  Galactic interacting double white dwarfs (DWD) are guaranteed gravitational
wave (GW) sources for the GW detector LISA, with more than 10^4 binaries
expected to be detected over the mission's lifetime. Part of this population is
expected to be eccentric, and here we investigate the potential for
constraining the white dwarf (WD) properties through apsidal precession in
these binaries. We analyze the tidal, rotational, and general relativistic
contributions to apsidal precession by using detailed He WD models, where the
evolution of the star's interior is followed throughout the cooling phase. In
agreement with previous studies of zero-temperature WDs, we find that apsidal
precession in eccentric DWDs can lead to a detectable shift in the emitted GW
signal when binaries with cool (old) components are considered. This shift
increases significantly for hot (young) WDs. We find that apsidal motion in hot
(cool) DWDs is dominated by tides at orbital frequencies above ~10^{-4}Hz
(10^{- 3}$Hz). The analysis of apsidal precession in these sources while
ignoring the tidal component would lead to an extreme bias in the mass
determination, and could lead us to misidentify WDs as neutron stars or black
holes. We use the detailed WD models to show that for older, cold WDs, there is
a unique relationship that ties the radius and apsidal precession constant to
the WD masses, therefore allowing tides to be used as a tool to constrain the
source masses.
