He is a hydrogenic ion with nuclear charge and a single electron

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Atoms in electric fields

Problem

^+

is a hydrogenic ion with nuclear charge

Z=2

and a single electron. Hydrogen's ground-state polarisability closure bounds are

\frac{16}{3}a_0^3 \;(\text{upper, closure}), \qquad 2.96\,a_0^3 \;(\text{lower, }2p\text{ term alone}).

For a hydrogenic ion of charge

Z

, lengths scale as

a_0/Z

and energy gaps scale as

Z^2\,E_{\rm h}

, both relative to hydrogen (

Z=1

). Use this scaling to find the corresponding upper and lower bounds on the ground-state polarisability of He

^+

, in units of

a_0^3

(the ordinary, unscaled Bohr radius).

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