands combining both positive and negative parity states are known in several nuclei. However, only recently it has been discovered in ${}^{240}$Pu an excited positive parity rotational band having an octupole nature and demonstrating strong anharmonicity of the octupole motion in the band head energies.Purpose: To suggest a model describing both ground state and excited alternating parity bands, which includes a description of the anharmonic effects in the bandhead excitation energies and can be used to predict the energies of the excited rotational bands of octupole nature and the $E1$ transition probabilities.Methods: The mathematical technique of the supersymmetric quantum mechanics with a collective Hamiltonian depending only on the octupole collective variable which keeps axial symmetry is used to describe the ground state and excited alternating parity rotational bands.Results: The excitation energies of the states belonging to the lowest negative parity and the excited positive parity bands are calculated for ${}^{232}$Th, ${}^{238}$U, and ${}^{240}$Pu. The $E1$ transition matrix elements are also calculated for ${}^{240}$Pu.Conclusions: It is shown that the suggested model describes the excitation energies of the states of the lowest negative parity band with the accuracy around 10 keV. The anharmonicity in the bandhead energy of the excited positive parity band is described also. The bandhead energy of the excited positive parity band is described with the accuracy around 100 keV.