The two-nucleon potential, with the necessary invariance requirements, is assumed to be a quadratic function of momentum: v= -VoJi(r) -(\/M) p-^Wp, where Ji(r) and J%(r) are two short-range functions. For simplicity -Ji{r) is assumed to be a square well of unit depth. The Schrodinger equation is solved (neglecting Coulomb forces) for three different choices of Ji (r). Numerical results for the phase shifts are given for these three potentials (vi, v 2 , and v$) for the singlet S, D, and G states. Reasonably good fits are obtained.

Ce is one of the few lanthanide elements to exhibit well-defined (III) and (IV) oxidation states in solid-state environments, and there is therefore ambiguity as to whether CeVO 4 should be formulated as Ce(III)V(V)O 4 or Ce(IV)V(IV)O 4 . To address this question, CeVO 4 and Ce 0.5 Bi 0.5 VO 4 have been studied by density functional theory calculations and X-ray photoemission spectroscopy. A peak above the main O 2p valence band in photoemission is attributed to localized Ce 4f states, in agreement with the calculations which show occupation of Ce 4f states. The Ce 3d core level spectrum is diagnostic of Ce(III) with no sign of a peak associated with 4f 0 final states that are characteristic of Ce(IV) compounds. The experimental and theoretical results thus confirm that both compounds contain Ce(III) and V(V), rather than Ce(IV) and V(IV). In agreement with experiment, the calculations also show that the tetragonal zircon phase adopted by CeVO 4 is more stable for Ce 0.5 Bi 0.5 VO 4 than the monoclinic clinobisvanite phase adopted by BiVO 4 , so that the formation of the stereochemically active Bi(III) lone pairs is suppressed by Ce doping.

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