2) Complete the following four problems from Textbook II, 15 points for each: 7.2 (a) Derive the expression given in (7.95) to (7.98) for the elastic magnetic cross-section when a magnetic field B is applied in the - direction to a paramagnet. (b) Show that ((S'))-S², 0, (S)→S(S+1)u. ((S))S(S+1) as →∞0, (S¹)→S. as 8.1 The magnetic ions of an antiferromagnet have a face-centred cubic structure. The reciprocal lattice, with unit cell vectors 7₁.2.3. is defined for the simple cubic lattice. The spins of the ions in a plane perpendic- ular to the third cube axis are all aligned, and are opposite to those in the neighbouring parallel planes. If x=++, what are the conditions on f₁, fa, fs for a magnetic Bragg reflection? 9.1 Show that, for neutrons whose wavelength is large compared to the distance between the protons of a hydrogen molecule, the total scattering cross-sections for ortho- and parahydrogen are -{(3b*+b¯)³+2(b*−b¯)). 4m para (3b*+b). where band bare the triplet and singlet scattering lengths respec tively for the proton. (The two proton spins are parallel in artho hydrogen, and antiparallel in parahydrogen. Hint: Use the operator form of the scattering length.) 9.2 MnF: has a body-centred tetragonal lattice with unit cell dimen- sions a, a, c. The atoms occupy the following positions (in units of a, ac) Mn (0, 0, 0), d.d.). F (, , 0), (1-1, 1-0), G+1-d-u+). -0.31. In the magnetically ordered phase, the spins of the Mn ions at (0, 0, 0) and d.1.) are in opposite directions. At which reciprocal lattice points does nuclear-magnetic interference occur in this phase?

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2) Complete the following four problems from Textbook II, 15 points for each: 7.2 (a) Derive the expression given in (7.95) to (7.98) for the elastic magnetic cross-section when a magnetic field B is applied in the - direction to a paramagnet. (b) Show that ((S'))-S², 0, (S)→S(S+1)u. ((S))S(S+1) as →∞0, (S¹)→S. as 8.1