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Register a new userAn attractive spin-orbit potential from the Skyrme model
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We derive the nucleon-nucleon isoscalar spin-orbit potential from the Skyrme model and find good agreement with the Paris potential. This solves a problem that has been open for more than thirty years and gives a new geometric understanding of the spin-orbit force. Our calculation is based on the dipole approximation to skyrmion dynamics and higher order perturbation theory.
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A lagrangian which describes interactions between a soliton and a background field is derived for sigma models whose target is a symmetric space. The background field modifies the usual moduli space approximation to soliton dynamics in two ways: by introducing a potential energy, and by inducing a Kaluza-Klein metric on the moduli space. In the particular case of the Skyrme model, this lagrangian is quantised and shown to agree with the leading pion-nucleon term in the chiral effective lagrangian, which is widely used in theoretical nuclear physics. Thus chiral perturbation theory could be considered a low energy limit of the Skyrme model.
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.
We present a first attempt to determine nucleon-nucleon potentials in the parity-odd sector, which appear in 1P1, 3P0, 3P1, 3P2-3F2 channels, in Nf=2 lattice QCD simulations. These potentials are constructed from the Nambu-Bethe-Salpeter wave functions for J^P=0^-, 1^- and 2^-, which correspond to A1^-, T1^- and T2^- + E^- representation of the cubic group, respectively. We have found a large and attractive spin-orbit potential VLS(r) in the isospin-triplet channel, which is qualitatively consistent with the phenomenological determination from the experimental scattering phase shifts. The potentials obtained from lattice QCD are used to calculate the scattering phase shifts in 1P1, 3P0, 3P1 and 3P2-3F2 channels. The strong attractive spin-orbit force and a weak repulsive central force in spin-triplet P-wave channels lead to an attraction in the 3P2 channel, which is related to the P-wave neutron paring in neutron stars.
We derive the generalized Skyrme model as a low-energy effective model of the Sakai-Sugimoto model. The novelty with the past is the presence of the sextic term equal to the topological charge squared. This term appears when the $omega$ meson, and the tower of states on top of it, are integrated out. We claim that, in the small t Hooft coupling limit, the instanton is well described by a Skyrmion arising from the low energy effective Lagrangian of the Sakai-Sugimoto model. The sextic term plays a dominant role in this limit. Moreover, when a pion mass term is added we recover the BPS Skyrme model in the small t Hooft coupling limit.
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric attractive cusp potential. The components of the spinor solution are expressed in terms of Whittaker functions. We compute the bound states solutions and show that, as the potential amplitude increases, the lowest energy state sinks into the Dirac sea becoming a resonance. We characterize and compute the lifetime of the resonant state with the help of the phase shift and the Breit-Wigner relation. We discuss the limit when the cusp potential reduces to a delta point interaction.
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