Interaction kernels for A = 4n binary cluster systems

Abstract

Bargmann transform techniques used to calculate norm kernels for nuclear cluster systems have been generalized to evaluate interaction kernels for central interactions of gaussian form for binary cluster systems made up of SU(4}scalar (A = 4n) cluster fragments with internal func tions of good SU(3) symmetry and equal oscillator width parameters . The technique involves a reduction from A-particle orbital states of space symmetry characterized by 4-columned Young tableaux to 4A-particle states of single-column symmetry . The interaction kernels are built partly through a convolution of the single~olumn Bargmann transforms of the Fourier components of basic one-body operators . Bargmann transforms of single-column type have been evaluated in algebraic form for a two-body gaussian interaction and for the one-body Fourier kernel,~~E xp (iq~r;), for the following A-particle systems and cluster decompositions : A = 12, x+"Be : A = 16, x+' 2 C, "Be+"Be ; A = 20, x+"'O, "Be+`Z C ; and A = 24, ' zC+' zC, "Be+'`'O, x+ Z°Ne .The construction of the Bargmann transform for the full A-particle system is illustrated with a simple example. The example also shows how the coordinate space matrix elements needed for the evaluation of RGM and GCM kernels can be extracted from appropriate expansions of this Bargmann transform by purely algebraic techniques . *

Precise solution of few-body problems with the stochastic variational method on a correlated Gaussian basis

“…The calculation consists of three steps: (A)The calculation of the matrix elements between the Slater determinants of the Gaussian wavepacket single-particle functions, (B)A transformation from the single-particle coordinate representation to the relative and center-of-mass coordinate representation, (C)An integral transformation from the Gaussian wave-packet functions to the correlated Gaussian basis. A procedure similar to steps (A) and (B) was used to manipulate algebraically the antisymmetrization operation and the transformation of the coordinates for complex cluster systems [21]. In step (A) the Slater determinant for the N-nucleon wave function is constructed by distributing the nucleons at positions (s 1 , ..., s N ).…”

“…These position vectors serve as the generator coordinates. The Slater determinant of the Gaussian wave packets is often used in nuclear theory, e.g., in cluster model [21][22][23][24] and fermionic or antisymmetrized molecular dynamics [25,26]. The Hamiltonian matrix elements are analytically evaluated with the use of technique of the Slater determinants [27,22], and can be expressed as a function of the generator coordinates.…”

6He + 6He Clustering of 12Be in a Microscopic Algebraic Approach

“…Both groups utilize the Bargmann space technique [14] and the SU (3)-scalar property of the norm kernels. Apart from the most tractable, so-called alpha-conjugated systems (A = 4n) [15], the most relevant to our case example of 6 Li+ 6 Li was considered in Ref. [13], where the norm kernel is tabulated.…”

Microscopic multicluster description of neutron-halo nuclei with a stochastic variational method

“…All these shortcomings call for fully microscopic treatments that preserve some elements of the few-body approaches as well. Although microscopic cluster models are general enough and their techniques are highly sophisticated [12,13,14], they have not been used too much to describe systems containing more than two clusters. It has been demonstrated recently for an α+p+n model of 6 Li that a microscopic approach, in which the treatment of the relative motion is comparable with the three-body approaches is feasible [15], and similar calculations for the 6 He- 6 Li-6 Be isospin triplet have been published in another paper [16].…”