(a) Obtain an expression for the lowest energy a neutron can have if it is to be elastically scattered backward along the [111] direction. Evaluate your expression in electron volts.
(b) Repeat part (a) for elastic scattering along the forward (incident) [111] direction.
(c) Due to the zero-point and thermal motion of the gold atoms, there is a difference between the intensity for the minimal energy scattering in cases (a) and (b). Which of these cases produces the greater intensity, and why?
Hint: The point of part (c) should become clear in class on Monday. Alternatively, you may be able to work out the answer using Ashcroft and Mermin Eqs. (N.20) and (24.28), once told that the quantity on the left-hand side of Eq. (N.20) is proportional to the scattering intensity.