Nuclear Bubble Configuration in Heavy-Ion Collisions

Round 1

Reviewer 1 Report

The article is on a topic that has been theoretically discussed for many decades. and it is based on a code developed recently by the same authors. The study is sound but suffers, as many other computational studies, of a lack of self-checks.

Questions will always remain about, e.g., what is the sensitivity of the results on the values of the coupling constants in the Lagrangian density (PC-PK1)? What is the effect of using the particular nucleon density profile or the mean field potentials used? What would happen if we repeat the calculation with different profile function of the test particle?  Should we study the effect of varying the impact parameter? Et cetera, et cetera, et cetera.

Since this is a common problem of most BUU articles, I feel I must approve the article for publication with the following mandatory changes:

The article needs a section, at least a long paragraph, describing how the bubble configurations affects the ratio of π−/π+, its connection to the variation of the compression and to the neutron to proton ratio of compression.

Add comments about the expected sensitivity (your "guess") of the results on:

-  variations of the values of the PC-PK1 coupling constants.

- why the particular nucleon density profile was chosen, and how the results would change if other profile had been used.

- why the particular mean field potentials were chosen, and how the results would change if another one had been used.

-  why the particular profile function of the test particle was used, and how the results would change if another one had been used.

-  What is the effect of starting the simulation with the nuclei initially in contact instead of being separated and approaching at high speeds.

Finally, to maintain the track record of this type of studies, references should be made to articles from older to recent, such as: 

- Bubble nuclei, C. Y. Wong, Physics Letters B, Volume 41, Issue 4, 16, 1972, Pages 451-454

- On the Formation of Hollow Configurations in Heavy-Ion Collisions, M. Borunda and J. A. López, Il Nuovo Cimento 107A, 2773 (1994)

- Hollow nuclear matter, Gao-Chan Yong, Phys. Rev. C 93, 014602, 2016

Author Response

We thank the referee for the very helpful comments.
The main modifications we made are:
1. We doubled the number of our simulation runs (from 5 to 10) and updated figures.
2. We added a few lines on symmetyr energy in our work in line 83-85.
3. We added Figure 6 for the neutron directed flow and two lines on this, line 132-133.
4. We added Table 1 for the charged pion ratio.
5. We added several lines on light bubble nuclei in line 170-179. 
Below, we provide our replies to the referee's comments.

"The article is on a topic that has been theoretically discussed for many decades. and it is based on a code developed recently by the same authors. The study is sound but suffers, as many other computational studies, of a lack of self-checks.
Questions will always remain about, e.g., what is the sensitivity of the results on the values of the coupling constants in the Lagrangian density (PC-PK1)? What is the effect of using the particular nucleon density profile or the mean field potentials used? What would happen if we repeat the calculation with different profile function of the test particle?  Should we study the effect of varying the impact parameter? Et cetera, et cetera, et cetera.
Since this is a common problem of most BUU articles, I feel I must approve the article for publication with the following mandatory changes:

The article needs a section, at least a long paragraph, describing how the bubble configurations affects the ratio of π?/π+, 
its connection to the variation of the compression and to the neutron to proton ratio of compression."

(our reply) 
We have added Table 1 for the charged pion ratio. We also added a paragraph for this in line 140-150.

Add comments about the expected sensitivity (your "guess") of the results on:

-  variations of the values of the PC-PK1 coupling constants.

(our reply) 
The PC-PK1 parametrization is not a unique one, as it is.
One can find out different coupling constants set which explains nuclear structure equally well compared to PC-PK1.
If this new set of coupling constants give difference in the bubble structure, then our results will change.
 We added  footnote 1 on this in page 2.

 
- why the particular nucleon density profile was chosen, and how the results would change if other profile had been used.

(our reply) 
Here, we use the nucleon density profile from RCHB with spherical symmetry which includes continuum and paring in a 
consistent way. RCHB has been proved to be successful in describing nuclear properties. This is basic reason why we
chose the density profile from RCHB. 
To emphasize the success of RCHB we added a few lines in Introduction, line 37-40.
Using a different nucleon density profile will give a different nuclear matter produced during the collsions
and so our results may accordingly change.
We also added a few lines on this, line 136-138  and line 168-171. 

- why the particular mean field potentials were chosen, and how the results would change if another one had been used.

(our reply) 
In this work we used the mean field potential by Liu et al as in our current manuscript.
This mean field potential has been widely used for The Transport Model Evaluation
Project (TMEP) and so it is well tested. We added a few lines, line 83-86, for this with some additional references.
We added a few lines on this, line 136-138  and line 168-171. 

-  why the particular profile function of the test particle was used, and how the results would change if another one had been used.

