It is possible to calculate quantities of the form

‘(E)R(E) dE

where ‘(E) is the fluence and R(E) is an additive and/or multiplicative response function from the MCNP cross-section library. It is very useful to find the reaction rates, the averaged cross-sections (over the flux) and so

on. Such quantities are obtained with FM cards (related to F (tally) cards); an FM card is written as

FMn C m-L R1

or

FMn (C mL Rl)(C m2 R2)

where n is the tally number, C is the multiplicative constant, mt is the material and R is a reaction code (or a list of reactions); table 5.3 gives some useful reaction codes.

But let us see some useful examples of FM cards. Suppose that cell 1, of volume V, is made of material 2 with a given density.

F4:n 1 F14:n 1

FM14 (1 2 102) (-1 2 102) (-1 2 -6:102) (-1 2 -6 -7)

Tally 4 just gives the flux in cell 1. Tally 14 gives:

• (1/V) J ‘(E)an7f (E) dE for material 2.

• (1/ V) ‘(E)^n7(E) dE for material 2; the density of cell 1 is used because the muJltiplicative constant is negative to calculate the number of atoms.

• (1/V'(E)(Xn,7(E) + Xfis(E)) dE for material 2; the ‘:’ means that reactions -6 and 102 are summed.

• (1/V) J" ‘(E)v(E)Xfis(E) dE for material 2; the ‘ ’ means that reaction-6 is multiplied by ‘reaction’ -7.

To calculate

‘(EK,7(E) dE ‘(E) dE

one just has to take the ratio of the first value of tally 14 by the value of tally 4 (for complex cells, MCNP is not able to calculate the cell volume and one has to specify it with an SD or VOL card).

It is also possible to calculate these quantities for a material which is not directly present in the geometry; it is just necessary to define this material. This is particularly interesting if one wants to see the contribution of individual nuclei to a mixture (for example the role of hydrogen and of oxygen in the water). Note that, in this case, the multiplicative constant C must be positive, because the density of this perturbing material is not given.