LINEAR PROGRAMMING AND CALCULATION OF UPPER AND LOWER BOUNDS OF ATOMIC MEAN EXCITATION ENERGIES

Linear programming is used to calculate upper and lower bounds to the mean excitation energies I of hydrogen, helium, neon, argon and krypton. Only the values of dipole oscillator strength sum rules are required. The bounds obtained for I are: H, 14·0 <or= I(eV) <or= 15·2; He, 41·1 <or= I(eV) <or= 43·5; Ne, 90 <or= I(eV) <or= 181; Ar, 64 <or= I(eV) <or= 295; Kr, 88 <or= I(eV) <or= 476. These bounds are rigorous in that they are the greatest upper and least lower bounds consistent with the presently available values of the sum rules.