For attractive zero-range interactions in a 1D light-heavy-heavy system, the nth eigenvalue satisfies E_n(ε) = -α² + |σ_n| α² ε^{2/3} + O(ε) with σ_n an Airy-function extremum or zero according to particle statistics, and the essential spectrum begins at -α²/(4+ε²).
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The Born-Oppenheimer approximation for a 1D 2+1 particle system with zero-range interactions
For attractive zero-range interactions in a 1D light-heavy-heavy system, the nth eigenvalue satisfies E_n(ε) = -α² + |σ_n| α² ε^{2/3} + O(ε) with σ_n an Airy-function extremum or zero according to particle statistics, and the essential spectrum begins at -α²/(4+ε²).