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General features and contact modeling of $N$-body isolated resonances near threshold
by Ludovic Pricoupenko
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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]
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2024-7-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202406_00010v1, delivered 2024-07-26, doi: 10.21468/SciPost.Report.9476
Report
The author has considerably improved the manuscript and addressed all
comments from the first report. He has also added a discussion of
6He as a possible two-neutron halo nucleus without a large s-wave neutron-core
scattering length. In this context, I remark that in the case of 6He there
is a very shallow p-wave resonance in the p_3/2 partial wave ("5He" channel)
which generates a large p-wave scattering volume of about -63 fm^3.
(See, e.g., the discussion in Bertulani et al., Nucl. Phys. A 712 (2002) 37
based on the phase shift analysis from Arndt et al., Nucl. Phys. A 209 (1973)
429.) This resonance is known to be important for the structure of 6He and
complicates the discussion of 6He in the framework of Refs. [8,9].
A brief comment on this complication in the paragraph on 6He would be
useful for the general reader not familiar with the details of 6He.
Apart from this minor issue, the manuscript is ready for publication in
SciPost Physics. I do not need to see the manuscript again.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
The author has made the corrections suggested in my previous report, and has answered my question. I think the paper is ready for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)