Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apro13013p&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
The response of a relativistic particle bound in a linear confining well is calculated as a function of the momentum and energy transfer, q, ν. At large values of |q| the response exhibits scaling in the variable tildey=ν-|q|, which is proportional to the Nachtmann variable, ξ. The approach to scaling is studied at smaller values of |q|. Scaling occurs at ν ~ |q| at relatively small |q|, and its validity extends over the entire ξ range as |q| increases; this behavior is observed in electron-proton scattering. About 10% of the response at large |q| is in the timelike region where ν>|q|, and it is necessary to include it to fulfill the particle number sum rule. The Gross-Llewellyn Smith and Gottfried sum rules are discussed in the context of these results as well as the effects final state interactions on the width of the response. At large |q| the response acquires a constant width independent of |q|. This width has a contribution from the final state interactions of the struck particle, which persists in the large |q| limit. The width of the response predicted using plane wave impulse approximation is smaller because of the neglect of final state interactions in that approximation. However, the exact response may be obtained by folding the approximate response with a function representing final state interaction effects. We also study the response obtained from the momentum distribution assuming that the particle is on the energy shell both before and after being struck. Quantitative results are presented for the linear confining potential. In this case the response predicted with the on-shell approximation has correct values for the total strength, mean energy and width, however its shape is wrong.
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