Exploring Many-Body Theories in Light Nuclei

Abstract

A brief review of several many-body theories is presented with applications to the 4H e nu.cleus in a simplified model which only considers Wigner type nucleon-nucleon Interactions. Exact results are obtained with the Diffusion Monte Carlo method, and the results from the Jastrow variational method as well as linearized version of coupled cluster theory are compared with them.

Variational Cluster Methods in Coordinate Space for Small Systems: Center of Mass Corrections Made Easy

“…We have only shown one set of data for the ICI-SUB(2) approximation as the two calculational schemes described above produce essentially the same ground-state energy in their respective converged limits. The results are very promising, with the energy relative to the Diffusion Monte Carlo results [1,4,5,6]missing at most 2 MeV for the MT-V and S3 potentials, whereas for the V7 potential we already have complete agreement by including only these one-and two-body TRI correlations. We need only between 4 and 7 terms in the expansion of Eq.…”

“…As before, we shall confine ourselves (at present) to the 4 He nucleus described by Wigner (central) forces, which allows us to view the system as four identical bosons. Thus the CC method [7,8)starts from the zeroth-order description (<I>o) of our four particles in the (Os) HO state, and builds up excitations via exponential correlations,…”

“…{11 has been described in detail elsewhere [4,5,61, and here we will only present a brief pedagogical sketch. The basic idea is that if we can somehow restrict the cluster operators Sn (or en) to act only on the intrinsic coordinates of the system, thus leaving the CM in the (Os) state, there will be no CM problem as the correction becomes trivial.…”

“…[1), we presented an alternative approach which circumvented the problem altogether by restricting the correlation operator to produce only those excitations which explicitly leave the CM in the (Os) HO ground-state, thereby rendering the CM correction trivial. Unfortunately, this approach as we chose to implement it, suffered from the usual very slow convergence of the HO basis [1,4,5,6]. Below, after a brief review of the old method, we present a new version, entirely in coordinate space, which retains the desired CM properties, but which avoids the aforementioned convergence problems.…”

Translationally-Invariant Coupled Cluster Theory Applied to the 4He Nucleus

“…The column labelled HOW F corresponds to the optimal value for a (OS)4 configuration, and the LT ICC and TICC columns correspond respectively to the linea.r and to the general translationallyinvariant coupled cluster calculation. The results are compared with the exact (within statistical errors) results of a diffusion Monte Carlo calculation (column DMC) [24,28]and with the results of a variational calculation for a simple trial Jastrow function depending on three parameters [28]. We see from this Table that the dominant contribution to the energy comes from the linea.rpart of the coupled cluster wave function, the contribution of quadratic terms being a rather small fraction of 1MeV.…”