  Although a generic uniformly distributed sequence has Poissonian pair
correlations, only one explicit example has been found up to now. Additionally,
it is even known that many classes of uniformly distributed sequences, like van
der Corput sequences, Kronecker sequences and LS sequences, do not have
Poissonian pair correlations. In this paper, we show that van der Corput
sequences and the Kronecker sequence for the golden mean are as close to having
Poissonian pair correlations as possible: they both have $\alpha$-pair
correlations for all $0 < \alpha < 1$ but not for $\alpha = 1$ which
corresponds to Poissonian pair correlations.
