  We present an incisive spectroscopic technique for directly probing redox
orbitals based on bulk electron momentum density measurements via
high-resolution x-ray Compton scattering. Application of our method to spinel
LixMn2O4, a lithium ion battery cathode material, is discussed. The orbital
involved in the lithium insertion and extraction process is shown to mainly be
the oxygen 2p orbital. Moreover, the manganese 3d states are shown to
experience spatial delocalization involving 0.16 electrons per Mn site during
the battery operation. Our analysis provides a clear understanding of the
fundamental redox process involved in the working of a lithium ion battery.
