For finite-range potentials, the compositeness of a bound state is exactly proportional to the probability of finding the particle outside a chosen radius, with a universal factor depending on angular momentum.
Role of the effective range in the weak-binding relation
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We study the range correction in the weak-binding relation, which relates the internal structure of hadrons with the scattering length and the binding energy. Utilizing the effective field theories, we show that the effective range originates from the derivative coupling interaction as well as from the channel coupling to the bare state, and that the different contributions are not distinguishable. By examining the compositeness in the effective field theories, it is demonstrated that the effective range induces the finite range correction for the weak-binding relation in addition to the previously known contributions. We thus propose to include the range correction in the uncertainty terms of the weak-binding relation.
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A variation on "compositeness" (including higher partial waves)
For finite-range potentials, the compositeness of a bound state is exactly proportional to the probability of finding the particle outside a chosen radius, with a universal factor depending on angular momentum.