  The spectroscopic properties of the doubly heavy spin-$1/2$ baryons
$\Xi_{QQ'}$, $\Xi'_{QQ'}$, $\Omega_{QQ'}$ and $\Omega'_{QQ'}$, with heavy
quarks $Q$ and $Q'$ being $b$ or/and $c$, are investigated in cold nuclear
matter. In particular, the behavior of the mass of these particles with respect
to the density of the medium in the range $\rho\in [0,1.4] ~\rho_{sat}$, with
$\rho_{sat}=0.11^3 ~GeV^3$ being the saturation density of nuclear matter, is
investigated. From the shifts in the mass and vector self energy of the states
under consideration, it is obtained that $\Xi_{QQ'}$ and $\Xi'_{QQ'}$ baryons
with two heavy quarks and one $u$ or $d$ quark are affected by the medium,
considerably. It is also seen that the $\Omega_{QQ'}$ and $\Omega'_{QQ'}$
states, containing two heavy quarks and one $s$ quark do not see the dense
medium, at all. The value of mass for the $\Xi_{cc}$ state obtained at
$\rho\rightarrow 0$ limit is nicely consistent with the experimental data. Our
results on parameters of other members can be useful in the search for these
states. The obtained results may also shed light on the future in-medium
experiments aiming to search for the behavior of the doubly heavy baryons under
extreme conditions.
