Quark tunneling in a one-dimensional nuclear model

Journal Article · Thu Mar 01 04:00:00 EST 1990 · Physical Review, C (Nuclear Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevC.41.1198· OSTI ID:6848271

Clerk, G J; McKellar, B H.J. ^[1]

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1. Research Centre for High Energy Physics, School of Physics, University of Melbourne, Parkville 3052, Australia (AU)

A general result for the eigenenergies of the one-dimensional Dirac equation for an arbitrary array of delta-function potentials of either Lorentz scalar or vector type is developed. This result is then used to discuss a finite one-dimensional model of the nucleus from which the energy bands of the constituent quarks may be obtained. The resulting energy eigenvalues are compared with those obtained previously via a similar model based on a Klein-Gordon equation. In contrast to this alternative treatment a system consisting of massless quarks confined to a regular periodic one-dimensional nucleus is found to be unbound. In the near ultra-relativistic limit binding to first order in the mass is found, thus conforming unexpectedly with the nonrelativistic limit. The possible surface states are examined and it is found that the so-called Dirac surface states are not expected for potentials of either Lorentz character. The existence and effect of quark surface states is also discussed in terms of our nuclear model. Finally the scattering coefficients for a relativistic particle in an arbitrary array of delta-function potentials are determined and their implications with regard to quark tunneling in nuclei are discussed.

• OSTI ID: 6848271
• Journal Information: Physical Review, C (Nuclear Physics); (USA), Journal Name: Physical Review, C (Nuclear Physics); (USA) Vol. 41:3; ISSN 0556-2813; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BINDING ENERGY
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EIGENVALUES
ELEMENTARY PARTICLES
ENERGY
ENERGY LEVELS
EQUATIONS
FERMIONS
KLEIN-GORDON EQUATION
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
QUARKS
TUNNEL EFFECT
WAVE EQUATIONS