Compact expressions for spherically averaged position and momentum densities

Compact expressions for spherically averaged position and momentum density integrals are given in terms of spherical Bessel functions (j_n) and modified spherical Bessel functions (i_n), respectively. All integrals required for ab initio calculations involving s, p, d, and f -type Gaussian functions are tabulated, highlighting a neat isomorphism between position and momentum space formulae. Spherically averaged position and momentum densities are calculated for a set of molecules comprising the ten-electron isoelectronic series (Ne- CH₄) and the eighteen-electron series (Ar- SiH ₄, F₂ - C₂ H₆).