Microscopic study of nuclei synthesis in pycnonuclear reaction $^{12}$C + $^{12}$C in neutron stars

TL;DR

This work addresses microscopic formation of compound nuclei in pycnonuclear reactions within neutron-star matter, focusing on $^{12}$C+$^{12}$C forming $^{24}$Mg. It develops a folding-cluster model paired with the Multiple Internal Reflections method to compute resonance formation probabilities at near-contact distances, comparing scalar folding (S-form) and a new F-form folding potential to traditional Woods–Saxon descriptions. The results reveal that quasibound states significantly enhance compound-nucleus formation relative to zero-point vibration states, and that folding potentials yield markedly different quasibound spectra, including two rotational bands and potential-dependent energy shifts of the first few quasibound levels. These findings imply that heavy-nucleus synthesis in dense stellar environments proceeds preferentially through specific resonant channels, and that fully microscopic inter-nucleon potentials provide a more accurate framework for pycnonuclear fusion predictions.

Abstract

Purpose To investigate synthesis of nuclei in pycnonuclear reactions in dense medium of neutron stars on the basis of understanding, how the compound nucleus is formed during collision of two nuclei. To implement microscopic formulation of nuclear interactions and fusion in pycnonuclear reactions in dense medium. Methods (1) Nuclei synthesis in pycnonuclear reaction in dense medium of neutron star is investigated in the folding approximation of the cluster model. (2) Formation of compound nucleus in dense medium is studied with the method of Multiple Internal Reflections. Results (1) Wave functions of resonance states of $^{24}$Mg are determined by interaction of two $^{12}$C nuclei. (2) Clear maxima of probability of formation of compound nucleus in dense stellar medium are established at first time. (3) Difference between quasibound energies for potential of Woods-Saxon type and folding potentials with the shell-model approximation for wave functions is essential. (4) Formation of the compound nucleus is much more probable in the quasibound states than in states of zero-point vibrations. (5) Only the first quasibound energies for $^{12}$C + $^{12}$Care smaller than the barrier maximums. At these energies compound nuclear system has barrier which prevents its decay going through tunneling phenomenon. This is the new excited nucleus $^{24}$Mg synthesised in the neutron star. \item[Conclusions] Cluster approach with folding potential provides significant modification of picture of formation of compound nucleus, previously obtained concerning the potential of Woods-Saxon type. The highest precision is provided by the folding potential, created by semi-realistic nucleon-nucleon potential and shell-model description of the internal structure of interacting $p$-shell nuclei.

Figures (17)

• Figure 1: (Color online) Potential of interaction between two nuclei [12]C [potential is defined in Eqs. (\ref{['eq.potentialWS.2a']})--(\ref{['eq.potentialWS.2']})].
• Figure 2: (Color online) The potential of Woods-Saxon type and the folding potential with the S-form.
• Figure 3: Folding potentials for the [12]C+[12]C system generated by the Minnesota and Hasegawa-Nagata potentials.
• Figure 4: The part of inter-cluster potential which is related to the Coulomb interaction of [12]C clusters.
• Figure 5: (Color online) Position of the $^{24}$Mg resonance states.