Modified scalar product for the effective range approach: the molecular contribution

TL;DR

This paper introduces a modified scalar product for the effective range approach, allowing the inclusion of molecular contributions in one-channel contact models, especially relevant for narrow Feshbach resonances.

Contribution

It derives a new scalar product that restores self-adjointness and incorporates molecular effects in the effective range framework for contact models.

Findings

Restores self-adjointness of the effective range approach.

Provides a way to implicitly include molecular contributions.

Applicable to narrow Feshbach resonances.

Abstract

The modified scalar product which permits to restore the self-adjoint character of the effective range approach is derived for one-channel contact models where a more general internal structure is included. In the case of the effective range approach, the modified scalar product is interpreted in the light of a generic two-channel model for a narrow Feshbach resonance as a way to take into account implicitly the molecular contribution of the closed channel.