  We consider the fractional Hartree model, with general power non-linearity
and space dimension. We construct variationally the "normalized" solutions for
the corresponding Choquard-Pekar model - in particular a number of key
properties, like smoothness and bell-shapedness are established. As a
consequence of the construction, we show that these solitons are spectrally
stable as solutions to the time-dependent Hartree model.
  In addition, we analyze the spectral stability of the Moroz-Van Schaftingen
solitons of the classical Hartree problem, in any dimensions and power
non-linearity. A full classification is obtained, the main conclusion of which
is that only and exactly the "normalized" solutions (which exist only in a
portion of the range) are spectrally stable.
