Effective field theory for vibrations in odd-mass nuclei

Abstract

Heavy even-even nuclei exhibit low-energy collective excitations that are separated in scale from the microscopic (fermion) degrees of freedom. This separation of scale allows us to approach nuclear vibrations within an effective field theory (EFT). In odd-mass nuclei collective and single-particle properties compete at low energies, and this makes their description more challenging. In this article we describe spherical odd-mass nuclei with ground-state spin I = 1 /2 by means of an EFT that couples a fermion to the collective degrees of freedom of an even-even core. The EFT relates observables such as energy levels, electric quadrupole transition strengths, and magnetic dipole moments of the odd-mass nucleus to those of its even-even neighbor, and allows us to quantify theoretical uncertainties. For isotopes of rhodium and silver the theoretical description is consistent with data within experimental and theoretical uncertainties. Several testable predictions are made.

Gamow-Teller and double- β decays of heavy nuclei within an effective theory

“…The ET developed in Refs. [54,55] describes the lowenergy properties of spherical even-even and odd-mass nuclei in terms of collective excitations that can be coupled to an odd neutron, neutron-hole, proton, or protonhole. The effective operators are written in terms of creation and annihilation operators, which are the DOF of the ET.…”

“…In Ref. [55], silver isotopes with 1 /2 − ground states were described both as an odd proton coupled to palladium cores and as an odd proton-hole coupled to cadmium cores. Both descriptions turned out to be consistent with each other.…”

“…In order to describe the allowed GT β decays of parent odd-odd nuclei, we extend the collective ET of Refs. [54,55] and write the low-lying positive-parity states in the odd-odd nucleus as…”

“…In combination with powerful ab initio methods, chiral interactions have been employed to calculate low-energy properties of light and mediummass isotopes (see, e.g., recent reviews [44][45][46][47][48]). Complementary, a different set of ETs has been proposed to describe heavy nuclei in terms of collective DOF [49][50][51][52][53][54][55]. In particular, the ET developed in Refs.…”

Two-neutrino double electron capture on 124Xe based on an effective theory and the nuclear shell model

“…One of the advantages of the ET is to provide consistent theoretical uncertainties. Similar ETs have been used to study electromagnetic transitions in spherical [53,54] and deformed [55][56][57][58][59][60][61] nuclei. In addition, we present the first large-scale nuclear shell model calculation for 124 Xe 2νECEC.…”