Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

41For the computer simulation outlined above, a trajectory going out of the system meansthat t for certain p-s n-« selected, QplprtpH the thp- inequality:inprmalitvjof Equation (3.3) cannot be fulfilled even with the largest j — the particle goes through al!regions without collision.Such a finite extension of the non-zero, cross-section region has the mathematicalconsequence that the p(R) function given in Equation (3.1) is not a PDF. If R 0is thecoordinate of the latest boundary crossing point in a certain trajectory (rj(R') ^ 0, ifR' > R 0), thenP(oc) - P(RJ < 1The leakage of the particles will be discussed in this latter way, that is as a problem ofhaving a not normalized probability density for the path length, in Sections 3.1.A and 4.IV.E.There is an alternative description of the isolated systems: a black absorber surface isplaced on the outer surface. This approach of absorbing all particles crossing the systemboundary is as acceptable as to let the particles fly away forever.*C. COLLISIONS — IN GENERALThere are many different ways in which an incident particle can interact with matter.The most general formulation of the interactions was given in Section 2.N.I). The quantitythe value of which is proportional to the probability that an interaction will take place in anelementary volume is the cross-section. If there are n elements composing the material inwhich the particle flies, and m different types of interactions then the total cross-section isexpressed by the sum:o-(E) = E S 0-(E) (3.5)i = i j = iwhere (J 13denotes the partial macroscopic cross-section of the j-th type interaction, if the ith type element is hit by a particle having an incident energy E.The cross-sections are assumed to be independent of the angle of incidence (w). Thisassumption is not fully true, however the influence of the orientation of the particle withrespect to e.g., the axis of a molecule containing the element hit is always negligible intransport calculations.The probability that at the next interaction the i-th element will be hit and the actualinteraction will be of the j-th type is:CT 1J(E)Py = -77J7 (3.6)CT(E)From Equations (3.5) and (3.6) it trivially follows that:nmS X P, -I* The author of this paragraph (L.K.) admits that, of these two physically fictional but very fruitful models hecan more easily imagine the system immersed in an infinite sea of vacuum than covered by an impenetrableabsorber.