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The n-th state of atomic hydrogen is 2n2 times degenerate X0
                    . ,0       where n is the principal
and has an energy Xn =0    n 
                           n
quantum number and X0 is the ground state energy level. On this basis, the partition function may be written explicitly as

             n c      (1 - 1X0/kT
        uH =  I 2n2 en-                          (5.3)
            n=l

where nc is the principal quantum number of the last bound state. Defining a reduced energy variable a t X0/kT, (5.3) is simplified as



        u  = 2e - n  n2 e /n                     (5.4)
                 n=l


For a sufficiently large quantum number, nL, the energy levels approach a continuum. For n > nL the integral approximation of Ivanov-Kholodnyi et a". (48) can be applied to the partition function. Replacing the nearcontinuum portion of (5.4) by an integral,



        UH = 2e -a FL ne e/n2 +  c n2e a/n2d     (5.5)
        F orn


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