# Low-energy neutron scattering on light nuclei and 19B as a 17B-n-n three-body system in the unitary limit

### Submission summary

 As Contributors: Jaume Carbonell Preprint link: scipost_201911_00038v1 Date submitted: 2019-11-18 01:00 Submitted by: Carbonell, Jaume Submitted to: SciPost Physics Proceedings Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.) Academic field: Physics Specialties: Nuclear Physics - Theory Approaches: Theoretical, Experimental, Computational, Phenomenological

### Abstract

We consider the evolution of the neutron-nucleus scattering length for the lightest nu- clei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in 18B. We describe 19B in terms of a 17B-n-n three-body system where the two-body subsystems 17B-n and n-n are unbound (virtual) states close to the unitary limit. The energy of 19B ground state is well repro- duced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in 20,21B.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission scipost_201911_00038v2 on 15 January 2020

Submission scipost_201911_00038v1 on 18 November 2019

## Reports on this Submission

### Report 1 by Eduardo Garrido on 2019-11-20 (Invited Report)

• Cite as: Eduardo Garrido, Report on arXiv:scipost_201911_00038v1, delivered 2019-11-20, doi: 10.21468/SciPost.Report.1328

### Report

Before publication of the paper there are a few issues, most of them just misprints, that I believe should be corrected or clarified.

The only relevant point that should be made clear refers to the discussion about the sign of the scattering length for the different processes given in Table 1. I agree with the authors when they write that "For a purely repulsive potential this quantity (the scattering length) is always negative", whereas "For a purely attractive one, its sign depends on the strength of the potential". This is somewhat the standard convention for the sign of the scattering length. However, in Fig.4 the repulsive potential has for any strength a positive value. It should be negative according to what written above.

Probably due to this confusion, the discussion of Table 1 is, at least for me, very confusing as well:
-In the paragraph discussing the N=1 cases, the S=1/2 states for n-$^2$H and n-$^2$He are mentioned. Shouldn't it be n-$^3$He instead of n-$^2$He? But, on the other hand, for the n-$^3$He case the value S=1/2 is not possible. In any case, the corresponding $a_+$ values in table 1 are positive, in apparent disagreement with the repulsive character assigned to them in the text (a few lines above it is written that repulsion means negative scattering length).
-In the same paragraph the S=1/2 states of these systems are mentioned as well. As before that makes sense for the n-$^2$He case, but not for the n-$^3$He. Then it is mentioned that they are naturally attractive "despite its positive value". But positive scattering length means attraction no matter what. Then I don't understand the "despite" term. Or perhaps the signs in the table are exchanged as apparently they are in Fig.4?
-The same for the other N cases. For N=2 it is written that all the scattering lengths are repulsive. Then they should be negative, but in the table they are all positive.
-By the way, it is not clear what the '*' that appears for some values in the table actually means. I suspect those are the cases where the "recommended value" is taken.

Summarizing, it seems to me there as a mixing of sign conventions for the scattering length in the text, in Fig.4, and in Table 1.

A second point I would like to mention refers to the n-$^{17}$B potential given in Eq.(1). If I understood well, the term in the potential containing the parameter R is just introduced to produce a repulsive hard core preventing the incoming neutron to penetrate too much in the target. But then the strengths given in the right panel of Fig.5 are all positive. Is that correct? If that is the case, then the term in the potential containing the R parameter is highly attractive.

Two more little things about the figures: In the right panel in Fig.2 I think it would be good to give the units of k, which I guess are fm$^{-1}$. The same for the right panel in Fig.5. Are the strenghts given in MeV? Also, in Fig.3 I'm not really sure to know what "MS" really means. Those states are not mentioned in the text.

Then I have found a series of misprints that should be corrected (there could easily be a few more):

1.- Introduction: Fourth Line: I think what the authors really mean is that "this process is very sensitive to the effects...." instead of "sensible".

2.- Section 2: Fourth line: "In the singlet..."

3.- Page 3: Paragraph "Despite all...": Second and third lines: "... as if the nA potential $V_{nA}$ were..." and "... acts as if there were..." instead of "was".

4.- Page 4: Paragraph "Apart from the Pauli forbidden....": Fourth line: There is a "." to be removed.

