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<blockquote data-quote="Spata" data-source="post: 2310165" data-attributes="member: 1455"><p>You need to consider the scattering of spin-1/2 nucleons, &#968;, due to the interaction with a real scalar &#64257;eld, &#966;. This theory is similar to Yukawa’s model for nucleon-meson interactions, except that the pions are pseudoscalar particles while here we are treating them as scalars. The Lagrangian density of this model is,</p><p></p><p>L = &#968;(i/&#8706;&#8722;M)&#968;+ 1/2(&#8706;µ&#966<img src="/images/smilies/wink.png" class="smilie" loading="lazy" alt=";)" title="Wink ;)" data-shortname=";)" />^2&#8722;1/2m^2&#966;^2&#8722;g&#968;&#966;&#968;.</p><p></p><p>What is the di&#64256;erential cross section d&#963;/d&#8486; in the center-of mass frame for unpolarized nucleon-nucleon scattering, summed over &#64257;nal state nucleon spins, to the lowest nontrivial order in g?</p><p>You should calculate all gamma matrix traces, and your &#64257;nal expression should be in terms of kinematical factors. You should evaluate all kinematical factors in terms of the total energy, particle masses, and scattering angle, but you do not have to simplify the &#64257;nal result. By comparing with the Born approximation in nonrelativistic quantum mechanics, what are the nonrelativistic potential and exchange potential due to the exchange of &#966; particles? Do nucleons attract or repel other nucleons in this theory? Do nucleons and antinucleons attract or repel in this theory?</p></blockquote><p></p>
[QUOTE="Spata, post: 2310165, member: 1455"] You need to consider the scattering of spin-1/2 nucleons, ψ, due to the interaction with a real scalar field, φ. This theory is similar to Yukawa’s model for nucleon-meson interactions, except that the pions are pseudoscalar particles while here we are treating them as scalars. The Lagrangian density of this model is, L = ψ(i/∂−M)ψ+ 1/2(∂µφ)^2−1/2m^2φ^2−gψφψ. What is the differential cross section dσ/dΩ in the center-of mass frame for unpolarized nucleon-nucleon scattering, summed over final state nucleon spins, to the lowest nontrivial order in g? You should calculate all gamma matrix traces, and your final expression should be in terms of kinematical factors. You should evaluate all kinematical factors in terms of the total energy, particle masses, and scattering angle, but you do not have to simplify the final result. By comparing with the Born approximation in nonrelativistic quantum mechanics, what are the nonrelativistic potential and exchange potential due to the exchange of φ particles? Do nucleons attract or repel other nucleons in this theory? Do nucleons and antinucleons attract or repel in this theory? [/QUOTE]
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