  The bulk Fermi surface in an overdoped ($x = 0.3$) single crystal of
La$_{2-x}$Sr$_{x}$CuO$_{4}$ has been observed by using x-ray Compton
scattering. This momentum density technique also provides a powerful tool for
directly seeing what the dopant Sr atoms are doing to the electronic structure
of La$_2$CuO$_{4}$. Because of wave function effects, positron annihilation
spectroscopy does not yield a strong signature of the Fermi surface in extended
momentum space, but it can be used to explore the role of oxygen defects in the
reservoir layers for promoting high temperature superconductivity.
