An ergodic automorphism T with singular spectrum of $ T⊗ n$ and Lebesgue one of $ T⊗ (n+1)$

For any natural n, and real α≥ 0 we construct an ergodic automorphism T such that its tensor powers T⊗ n have singular spectra if n≤ 1+α /2, and Lebesgue if n\, > 1+α/2.