On the concept of “Partitions” in the perturbation theory of n-electron systems

✍ Scribed by H. M. Schmidt

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 1019 KB
• Volume: 24
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560240604

✦ Synopsis

Abstract

This paper deals with the perturbation theory of an n‐electron Hamiltonian of the general form H = ∑^n^ ƒ(i) + λ∑^n^ g(i, j) = H (f, g; n). In comparison to the Brueckner–Goldstone diagrammatic perturbation theory, we adopt the more general standpoint of admitting, for the construction of an n‐particle state, component states of 1, 2, 3, and more particles [O. Sinanoglu, Phys. Rev. 122, 493 (1961) and C. D. H. Chisholm and A. Dalgarno, Proc. R. Soc. (London) Sec. A 292, 264 (1966)]. We show that this leads to the concept of a “partition” of a perturbational eigenstate (or energy) of H. A “partition” is a natural decomposition which: (i) is finite; (ii) relates the eigenvalue problem of the system H = H (f, g; n) to those of certain subsystems H (f, g; n~1~)(n~1~ < n); (iii) uses “nonseparable” components. We domonstrate (under the preliminary assumption of “strict” nondegeneracy) the second‐order energy to possess a “partition.” The components therein are second‐order energies of two‐ and three‐particle states. The proof uses an extension of Racah's concept of the fractional‐parentage expansion.