Consider an electric dipoles consisting on two electric charges +e and -e located at +a and...

 

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Consider an electric dipoles consisting on two electric charges +e and -e located at +a and -a, respectively. Consider also another particle of mass m and charge e approaching the dipole with an incident wave vector k = k perpendicular to the direction of the dipole. a) Write down the expression of the interaction potential V(F) between the dipole and the incoming particle, located at a generic point P in space, in terms of {e, a, }, where is the position vector of P with respect to the origin. Assume 1/40 = 1. b) Write down the corresponding integral expression of the scattering amplitude f(E,E) in the Born approximation, in terms of vector q=k-. Show that, since we are considering elastic scattering, the magnitude of a reads q= || = 2k sin where a is the angle formed by vectors k and k'. c) Solve the resulting integral :) This can be done expressing it in 3D spherical coor- dinates (r,,) and using the prescription dz sin(qz) lim = +04-11 Lodze 1 dz ez sin(qz) q d) Considering m, a and k fixed, find the the value of a that maximizes the obtained scattering amplitude. You can assume q is on the XZ plane due to the rotational symmetry of the problem around the axis. Consider an electric dipoles consisting on two electric charges +e and -e located at +a and -a, respectively. Consider also another particle of mass m and charge e approaching the dipole with an incident wave vector k = k perpendicular to the direction of the dipole. a) Write down the expression of the interaction potential V(F) between the dipole and the incoming particle, located at a generic point P in space, in terms of {e, a, }, where is the position vector of P with respect to the origin. Assume 1/40 = 1. b) Write down the corresponding integral expression of the scattering amplitude f(E,E) in the Born approximation, in terms of vector q=k-. Show that, since we are considering elastic scattering, the magnitude of a reads q= || = 2k sin where a is the angle formed by vectors k and k'. c) Solve the resulting integral :) This can be done expressing it in 3D spherical coor- dinates (r,,) and using the prescription dz sin(qz) lim = +04-11 Lodze 1 dz ez sin(qz) q d) Considering m, a and k fixed, find the the value of a that maximizes the obtained scattering amplitude. You can assume q is on the XZ plane due to the rotational symmetry of the problem around the axis.