Charge exchange operators sum rules and proton-neutron T=0 and T=1 pairing interactions

Abstract

We study sum rules for charge exchange operators of the Gamow-Teller and Fermi type and explore what can be learned from them about proton-neutron pairing in T=0 and T=1 channels. We consider both energy weighted (EWSR) and non-energy weighted (NEWSR) sum rules. We use a schematic Hamiltonian to stress the distinctive roles of T=1 and T=0 pair interactions and correlations in the sum rules. Numerical results for 44Ti are presented for both schematic and realistic interactions.

arXiv comment17 pages, new section added. To appear in Nucl. Phys. A

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• $N=Z$ nuclei: A laboratory for neutron-proton collective mode
• Competition between $T$=1 and $T$=0 pairing in $pf$-shell nuclei with $N=Z$
• Energy expressions for n=3 and 4 systems in a single-j shell
• Odd- J Pairing in Nuclei
• Cooperation of anti-aligning and aligning shell-model forces for N=Z
• Expressions for the number of J=0 pairs in even-even Ti isotopes
• J=0 T=1 Pairing Interaction Selection Rules
• Isoscalar neutron-proton pairing and SU(4)-symmetry breaking in Gamow-Teller transitions
• Isospin mixing and Fermi transitions: Selfconsistent deformed mean field calculations and beyond
• Relations for Four Nucleons in a Single j Shell-using 9j Symbols to get rid of 9j Symbols
• Isobaric analog state energy in deformed nuclei: a toy model
• Odd J states of isospin zero and one for 4 nucleon systems: near degeneracies
• A critical look at the vibrational model for ^{92}Pd and comparison with ^{48}Cr
• Shell Model Symmetries-Honoring Franco Iachello