The cross-correlation function: main properties and first applications

When a model structure, and more generally a model electron density rho(M)(r), is available, its cross-correlation function C(u) with the unknown true structure rho(r) cannot be exactly calculated. A useful approximation of C(u) is obtained by replacing exp[i(phi(h) - phi(Mh))] by its expected value. In this case C'(u), a potentially useful approximation of the function C(u), is obtained. In this paper the main crystallographic properties of the functions C(u) and C'(u) are established. It is also shown that such functions may be useful for the success of the phasing process.