Spin-dependent Polarizability of Nucleon with Dispersion Relation in the Skyrme Model

We calculate the spin-dependent polarizability of the nucleon in the Skyrme model. The result is compared with that of a heavy baryon chiral perturbation theory(HBChPT), and is shown to be the same as that of HBChPT up to the $\mathrm{\Delta }$-pole terms in the narrow width limit of the $\mathrm{\Delta }$ state and with the experimental physical constants. The effect of the $\mathrm{\Delta }+\pi$ channel is rather small and is numerically quite similar to that of the $\mathrm{\Delta }$ loop in the HBChPT. The electric and magnetic polarizabilities are recalculated using the transverse photon and a consistent inclusion of the $\mathrm{\Delta }$ width.