Cluster transfer reactions with the combined R-matrix and Lagrange-mesh methods

Abstract

We have recently applied the R-matrix method to transfer reactions in the distorted wave Born approximation (DWBA) framework. In our approach the wave function in the internal region is expanded in terms of Lagrange basis, which provides a fast and efficient way to compute the matrix elements. This paper is a short review of our work on transfer reactions. I discuss applications of our approach by considering the 16 O(d, n) 17 F and 12 C( 7 Li, t) 16 O reactions, which are specific examples of neutron and α transfer, respectively. In particular, I discuss the role of the remnant terms, post-prior form equivalence, peripherality of the reaction and sensitivity of the transfer cross sections to the bound state wave functions. Effects of the remnant terms and of the supersymmetric bound state potentials on the extracted spectroscopic factors are also discussed.

Application of R-Matrix and Lagrange-Mesh Methods to Nuclear Transfer Reactions

“…which is quite similar to the scattering matrix in the DWBA framework (see for example Ref. [6][7]), except that the distorted wave χ 1…”

“…[6], we then simplify the scattering matrix [Eq. (7)] which is further computed to obtain the cross sections. As discussed in Refs.…”

“…As discussed in Refs. [6][7], typically N ≈ -30 40 basis functions are sufficient to achieve the convergence which are significantly lesser than the number of points needed in other methods, like the finite difference method, where normally around 500 points are used. This makes the method very efficient and speedup our computations.…”

“…Modern calculations, like in the CDCC and Faddeev's methods are more demanding in terms of the computer capabilities and hence require efficient numerical techniques. In this regard, as a first step, recently we have applied the R-matrix method [4] along with the Lagrange-mesh method [5] in the DWBA framework of transfer reactions [6][7]. We have shown that these methods lead to the faster and accurate numerical computations.…”

“…Our aim is to utilize the Lagrange-mesh and R-matrix method as we did in Refs. [6][7] in the DWBA framework of transfer reactions.…”