Calculation of deformed double-folding potentials in the context of the generalized rotation-vibration model

Abstract

We present a procedure to calculate quite accurately double-folding potentials involving deformed densities. The calculations are performed in the context of the generalized rotation-vibration model, which is a general approach to describe rotations and vibrations of nuclear densities for heavy nuclei. The present method is appropriate for obtaining the coupling potentials intended for future applications in coupled-channel calculations. We compare our results with those obtained from other models usually assumed in coupled-channel analyses.

Folding-type coupling potentials in the context of the generalized rotation–vibration model

“…The calculation of the six-dimensional integral (5) can be performed through the Fourier transform method (e.g. [4,7,11]):…”

“…( 1 ) and ( 2 ) indexes in (7) mean calculations relative to the projectile and target nuclei. The double-folding potential for deformed densities can thus be calculated through (6) to (9).…”

“…However, the corresponding numerical calculation requires considerable computer time and, therefore, it is not appropriate to obtain coupling potentials in practical applications. Aiming to avoid this problem, we adopt the method presented in [7] to calculate the folding potential in an approximate but accurate form. Through the expansion of (1) up to second-order in the deformation parameters, we obtain:…”

“…The (27) are the reduced matrix elements of the spherical tensor V lm of (7). The Wigner-Eckart theorem provides the following relation:…”

“…Indeed, as an approximation, many times the coupling potentials are associated to the derivative of the central one, through expansions involving the nuclear deformations. In [7], we have presented a method to calculate deformed potentials using the double-folding procedure. In the present work, we show how to use that method to obtain folding-type coupling potentials for inelastic states involved in heavy-ion collisions.…”