Rydberg Atom - Hydrogenic Potential

Hydrogenic Potential

An atom in a Rydberg state has a valence electron in a large orbit far from the ion core; in such an orbit the outermost electron feels an almost hydrogenic, Coulomb potential, U_C from a compact ion core consisting of a nucleus with Z protons and the lower electron shells filled with Z-1 electrons. An electron in the spherically symmetric Coulomb potential has potential energy:

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The similarity of the effective potential ‘seen’ by the outer electron to the hydrogen potential is a defining characteristic of Rydberg states and explains why the electron wavefunctions approximate to classical orbits in the limit of the correspondence principle. In other words, the electron's orbit resembles the orbit of planets inside a solar system, much like the obsolete but visually useful Bohr and Rutherford models of the atom used to show.

There are three notable exceptions that can be characterized by the additional term added to the potential energy:

• An atom may have two (or more) electrons in highly excited states with comparable orbital radii. In this case the electron-electron interaction gives rise to a significant deviation from the hydrogen potential. For an atom in a multiple Rydberg state, the additional term, U_ee, includes a summation of each pair of highly excited electrons:

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• If the valence electron has very low angular momentum (interpreted classically as an extremely eccentric elliptical orbit) then it may pass close enough to polarise the ion core, giving rise to a 1/r4 core polarization term in the potential. The interaction between an induced dipole and the charge that produces it is always attractive so this contribution is always negative,

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where α_d is the dipole polarizability. Figure 2 shows how the polarization term modifies the potential close to the nucleus.

• If the outer electron penetrates the inner electron shells, it will 'see' more of the charge of the nucleus and hence experience a greater force. In general the modification to the potential energy is not simple to calculate and must be based on knowledge of the geometry of the ion core.