Multipole Analysis of Particle-Particle or Particle-Hole Multiplets

Recent data on particle-hole multiplets in ${\mathrm{Bi}}^{208}$ have been analyzed in terms of the Racah multipole decomposition. The resulting multipole coefficients are very similar for the various multiplets. A comparison with other known multiplets in ${\mathrm{Cl}}^{38}$, ${\mathrm{K}}^{30}$, ${\mathrm{Sc}}^{42}$, ${\mathrm{Sc}}^{48}$, ${\mathrm{Sc}}^{50}$, ${\mathrm{Nb}}^{92}$, and ${\mathrm{Bi}}^{210}$ also shows a remarkable similarity. These empirical results show that the spectra of such multiplets are determined reasonably well by one set of multipole coefficients, independent of the single-particle orbits involved. It has been pointed out by Kurath that a simple $\delta$-function two-body force with spin exchange fits these average multipole coefficients as well as more complicated interactions.