Existing magneto-optical data on shallow donors in InSb subjected to high magnetic fields and strong hydrostatic pressures are analysed theoretically using variational wavefunctions and taking into account the realistic energy band structure. The data are successfully described assuming that, in addition to a pressure variation of the effective mass, the static dielectric constant varies from 16.4 at zero pressure to 14.8 at 9 kbar. It is argued that the strong pressure dependence of the dielectric constant of InSb is due to the narrow-gap band structure of the material.
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