Influence of the particle-number fluctuation on theE1ΔK=±1transitions in deformed odd-mass nuclei

Abstract

Dipole electric transitions with $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}1$ are studied theoretically for odd-mass nuclei in the rare-earth region (i) in the frame work of an elaborated Nilsson model with rotation-particle coupling and with isospin-dependent parameters, (ii) with the usual BCS wave function, and (iii) with sharp particle-number-projected BCS wave functions. These projected wave functions are the limit of very speedily converging sequences of functions. General formulas for the pairing reduction factors with strict nucleon number conservation are established. The unphysical effects due to particle fluctuation in the usual BCS wave functions are found to be very important in the theoretical BCS evaluation of reduction factors and half-lives. In most of the analyzed $E1$ transitions, the hindrance factors are improved by the elimination of the unphysical effects due to particle fluctuation. The blocking effect is systematically taken into account. The importance and validity of the physical and mathematical approximations used is discussed.RADIOACTIVITY $^{153,155}\mathrm{Eu}$; $^{159,161}\mathrm{Tb}$; $^{175,177}\mathrm{Lu}$; $^{179,181}\mathrm{Ta}$; $^{155,157}\mathrm{Gd}$; $^{161}\mathrm{Dy}$; $^{169,171,173,177}\mathrm{Yb}$; $^{175,177,179}\mathrm{Hf}$; $E1$ $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}1$ particle-number-projected pairing reduction factor and ${T}_{\frac{1}{2}}$.