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General features and contact modeling of $N$-body isolated resonances near threshold
by Ludovic Pricoupenko
Submission summary
| Authors (as registered SciPost users): | Ludovic Pricoupenko |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00010v1 (pdf) |
| Date submitted: | 2024-06-05 17:07 |
| Submitted by: | Pricoupenko, Ludovic |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the effective range approximation. This two-parameter description can be used in various contexts from ultra-cold to hadronic physics. The universal character of these states makes it possible a formulation in terms of a contact model. The singularity at the contact imposes the introduction of a modified scalar product to solve the normalization catastrophe and to restore the self-adjoint character of the model. An equivalence with the standard scalar product used for realistic finite range models is derived.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
In this new version of the manuscript, I have taken into account all the remarks and comments of both referees (see my previous reply to referee 1). I am very indebted to both of them for their relevant reports. They drew my attention on interesting issues (especially halo physics, regarding possible experimental perspectives and also the link with the work of Hammer and Lee). I am also very grateful to referee 2 for the improvements he made to the text.
My answer to the question 4 of referee 2 is as follows. The regime 1/2<s<1 can be reached for a system made of two identical fermions (mass M) interacting resonantly in the s wave with an impurity (mass m) for a mass ratio 8.61...<M/m<12.31... Then, similarly to a narrow s-wave two-body resonance, a large range parameter regime for a three-body resonance can be obtained if one considers a Feshbach resonance in the limit of a small coupling between the three particles and a three-body molecular state in a closed channel.
Best regards
List of changes
-All the text corrections of referee 2 have been implemented
-Minor typos / text changes have been implemented
-To simplify the reading, a change of notations has been implemented E_sep -> E_0 ; Rsep->R_0 ; k_0 -> k
-Eqs.(4,13) have been added (comments 2 and 3 of referee 2)
-Last paragraph of Sec. III-C has been added (comment 2 of referee 1)
-A technical precision on the parameter eta has been added in the paragraph before Eq. 58
-Last paragraph of Sec. IV-A-2 has been enlarged (comment 3 of referee 1)
-Last paragraph of Sec.IV-C-3 has been enlarged (comment 1 of referee 1)
-First paragraph of Sec. VII has been added
-The conclusion has been enlarged :
*paragraph 1 has been enlarged (comment 4 of referee 2 and comment 3 of referee 1) ; there was also an error on the interval for the mass ratio such that 1/2<s<1.
*paragraph 2 has been added
*paragraph 3 has been enlarged (answer to comment 3 of referee 1)
-Few references have been added [32,33,35,36,37,38,39,46,47,57,58]