# An investigation of the appearance of a long range nuclear potential in ultra low energy nuclear synthesis

### Submission summary

 As Contributors: Shinsho Oryu Preprint link: scipost_201910_00041v1 Date submitted: 2019-10-30 Submitted by: Oryu, Shinsho Submitted to: SciPost Physics Proceedings Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.) Discipline: Physics Subject area: Nuclear Physics - Theory Approaches: Theoretical, Computational

### Abstract

A new potential, the so called GPT'', represents a Yukawa-type potential for shorter range, but a $1/r^n$-type potential for longer range where $n=2$ includes the Efimov-like potential. In order to confirm the existence of a GPT potential, we investigate the possibility of creating the lanthanum (La)-nucleus via the {\it ultra low energy reaction}: Cs(2d,$\gamma$)La on the three-ion quasi-molecule CsD$_2$ in a CsD$_2$Pd$_{12}$-cluster. Here, the D-Cs-D (or d-Cs-d) three-body bound state and wave function are used to calculate the electro-magnetic (EM) transition from the molecular states to the nuclear states in the Cs(2d,$\gamma$)La reaction. We obtain an approximate E2-transition ratio between the $1/r^2$-type long range potential in combination with the short range nuclear potential and the short range nuclear potentials of $W_{i\rightarrow f}^{E2';L}/W_{i\rightarrow f}^{E2';S}\approx 10^8$ which implies that the quasi molecular state is stable for the usual transition $W_{i\rightarrow f}^{E2';S}$, but nuclear synthesis occurs for $W_{i\rightarrow f}^{E2';L}$ with long range. We conclude that if the reaction Cs(2d,$\gamma$)La occurs, then the existence of the GPT potential is confirmed.

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

### Submission & Refereeing History

Resubmission scipost_201910_00041v2 on 11 December 2019
Submission scipost_201910_00041v1 on 30 October 2019

## Reports on this Submission

### Report 1 by LAURO TOMIO on 2019-12-4 Invited Report

• Cite as: LAURO TOMIO, Report on arXiv:scipost_201910_00041v1, delivered 2019-12-04, doi: 10.21468/SciPost.Report.1367

### Strengths

The submitted work is enough interesting and appropriate to a few-body contribution in the SciPost Physics Proceedings. The authors, by following previous work are giving some more details on a proposal of a "general particle transfer" potential (named as GPT potential), applied to atomic-molecular systems.

### Weaknesses

1-) A text revision is necessary, considering my comments and recommendations in the full report.
2-) Formalism should be corrected
and re-checked, by considering some sample mistakes being detailed in my report.

### Report

I found the submitted work enough interesting and appropriate as a contribution to the
SciPost Physics Proceedings. The text is well organized and of general interest, following
some other previous works by the authors.
However, it needs some general text corrections to avoid misprints or language mistakes,
as well as a revision in the presented formalism.

I can make one general remark, which is happening when the authors are citing
references of some of them (not all the authors) by "we...".
See, for example the paragraph starting after Eq.(2).
In such a case, it will be more appropriate to use the passive voice (non-personal) format:
Instead "... we proposed the GPT potential,...", better replace by "...the GPT potential was proposed,... ".

In the following, I am including other specific comments with recommendations, which are indicating that a
throughout revision is necessary, to improve the manuscript presentation.

Abstract

As considering that the abstract is usually being used to advertise a work, even before the
interested reader can access the full paper, I have the following suggestions:

- To define the acronymous GPT in the first time that is appearing in the abstract.
- Revise the abstract in a succinct way, avoiding details on specific reactions (which require
further explanations or definitions that are not easy to be clearly included in an abstract).
- One sentence may be included on the motivation to investigate interactions for
ultra-low energy nuclear synthesis.

Sections 1-4

- Chemical elements should be clearly defined, when appearing for the
first time, to be comprehensive to a general reader. Without clear definitions, one
could be confused with the use of symbols such as D (deuterium atom) and d
(deuteron nucleus) along the text.
- "Pd-cage" should also be explained in a short way.
- Second paragraph after eq.(2), punctuation are required in the starting sentence:
"Let us recall our theory briefly at the Q2T. The Born...".
- Eq.(3) needs to be corrected: $Z$ is defined in the lhs as a function of $q,q^\prime$.
But in the rhs, we have $p$, $p^\prime$ and $q$. The authors should also revise some other
expressions following that; as well as vector notations wherever are necessary.
- The statement, in the last phrase of section 4 (conclusion and discussion) that their
calculation is done at "room temperature nuclear synthesis based upon the Faddeev approach",
needs to be clarified (or removed).
Where "temperature" is introduced (and being effective) in their formulation or calculations?

Formalism

- The authors need to revise the formalism for the notations, considering that all the vector positions (and
corresponding vector momenta) are expressed as being non-vectors. For that, they may follow some
of their previous works.
- Before the Eqs.(16) - (19), they need to define $V_e\equiv V_e(\vec{r}_1,\vec{r}_2,\vec{r}_3)$.
- For clarity on the conditions of (16) and (17), better say (for $\vec{r}_{ki}=\vec{r}_{jk}=0$) in (16);
and [for $\vec{r}_{ki}=0$ ($\vec{r}_{jk}\ne 0$) or $\vec{r}_{jk}= 0$ ($\vec{r}_{ki}\ne 0$)] in (17).
- In Eq.(20), it should be $3\cos^2\theta_k$ instead of $2\cos^2\theta_k$.

References

- Include details of Ref.[6], if available.
- Ref.[10]: replace "Phys. Rev. {\bf 76}" by "Phys. Rev. C{\bf 76}".
- Ref.[14]: "T-matrix", instead of "T-matarix".

### Requested changes

The requested changes are described in attached report. Within the recommendations enumerated, particular attention should be given to the formalism.

• validity: good
• significance: good
• originality: good
• clarity: ok
• formatting: perfect
• grammar: good