Electrons on a sphere in disorder potential

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We investigate, both analytically and numerically, the behavior of the electron gas on a sphere in the presence of point-like impurities. We find a criterion when the disorder can be regarded as small one and the main effect is the broadening of rotational multiplets. In the latter regime the statistics of one impurity-induced band is studied numerically. The energy level spacing distribution function follows the law P(s) s exp(-a sᵇ) with 1<b<2. The number variance shows various possibilities, strongly dependent on the chosen model of disorder.