Global Spectral Gap in Bosonic Molecular Hamiltonians

Abstract

We consider a neutral bosonic molecule in the Born-Oppenheimer approximation without spin and assume the physically obvious assertion that a neutral molecule prefers to break into smaller neutral clusters. We prove the existence of a global in space/uniform spectral gap between the ground state and first excited state energies. To do so, we improve upon previous results using a different tool, the time-independent Feshbach-Schur map.