Nuclear quantum shape-phase transitions in odd-mass systems

Abstract

Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -the number of nucleons -theoretical low-energy spectra, twoneutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and E2 reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuities at neutron number N = 90, compared to the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared to the corresponding Sm isotopes.PACS numbers: 21.60. Jz, 21.60.Ev, 21.10.Re, 21.10.Tg Quantum mechanical systems can undergo zerotemperature phase transitions upon variation of a nonthermal control parameter. Quantum phase transitions (QPTs) present a very active field of research and have found a variety of applications in many areas of physics and chemistry [1,2]. Nuclear QPTs, in particular, correspond to shape transitions between competing groundstate phases induced by variation of a non-thermal control parameter (number of nucleons) [3][4][5][6][7]. Most experimental and theoretical studies of first-and second-order nuclear QPTs have considered systems with even numbers of protons and neutrons [8][9][10][11][12][13][14][15][16][17][18][19]. QPTs in odd-A nuclei present a more complex phenomenon because of the coupling between single-particle and collective degrees of freedom. The crucial issues for QPTs in odd-A systems are the influence of the unpaired fermion(s) on the precise location and nature of the phase transition, empirical signatures of QPTs, and the definition and computation of order parameters [20,21]. In recent years phenomenological geometric models with single-or multij state coupling [22][23][24][25], the interacting boson-fermion framework [25][26][27], and microscopic energy density functionals [28,29] have been employed in extensive studies of QPTs in odd-mass nuclei.In this paper we report a microscopic study of QPT in odd-mass Eu isotopes, calculate a series of observables that can be related to order parameters (low-energy spectra, two-neutron separation energies, isotope shifts, spectroscopic quadrupole moments, and reduced transition matrix elements), both for odd-mass nuclei and the adjacent even-even isotopes, and analyze the polarization * zpliphy@swu.edu.cn effect of the unpaired nucleon on the QPT. The choice of Eu isotopes is motivated by the fact that probably the best example of a QPT in atomic nuclei is in the rare earth region with N ≈ 90 neutrons, where a transition b...

Ground state properties and potential energy surfaces of 270Hs from multidimensionally-constrained relativistic mean field model

“…As reviewed in Ref. [78], this empirical functional has been very successful in describing nuclear ground state properties, e.g., the Coulomb displacement energies between mirror nuclei [79], nuclear binding energies [80][81][82] and quadrupole moments [83][84][85] and phase transitions in the nuclear shape [86], and low-energy excited states including nuclear chiral rotations [87] and magnetic and antimagnetic rotations [88][89][90][91][92]. PC-PK1 has also been used to study properties of SHN [93][94][95].…”

Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

“…Evidence of quantum phase transitions in odd systems were reported in recent works [27][28][29][30][31][32][33][34]. The experimental evidence for transition from spherical to the γ-unstable shapes in odd-mass 127−137 Ba and 101−109 Rh, and 123−135 Xe nuclei was presented in Refs.…”

“…A microscopic description of the quantum shape phase transition was performed for the the axially-deformed odd-mass 147−155 Sm and 147−155 Eu nuclei [29] by taking into consideration their common bosonic cores 148−154 Eu that show the transition from spherical to axially-deformed shape. Another description along the same transition path was carried out for odd-mass 149−155 Eu isotopes and their even-even neighbors, 148−154 Sm and 150−156 Gd nuclei [33]. In this study, the energy surfaces were presented for even-even nuclei, later the energy spectra of odd-mass 149−155 Eu isotopes were analyzed and their two-neutron separation energies, isotope shifts, quadrupole moments, and E2 reduced transition matrix elements were calculated along the isotopic chain and the results show good agreement with experimental data [33].…”

“…Another description along the same transition path was carried out for odd-mass 149−155 Eu isotopes and their even-even neighbors, 148−154 Sm and 150−156 Gd nuclei [33]. In this study, the energy surfaces were presented for even-even nuclei, later the energy spectra of odd-mass 149−155 Eu isotopes were analyzed and their two-neutron separation energies, isotope shifts, quadrupole moments, and E2 reduced transition matrix elements were calculated along the isotopic chain and the results show good agreement with experimental data [33]. The prolate to oblate shape phase transition was studied in neutron-rich odd-mass 185−193 Os, 185−195 Ir, and 185−199 Pt nuclei in the A ≈ 190 mass region to see the effect of the odd particle [34].…”

“…We would like to mention that other relevant contributions to the topic of shape phase transitions in odd-even nuclei have been presented in the last 15 years in Refs. [10,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”