Hierarchical Tensor Coupling and Parity-Projected Langevin Dynamics in Cryogenic HeH+ Collisions

Abstract

Recent cryogenic storage ring (CSR) experiments have confirmed that low-temperature reaction rates for the primordial molecular ion HeH+ remain remarkably constant down to the sub-Kelvin regime. We formulate an analytical framework based on a hierarchical tensor contraction to explain both internal energy redistribution and asymptotic capture. A rank-3 trilinear coupling tensor (T_ijk), allowed by the explicit inversion symmetry breaking of the 2:1 nuclear charge asymmetry, accelerates spontaneous rovibrational de-excitation into the ground state |v=0, J=0>. In this isotropic manifold, the expectation value of the rank-1 dipole tensor vanishes identically (<μ_i> = 0), suppressing permanent dipolar orientation effects. Asymptotic interaction is therefore exclusively governed by the scalar trace of the neutral partner's rank-2 polarizability tensor (α_ij). The resulting V(R) ∝ -R^-4 potential dictates a Langevin capture cross-section σ(v) ∝ v^-1, yielding a strictly temperature-independent rate coefficient k(T) = 2π q sqrt(α_bar / μ). Note: The analytical formulation, tensor structuring, and LaTeX typesetting were developed in collaboration with artificial intelligence assistance.