Electron correlation effects in some S and P states of helium and lithium
In Section (I), the origins and nature of the correlation problem are discussed, and two approaches to its solution are outlined. Some of the methods by which correlation effects in the ground state of helium have been analysed in the past are briefly reviewed. In Section (II.1), position-space correlation effects in the 21S, 23S, 21P and 23P states of helium are studied. The investigation is performed by examining the effects of correlation on various radial, angular and interparticle distribution functions and expectation values; where possible, comparisons are made with the ground state. For each of the four excited states studied, it was found that correlation causes a significant inward movement of electron density from the outer regions of the atom, due to a reduction in nuclear shielding. In the light of the results obtained in position space, a3 parallel momentum-space investigation of the 23S, 21P and 23P states was performed, and the results are presented in Section (II.2). Differences between the interparticle correlation properties of the three states were rationalised by considering the varying interactions between the radial and angular components of correlation in each instance. For 23S and 21P, as for the ground state, radial and angular correlation have opposing effects on the interparticle momentum distributions; for 23P, on the other hand, the two effects act together. In Section (III), a partitioning technique used previously to examine correlation effects in individual electron pairs within many-electron atoms is applied to a momentum-space study of the (1s2 2s)2S and (1s2 2p)2P states of lithium. For both states, the effects of correlation observed in the K-shell electron pairs show a strong resemblance to those found in Li+. As for the excited states of helium, the rationalisation of the behaviour of, and differences between, the interparticle correlation properties of the intershell electron pairs was achieved by considering the varying interactions between the radial and angular components of correlation in each instance.