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How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range
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abstract
We present an approach that allows one to obtain information on the compositeness of molecular states from combined information of the scattering length of the hadronic components, the effective range, and the binding energy. We consider explicitly the range of the interaction in the formalism and show it to be extremely important to improve on the formula of Weinberg obtained in the limit of very small binding and zero range interaction. The method allows obtaining good information also in cases where the binding is not small. We explicitly apply it to the case of the deuteron and the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ states and determine simultaneously the value of the compositeness within a certain range, as well as get qualitative information on the range of the interaction.
Forward citations
Cited by 2 Pith papers
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Correlation functions for $n\,\bar{D}_{s1}(2460)$ and $n\,\bar{D}_{s1}(2536)$
The neutron-D_{s1}(2460) and neutron-D_{s1}(2536) systems are predicted to have bound states, with correlation functions sensitive to the molecular structure of the D_{s1} mesons.
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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.
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