# Dynamical Pair Production at Sub-Barrier Energies for Light Nuclei

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Schwinger Mechanism

## 3. Cross Section of Pair Production

^{12}C nuclei with their surfaces touching, Equation (21) gives a maximum transverse mass of 3.14 MeV. For

^{238}U in the same condition, ${m}_{T,max}$ = 17.8 MeV. The corresponding effective potential for the two solutions is

^{12}C+

^{12}C, we find the maximum number of pairs produced in the collisions by summing over the trajectory without taking into account the energy loss after a pair is produced. The maximum is attained near ${E}_{c.m.}$= 4 MeV ($\Delta {E}_{k}=2{m}_{e}$) in Figure 4. Clearly, the maximum number of pairs produced in the collisions, and the relative cross-section of Figure 4, critically depends on the ultraviolet cutoff ${x}_{s}$ discussed above and it must be confirmed or modified by future experimental data. Furthermore, microscopic calculations following the heavy ion trajectory and the dynamics of one or more pairs created during the time evolution must be implemented in order to make predictions for heavier colliding nuclei and collisions of different mass number nuclei.

## 4. Summary

^{12}C+

^{12}C collisions, we predict ${E}_{c.m.}\ge 1$ MeV for this effect to occur. The cross-sections are of the order of mb or less. These predictions call for detailed experimental investigation of pair production for this system, and also their energies, in coincidence with fusion fragments to be able to extract correlation functions. An enhancement may be shown by performing a correlation between fusion events with and without pair production.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(Color online) An illustrative example when ${V}_{eff}(R,0)=0$. In the bottom panel we plot ${V}_{eff}$ vs. x and the corresponding potential with full line ($\pm {m}_{T}={m}_{e}$—top panel, dashed and dotted lines) seen by the positron. The calculations are performed for

^{12}C+

^{12}C collisions.

**Figure 3.**(Color online) Tunneling probability for the positron as a function of the relative distance of the two C ions and ${E}_{c.m.}$= 9.4 MeV and different values of $\Delta {E}_{k}$.

**Figure 4.**(Color online) Upper limit for the integrated cross-section for ${e}^{+}{e}^{-}$ production in

^{12}C+

^{12}C scattering below the Coulomb barrier for different values of $\Delta {E}_{k}$. We stress that $\Delta {E}_{k}\ge 0$.

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**MDPI and ACS Style**

Settlemyre, T.; Zheng, H.; Bonasera, A.
Dynamical Pair Production at Sub-Barrier Energies for Light Nuclei. *Particles* **2022**, *5*, 580-588.
https://doi.org/10.3390/particles5040041

**AMA Style**

Settlemyre T, Zheng H, Bonasera A.
Dynamical Pair Production at Sub-Barrier Energies for Light Nuclei. *Particles*. 2022; 5(4):580-588.
https://doi.org/10.3390/particles5040041

**Chicago/Turabian Style**

Settlemyre, Thomas, Hua Zheng, and Aldo Bonasera.
2022. "Dynamical Pair Production at Sub-Barrier Energies for Light Nuclei" *Particles* 5, no. 4: 580-588.
https://doi.org/10.3390/particles5040041