5.- Page 4: Fourth line from the bottom: In the sentence "In the latter case..." it seems that some verb is missing somewhere. You might perhaps mean "In the latter case a negative imaginary part APPEARS due to its coupling..." or something similar.

6.- Same page: Second line from the bottom: "... all the scattering lengthS are repulsive."

7.- Page 5: Second line: There is a series of strange question marks after $^4$He.

8.- Page 6: Seventh line: "Since the precise value of $a_S$ is not knowN...". And in the following line there is a ")" to be removed.

9.- Page 7: Fourth line from the bottom: "curves" instead of "cuves".

10.- Page 9: Paragraph "Finally, it is worth...". As written, I find the paragraph difficult to read. I believe the "attempts" are "made" instead of "used". At least to me, the paragraph makes more sense if writing "...although a purely attractive (non-local) n-$^{17}$B interaction was chosen, overbinding the $^{19}$B ground state and predicting bound excited states."

11.- Conclusions: Paragraph "The possibility...": Third line: There is an extra ",". And, right after, "Such an extremely fragile nuclear structure..." or "Such extremely fragile nuclear structures...".

12.- Conclusions: Paragraph "We have constructed...": Second last line: "... accommodateS two resonant stateS..."

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Jaume Carbonell  on 2019-11-28  [id 661]

(in reply to Report 1 by Eduardo Garrido on 2019-11-20)

You are totally right that there was a confusion with the sign of the scattering length: we made a stupid mistake in the very first sentence when we wrote "For a purely repulsive potential this quantity is always negative".
Our convention (which I agree is arbitrary) was just the opposite one, i.e. the one used in nuclear physics which states just the contrary, that is "For a purely repulsive potential this quantity is always positive".
I am very sorry for this "flop" and I am even surprised that before you nobody had realized it.
Of cours the rest of the text was not clear. We have now made the necessary changes.

Concerning the discussion for N=1, you are also right that we were talking about n+3He and not about n+2He !
The a_+ values (i.e. S=3/2 for n-2H and S=1 for n+3He) are positive and repulsive according to our (now corrected convention in Fig 4).
The a_- (i.e. S=1/2 for n-2H and S=0 for n+3He) are also positive but attractive because below them one finds respectively the 3H bound state (in the n+2H case) and the p-3H thresholds (hence its imaginary part) and the 4He ground and first excited state (in the n+3He case).
We have also corrected and better explain that in the revised text.

We denoted with and asterisk (*) a positive value of the scattering length that, instead of being repulsive following the usual (now corrected) convention, it corresponds to an attractive channel. This is for instance the case of np in the S=1 channel (deuteron), where we wrote a^_+=5.42*. The notation was introduced in the text (previous version) when discussing this channel.
However the same will happens for the n+2H in the S=1/2 triton channel for which we wrote a_-=0.65*.

To finished with this point, we fully agree that "there as a mixing of sign conventions for the scattering length in the text, in Fig.4, and in Table 1".
Hope is now corrected.

Refere remark:
"B potential given in Eq.(1). If I understood well, the term in the potential containing the parameter R is just introduced to produce a repulsive hard core preventing the incoming neutron to penetrate too much in the target. But then the strengths given in the right panel of Fig.5 are all positive. Is that correct? If that is the case, then the term in the potential containing the R parameter is highly attractive."

Yes, you are totally right.
According to e. (1), when r>R, the term e^{-mu*r) becomes negligible with respect
the term e^{-mu*R) and the the potential is attractive (with V_r>0).

Refere remark:
Two more little things about the figures: In the right panel in Fig.2 I think it would be good to give the units of k, which I guess are fm−1
. The same for the right panel in Fig.5. Are the strengths given in MeV? Also, in Fig.3 I'm not really sure to know what "MS" really means. Those states are not mentioned in the text.

We have made the necessary changes to account for that.
We have also corrected the misprints you quoted.
Sensible-> sensitive ...
as well as Figs. 2,5 and 3 (right panel)

We hope that our manuscript is now acceptable for publication.

### Eduardo Garrido  on 2019-12-02  [id 662]

(in reply to Jaume Carbonell on 2019-11-28 [id 661])

After the corrections made, I think the manuscript is ready for publication.