Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule H¯(v) and extracule D¯(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities H¯(v) and D¯(P) are found to have either one maximum or two maxima, and the numbers of maxima in H¯(v) and D¯(P) are the same for 98 atoms. For these atoms, the locations υmax and Pmax and the heights H¯max and D¯max of the corresponding maxima satisfy the approximate relations υmax ≅ 2Pmax and H¯max≅D¯max/2. On the basis of their Z-dependence, the maxima in H¯(v) and D¯(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms.