Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: A time-dependent microscopic description

Abstract

The effect of pairing correlation on transfer reaction below the Coulomb barrier is investigated qualitatively and quantitatively using a simplified version of the time-dependent Hartree-$\mathrm{Fock}+\mathrm{BCS}$ approach. The effect of particle-number symmetry breaking on the description of reaction and dedicated methods to extract one- and two-nucleon transfer probabilities (${P}_{1n}$ and ${P}_{2n}$) in a particle-number symmetry breaking approach are discussed. The influence of pairing is systematically investigated in the ${}^{40}\mathrm{Ca}+{}^{40,42,44,46,48,50}\mathrm{Ca}$ reactions. A strong enhancement of the two-particle transfer probabilities owing to initial pairing correlations is observed. This enhancement induces an increase of the ratio of probabilities ${P}_{2n}/{({P}_{1n})}^{2}$ compared to the case with no pairing. It is shown that this ratio increases strongly as the center-of-mass energy decreases with a value that could be larger than ten in the deep sub-barrier regime. An analysis of the pair transfer sensitivity to the type of pairing interaction, namely surface, mixed, or volume, used in the theory is made. It is found that the pair transfer is globally insensitive to the type of force and depends mainly on the pairing interaction strength.