Abstract
We compute the nuclear spin-orbit coupling from the Skyrme model. Previous attempts to do this were based on the product ansatz, and as such were limited to a system of two well-separated nuclei. Our calculation utilises a new method, and is applicable to the phenomenologically important situation of a single nucleon orbiting a large nucleus. We find that, to second order in perturbation theory, the coefficient of the spin-orbit coupling induced by pion field interactions has the wrong sign, but as the strength of the pion-nucleon interactions increases the correct sign is recovered non-perturbatively.
Highlights
The spin-orbit coupling is an important ingredient in nuclear structure theory
The experimentally observed nuclear spin-orbit coupling arises from a rolling motion of a nucleon over the surface of a larger nucleus
Understanding why such a rolling motion is energetically preferred remains something of a mystery
Summary
The spin-orbit coupling is an important ingredient in nuclear structure theory. Its presence implies that it is energetically favourable for the spin and orbital angular momentum of a nucleon to be aligned, if this nucleon is moving close to the surface of a larger nucleus. When the parameter is larger (but not too large), the spin-orbit coupling for the Skyrmion has the correct sign In this latter regime, a better approximation to the Skyrmion wavefunction is to say that the orientation has its probability concentrated near the minimum of the orientational potential, with this minimum varying with the Skyrmion’s location on the surface. The quantum state is close to the classical picture of a Skyrmion rolling over the nuclear surface, maintaining a minimal orientational potential energy This classical rolling motion gives the correct sign for the spin-orbit coupling. We solve the first of these problems by working in the lightly bound version of the Skyrme model [15], for which multi-Skyrmions and their interactions are accurately captured by a point particle description, the particles still have orientational degrees of freedom.
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