Neutron-nucleus interaction function

If this equation is compared to (2.2), we arrive at one of the basic probability functions for neutron-nucleus interactions ... 

Notice that one can only measure the product pao with this technique. Notice also that the event rate at energy E depends on the WIMP velocity distribution at speeds v > ME/2p . This integration limit depends on the nuclear mass, and thus detectors with different kinds of nuclei are sensitive to different regions of the WIMP velocity space. Moreover, the cross section gq scales differently for spin-dependent and spin-independent WIMP-nucleus interactions. Finally, while there is a consensus on the spin-independent nuclear form factors, spin-dependent form factors are sensitive to detailed modeling of the proton and neutron wave functions inside the nucleus , seeand references therein] Jungman 1996. 

A. Theoretical basis. The theoretical basis for the calculation of slow neutron scattering from chemically bound systems is the pseudo-potential approximation. This approximation can be derived [13] by replacing the strong, short-range /S-wave interaction between neutron and nucleus by a boundary condition on the wave function at small neutron-nucleus separation. This corresponds to replacing the actual interaction by a pseudo-potential interaction... 

Neutrons interact with the nucleus and because they possess zero charge the interaction occurs over a much shorter distance (10 instead of 10 m). The nucleus acts as a point scatterer, and there is no form factor as a function of angle. The difference in scattering as a function of angle is shown in Figure 3.16. 

The parameter 2 is to be computed from the properties of this ith medium, using the known and the density AT, from Eq. (2.54). Now imagine these various media to be combined to give the resultant mixture. Furthermore, let us assume that collisions with the various nuclear species are independent events, that is, the presence of other nuclear species in no manner affects the interaction between a given nuclear type and a neutron. Then the probability in the mixture that a neutron reach distance x without suffering a collision with a nucleus of type i is given by 1 — F,(x). If a neutron is to survive a distance x without collision in the mixture, it must avoid collision with each nuclear type. Thus, the joint probability is some function 1 — where... 

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