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

Abstract

A reexamination of the center of mass problem for light systems in the context of coupled cluster theory has produced a new variational version of the method which is developed entirely in coordinate space. It involves independent cluster functions which depend only on the relative coordinates of the sub clusters of the system. In applications to the 4 He nucleus described via a number of phenomenological and quasireaIistic microscopic Wigner potentials, the method is shown to be quantitatively rather accurate, producing in all cases almost exact results for the ground-state energies at the SUB(3) level of approximation.

An overview of coupled cluster theory and its applications in physics

“…More recently, two other such extensions of the CCM have been discussed. Thus, sixthly, in a recent series of papers [76,77] the CCM has been the subject of intense investigation in order exactly to incorporate translational invariance into it, for use with such light finite systems as the alpha-particle. As a consequence, the emphasis has been to formulate the CCM and the underlying correlations directly in coordinate space rather than in the more usual multiconfigurational Fock-space representation.…”

“…As a consequence, the emphasis has been to formulate the CCM and the underlying correlations directly in coordinate space rather than in the more usual multiconfigurational Fock-space representation. In this way contact has been made both with more traditional generalized nuclear shell-model calculations of the CI type, with the result that the number of configurations can be dramatically reduced [76], and also with variational approaches [77]. This latter work holds out real possibilities of combining the best elements of the CL, variational and CCM approaches.…”

The coupled cluster method

“…Thus, sixthly, in a recent series of papers [70][71][72][73][74] the CCM (and the CIM) have been the subjects of intense investigation in order to incorporate exactly the translational invariance property, which is vital for the accurate treatment of such light nuclei as the alpha-particle. As a consequence, the emphasis has been to formulate the CCM and the underlying correlations directly in coordinate space, rather than in the more usual multiconfigurational Fock-space representation discussed at length in Sects.…”

“…2 and 3 below. In this way contact has been made both with more traditional generalised (many-body) nuclear shell-model calculations of the CIM type, with the result that the number of independent configurations can be dramatically reduced [70,71], and also with variational approaches [72,73]. This work now holds out the possibility of combining some of the best elements of the CIM, CCM, and variational approaches.…”

“…Without any attempt to be exhaustive, we note that some of the most important applications of the CCM have been to the following systems: -Atomic Nuclei: The NCCM has very successfully been applied to the ground and excited states of both closed-shell nuclei (e.g., 4He, 160,4°Ca) and to the open-shell nuclei (e.g., lSN, 170, 14C, lSO, lSF) formed from the addition to the closed-shell nuclei of one or two valence particles or holes. Calculations have been performed [8,9,[70][71][72][73][74][75]100,107,122,1431 for a variety of phenomenological two-body (and three-body) internucleon potentials, using the HCSUBn truncation scheme essentially up to the n = 4 level. Numerical convergence has been demonstrated at this level;…”