Ab Initio Study on the Halo Structure in ¹¹Be

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a conference report that provides a nice complement to a recent Physical Review Letter (MS ref. [23]) by the same set of authors. That publication reported on calculations of the Beryllium isotopic chain using Nuclear Lattice EFT and the wave-function-matching technique. Here a set of results pertinent to the structure of the 11Be nucleus is presented. The paper is nicely laid out, with a good explanation, a summary of the method, interesting results, and clear conclusions. 

However, one point is lacking to ensure that the results fully support the conclusions. I would like to see a clearer demonstration of the claim that the valence neutron in 11Be is in a sigma-orbital, in contrast to the neutrons in 10Be, which are in pi-orbitals. This sounds very plausible, but the figures provided don't demonstrate it clearly. First, it is quite difficult to subtract the left panel of Fig. 1 from the right panel with the naked eye, and deduce that the result is a sigma orbital. Thus to say "The extra neutron...makes the density distribution of 11Be more prolate, and the two clusters are connected closer" is a claim that needs more explanation and/or support from figures presented later in the paper.

Second, I am very puzzled as to how Fig. 4(b) can be consistent with the neutrons in 10Be being in a pi-orbital. If they are in a pi-orbital then wouldn't I expect to see a P_1(cos theta) structure for the neutrons that are in 10Be, but a P_0(cos theta) structure for the last neutron? What am I missing here?

There are also two details of the NLEFT calculation I would like to see explained in the manuscript. I understand that these can probably be found in earlier works, but including them here would make this manuscript more self-contained. First, I'd like to know to what order in perturbation theory is the perturbative correction that corrects the results of Eq. (2) for the difference between H' and H_S computed? And, I'd also like it stated in the text, how bound 10Be is with respect to the alpha-alpha-neutron-neutron and Be9-neutron thresholds. 

The second point is related to a concern that I have, which is that it seems that the last neutron in 11Be is bound by 1.9 MeV compared to the 10Be threshold in the NLEFT calculation. This makes it significantly more bound than the 500 keV of binding in nature. This should be mentioned in the manuscript. Can the authors comment--either in the manuscript or in their response to this report--on whether the asymptotic fall off of the neutron distribution shown in Fig. 2(c) is consistent with S_{1n}=1.9 MeV?

Lastly, there are two more points, which I think are just typos: 

(1) The text says that the density distribution for the first excited state of 11Be is shown in Fig. 1, but it is not. 

(2) There is a typo in the first line of Sec. 3: "Eculidean" should be "Euclidean". 

With these changes the manuscript will be suitable for publication. 

Comments on the Quality of English Language

The English is very good apart from the one typo listed above.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report on Ab initio study of the halo structure of 11Be

This paper extends the work of ref [23] by investigating the detailed structure of 11Be, a halo nucleus. 

Overall the work is interesting and worth publishing. I have a few small questions/comments to be addressed to help the paper be more digestible by readers.

1.  Equation (2) defines a variable Z in terms of the many-body density operator. Immediately before Eqn (2), ref [30], which introduced the pinhole algorithm, is referenced, as is ref [27], which discussed wavefunction match. However Z is not defined in either [30] or [27], nor is any part of eqn (2). Furthermore the symbol M in Eqn (2) is not defined. Either this needs to be explicated in more detail, or an accurate citation to a paper that will help the reader to truly understand how Eq. (2) is to be used is needed.

2. In the first paragraph of section 3, "experimental" is misspelled as 'experiemntal.'

3. The radii are presented in Table I. While the qualitative trends between theory and experiment somewhat agree, the actual increase--the ratio between 11Be and 10Be--is far smaller in theory than in experiment. Can the authors discuss briefly why this might be? I could actually understand the absolute magnitudes being off--radii are well known to be difficult to compute in ab initio methods, though it is better in NLEFT than in, say, the no-core shell model, but often ratios of radii are more accurate, but this seems to be the opposite. Some discussion would be appreciated.

4. In the 4th paragraph of section 3, it would be better to write "two-cluster" rather than "2 cluster."  Also, I have to say, although Fig 1 is worth publishing, I disagree with the assertion that 'the two nuclear show a quite different pattern of shapes,' at least based upon Fig. 1. They look very similar.  Are there other observables here that support the extra neutron going into the sigma orbital here? 

5. Fig 2, insets show exponential fall-offs in the tails of the wavefunctions. In general, the argument of the exponential fall-off--the slope on the log-linear plot--is easily explained by the separation energy, and so I would interpret these inset figures as meaning, unsurprisingly, that the various decompositions of the wave function 10Be is more strongly bound that 11Be. Furthermore, if you know the separation energy, you can calculate the slope. It's a simple exercise, but would reinforced our intution. Is this the case here?

Addressing these questions would help the reader to better understand these systems and these calculations and their interpretations.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have included additional details which clarify both the methods they have used and the results they have obtained. The paper is now suitable for publication. 

Comments on the Quality of English Language

In a few places, the English is a little idiosyncratic in the additions that were made in response to my first report. But the additional text is  completely understandable. 

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have adequately responded to my comments and significantly improved and clarified the paper. In my opinion, it is now ready for publication.