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Abstract

This paper considers two types of 2 × 2, 3 × 3, and 4 × 4 determinantal inequalities. The elements of one type are 〈rn〉, while the elements of the other type are crn〉;, where c = 3 + n. The 2 × 2, 3 × 3, and 4 × 4 determinantal inequalities involve n = −1, 0, 1, n = −1, 0, 2, 3, 4, and n = −1, 0, 1, 2, 3, 4, 5. The two types of 2 × 2, 3 × 3, and 4 × 4 inequalities are used to obtain lower bound estimates of 〈r〉, 〈r3〉, and 〈r5〉 for the noble gas atoms He, Ne, Ar, Kr, and Xe. The values of these quantities obtained from the inequalities are compared with the quantum mechanical values of Boyd, who calculated them with the near Hartree–Fock analytical wave functions of Clementi and Roetti. © 1993 John Wiley & Sons, Inc.