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On the dipole polarizability of a hydrogen-like atom confined in an impenetrable spherical box

First-order 1s and 2p wavefunctions of a hydrogen-like atom, confined at the centre of a spherical ‘box’ with impenetrable walls, are derived and used to predict the large-box asymptotic forms of the 1s–2p oscillator strength and the ground-state static dipole polarizabilty. It is found that the deviations from the unconfined values behave as e−ZR in the case of the oscillator strength and as e−2ZR in the case of the dipole polarizability, where R is the box radius. For smaller boxes, Rayleigh–Schrödinger perturbation theory is employed to calculate dipole polarizabilities.