  Monolayer graphene is an example of materials with multi-valley electronic
structure. In such materials, the valley index is being considered as an
information carrier. Consequently, relaxation mechanisms leading to loss of
valley information are of interest. Here, we calculate the rate of valley
relaxation induced by charged impurities in graphene. A special model of
graphene is applied, where the $p_z$ orbitals are two-dimensional Gaussian
functions, with a spatial extension characterised by an effective Bohr radius
$a_\textrm{eB}$. We obtain the valley relaxation rate by solving the Boltzmann
equation, for the case of noninteracting electrons, as well as for the case
when the impurity potential is screened due to electron-electron interaction.
For the latter case, we take into account local-field effects and evaluate the
dielectric matrix in the random phase approximation. Our main findings: (i) The
valley relaxation rate is proportional to the electronic density of states at
the Fermi energy. (ii) Charged impurities located in the close vicinity of the
graphene plane, at distance $d \lesssim 0.3\,\textrm{\AA}$, are much more
efficient in inducing valley relaxation than those farther away, the effect of
the latter being suppressed exponentially with increasing graphene-impurity
distance $d$. (iii) Both in the absence and in the presence of
electron-electron interaction, the valley relaxation rate shows pronounced
dependence on the effective Bohr radius $a_\textrm{eB}$. The trends are
different in the two cases: in the absence (presence) of screening, the valley
relaxation rate decreases (increases) for increasing effective Bohr radius.
This last result highlights that a quantitative calculation of the valley
relaxation rate should incorporate electron-electron interactions as well as an
accurate knowledge of the electronic wave functions on the atomic length scale.
