Eigenvalues and expectation values for the 1s22s2S, 1

Abstract

High-precisipn varlatipnal eigenvalues fpr the 1& 2s S, 1+ 2p P, and 1z 3d D states pf hthium are calculated using multiple basis sets in Hylleraas coordinates. Convergence to a few parts in 10' -10" is achieved. The nonrelativistic energies for infinite nuclear mass are -7.478060323 10(31) a.u. for the ls 2s S state, -7.410156 521 8(13) a.u. for the ls 2p P state, and -7.335 523 541 10(43) a.u. for the 1s 3d D state. The corresponding specific isotope shifts due to mass polarization are also calculated with similar accuracy. The 1s 2s S -1s 2p P and 1s 2p P -1s 3d D transition energies for Li and Li, as well as the isotope shifts, are calculated and compared with experiment. The results yield an improved ionization potential for lithium of 43487.167(4) cm '. Expectation values of powers of r; and r; and the delta functions 8(r;) and 6(r;,) are evaluated.PACS number(s): 31.15.Ar, 31.50.+w

Lower Rydberg2Dstates of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions

“…,7, configurations, they also contain small contributions from other configurations, in particular the 1s 1 2p 2 configuration. To effectively describe all these contributions with ECGs the following functions need be included in the basis set [3]: (2) where electron labels i k and j k are either equal or not equal to each other and they can vary from 1 to n. A k in (2) is an n × n symmetric matrix, ⊗ is the Kronecker product, I 3 is a 3 × 3 identity matrix, and r is a 3n vector that has the form…”

“…, 12. A literature search reveals that only the lowest state of this series has been calculated with high accuracy using the variational method by Yan and Drake [2]. Their energy obtained using the infinite-nuclear-mass approach was −7.335 523 541 10(43) a.u.…”

Electron affinity of Li7 calculated with the inclusion of nuclear motion and relativistic corrections

“…[3][4][5][6][7] The most accurate atomic calculations for systems with two and three electrons have been done with Slater-type or Hylleraas-type explicitly correlated functions. 2,[8][9][10][11] Those calculations demonstrated that by accurately accounting for the electron correlation effects and by including the leading relativistic and QED corrections, the accuracy of the results of the calculations matches the accuracy of the state-of-theart high-resolution experiment. The Slater-type and Hylleraas-type functions are more effective than ECGFs in describing the cusp behavior of the wave function, but their implementation to systems with more than three electrons has not been achieved due to technical difficulties related to calculating the matrix elements.…”

Singular Hylleraas three-electron integrals

“…The calculation of the nonrelativistic energy involves integrals with nonnegative n i . Such integrals have been worked out by King et al in the series of works [4], and more recently by Yan and Drake [1,5], Sims and Hegstrom [6], and by us in Ref. [7].…”

“…This wave function ψ is next used to obtain relativistic and quantum electrodynamics (QED) effects including finite nuclear mass corrections. The most accurate representation of the threeelectron wave function ψ achieved so far [1,2] uses the Hylleraas basis set [3], namely ψ = i c i φ i φ = e −w 1 r 1 −w 2 r 2 −w 3 r 3 r n 1 23 r n 2 31 r n 3 12 r n 4 1 r n 5 2 r n 6 3 ,…”