  We develop a method to compute shakeup effects on photoluminescence from a
strong magnetic field induced two-dimensional Wigner crystal. Only localized
holes are considered. Our method treats the lattice electrons and the tunneling
electron on an equal footing, and uses a quantum-mechanical calculation of the
collective modes that does not depend in any way on a harmonic approximation.
We find that shakeup produces a series of sidebands that may be identified with
maxima in the collective mode density of states, and definitively distinguishes
the crystal state from a liquid state in the absence of electron-hole
interaction. In the presence of electron-hole interaction, sidebands also
appear in the liquid state coming from short-range density fluctuations around
the hole. However, the sidebands in the liquid state and the crystal state have
different qualitative behaviors. We also find a shift in the main luminescence
peak, that is associated with lattice relaxation in the vicinity of a vacancy.
The relationship of the shakeup spectrum with previous mean-field calculations
is discussed.
