The low-field effect in radical pairs: A zero-field singlet–triplet basis picture

Abstract

We present a new formulation of the low-field effect (LFE) in spin-correlated radical pairs based on a zero-field singlet–triplet basis for the isotropic spin Hamiltonian. The aim is to provide a description that is both formally rigorous and mechanistically transparent, especially in the regime of weak magnetic fields such as the geomagnetic field. For the standard model radical pair containing a single spin-12 nucleus, we show that the usual electron singlet–triplet basis obscures the distinct dynamical roles of the hyperfine and Zeeman interactions. In a zero-field S–T basis constructed from the angular-momentum structure of the zero-field Hamiltonian, by contrast, the mechanism separates cleanly: isotropic hyperfine coupling mixes singlet–doublet and triplet–doublet states, whereas the weak-field Zeeman interaction mixes triplet–quartet and triplet–doublet states without directly introducing an additional singlet–triplet coupling. The LFE is, therefore, revealed as a sequential process in which a weak field unlocks access from a triplet-only manifold to a singlet-accessible triplet manifold, from which hyperfine-driven singlet–triplet interconversion can occur. We then generalize this picture to radical pairs with arbitrary isotropic hyperfine structures by identifying maximal, interior, and, when present, minimal triplet-only manifolds in the zero-field spectrum. Finally, we introduce a practical blockwise triplet-only state recruitment measure for the triplet-only zero-field state space made singlet-accessible by a weak field and show how this quantity depends on hyperfine symmetry, including the effects of equivalent nuclei. The resulting framework provides both a simple physical picture of the LFE and a general route for estimating its structural upper bound for arbitrary radical pairs.