Starting from a first principle many-body theory, we derive a general formula to describe overall features in core-level photoemission including plasmon losses and peak asymmetry due to X-ray singularity. In the high-energy region we can derive quantum Landau formula which is directly compared with the corresponding classical theory where electron propagation in solids is classically described. In this quantum Landau formula elastic scatterings before and after the loss is completely taken into account. The total photoemission intensity is factorized as (elastic part)×(inelastc part): For the latter we have a quantum Landau formula. Explicit numerical calculations are also shown for rather high energy region, 7-10 KeV from Al 2p level. Although the interference term should drop out as a function of photoelectron energy, we find that the rate is very slow. [DOI: 10.1380/ejssnt.2008.263]