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

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Average low < p< > and high < p> > momenta are examined for 28 singly-excited 1snl singlet and triplet states (0 ≤ l < n ≤ 5) of the He atom. The low momentum < p< > decreases with increasing n and decreasing l, while the high momentum < p> > is nearly equal to 16/(3π)≅1.698, independent of n and l. Comparing the low < p< > and high < p> > 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 < r >< p > finds that the largest contribution to < r >< p > comes from an outer electron and a high momentum electron, where < r > and < p > are the usual average electron radius and momentum, respectively.

Affiliations: 1: Department of Applied Chemistry, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan


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