Effect of Pairing Correlations on Nuclear Gamma-Ray Transitions

Several examples of the effect of pairing correlations on nuclear gamma-ray transitions are presented. It is shown that even if collective coupling exists, gamma-ray transitions of electric multipole type between low-lying quasiparticle states whose free shell-model orbit energies are symmetrically related to the Fermi energy may be extremely retarded. In this work the factor ($U_i{U}_f-V_i{V}_f$) which arises from the pairing correlation is directly estimated from empirical even-odd mass difference data. The agreement of the calculated transition probabilities with experimental results is good. A shell-model calculation taking into account the pairing correlation has been made for transitions of $E2\mathrm{}$ type between $d_{\frac{3}{2}}$ and $s_{\frac{1}{2}}$ orbits in ${\mathrm{Sn}}^{117}$ and ${\mathrm{Sn}}^{118}$ and the results are compared with that of the quasiparticle approximation. It is shown that the quasiparticle approximation is more improved by using renormalized wave functions which are obtained by projecting out only the terms having the correct number of particles than by taking into account only the blocking effect except for special cases.