(our reply) 
Many transport models adopt the Gaussian type profile functions, while DJBUU has a polynomial type which is exactly integrable.
Using the Gaussian type profile functions may change our results,  but we don't expect any substantial change.
Rather, changing the constants (a, m, n) in our profile function may affect our results significantly.
We added a few lines on this, line 90-92.

-  What is the effect of starting the simulation with the nuclei initially in contact instead of 
being separated and approaching at high speeds.

(our reply) 
If the initialized projectile and target are stable enough, both cases (contact or separated) should give the same result if
the relative speeds between projectile and target nuclei are the same in the both cases. 
In our case  since the two different mean field models are used for initialization and propagation, 
the initialized nucleus can be a bit unstable. 
If we start our simulations with the nuclei initially being separated and approaching each other, the nuclei can lose their intrinsic
properties such as the nucleon density distribution or bubble structure at the time when they collide. 
In this case we may not be able to clearly study the effect of bubble configuration in our simulation runs.  
Therefore, as stated, we put them close enough and start the simulations.
We added a few lines on this, line 94-98.

Finally, to maintain the track record of this type of studies, references should be made to articles from older to recent, such as: 
- Bubble nuclei, C. Y. Wong, Physics Letters B, Volume 41, Issue 4, 16, 1972, Pages 451-454
- On the Formation of Hollow Configurations in Heavy-Ion Collisions, M. Borunda and J. A. Lopez, Il Nuovo Cimento 107A, 2773 (1994)
- Hollow nuclear matter, Gao-Chan Yong, Phys. Rev. C 93, 014602, 2016

(our reply) 
We added these references:  [5, 6, 9] in the revised version.

Author Response File: Author Response.pdf

Reviewer 2 Report

This study is interesting for nuclear structure exploration. To improve the quality of the study, the following aspects should be considered:

1. The proton flow may be evidently affected by the Coulomb actions, thus cannot reflect entirely the bubble structure of colliding nuclei. Other flow, such as, neutron flow, triton flow may has larger effects.

2. It is not clearly whether the transport model used includes the symmetry energy, since the pion ratio is sensitive to the symmetry energy and different maximum compression densities may cause different different effects of the symmetry energy on the pion ratio.

3. The error bars can be reduced by accumulating more events.

4. Two bubble nuclei or one bubble nuclei with a very light nuclei may have more clear effects.

Author Response

We thank the referee for the very helpful comments.
The main modifications we made are:
1. We doubled the number of our simulation runs (from 5 to 10) and updated figures.
2. We added Figure 6 for the neutron directed flow.
3. We added Table 1 for the charged pion ratio.
4. We added three references  [5, 6, 9] on bubble nuclei in the revised version.
5. To emphasize the success of RCHB we added a few lines in Introduction, line 37-40,
   and added four more references [24-27].
6.  We added a few lines, line 83-86, on the adopted mean field potential with some additional references.
7.  We revised our comments in line 94-98.
Below, we provide our replies to the referee's comments.

"Comments and Suggestions for Authors"
This study is interesting for nuclear structure exploration. 
To improve the quality of the study, the following aspects should be considered:

1. The proton flow may be evidently affected by the Coulomb actions, 
thus cannot reflect entirely the bubble structure of colliding nuclei. 
Other flow, such as, neutron flow, triton flow may has larger effects.

(our reply)
Yes, we added a figure of the neutron flow, Figure 6, and two lines on this, line 132-133.

2. It is not clearly whether the transport model used includes the symmetry energy, 
since the pion ratio is sensitive to the symmetry energy and
 different maximum compression densities 
may cause different different effects of the symmetry energy on the pion ratio.

(our reply)
Yes, we use the mean field potential in Liu et al, where
the symmetry energy at the saturation density is 30.5 MeV and the slope parameter  is 84 MeV.
We added a few lines in line 83-85.

3. The error bars can be reduced by accumulating more events.

(our reply)
To improve our results we performed additional five simulation runs and updated our results.
The error bars are reduced as expected. However, we observed that our main conclusion does not change.

Instead, we discussed other possibilities such as different mean potentials, etc. 
We added a several lines on this, line 90-92, line 136-138  and line 168-171. 

4. Two bubble nuclei or one bubble nuclei with a very light nuclei may have more clear effects.

Yes, we agree with you. 
One practical difficulty is that as discussed in our manuscript, due to the finite width of the test particles
there is finite density contribution to the central density by nearby nucleons (test particles), which makes
difficult to initialize the bubble nuclei. For light nuclei, we have observed that realizing bubble nuclei 
is even more difficult since the nucleons in a light nucleus are gathered near the center of the nucleus.
We may try this after we make the width extremely small (after confirming that DJBUU with this
very small width can reasonably describe heavy ion collisions), which may be considered in our future studies.
We added several lines on this in line 170-179. 

 

Author Response File: Author Response.pdf