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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: | https://arxiv.org/abs/2311.18372v2 (pdf) |
| Date submitted: | 2023-12-22 12:17 |
| 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.
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"General features and contact modeling of N-body isolated resonances near
threshold"
by L. Pricoupenko
The author investigates the emergence of N-body bound and quasi-bound
states (collectively denoted as resonances) in systems with short-range
interactions in the non-Efimovian regime. In this case the long-range
potential in the hyperradial equation is repulsive. Furthermore, it is
assumed that no M-body 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 finite-range reference model for the considered states.
The methodology is reminiscent of description of a scattering state in a
channel with a shallow two-body state in terms of a pole position (binding
energy) and an asymptotic normalization constant. Here the formalism is
extended to N-body resonances by using hyperspherical coordinates.
The paper discusses a new class of universal of few-body states,
an important problem in few-body 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 two-neutron halo nuclei. However, most two-neutron halos have
shallow resonances (using the terminology of the current paper)
in the neutron-core and neutron-neutron 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
neutron-core 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) 500-503]
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
N-body resonances in the conclusions would be useful.