A Nuclear Cross Section Data Handbook

neutron heating. For a detailed explanation of this phenomenon, please see Ref. 12
(page 5) and 13 (page 91).
In his description 14 of the HEATR module in NJOY, McFarlane pointed out
that the heating number could be calculated in a “forward” way using KERMA15
factors (Kinetic Energy ~eleased in I&erial). In the energy density terms used by
NJOY of eV/cm3, the heating rate in a material is,
xx ~i~ij(~)+(~)
i 3
interactions reactions
where E is the incident energy, ni is the atotic density of material i, @(E) is the
scalar flux of either neutrons or gammas, and k is the Kerrna factor and is in eVbarns.
The kerma factor is obtained by multiplying each interaction cross-section
by the locally deposited energy produced, thus:
where the sum is over the 1 species of charged particles produced, including recoil,
in the interaction j, on the mat~rial i, at the incident neutron energy E, producing
the mean energy per collision, E’ijt. MCNP needs
as the heating number. Unfortunately, ENDF/B evaluations do not include the
detailed spectral information needed to calculate Eijl.
The alternative approach which is used in NJOY to cilculate the heating numbers
is the “energy balance method.” The energy carried away by the neutrons and
photons is subtracted from the total energy available; the remainder is assumed to
be the charged-particle and recoil energy, all of which is locally deposited. Hence
the kerma factor is:
kij(E) = (E + Qij – Aij.(E)– fiij7(~))~:j(~) (6)
and the heating number is effectively kij/aij where Qi~ is the Q-Value (mass differ-
ence) for reaction i on the target j, &ijn is the mean outgoing neutron energy, and
&ij7 is the mean outgoing gamma energy. Thus,
Equation (7) while theoretically correct is of little practiczd value, since photonproduction
information is not available on a reaction-by-reaction basis. Instead the
kermas are redefined viz:
(3)
(4)
(5)
(7)
7