Independent clusters in coordinate space: an efficient alternative to shell-model expansion

Abstract

A previous shell-model-style calculation for the ground-state energy of the 'He nucleus, based on coupled cluster techniques, was able to treat exactly the centre-of-mass motion. It is now recast in a precisely equivalent but vastly more computationally efiaent form, directly in terms of coordinate-space correlation functions which are expanded in a Gaussian geminal basis and determined variationally. This reformulation further leads in a straightforward manner to a natural procedure for including higher-order correlations. Its implementation at even the simplest level produces a significant improvement in the already very good upper bounds achieved far the ground-state energy. Further extensions are also discussed.

Effective interactions and the nuclear shell-model

“…The lowering in energy of the 2 + 1 state supports this interpretation. The most thoroughly studied case, and the one which most convincingly demonstrates these phenomena, is 32 Mg with its extremely large B(E2) = 454 ± 78 e 2 fm 4 and corresponding β 2 = 0.513 [104]; however, a word of caution is necessary when deciding on the basis of this limited information that we are in the presence of well-deformed rotors: for 22 Mg, we would obtain β 2 = 0.67, even more spectacular, and for 12 C, β 2 = 0.8, well above the superdeformed bands.…”

“…Two sets of these nuclei that have received particular attention are those with neutron number N in the vicinity of the 1s0d and 0f 7/2 shell closures (N ≈ 20 and N ≈ 28). Experimental studies of neutron-rich Mg and Na isotopes indicate the onset of deformation, as well as the modification of the N = 20 shell gap for 32 Mg and nearby nuclei [104]. Inspired by the rich set of phenomena occurring near the N = 20 shell closure when N ≫ Z, attention has been directed to nuclei near the N = 28 (sub)shell closure for a number of S and Ar isotopes [105,106] where similar, but less dramatic, effects have been seen as well.…”

Translationally invariant treatment of pair correlations in nuclei II. Tensor correlations

“…The kinetic energy and norm matrices are calculated straightforwardly, and we concentrate therefore on the more complicated matrix element of the potential energy operator where the indices in parentheses identify the particles on which the corresponding operator acts. Many of the terms in the previous expression are similar, and a convenient way of dealing with them is to make a diagrammatic analysis [10] and get the topologically distinct diagrams to expand the matrix elements. The topologically distinct diagrams are schematically indicated in Fig.…”

“…The Gaussian expansion has proven to give a very accurate representation of the correlation function f when both negative and positive values of β [10] are included. In practice we use a set of around 10 Gaussians with fixed length parameters covering a sufficiently wide range of distances.…”

“…Inspired by the CCM we have constructed a variational method that is explicitly translationally invariant, but which includes only a linearised correlation operator. This procedure, the translationally invariant configuration-interaction (TICI) method [9,10], is the subject of this paper. The procedure has mainly been used in a two-body implementation, called TICI2.…”