Useful Bases for Problems in Nuclear and Particle Physics

Abstract

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly Fourier-Bessel transformed. The configuration space functions are associated Laguerre polynomials multiplied by an exponential weight, and their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in $\Lambda^2/(k^2 + \Lambda^2)$. A simple model of a meson containing a confined quark-antiquark pair shows that this basis is much better at describing the high-momentum properties of the wave function than the harmonic-oscillator basis.Comment: 12 pages LaTeX/revtex, plus 2 postscript figure

Lithium isotopes within theab initiono-core full configuration approach

“…One-dimensional and three-dimensional translationally-invariant one-body density distributions were calculated for various ground and excited states of 6 Li, 7 Li, and 8 Li. These one-body density distributions provide an excellent framework for visualization of nuclear shape distortions and clustering effects.…”

“…9 for the gs of 7 Li. The top panel shows the space-fixed (sf) density including the cm motion, ρ invariant density, ρ ti ( r).…”

“…As N max increases, the dimension of the many-body basis increases exponentially, and there is a clear need for high-performance computing. For the Li isotopes we investigate here, we have limited the basis space to about 1 billion: for 6 Li the largest basis space is N max = 16, with a dimension of 805,583,856; for 7 Li the largest basis space is N max = 14, with a dimension of 1,244,131,981; and for 8 Li the largest basis space is N max = 12, with a dimension of 1,222,330,036. We use the code MFDn (Many Fermion Dynamics for nuclear structure) [13,14], which is a state-of-the-art numerical code for no-core configuration interaction calculations.…”

“…Since we address light nuclei, we feel this capability is an important ingredient. A further advantage in using the (HO) basis is its ease in performing analytical evaluations and straightforward matrix element calculations though certain alternative basis choices also have these advantages [7,8]. In this context, the NCFC approach is similar to the no-core shell model (NCSM) [9].…”

First order relativistic three-body scattering

“…The irreducible representation space is the space of square integrable functions of the eigenvalues of the four commuting operators. The generators can be expressed as functions of these four operators, their conjugates, and the Casimir invariants [26,27,28].…”