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We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts$(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t -\tau_t$ belongs to a certain Schatten-von Neumann class $\gS_p$ with $p\ge 1$.We show that, for the unitary component in the Wold-Kolmogorov decomposition ofthe cogenerator of the semigroup $(\tilde\tau_t)_{t\ge 0}$, {\it any singular}spectral type may be achieved by $\gS_1$ perturbations. We provide an explicitconstruction for a perturbation with a given spectral type based on the theoryof model spaces of the Hardy space $H^2$. Also we show that we may obtain {\itany} prescribed spectral type for the unitary component of the perturbedsemigroup by a perturbation from the class $\gS_p$ with $p>1$.

On perturbations of the isometric semigroup of shifts on the semiaxis