On the Skyrme model prediction for the N - N spin - orbit force

Abstract

In the framework of the product ansatz as an approximation for the two-baryon system we review in details the derivation of the isoscalar nucleon-nucleon spin orbit potential coming from the sixth order term of the extended Skyrme model. We show that the sixth order term contributes with a positive sign, as is the case for the Skyrme term, contrary to the claims of Riska and Schwesinger. Those authors considered only one part of the force due to the sixth order term and omitted the second part which turns out to be the dominant one. Our result is independent of the parameters of the model. PACS: 11.10Lm, 12.39Dc, 13.75Cs.

Isoscalar NN spin-orbit potential from a Skyrme model with scalar mesons

“…Indeed, these authors ignored the baryon exchange current contribution to the spin-orbit force in their calculations, and we have shown in Ref. [13] that this contribution is significant, with respect to the direct term [12,17], and should be taken into consideration. It is then legitimate to question whether the qualitative results of Ref.…”

“…However the asymptotic expression of the second part of V 6 , which arises from the baryon exchange current [13],…”

“…As reported in Ref. [10,13], generally, one has to treat with care the conversion from velocities to canonical momenta before identifying and extracting the spin-orbit potential. Indeed, one has to start from a Lagrangian formalism, take its "classical" kinetic energy and extract from it the mass matrix and then invert it properly in order to move to a Hamiltonian formalism.…”

“…distance r, the region of validity of the product ansatz, this procedure [10] is equivalent to that of Refs. [9,12,13] which we will use here. In this latter one starts, in the case (2), directly from…”

“…The rather lengthy expressions of the Skyrmeterm contribution V 4 and the sixth-order term contribution V 6 can be found explicitly in Refs. [9,10,17] and [13], 2 Due to the projection theorem, the terms proportional to D(A + 1 A2) contribute to the isospin dependent force.…”