A Nuclear Cross Section Data Handbook

~Uij(E)
j
The “total” heating number includes the energies of all photons produ~, the
“local” heating number has the photon energies removed. The distinction between
j and jt is significant. The cross sections for the j~ photon production reactions
are independent of the j neutron reactions. In calculating H~l(E) one takes the
difference between two large numbers. Extreme care must be taken in the calculation
of k~(l?) and k~,(E) but - more importantly - extreme care is needed
in the preparation of the evaluated data to insure that proper energy balance is
maintained. When energy balance is considered appropriately, the local heating
numbers H~ti~(E) will be positive.
An alternative and somewhat simpler depiction of the heating number is the
difference calculation employed by Carter and Cashwell (Ref. 13). In this caae
(8)
H=lJ+~--Et-rt (9)
where E is the incident neutron energy, ~ is the average Q-Value, E’ is the average
energy of the secondary neutrons, and 17’ is the average energy of the outgoing
photons.
The difference (E+~)-(E’+1”) is the charged particle heating assumed to be
deposited within a negligible distance from the reaction (hence the term local neutron
heating). The assumption is that neutrons and photons escape the immediate
volume and deposit their energy elsewhere.
Equation (9) again reinforces the fact that the incorrect calculation of P will
result in negative heating numbers. In the past this problem has been particularly
troublesome as illustrated in the work of Soran and Seamen (Ref. 12) where 26 of
the 68 evaluations on the RMCCS library at that time had negative local heating
numbers. Compare that with the present MCNP library which has 28 of the 129
evaluations with at least one negative local heating number; those evaluations are
listed in Table V. Two factors essential in the improvement of the heating number
calculation are a) better energy balance considerations and b) significantly improved
evaluations and evaluational methods. Incidentally, the Monte Carlo code
8