  A recombination emission spectrum is applied to study the local lattice
distortion due to core excitation in graphite. The recombination emission
spectrum reveals a long low-energy tail when the C $1s$ electron is excited to
the $\sigma^*$ core exciton state. This indicates a large local lattice
distortion around the excited carbon atom within a core hole lifetime
($\sim$10fs). Theoretical calculation based upon an ionic cluster model well
reproduces the experiments. The strong polarization correlation between
incident and emitted X-rays is conclusive evidence of symmetry breaking in the
core exciton state due to coupling with asymmetric vibrational modes.
