Effect of radio frequency fields on the radical pair magnetoreception model

Although the radical pair (RP) model is widely accepted for birds' orientation, the physical mechanism of it is still not fully understood. In this paper we consider the RP model in the total angular-momentum representation and clearly show a detailed mechanism for orientation. When only the vertical hyperfine (HF) coupling component is considered, analytical expressions of singlet yield angular profiles are obtained with and without considering the radio frequency field, and when the horizontal HF coupling components are considered, a numerical calculation of the singlet yield is given. Based on these analytical and numerical results we present a detailed account of the following issues: how the HF coupling induces the singlet-triplet conversion; why the vertical radio frequency field can disorient the birds, while the parallel one cannot; and why the birds are able to "train" to different field strengths. Finally, we consider a multinuclei RP model.