Average Low and High Momenta in Singly-Excited 1snl States of the He Atom

Abstract

Average low and high > momenta are examined for 28 singly-excited 1snl singlet and triplet states (0 ≤ l decreases with increasing n and decreasing l, while the high momentum > is nearly equal to 16/(3π)≅1.698, independent of n and l. Comparing the low and high > momenta with the average electron momentum of a hydrogenlike atom, we show that an electron with a lower momentum behaves like an nl electron of the hydrogen atom and another electron with a higher momentum behaves like the 1s electron of the helium cation. A decomposition of an uncertainty product finds that the largest contribution to comes from an outer electron and a high momentum electron, where and are the usual average electron radius and momentum, respectively.