  Angular resolved photoelectron spectra of metal clusters have been
experimentally measured for the first time only recently. These measurements
have been performed systematically for sodium clusters in a broad range of
cluster sizes. This work attracted a lot of attention and was reported
practically at all major international cluster conferences because it revealed
a very non-trivial behavior of the angular anisotropy parameter with respect to
photon energy and provided a method for probing the angular momentum character
of the valence orbitals of free nanoclusters. Initial attempts to explain these
observations within single particle approximations fail completely. In this
Letter we present a consistent many-body theory for the description of angular
resolved photoelectron spectra of metal clusters. Jellium model formalism is
employed. Our calculations demonstrate the dominant role of the many-body
effects in the formation of angular distributions of photoelectrons emitted
from sodium clusters and are in a good agreement with experimental data
reported in. The concrete comparison of theory and experiment has been
performed for the photoionization of $Na_7^{-}$ and $Na_{19}^{-}$ anions being
characterized by the entirely closed shells of delocalized electrons.
