Dynamical probes of pairing correlations: two-particle transfer and two-particle break-up reactions

We investigate the role played by pairing correlations in two typical classes of nuclear reactions specifically involving pairs of particles: two-particle transfer reactions, where a pair of nucleons is exchanged between the reaction partners, and two-particle break-up reactions, where a pair of nucleons is emitted. In both cases we find that, although the process is mainly induced by the repeated action on each particle by the one-body field created by the reaction partner, a coherent enhancing effect is generated by the pair correlation present in the initial wave function, acting during the process and again present (in the case of two-particle transfer) in the final wave function. In the case of reactions involving weakly-bound nuclei the low-density features characterizing the vicinity of the drip line and the suggested consequent enhancement of the pairing correlations should show up as clear signature in both processes. From the point of view of their theoretical description, the vicinity of the drip lines will involve heavily the continuum part of the spectrum and we will test in simple models the validity of different discretization procedures used in the description of both structure and reaction. 1. Pairing correlations and two-particle trasfer proceeses Two-particle transfer processes induced by light ions (reactions as (t,p), (p,t), (3He,n), (α,d)) or heavy ions are considered the ideal tool to study the dynamical effects of pairing correlations. All these reactions do explore precisely the radial properties of pair correlations. Unfortunately, the situation is different, for example, from low-energy one-step Coulomb excitation, where the excitation probability is directly proportional to the B(Eλ) values. Here the reaction mechanism is much more complicated and not well established, so that the possibility of extracting spectroscopic information on the pairing field is not obvious. It is often assumed that the cross section for two-particle transfer will scale with the square of the matrix element of the pair creation (or removal) operator. In this perspective in order to define and measure the collectivity of pairing modes one could compare with single-particle pair matrix elements to define some pairing single-particle units and therefore pairing enhancement factors. But the two-particle transfer process in not sensitive to just the pair matrix element. We have to look at the radial dependence of the pair transition density, which is relevant for the 13th Conference on Theoretical Nuclear Physics in Italy IOP Publishing Journal of Physics: Conference Series 336 (2011) 012018 doi:10.1088/1742-6596/336/1/012018 Published under licence by IOP Publishing Ltd 1 reaction mechanism associated with pair transfer processes. As examples we show in figures 1 and 2 the comparison with pure single-particle configurations in the case of the addition mode around 16O (i.e. the ground state of 18O) and the removal mode around 208Pb (i.e. the ground state of 206Pb). The comparison is done in figure 1 directly on the local transition density (δρP (r, r)). In figure 2 the comparison is done on the non-local transition density δρP (r1, r2) by fixing the position on one particle and plotting as contour plots in space the probability of finding the second one. One immediately sees that while for pure configuration one has equal probablity of finding the second particle on the same or on the opposite side with respect to the core, the pairing correlation induces a correlation in space, favouring the clustering of the pair. r (fm) ' # (r ,r ) (1d5/2)2 0.8 (1d5/2)2 + 0.6(2s1/2)2