Charge-exchange pigmy resonances of tin isotopes

Charge-exchange states, the so-called “pigmy” resonances, which are below the giant Gamow–Teller resonance, have been studied in the self-consistent theory of finite Fermi systems. Microscopic numerical calculations and semiclassical calculations are presented for nine tin isotopes with the mass numbers $A =112, 114, 116, 117, 118, 119, 120, 122$, and $124$, for which experimental data exist. These data have been obtained in the $\mathrm{Sn(^3He},t\mathrm{)Sb}$ charge-exchange reaction at the energy $E\mathrm{(^3He)=200}$ MeV. The comparison of calculations with experimental data on the energies of charge-exchange resonances gives the standard deviation $\delta E < 0.40$ MeV for microscopic numerical calculations and $\delta E < 0.55$ MeV for calculations by semiclassical formulas, which are comparable with experimental errors. The strength function for the $^{118}\mathrm{Sn}$ isotope has been calculated. It has been shown that the calculated resonance energies are close to the experimental values; the calculated and experimental relations between heights of pygmy resonance peaks are also close to each other.