SciPost Submission Page
General features and contact modeling of $N$body isolated resonances near threshold
by Ludovic Pricoupenko
This is not the latest submitted version.
Submission summary
Authors (as registered SciPost users):  Ludovic Pricoupenko 
Submission information  

Preprint Link:  https://arxiv.org/abs/2311.18372v2 (pdf) 
Date submitted:  20231222 12:17 
Submitted by:  Pricoupenko, Ludovic 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
$N$body non efimovian bound or quasibound 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 twoparameter description can be used in various contexts from ultracold 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 selfadjoint character of the model. An equivalence with the standard scalar product used for realistic finite range models is derived.
Current status:
Reports on this Submission
Report
The author considers some general features of Nbody resonances in D spatial dimensions, in the absence of the Efimov effect. There is an effective repulsive potential that is inversely proportional to the square of the hyperradius rho, with a strength characterized by the parameter s. This problem is of broad interest in both ultracold atoms physics and nuclear physics. The method the author presents is interesting, although I did not check for myself whether it is accurate (in particular the approximation made in Eq.(15)).
This work seems to be an extension of Ref.[26] by the author.
Because of the importance of the topic and because of the author's expertise on
the subject, I support the publication of the paper.
Some comments and questions which I hope the author can address:
1. Some grammatical changes are desired. It may be helpful to ask a native English
speaker to make such changes.
Some necessary changes, not a complete list:
A. in the introduction,
"Although the huge different scales"
>
"In spite of the enormously different scales"
B. "ultracold atoms experiments gives the marvelous opportunity"
> "ultracold atoms experiments provide marvelous opportunities"
C. "Efimov states, can be observed"
> "Efimov states can be observed"
D. "s wave"
> "swave" (where the letter "s" should be in italic face)
E. "At the heart of this universality, is the scale"
> "At the heart of this universality is the scale"
F. "The beauty of this effects"
> "The beauty of this effect"
G. "no more separable" (several places in the paper)
> "no longer separable"
H. "First studies of this regime using a contact model, was done"
> "First studies of this regime using a contact model were done"
I. "verify" or "verifying" (on pages 6,7,10,11,12,13,15)
> "satisfy" or "satisfying".
J. "verified" (pages 7, 11, 12, 17)
> "satisfied"
K. "traduce" (page 3)
> "replace"
L. "traduces" (page 16)
> "models"
M. "and effective angular momentum" (page 3)
> "an effective angular momentum"
2. Around Eq.(4), the hyperradius rho is introduced.
I suggest that the author define rho in terms of the position vectors of the N particles
or in terms of the Jacobi coordinates.
3. Immediately after Eq.(11), it may be helpful to show the explicit formula for s:
s=K+\frac{d}{2}1.
4. In the Conclusions section, the author writes
"The identification of possible longlived quasibound states in this last regime for small but finite detuning, when \frac{1}{2} \leq s < 1, is perhaps the most important physical result of this paper."
Could the author show a possible physical system in which this effect may be realized?
Recommendation
Ask for minor revision
Report
Referee report
"General features and contact modeling of Nbody isolated resonances near
threshold"
by L. Pricoupenko
The author investigates the emergence of Nbody bound and quasibound
states (collectively denoted as resonances) in systems with shortrange
interactions in the nonEfimovian regime. In this case the longrange
potential in the hyperradial equation is repulsive. Furthermore, it is
assumed that no Mbody resonances with M<N occur.
The author generalizes his previous work for 3d systems close to the unitary
limit in [26] to system away from the unitary limit and to 1d and 2d systems.
A contact model with two parameters is constructed that reproduces the
main features of a finiterange reference model for the considered states.
The methodology is reminiscent of description of a scattering state in a
channel with a shallow twobody state in terms of a pole position (binding
energy) and an asymptotic normalization constant. Here the formalism is
extended to Nbody resonances by using hyperspherical coordinates.
The paper discusses a new class of universal of fewbody states,
an important problem in fewbody physics.
It is carefully written and it is obvious that the author has
made some effort to present the results in a comprehensive way,
for example by including a summary of the main results in the introduction.
Despite this, the paper is still rather technical and the connection to
experiment is not obvious. The paper could be published in SciPost after
the author has adressed the comments below.
1) p.4, 1st column, end of first paragraph:
The last sentence implies that the scenario of Ref. [8,9] is common
in twoneutron halo nuclei. However, most twoneutron halos have
shallow resonances (using the terminology of the current paper)
in the neutroncore and neutronneutron channels. They are bound by the
Efimov effect, even though there might be only one state in the universal
region (see the discussion in [4]). The scenario of Ref. [8,9] (no
neutroncore resonance) may be applicable to 22C but there is conflicting
information from experiment.
2) Sec. IIC:
The results on the occupation probability for the small hyperradius region
are interesting. In [Hammer, Lee, Phys.Lett.B 681 (2009) 500503]
causality bounds on the occupation probability for large distances in the
limit E > 0 were derived. Are these bounds consistent with the results
on the occupation probability for small hyperradii in the paper?
3) While some references to similar results obtained using other
methods are made in the conclusions no connections to actual physical
systems or experimental results are made. Are the states discussed in the
manuscript theoretical artifacts or can they be observed in experiment?
A brief discussion of experimental prospects for the observation of the
Nbody resonances in the conclusions would be useful.
Author: Ludovic Pricoupenko on 20240531 [id 4528]
(in reply to Report 1 on 20240403)Please find attached my reply to this report.
Attachment:
Answer.pdf