Double charge-exchange phonon states

Abstract

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 ${\sum }_{i,j=1}^A{t}_{-}(i)t_{-}(j)$ and spin-isospin operator ${\sum }_{i,j=1}^A\sigma (i)t_{-}(i)\sigma (j)t_{-}(j)$, respectively. We employ quartic commutator relations to evaluate the average energies $E_{\mathrm{DIAS}}-2E_{\mathrm{IAS}}$ and $E_{\mathrm{DGTR}}-E_{\mathrm{DIAS}}-2(E_{\mathrm{GTR}}-E_{\mathrm{IAS}})$, and conventional double commutator relations to evaluate the average energies of $E_{\mathrm{GTR}}-E_{\mathrm{IAS}}$ and $E_{\mathrm{IAS}}$. We have found that the corrections due to quartic commutators follow the approximate laws: $E_{\mathrm{DIAS}}-2E_{\mathrm{IAS}}\approx \frac{3}{2}{A}^{-1/3}$ MeV and $E_{\mathrm{DGTR}}-E_{\mathrm{DIAS}}-2(E_{\mathrm{GTR}}-E_{\mathrm{IAS}})\approx 16A^{-1}$ MeV. While the former is dominated by direct Coulomb effects, since Coulomb exchange cancels out to some extent with isospin symmetry breaking contributions originated form the nuclear strong force, the latter is sensitive to the difference in strength between the spin and spin-isospin chanels of the strong interaction.

References in corpus (5)

• A new Skyrme interaction with improved spin-isospin properties
• Double Gamow-Teller transitions and its relation to neutrinoless $\beta \beta$ decay
• The nuclear symmetry energy and the breaking of the isospin symmetry: how do they reconcile with each other?
• Sum rule study for Double Gamow-Teller states
• Nuclear structure studies of double Gamow-Teller strength

Cited by in corpus (6)

• Toward the discovery of matter creation with neutrinoless double-beta decay
• $\gamma \gamma$ decay as a probe of neutrinoless $\beta \beta$ decay nuclear matrix elements
• Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness
• Isobaric analog state energy in deformed nuclei: a toy model
• Systematic analysis of double Gamow-Teller sum rules
• Neutrinoless $\beta \beta$-Decay in DCEQTDA