Semiclassical triton

Abstract

The symmetric components of the spatial part of $S$- and $D$- states' wavefunctions for triton ${(}^{3}H)$ are investigated utilizing semiclassical expansion (in the powers of $\hslash$). Analysis of the diagonalized Hamiltonian reveals the existence of two different mass states within the ground state of triton. We have solved the coupled differential equations for the two admixed states ${}^2{S}_{1/2}$ and ${}^4{D}_{1/2}$ owing to tensor interactions exploiting classical WKB-theory using phenomenological Feshbach-Pease potentials. The relative probability of the $D$-state is found to be in good agreement with the experimentally inferred value (4 - 5 \%).