PHY304 Particle Physics Dr C N Booth

Particle Physics  -  Homeworks

Yukawa potential

Note. Marks are obtained for a proper explanation of your working, not simply for obtaining the correct numerical or algebraic results!

Earlier in the course, we used the Born approximation to show that in the case of scattering with a momentum transfer q from a spherically symmetric potential V(r), the matrix element is given by

.

For the case of the Yukawa potential,

 
(with Rħ/mc, and m the mass of the exchanged boson mediating the force) show that the matrix element evaluates to
.


When an electron scatters electromagnetically off a nucleus, the exchanged boson is the massless photon, and at low energies the nucleus can be considered to remain effectively at rest.  Starting from the definition of q,   q = pipf, derive an expression for q2 in terms of θ for elastic scattering, and show that the angular dependence of the scattering is then given simply by the Rutherford formula

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