Three-alpha force and the 3-? model of12C

Abstract

We postulate a Gaussian three-body potential among c~ particles and adjust its parameters so that, when it is added to the Ali-Bodmer c~-~ potential, a good fit to experimental energies of low-lying 0 + and 2 + states of 12C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-~ system. The 3-c~ potential improved results found with the Ali-Bodmer potential alone. We find the 0 + state to be a (non-rigid) linear chain and the ground state to be a triangle of c~ particles.

Breaking and restoration of rotational symmetry on the lattice for bound state multiplets

“…where R α = 1.44 fm is the radius of the α particle, e is the unit of charge and erf denotes the error function. We also employ the three-body interaction [38] V (r r r 1 , r r r 2 , r r r 3 ) = V 0 e −λ (r 2 12 +r 2 13 +r 2…”

“…We take the Gaussian width parameter to be the same as in Ref. [38], Figure 1. The fitted α − α nuclear potential as a function of distance.…”

“…We take the Gaussian width parameter to be the same as in Ref. [38], λ = 0.00506 fm −2 , and we set V 0 = −4.41 MeV to recover the binding energy of the ground state of 12 C.…”

“…For some even-even N = Z nuclei, the system can be approximately described in terms of α-clusters that interact via effective α-α interactions. The most frequently used interactions are local potentials involving a strongly repulsive core [37,38], non-local "fish-bone" potentials [39,40] and other "folding" potentials extracted using the resonating-group method [41][42][43]. In some cases a three-α interaction [38] and/or forbidden state projection [44] are also needed to reproduce the empirical data.…”

Convergence properties ofab initiocalculations of light nuclei in a harmonic oscillator basis

“…The basis functions can also depend upon a parameter (such as the harmonic oscillator energy ω which sets a scale) that then becomes a non-linear variational parameter additional to the linear expansion coefficients. Such variational approaches were the standard for calculating properties of the trinucleon in the decade following the 1960's [5,7] and have also been applied to three and four body alpha particle models of light nuclei and hypernuclei, see [8][9][10]). No-core shell model (NCSM) calculations and no-core full configuration (NCFC) calculations with a "bare" potential are more recent examples of a variational calculation with a linear trial wave function.…”