A solution energy term (Eimp) must be considered to explain the surface core-level shift (SCS) of photoemission spectroscopy (PES) ((PES)) for the occupied core-level of a Z-atom metal and the SCS of inverse photoemission spectroscopy (IPES) ((IPES)) for the unoccupied core-level of a (Z+1)-atom metal. In addition, the Coulomb interaction of surface atoms (US ff ) of Eu metal must be different from that of bulk atoms (UB ff ) of Eu metal to explain consistently the (PES) of Eu metal and the (IPES) of Gd metal.