22.54 Neutron Interactions and Applications (Spring 2004)
Problem Set No. 3
Due: Mar. 11, 2004
Problem 1
State the assumptions on which the energy transfer kernel F ( E → E ') , given in Eq.(6.12)
of the Lecture Notes, is based. Find the corresponding energy distribution for the
recoiling nucleus G ( E A ) , where EA is the recoil energy. Sketch your result and discuss
how it will change if the above assumptions were relaxed.
Problem 2
Write out in words the physical justification for relating the theoretical and observed
cross sections, as given in Eq.(7.1) of the Lecture Notes. Carry out the integration to
arrive at Eq.(7.5). Examine the low and high neutron energy limits to obtain Eqs. (7.9)
and (7.10). What is the quantity in Eq.(7.5) that should be identified with the cross
section observed in the laboratory?
Problem 3
Refer to Fermi's Golden Rule No. 2 as stated in Lec2 (2003). Go through the argument
that shows the cross section for elastic scattering σ (n, n) should be a constant in energy.
How does one reconcile this behavior with what you have just gone through in the
preceding problem?
Problem 4
Sketch the neutron cross section of polycrystalline carbon (see Fig. 3) in Chap 7 of the
Lecture Notes. Explain the various features in the energy variation of the cross section in
terms of the underlying processes (sometimes referred to as the "collision mechanism").
Compare this result with that of water given in Fig. 2, and discuss similarities and
differences.