Elastic scattering of an x-ray photon by a free atom: the form-factor of an atom with an open shell

The general analytical structure of the form-factor for an atom with a L-2S +1(J) term for the ground state is established. The influence of non-spheri cal effects of atomic shapes with one open shell and total momentum J = 0, 1/2, 3/2 of the ground state on the theoretical structure of their form-fac tors is investigated. It is found that in the x-ray range of ionization thr eshold energies of atomic 1s-shells, the non-spherical effects change the a bsolute form-factors values of the spherically symmetrical approximation in the range of -2% to +3%.