Lattice models for quark, nuclear structure and nuclear reaction studies

Abstract

Because of their computational simplicity, lattice models have found various uses in quark, nuclear structure and nuclear reaction (multifragmentation and heavy-ion) studies. However, differences in the mean density of particles among crystal types lead to significantly different properties, indicating that simulations using nucleon lattices should compare several lattice structures. The characteristics of five important lattice groups are discussed and fundamental algorithms are provided.

Valence quark distribution inA=3nuclei

“…The potential is composed of individual, linearly confining (nucleonlike) potential wells, set out in a regular array (equilateral triangle for A=3 and tetrahedron for A=4) in a bodyfixed frame, separated by a variationally determined distance scale d (common side length) and truncated on the midplanes between each pair of wells. The structure of this "egg-crate" potential, if extended to larger A, may be relevant to the observations of Cook and others [19].…”

From Quark and Nucleon Correlations to Discrete Symmetry and Clustering in Nuclei

“…Hence, an antiquark can be replaced by two correspondingly colored quarks to create a color singlet baryon; now destructive interference takes place between color fields of three valence quarks (VQs). Putting aside the mass and charge differences of valence quarks one may say that inside the baryon three quarks oscillate along the bisectors of equilateral triangle under the potential (5). The larger separation of the color quarks is controlled by the linear growing confining potential.…”

“…Within nuclei constructed this way the nucleons aggregate into a face-centered cubic (FCC) lattice with alternating spin and isospin layers. It turns out that this arrangement is the basis of the FCC-lattice model of the nuclear structure [4,5,6], developed more than 30 years ago. For finite nuclei the FCC arrangement appears as a tetrahedron ( 4 He) and truncated tetrahedrons (for larger nuclei).…”

“…It turned out (Section 4) that the received geometry of nuclear structure corresponds to symmetry of the face-centered cubic (FCC) lattice. The SCQM together with the FCC lattice model developed by N.D. Cook [4,5,6] are applied to describe the nuclear properties.…”

Fragmentation of nuclei at intermediate and high energies in modified cascade model

“…where r is the Euclidean distance of each nucleon, x Nucleon coordinates (4 -6) for the target (projectile) nucleus are generated in accordance with the algorithm given in reference [10]. For each nuclear collision, lattices of target and projectile nuclei are oriented randomly in relation to the collision axes.…”