Transfer reactions with the Lagrange-mesh method

Abstract

We apply the R-matrix method in Distorted Wave Born Approximation (DWBA) calculations. The internal wave functions are expanded over a Lagrange mesh, which provides an efficient and fast technique to compute matrix elements. We first present an outline of the theory, by emphasizing the R-matrix aspects. The model is applied to the 16 O(d, p) 17 O and 12 C( 7 Li, t) 16 O reactions, typical of nucleon and of α transfer, respectively. We illustrate the sensitivity of the cross sections with respect to the R-matrix parameters, and show that an excellent convergence can be achieved with relatively small bases. We also discuss the effects of the remnant term in DWBA calculations, and address the question of the peripherality in transfer reactions. We suggest that uncertainties on spectroscopic factors could be underestimated in the literature.

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

“…The latter reaction we have studied in Refs. [22,23] along with the 16 O(d, p) 17 O, but our results for the former have not been presented before.…”

“…2.1 DWBA theory of transfer reactions I give here brief details of the DWBA formalism, which of course has been discussed in many textbooks and reviews [5][6][7][8]27]. For more details about the current approach one is referred to [22]. We consider a projectile A which transfers a cluster/nucleon c to the target t (spin-less in our case) leading to the formation of a residual nucleus B and an outgoing core a in the final channel.…”

“…In the above equation, J = [ m A m B mc(m A +mt) ] 3 (m i is the mass of particle i) is the Jacobian [22] which is introduced to take care of transformations from the natural sets of independent variables (R R R, r r r A ), (R R R , r r r B ) to the set (R R R, R R R ) which is usually adopted for symmetry reasons. Calculation of the transfer kernel [Eq.…”

“…[13], the 16 O( 3 He, d) 17 F reaction was measured to analyze the states of 17 F and the deduced ANCs were then used to determine the low energy radiative capture cross sections of the 16 O(p, γ) 17 F reaction. Similarly, the cluster transfer reactions such as ( 6 Li, d) and ( 7 Li, t), where an α cluster transfer from the projectile to the target, have been used to study the important astrophysical reactions like 12 C(α, γ) 16 O, 13 C(α, n) 16 O, 22 Ne(α, γ) 26 Mg, (for details see for example the review article [10]). It is now well established that cross sections of low energy peripheral radiative capture reactions are mainly determine by the ANCs.…”

“…As a first step in this direction, in Refs. [22,23] we have applied the combined R-matrix [24,25] and the Lagrange mesh [26] methods, to the transfer reaction study in the DWBA frame work. Apart from simplifying the calculations, usage of these methods lead to fast and accurate numerical computations.…”