Islands of shape coexistence from single-particle spectra in covariant density functional theory

Abstract

Shape coexistence in even-even nuclei is observed when the ground state band of a nucleus is accompanied by another K=0 band at similar energy but with radically different structure. We attempt to predict regions of shape coexistence throughout the nuclear chart using the parameter-free proxy-SU(3) symmetry and standard covariant density functional theory. Within the proxy-SU(3) symmetry the interplay of shell model magic numbers, formed by the spin-orbit interaction, and the 3-dimensional isotropic harmonic oscillator magic numbers, leads to the prediction of specific horizontal and vertical stripes on the nuclear chart in which shape coexistence should be possible. Within covariant density functional theory, specific islands on the nuclear chart are found, in which particle-hole excitations leading to shape coexistence are observed. The role played by particle-hole excitations across magic numbers as well as the collapse of magic numbers as deformation sets in is clarified.

Signatures for shape coexistence and shape/phase transitions in even–even nuclei

“…In particular (a) N = 90 signifies the beginning of participation of the intruder 1i 13/2 orbital. As seen in [10,11] The present findings further emphasize the difference between SC seen in the regions around Z = 82, 50 and in the regions around N = 90, 60. In the first set, SC is due to proton particle-hole (p-h) excitations caused by the neutrons (neutron-induced SC), while in the second set SC is due to neutron particle-hole excitations caused by the protons (protoninduced SC).…”

“…It has been accepted over the years that SC occurs when particle-hole (p-h) excitations across major shells are possible [1][2][3][4], the regions around Z = 82 and Z = 50 providing the most robust examples. Calculations of single-particle energy spectra using covariant density functional theory have recently corroborated this assumption, indicating that proton p-h excitations leading to SC occur in certain islands of the nuclear chart, centered around the Z = 82 and Z = 50 major shell gaps [10,11]. This has been called neutron-induced SC since they are caused by the varying number of neutrons acting on the same set of protons.…”

“…This has been called proton-induced SC, since they are caused by the varying in number protons acting on the same set of neutrons. In addition, a region around N = 40, Z = 40 has been found, in which both proton p-h excitations and neutron p-h excitations are possible [11].…”

“…This has been called neutron-induced SC since they are caused by the varying number of neutrons acting on the same set of protons. Furthermore, it has been suggested that islands of SC occurring around N = 90 and N = 60 can be attributed to neutron p-h excitations across the N = 112 and N = 70 shell closures of the three-dimensional isotropic harmonic oscillator (3D-HO), signifying the beginning of the participation of the intruder (opposite parity) orbitals 1i 13/2 and 1h 11/2 to the onset of nuclear deformation [10,11]. This has been called proton-induced SC, since they are caused by the varying in number protons acting on the same set of neutrons.…”

Prolate-oblate shape transitions and O(6) symmetry in even–even nuclei: a theoretical overview

“…A by-product of proxy-SU(3) symmetry and the dominance of the highest weight irreps is the resolution [60,104,191,199] of the long standing problem of the dominance of prolate over oblate shapes [17,18] in the ground states of even-even nuclei. Another by-product of the proxy-SU(3) symmetry is the dual shell mechanism [200], which predicts that shape coexistence can occur only on specific islands of the nuclear chart [77,201,202], recently corroborated through CDFT calculations [203,204].…”