Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrödinger equation (n = 3, 4) is solved. A new family of variable separation solutions with arbitrary functions is derived.

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This paper estimates the orbital shielding of metallic nuclei. The model is that of a nucleus at the centre of a single spherically symmetric potential, immersed in an otherwise free electron gas. The analytic result for the shielding constant has a rather simple form. An approximation leads to a simple relation between the orbital shielding constant and the orbital susceptibility ; however. exact calculations for several metals of the paramagnetic van Vleck contribution using a muffin-tin potential proved easy.The results indicate that in indium, at least, the orbital contributions are not small.

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