A useful way to characterize the hole-energy spectrum excited in a direct particle-removal reaction like ($p,2p$) or ($e,e^{\prime }p$) is through the centroid or mean removal energy. We derive the rules for computing this quantity in a linked-cluster expansion, and give some examples. We demonstrate the close relation of the mean removal energy to Brandow's self-consistent orbital energy, and discuss briefly the connection with Green's function theory.

[NUCLEAR STRUCTURE Linked-cluster theory of mean or centroid removal energies measured in ($p,2p$) or ($e,e^{\prime }p$); applications and relation to other hole energies.]

• Received 4 September 1973

DOI:https://doi.org/10.1103/PhysRevC.9.484