Phenomenological α-α potentials

Abstract

Phenomenological l-dependent α-α potentials are obtained for l = 0, 2 and 4 from fitting the relevant phase shifts for c.m. energies ⪅ 12 MeV. For the nuclear part of the potentials, a superposition of repulsive and attractive Gaussian shapes was used. Following theoretical indications, we try to obtain fits with an l-independent attractive part having a longer range than the repulsive parts. Further, we attempt to obtain, at first, the attractive part from just the l = 4 phase shift in view of the effect of the large l = 4 centrifugal barrier in masking the inner repulsive part. It is, in fact, found possible to obtain acceptable potentials with a common attractive part. These potentials are, however, strongly l-dependent through the repulsive part which becomes weaker as l increases. For l = 4, only a quite weak repulsive part is found to be permissible. Our potentials are in good agreement with those recently obtained by Darriulat et al. The possible importance of the attractive tail of the α-α potential as a selective probe into just the central, spin-independent, isospin-independent part of the nuclear force is pointed out and discussed.