Quantitative study of coherent pairing modes with two-neutron transfer: Sn isotopes

Abstract

Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions in superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. The case studied in the present paper is that of the Sn isotopes [essentially from closed (Z=N=50) to closed (Z=50, N=82) shells]. The static and dynamic off-diagonal, long-range order phase coherence in gauge space displayed by pairing rotations and vibrations, respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular, BCS plus quasiparticle random-phase approximation and Hartree-Fock mean field plus random-phase approximation, respectively. The associated two-nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially "exact." This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely A +2Sn+p, A+1Sn+d, and ASn+t, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above-mentioned nuclear structure and optical potential inputs, within the framework of second-order distorted-wave Born approximation, taking into account simultaneous, successive, and nonorthogonality contributions, provide, within experimental errors in general, and below 10% uncertainty in particular, an overall account of the experimental findings for all of the measured A+2Sn(p,t)ASn(gs) reactions, for which absolute cross sections have been reported to date.