# 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_00041v2 Date accepted: 2019-12-12 Date submitted: 2019-12-11 01:00 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 $general$ $particle$ $transfer$ $potential$: so called GPT'' potential was represented in the previous paper which indicates 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 the hadron system. In order to confirm the existence of a GPT potential, we investigate the possibility of Cs+2d$\rightarrow$La reaction on the three-ion quasi-molecule CsD$_2$ which is covered by twelve Pd or a CsD$_2$Pd$_{12}$-cluster, where the three-body bound states and wave functions for D-Cs-D molecular and d-Cs-d nuclear systems are calculated. We obtain an approximate E2-transition from the molecular states to the nuclear states. The transition ratio between the short range nuclear potential with the $1/r^2$-type long range potential and without long range potential is $W_{i\rightarrow f}^{E2';L}/W_{i\rightarrow f}^{E2';S}\approx 10^8$. If the reaction Cs+2D$\rightarrow$La is experimentally observed, then the existence of the GPT potential could be confirmed.

Published as SciPost Phys. Proc. 3, 050 (2020)

We rewrite our paper by refree comments.

### List of changes

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.
Ans. Rewritten.

- 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).
Ans. Rewritten.

- One sentence may be included on the motivation to investigate interactions for
ultra-low energy nuclear synthesis.
Ans. Rewritten.

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.
Ans. Being explained.

- "Pd-cage" should also be explained in a short way.
Ans. Being explained.

- Second paragraph after eq.(2), punctuation are required in the starting sentence:
"Let us recall our theory briefly at the Q2T. The Born...".
Ans. corrected.

- Eq.(3) needs to be corrected: ZZ is defined in the lhs as a function of q,q′q,q′ .
But in the rhs, we have pp , p′p′ and qq . The authors should also revise some other
expressions following that; as well as vector notations wherever are necessary.
Ans. Vector notation is given.

- 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?
Ans. The usual fusion is performed in the high temperature in the pile, however, in the present theme, the room temperature is commonly used in the technology field. However, in physics, the temperature should be defined by the Boltzmann distribution function. In order to concentrate our discussion, we don’t touch with the detail, we have used a word “the ultralow energy”, but partly we used room temperature without notice. By the referee’s suggestion, the word should be unified in the physics stile. In my Surry talk, we compared the different temperature cases for T=10^9K, T=10^6K, and T=500K. In this paper, the discussions were not mentioned about the temperature but the ultralow energy region. Thanks to the referee!!

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.
Ans. Corrected.

- Before the Eqs.(16) - (19), they need to define Ve≡Ve(→r1,→r2,→r3)Ve≡Ve(r→1,r→2,r→3) .
- For clarity on the conditions of (16) and (17), better say (for →rki=→rjk=0r→ki=r→jk=0 ) in (16);
and [for →rki=0r→ki=0 (→rjk≠0r→jk≠0 ) or →rjk=0r→jk=0 (→rki≠0r→ki≠0 )] in (17).
Ans. Corrected.

- In Eq.(20), it should be 3cos2θk3cos2⁡θk instead of 2cos2θk2cos2⁡θk .
Ans. Corrected.

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".
Ans. Corrected.