# 1. A beam of neutrons of constant velocity, mass M.

1. A beam of neutrons of constant velocity, mass M. (M. 1.67 x 10 * kg) and energy E, is incident on a linear chain of atomic nuclei, arranged in a regular fashion as shown in the figure ........................................

1. A beam of neutrons of constant velocity, mass M, (M, 1.67 x 10-27 kg) and energy E, is incident on a linear chain of atomic nuclei, arranged in a regular fashion as shown in the figure (these nuclei could be, for example, those of a long linear molecule). We call / the distance between two consecutive nuclei, and d, their size (d < I). A neutron detector D is placed far away, in a direction which makes an angle of 6 with the direction of the incident neutrons. a) Describe qualitatively the phenomena observed at D when the energy E of the incident neutrons is varied. b) The counting rate, as a function of E, presents a resonance about E = E,. Knowing that there are no other resonances for E < E, show that one can deter- mine I. Calculate I for 6 30° and E, 1.3 x 10-20 joule. c) At about what value of E must we begin to take the finite size of the nuclei into account ? 0oo0000