Low-lying12C continuum states in three-αmodel

Souichi Ishikawa,C Elster,D.R Phillips,C.D Roberts

doi:10.1051/epjconf/201611306004

Abstract

The electromagnetic monopole (E 0) transition of the 12 C nucleus, the 0+ ground state to three α -particles (3α ) continuum states, is calculated by applying the Faddeev three-body formalism in coordinate space accommodating the long range Coulomb potential between α particles. Results show that there are two 0+ states, 12 C(03 + ) and 12 C(04 + ) states at excitation energies around 10 MeV, which is consistent with results of recent semi-microscopic calculations and analysis of α-12 C inelastic scattering.

Highlights

Low-lying states in 12C nucleus are interesting subjects to study as a 3α system
There still have been uncertainties in the 12C energy level structure at these energies (Ex ≈ 10 MeV): While a 0+ state was tentatively listed at Ex = 10.3 MeV in the compilation of experimental data near Ex = 10 MeV
I will consider a transition of the 12C ground state 12C(0+1 ) to 3α 0+ continuum states by the E0 operator and calculate the transition strength as a function of 3α energy E at the center of mass (c.m.) system above the 3α threshold

Summary

Introduction

Low-lying states in 12C nucleus are interesting subjects to study as a 3α system. For example, it is widely known that the first 0+ resonant state 12C(0+2 ) at the excitation energy Ex = 7.65 MeV (so called the Hoyle state) plays an essential role in the synthesis of 12C from a 3α continuum state (the triple-α process). I will consider a transition of the 12C ground state 12C(0+1 ) to 3α 0+ continuum states by the E0 operator and calculate the transition strength as a function of 3α energy E at the center of mass (c.m.) system above the 3α threshold This is an extension of recent works [5, 6], in which 3α continuum states up to E = 0.6 MeV were studied to calculate the reaction rate of the triple-α process at stellar temperature T ∼ 109 K, and clarify the decay mode of the Hoyle state. In such a treatment, every complicacies arising from nucleon structure of the α-particle are assumed to be incorporated in interaction potentials among the α-particles, which usually consist of two-α potential (2αP) as well as three-α potential (3αP).

Formalism

Results

Summary