By James Avery and John Avery
This booklet describes the generalized Sturmian process, which deals a clean method of the calculation of atomic spectra. Generalized Sturmians are isoenergetic suggestions to an approximate many-electron SchrÃ¶dinger equation with a weighted strength. The weighting elements are selected in this kind of approach as to make all the options correspond to a given power. the good thing about such an isoenergetic foundation set is that each foundation functionality has the proper turning aspect habit wanted for effective synthesis of the wave functionality.
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Additional info for Generalized Sturmians and atomic spectra
3) The interelectron repulsion matrix is energy-independent. 26)). Because the effective nuclear charges that characterize the basis functions depend on pK, the basis set is not completely known before the secular equations have been solved. Only the form of the basis functions is known, but not their scale. Solving the secular equations gives us at one stroke a spectrum of energies, and a near-optimal set of basis functions for representing the corresponding states. The Slater-exponents that appear in the hydrogenlike orbitals of the Goscinskian configurations turn out to be almost exactly those that would have been found by a variational optimization of the basis.
4. -blocks for the He-like, Li-like, Be-like and B-like isoelectronic series. These have 1ZV values and dimensions given respectively by He-like : Li-like: ft„ Be-like : 1ZU B-hke: 8 Tlv = \j ^ = V2 = A 2 /_ + 8! (8- 0)! = 1 ) 1 3 _ = _ 0- 8! (8- 1)! 8! (8- 2)! 64) 28 3! (8-3)! 4. Similarly, the lowest 7£-blocks of the interelectron repulsion matrix for the N-like, O-like, 38 GENERALIZED STURMIANS AND ATOMIC SPECTRA F-like and Ne-like isoelectronic series are characterized respectively by — w£+£-¥ J -aorhr" — *-4 (S) = asnhir» F-like: 7t„ + *~*r 2 I2 7 22 Vl5 2 Ne-like: ft„ = \ / l42 + £22= 2 /8\ V7/ 8!
Islld lD expt. IsUd lD expt. 4: STURMIANS AND ATOMIC SPECTRA Doubly-excited (autoionizing) 3 S states of the 2-electron isoelectronic series with n = 2 and n ' = 3 , 4, 5. 1. C4+ expt. N 5+ expt. 0 6+ expt. F7+ expt. Ne8+ expt. Na 9 + expt. Mg 10 + expt. Al 1 1 + expt. Si12+ expt. pl3+ expt. S14+ expt. C115+ expt. Ar16+ expt. K17+ expt. Ca 18 + expt. Sc19+ expt. expt. 2= Z* 2 v 1 1 I 2n2 2n' 2 2n" 2 (or,) y ' In other words, if interelectron repulsion is totally neglected, the energy levels of an iV-electron atom correspond to those of a set of N entirely independent electrons moving in the attractive potential of a nucleus with charge Z.