Geometric factors in the volume dependence of many-body bound states

Abstract

I derive the volume dependence of bound states from a cluster-cluster picture with nucleon degrees of freedom. A constant factor called the geometric factor appears in the generalization from point-like particles to clusters. I show that this factor is obtained explicitly when the underlying overlap integral is evaluated directly in the original many-body space. I achieve this by constructing Jacobi coordinates on the lattice with periodic boundary conditions. The derivation requires only the interaction between the clusters to be short-ranged, with the nonperturbative Coulomb force included. The factor emerges as a geometric property of the many-body configuration space rather than a multiplicity of physical channels. I validate my derivation using many-body calculations; in particular, I find this factor to be essential in extracting asymptotic normalization constants from lattice calculations of the \isotope[16]{O} ground state.

arXiv comment14 pages, 7 figures, matched published version