Useful Bases for Problems in Nuclear and Particle Physics

✍ Scribed by B.D. Keister; W.N. Polyzou

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 282 KB
• Volume: 134
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5688

✦ Synopsis

part of the one-gluon-exchange interaction leads to momentum-space wave functions that fall off algebraically A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. rather than like Gaussians. This algebraic falloff is also These basis functions are distinguished by the property that they consistent with predictions of asymptotic QCD.

fall off algebraically in momentum space and can be exactly Fourier-

The purpose of this paper is to suggest the use of basis Bessel transformed. The configuration space functions are associfunctions that have all of the advantages of the oscillator ated Laguerre polynomials multiplied by an exponential weight, basis with the additional property that they fall off algebraiand their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in ⌳ 2 /(k 2 ϩ ⌳ 2 ). A simple model of a meson cally in momentum space.

containing a confined quark-antiquark pair shows that this basis is

The configuration-space basis functions, sometimes much better at describing the high-momentum properties of the called ''Sturmians' ' [3], have been used successfully in wave function than the harmonic-oscillator basis. ᮊ 1997 Academic atomic and chemical physics [4,5] calculations. In this Press paper, we exploit the fact that they have analytic Fourier-Bessel transforms, and these transforms fall off like polynomials in momentum space. This makes them well suited