Double beta decay

A review is given of our present knowledge of collective spin-isospin excitations in nuclei. Most of this knowledge comes from intermediate-energy charge-exchange reactions and from inelastic electron- and proton-scattering experiments. The nuclear-spin dynamics is governed by the spin-isospin-dependent two-nucleon interaction in the medium. This interaction gives rise to collective spin modes such as the giant Gamow-Teller resonances. An interesting phenomenon is that the measured total Gamow-Teller transition strength in the resonance region is much less than a model-independent sum rule predicts. Two physically different mechanisms have been discussed to explain this so-called quenching of the total Gamow-Teller strength: coupling to subnuclear degrees of freedom in the form of $\ensuremath{\Delta}$-isobar excitation and ordinary nuclear configuration mixing. Both detailed nuclear structure calculations and extensive analyses of the scattering data suggest that the nuclear configuration mixing effect is the more important quenching mechanism, although subnuclear degrees of freedom cannot be ruled out. The quenching phenomenon occurs for nuclear-spin excitations at low excitation energies ($\ensuremath{\omega}\ensuremath{\sim}10\ensuremath{-}20$ MeV) and small-momentum transfers ($q\ensuremath{\le}0.5$ ${\mathrm{fm}}^{\ensuremath{-}1}$). A completely opposite effect is anticipated in the high ($\ensuremath{\omega}$, $q$)-transfer region ($0\ensuremath{\le}\ensuremath{\omega}\ensuremath{\le}500$ MeV, $0.5\ensuremath{\le}q\ensuremath{\le}3$ ${\mathrm{fm}}^{\ensuremath{-}1}$). The nuclear spin-isospin response might be enhanced due to the attractive pion field inside the nucleus. Charge-exchange reactions at GeV incident energies have been used to study the quasifree peak region and the $\ensuremath{\Delta}$-resonance region. An interesting result of these experiments is that the $\ensuremath{\Delta}$ excitation in the nucleus is shifted downwards in energy relative to the $\ensuremath{\Delta}$ excitation of the free proton. The physical origin of this shift is discussed, and it is shown that it may be related to the energy-dependent, attractive one-pion exchange interaction in the medium.

Nuclear spin and isospin excitations

Pionic modes of excitation in nuclei

https://digital.library.unt.edu/ark:/67531/metadc688058/m2/1/high_res_d/405725.pdf

Shell model Monte Carlo methods

Quenching of spin matrix elements in nuclei

Consideration of core polarization, meson exchange, and relativistic corrections gives a satisfactory, quantitative understanding of mirror Gamow-Teller $\ensuremath{\beta}$-transitions in $A=3, 15, 17, 39, \mathrm{and} 41$ nuclei.

Quenching of Allowed Gamow-Teller β Transitions in Mirror Nuclei

The dynamical form factor $S(Q,\ensuremath{\omega})$ of liquid $^{3}\mathrm{He}$, including both the coherent and the incoherent contributions, is calculated within the random-phase approximation. At low temperature a sharp zero-sound mode is obtained. At higher temperature this mode becomes a broad resonance in the particle-hole spectrum. This temperature effect may help account for the difference in $S(Q,\ensuremath{\omega})$ observed in two recent neutron-scattering experiments.

http://www.physics.udel.edu/~glyde/Pubs/PhysRevLett.37.1692.pdf

F. C. Khanna

Papers

Quenching of Allowed Gamow-Teller β Transitions in Mirror Nuclei

Neutron Scattering from Liquid He 3