Ground-State Energy of a Mixture of Fermions and Bosons in One Dimension with a Repulsiveδ-Function Interaction

The ground-state energy of a mixture of spin-½ fermions and bosons in one dimension, interacting with a repulsive $\delta$-function potential, is analyzed. The wave function is given by repeated use of a generalized Bethe hypothesis. The "momenta" in the hypothesis are determined by coupled Fredholm integral equations. Numerical solutions are given. No phase separation is found.