Coexistence, mixing and fluctuation of nuclear shapes

Abstract

The coexistence between near-spherical and well-deformed shapes in nuclear systems is studied by a schematic collective model employing a double-minimum phenomenological potential with an accounted centrifugal contribution from the kinetic energy. The quantum tunneling between the two deformation minima depends on the characteristics of the separating barrier and is gauged by the density probability distribution of deformation in the ground and excited states. Various degrees of overlap between the two states are associated to shape coexistence with and without mixing or to simple shape fluctuation phenomena. The effect of the interaction between deformation configurations on the transition observables is exemplified on the 76 Kr nucleus.

Shape Coexistence in 74Ge, 74Se and 74Kr Investigated by Phenomenological and Microscopic Models

“…These three states are very well described by the τ = 3 multiplet, which in the present model is slightly splitted over the total angular momentum such that to obtain also a quantitative agreement with the experimental data. Another important remark is that the first excited 0 + is very low in energy, especially for 74 Kr, while the monopole transition between this state and ground state has large value, which could be an indication for the presence of the shape mixing and coexistence phenomena [16,31]. Nevertheless, the phenomological model succeeds to describe such a lower excited 0 + state, as well as the monopole transition ρ 2 (E0; 0 + 2,0 → 0 + 1,0 ) even if for the latter one is used the value of β M fixed for the B(E2; 2 + 1,1 → 0 + 1,0 ) transition.…”

“…A sixth order anharmonic oscillator potential (sextic) is used for the Bohr Mottelson Hamiltonian, being numerically diagonalized [12] in a basis of Bessel functions of the first kind [13], which in turn are solutions for the infinite square well potential [14,15]. This method has been already involved with success to describe shape coexistence phenomenon within some nuclei as 76 Kr [16], 72,74,76 Se [17] and 96,98,100 Mo [18]. Additionally, it can be used to investigate the shape mixing and coexistence phenomena by increasing the height of the barrier [16,19].…”

“…This method has been already involved with success to describe shape coexistence phenomenon within some nuclei as 76 Kr [16], 72,74,76 Se [17] and 96,98,100 Mo [18]. Additionally, it can be used to investigate the shape mixing and coexistence phenomena by increasing the height of the barrier [16,19]. The free parameters of the phenomenological model are determined by fitting the experimental data [20] and then are used to calculate the energy spectrum of the ground, β and γ bands, the quadrupole (E2) and monopole (E0) transitions, respectively the shape of the ground and excited states.…”

Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth

“…Some numerical applications for experimental data have been made in [1]. Also, other two papers on this subject have been published in the meantime [28,29] with new interesting results for the critical point of the nuclear shape phase transition from the spherical vibrator to the axial symmetric rotor. The diagonalization method discussed here can be easily extended for more complex polynomial potentials in the β variable or to take into account other γ axial deformations.…”

Shape transitions between and within Zr isotopes

“…The extreme and intermediate cases of the abovementioned extremes have recently been worked out in Ref. [2]. In the following, we will concentrate on the highbarrier case, where eigenstates are located almost purely in either potential minimum, spherical or deformed.…”