Double charge-exchange phonon states

We study double charge-exchange phonon states in neutron-rich nuclei, in particular the double isobaric analog states and the double Gamow-Teller excitations, induced by the double isospin operator -i,j=1At-(i)t-(j) and spin-isospin operator -i,j=1Aσ(i)t-(i)σ(j)t-(j), respectively. We employ quartic commutator relations to evaluate the average energies EDIAS-2EIAS and EDGTR-EDIAS-2(EGTR-EIAS), and conventional double commutator relations to evaluate the average energies of EGTR-EIAS and EIAS. We have found that the corrections from quartic commutators follow the approximate laws: EDIAS-2EIAS≈32A-1/3MeV and EDGTR-EDIAS-2(EGTR-EIAS)≈16A-1MeV. While the former is dominated by direct Coulomb effects because Coulomb exchange cancels out to some extent with isospin symmetry breaking contributions originated from the nuclear strong force, the latter is sensitive to the difference in strength between the spin and spin-isospin channels of the strong interaction.