Shape fluctuations in the ground and excited0+states of30,32,34Mg

Abstract

Large-amplitude collective dynamics of shape phase transition in the low-lying states of 30−36 Mg is investigated by solving the five-dimensional (5D) quadrupole collective Schrödinger equation. The collective masses and potentials of the 5D collective Hamiltonian are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random phase approximation method. Good agreement with the recent experimental data is obtained for the excited 0 + states as well as the ground bands. For 30 Mg, the shape coexistence picture that the deformed excited 0 + state coexists with the spherical ground state approximately holds. On the other hand, large-amplitude quadrupole-shaped fluctuations dominate in both the ground and the excited 0 + states in 32 Mg, providing a picture that is different from the interpretation of the "coexisting spherical excited 0 + state" based on the naive inversion picture of the spherical and deformed configurations.Nuclei exhibit a variety of shapes in their ground and excited states. A feature of the quantum phase transition of a finite system is that the order parameters (shape deformation parameters) always fluctuate and vary with the particle number. Especially, the large-amplitude shape fluctuations play a crucial role in transitional (critical) regions. Spectroscopic studies of low-lying excited states in transitional nuclei are of great interest to observe such unique features of the finite quantum systems.Low-lying states of neutron-rich nuclei at approximately N = 20 attract great interest, as the spherical configurations associated with the magic number disappear in the ground states. In neutron-rich Mg isotopes, the increase of the excitation energy ratio E(4 1 + )/E(2 1 + ) [1-3] and the enhancement of B(E2; 2 1 + → 0 1 + ) from 30 Mg to 34 Mg [4-6] indicate a kind of quantum phase transition from spherical to deformed shapes taking place around 32 Mg. These experiments stimulate microscopic investigations on quadrupole collective dynamics unique to this region of the nuclear chart with various theoretical approaches: the shell model [7-10], the Hartree-Fock-Bogoliubov (HFB) method [11,12], the parityprojected Hartree-Fock (HF) [13], the quasiparticle random phase approximation (QRPA) [14,15], the angular-momentum projected generator coordinate method (GCM) with [16] and without [17,18] restriction to the axial symmetry, and the antisymmetrized molecular dynamics [19]. Quite recently, excited 0 + states were found in 30 Mg and 32 Mg at 1.789 MeV and 1.058 MeV, respectively, and their characters are presently under hot discussion [20-23]. For 30 Mg, the excited 0 2 + state is interpreted as a prolately deformed state which coexists with the spherical ground state. For 32 Mg, from the observed population of the excited 0 2 + state in the (t,p) reaction on 30 Mg, it is suggested [22] that the 0 2 + state is a spherical state coexisting with the deformed ground state and that their relative energies are inverted at N = 20. However, available shell-mod...

Self-consistent collective coordinate for reaction path and inertial mass

“…It is named "adiabatic self-consistent collective coordinate (ASCC) method" [19]. The ASCC provides an alternative practical solution to the SCC [19]: The state is determined at each value of q by solving the equation expanded up to the second order in p. The ASCC method has been successfully applied to nuclear structure problems with large-amplitude shape fluctuations/oscillations for the Hamiltonian of the separable interactions [3,[22][23][24][25][26][27][28]. It should be noted that a solution to the non-uniqueness problem of the ATDHF was given by higher-order equations with respect to momenta [17,18], which are similar to the ASCC equations.…”

Skyrme energy-density functional approach to collective dynamics

“…We thus take the quadrupole collective Hamiltonian approach with the local QRPA (LQRPA) method [15] in the present paper. For evaluation of the collective masses, the LQRPA equations are solved on the constrained HFB states along the collective coordinate.…”

Quantal rotation and its coupling to intrinsic motion in nuclei

“…In BM2 (pp.168-175), the band mixing between the ground and the β bands in 174 Hf are presented to explain the observed intensity relations. An effect of hindrance of the shape fluctuation induced by the rotation, suggested in references [49,50,51], may also play an important role. The Coriolis coupling effects may be a key ingredient to understand the peculiar B(E2) properties of the β-vibrational bands.…”