As already said, particle transport looks like a theoretical experiment: a particle is followed from its birth (the source), throughout its life, to its death (absorption, escape). Probability distributions are randomly sampled using transport data to determine the outcome at each step of its life (figure 5.1). Specific techniques have to be implemented for critical problems, where the neutron chain length can reach infinity. In MCNP, critical calcula­tions are known as KCODE calculations. In all cases one has to know:

• if the neutron interacts or not in a medium

• if yes, on which nuclei of the medium

• what kind of reaction occurs

• what are the ‘secondary’ particles emitted

Let us see how these steps are handled in MCNP.

Interaction: yes or no?

If one considers a neutron in a material, this neutron can escape or interact in the material. The probability for a collision to occur between / and / + d/ is

p(/) d/ = exp(—XT/)XT d/

where XT is the macroscopic total cross-section. One has to sample / accord­ing to this exponential probability law. Let £ be a random number in [0,1[ uniformly distributed. One can write

p/

p(/) d/ = 1 — e—StZ

0

that is to say / = — (1/XT) ln(1 — £) which can be replaced by / = — (1/XT) ln £ because 1 — £ and £ have the same distribution. The probability distribution of / is obtained by estimating the length of the interval A£ corresponding to the interval d/,

d — = d = exp(—St/)St (5.12)

which verifies that p(/) obeys the distribution given in equation (5.10).

• If / is greater than the distance to the edge of the material, the neutron escapes; the neutron is then placed on the surface separating the medium being exited and the test for the medium being entered is done again.

• Otherwise, an interaction occurs at distance /.

What is the interaction? Depending on the interaction, MCNP answers the following:

1. What is the velocity of the target nucleus?

2. On which nucleus does the collision happen?

3. How many photons are emitted? (This is optionally done if MCNP follows neutrons and photons; but here, we will not discuss that process.)

4. Is the neutron still alive or is it captured?

5. Is it an elastic scattering or an inelastic reaction?

6. What are the energies and directions of the new outgoing particles (if any)?

In the following, we show the main ways to answer these questions. £ will denote a random number in [0,1[ uniformly distributed.