Eur. Phys. J. A (2005) 26: 201-207
https://doi.org/10.1140/epja/i2005-10165-4

Original Article

Effective three-body interactions in the α-cluster model for the ¹²C nucleus

Joint Institute for Nuclear Research, 141980, Dubna, Russia

^* e-mail: oik@nusun.jinr.ru

Received: 9 September 2005
Accepted: 18 October 2005
Published online: 1 December 2005

Abstract

Properties of the lowest 0⁺ states of ¹²C are calculated to study the role of three-body interactions in the α-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the α-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited 0₂ ⁺ state and the monopole 0₂ ⁺↦0₁ ⁺ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the 0₂ ⁺ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.