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                              2
                    E   =f                          (4.41)
                       n    2h2n2

where I is the reduced mass, Z the nuclear charge, e the electrostatic electron charge, h the reduced Planck's constant, and n the principal quantum number. For the multi-electron atoms and ions in the uranium plasma, the energy levels and principal quantum numbers are not explicitly related by expressions such as (4.41). However, it can be argued that a highly excited electron in a multi-electron atom is nearly hydrogenic, since the atom can be regarded as a nucleus having an electron moving about it in a large orbit. Based on this reasoning, Drellishak et aZ. (46) have empirically treated the lowering of the ionization potential by assuming that the amount of potential lowering should vary inversely with the square of the cut-off quantum number, according to

                            E.
                    AE  =    1                      (4.42)
                          n 2(i)
                          c

where the symbols are defined as before. This relation will be used in the following section to obtain initial estimates of the cut-off quantum numbers of uranium atoms and ions.