Global-vector representation of the angular motion of few-particle systems II

Abstract

Abstract. The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three-and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0 − 1 state of 4 He. Twoparticle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.

Harmonic-oscillator excitations of precise few-body wave functions

“…Noting that the Fourier transform of the HO function in the coordinate space is again the HO function in the momentum space, the HO functions with large Q certainly contain largemomentum components. References [10,14,30,31] showed that the momentum distribution has a long tail due to the tensor and short-range correlations. The HO functions with large Q play a role in enhancing the high-momentum tail of the momentum distribution, whereas those with small Q describe the mean-field structure below the Fermi momentum.…”

“…(8) can be obtained analytically from the one between the generating functions (3) in a systematic, algebraic procedure prescribed in Refs. [9][10][11]. The CG basis (8) 4 He and the excited states of 4 He are obtained by using the stochastic variational method [8,9].…”

“…For this purpose, by extending the formulation of Ref. [5], we calculate the occupation probability of the number of total HO quanta in the wave function obtained with an ab initio few-body method; in particular, by using a correlated Gaussian (CG) basis with global vectors [8][9][10][11]. We calculate the HO occupation probability of the wave functions of two-to fournucleon systems and discuss its properties, especially focusing on the 4 He system.…”

Kaonic deuterium and low-energy antikaon-nucleon interaction

“…The so-called global vector representation [17] is applied to describe rotational degrees of freedom, such that the form of the variational wave function does not change under linear transformations of the three-body coordinates. This permits to optimize choices of the Jacobi coordinates for the K − pn andK 0 nn channels with their different masses.…”

Unified description of shell and cluster coexistence in16O with a five-body model

“…The 4 × 4 matrix A and 4-dimensional vectors u 1 and u 2 are variational parameters to be optimized and a tilde denotes a transpose of a matrix. It is noted that all coordinates are explicitly correlated, which enables us to obtain a precise solution of a many-body Schrödinger equation [5]. An advantage of this method is that its functional form does not change under any coordinate transformation, and thus both cluster-and shell-model like configurations can be expressed in a single scheme.…”