Description of the low-lying collective states of ${}^{96}$Zr based on the quadrupole-collective Bohr Hamiltonian

Abstract

Experimental data on ${}^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. Several collective low-lying states and E2 and M1 transitions are observed for this nucleus. The quadrupole-collective Bohr Hamiltonian depending on both $\beta$ and $\gamma$ shape variables with a potential having spherical and deformed minima, is applied consideration of these data. The relative depth of two minima, height and width of the barrier, rigidity of the potential near both minima are determined so as to achieve a satisfactory description of the observed properties of the low-lying collective quadrupole states of ${}^{96}$Zr. Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1;2_2^{+}\to 2_1^{+})$ reduced transition probabilities is obtained. It is shown that the low-energy structure of ${}^{96}$Zr can be described in a satisfactory way within the Geometrical Collective Model with a potential function supporting shape coexistence without other restrictions of its shape. However, the excitation energy of the $2_2^{+}$ state can be reproduced only if the rotation inertia coefficient is taken by four times smaller than the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1;2_2^{+}\to 2_1^{+})$ and $B(M1;3_1^{+}\to 2_1^{+})$ transition probabilities. An indication for the influence of the pairing vibrational mode on the $0_2^{+}\to 0_1^{+}$ transition is confirmed in agreement with the previous result.

9 pages, 8 figures

References in corpus (8)

• Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
• First Measurement of Collectivity of Coexisting Shapes based on Type II Shell Evolution: The Case of ${}^{96}$Zr
• Microscopic description of nuclear quantum phase transitions
• Bohr Hamiltonian with deformation-dependent mass term for the Davidson potential
• Intertwined Quantum Phase Transitions in the Zr Isotopes
• Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality
• Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients
• Description of shape coexistence in ${}^{96}$Zr based on the collective quadrupole Bohr Hamiltonian

Cited by in corpus (3)

• Shape coexistence in even-even nuclei: A theoretical overview
• Evolution of the phenomenologically determined collective potential along the chain of Zr isotopes
• Influence of triaxiality on the description of low-energy excitation spectrum of ${}^{96}$Zr