  X-ray absorption and resonant inelastic x-ray scattering measurements are
carried out on lithium nitrate LiNO$_3$. The $\sigma$ orbitals around the
nitrogen atoms exhibit a large lifetime effect. Experimentally, this is
manifest as an apparent weakening of the x-ray emission signal from these
states, but a closer examination shows that instead it is due to extreme
broadening. This echos previous studies on ammonium nitrate, which, despite
large differences in the cation and space group, showed a similar effect
associated with the nitrate. Using first-principles $GW$ self-energy and
Bethe-Salpeter equation calculations we show that this effect is due in part to
short quasi-hole lifetimes for the orbitals constituting the NO $\sigma$ bonds.
