General spin precession and betatron oscillation in storage rings

Spin precession of particles having both anomalous magnetic and electric dipole moments (EDMs) is considered. We give the generalized expression of spin precession of these particles injected with transversal extent in magnetic storage rings. This is the generalization of the Farley's pitch correction [F. J. N. Farley, Phys. Lett. B 42, 66 (1972)], including radial oscillation as well as vertical one. The transversal betatron oscillation formulae of these particles are also reproduced.