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Study and Applications of the Proportionally Off-Mass-Shell Equation

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Abstract

The Proportionally Off-mass-shell equation is a relativistic, three-dimensional equation for two particle systems. It is proven to be a superior alternative to the traditional three-dimensional equations, which either place one particle on-mass-shell or place the two particles equally off-mass-shell. In this work it is shown that the Proportionally Off-mass-shell equation takes the difference in masses of any two-body system into account while obeying the unitarity relation. It further shows that the unitarity relation is independent of any free parameters. This equation is manifestly covariant. It is also demonstrated that in order to ensure the one-body limit for this equation, it is necessary to use the Wightmann-Garding variables to define the relative momenta. As an application of the Proportionally Off-mass-shell equation, a relativistic multiple scattering series for an A1-body projectile and an A2-body target in the context of meson exchange is developed. The Proportionally Off-mass-shell equation is shown to be the most appropriate choice in calculating the transition matrix. As a specific application of the relativistic multiple scattering series, a first order optical potential calculation for K+-12C elastic scattering is performed. The results for this model are compared with experimental results and show excellent agreement.
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Differential Crossection (mb)
Kaon-Nucleus CM angle in degrees
’c12.dat’
’fort-rel.2’ using 1:3
’fort-nr.2’ using 1:3
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