Calculation of Energy Spectrum of 12C Isotope by Relativistic Cluster model

TL;DR

This paper calculates the energy spectrum of the 12C isotope using a relativistic cluster model with a three-alpha structure, employing a modified Yukawa potential and Klein-Gordon equation, aligning well with experimental data.

Contribution

It introduces a relativistic cluster model with a modified Yukawa potential to accurately compute the 12C energy spectrum, emphasizing the three-alpha cluster structure.

Findings

The 12C isotope has a well-developed three-alpha cluster structure.

The modified Yukawa potential effectively models cluster interactions.

Calculated energy spectrum aligns with experimental data.

Abstract

In this paper, we have calculated the energy spectrum of 12C isotope by cluster model. The experimental results show that the "Hoyle" state at 7.65 MeV in 12C isotope has a well-developed three-alpha structure. Hence, we select a three-body system and for interaction between the clusters we use modified Yukawa potential plus coulomb potential. Then, we solve the relativistic Klein-Gordon equation using Nikiforov-Uvarov method to calculate the energy spectrum. Finally, the calculated results are compared with the experimental data. The results show that the isotope 12C should be considered as consisting of three-alpha cluster and the modified Yukawa potential is adaptable for cluster interactions.