Accurate upper and lower bounds to the 2S states of the lithium atom

The first nonrelativistic lower bound to the ground state of the lithium atom is give with E0 > −7.47816 au using the method of variance minimization and an extension of Temple's formula. With large Hylleraas–CI basis sets, high-precision upper bounds and isotope shifts are calculated for the three lowest 2S states of the lithium atom, which are best to date. © 1994 John Wiley & Sons, Inc.

[1]  King Analysis of some integrals arising in the atomic three-electron problem. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[2]  L M Delves,et al.  On the Temple lower bound for eigenvalues , 1972 .

[3]  Bounds for energies of radial lithium , 1972 .

[4]  King,et al.  Calculation of some integrals for the atomic three-electron problem. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[5]  A. H. Wapstra,et al.  The 1983 atomic mass evaluation: (I). Atomic mass table , 1985 .

[6]  Bunge,et al.  Nonrelativistic energy of the Li ground state. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[7]  King Calculations on the 2S ground states of some members of the Li I isoelectronic series. , 1989, Physical review. A, General physics.

[8]  R. Hughes Isotope Shift in the First Spectrum of Atomic Lithium , 1955 .

[9]  J. Pipin,et al.  Accurate variational wavefunctions for some members of the lithium isoelectronic sequence , 1983 .

[10]  H. Kleindienst,et al.  Atomic integrals containing r 23λr 13μr 12ν with λ, μ, ν ≥ −2 , 1993 .

[11]  H. Kleindienst,et al.  Minimization of the Variance. A Method for Two-Sided Bounds for Eigenvalues of Selfadjoint Operators , 1991 .

[12]  H. Kleindienst,et al.  Variance minimization. A variational principle for accurate lower and upper bounds of the eigenvalues of a selfadjoint operator, bounded below , 1980 .

[13]  King,et al.  Calculations on the 2S ground state of the lithium atom. , 1986, Physical review. A, General physics.

[14]  L. Veseth Many-body calculations of atomic isotope shifts , 1985 .

[15]  King Calculations on the low-lying excited 2S states of some members of the Li isoelectronic series. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[17]  H. Kleindienst,et al.  Hylleraas–CI with linked correlation terms , 1993 .

[18]  S. Salomonson,et al.  Specific mass shifts in Li and K calculated using many-body perturbation theory , 1982 .

[19]  Y. K. Ho Improved Hylleraas calculations for ground state energies of lithium ISO–electronic sequence , 1981 .

[20]  K. Niemax,et al.  Level isotope shifts of 6,7Li , 1982 .

[21]  King,et al.  Calculations on the 2S ground state of the lithium atom. , 1986, Physical review. A, General physics.

[22]  H. Kleindienst,et al.  An efficient basis selection procedure for the reduction of the dimension in large Hylleraas-CI calculations , 1992 .

[23]  R. Neumann,et al.  Two-photon intracavity dye laser spectroscopy of the 4S and 3D term in6, 7Li , 1978 .

[24]  A. A. Frost The use of interparticle coordinates in electronic energy calculations for atoms and molecules , 1962 .

[25]  K. Niemax,et al.  Isotope shift of the 3s2S12 and 3p2PJ levels in 6,7Li , 1987 .

[26]  B. Lévy,et al.  Calculations of specific mass shifts in Li+(1s2) and Li(1s22s, 1s22p) , 1984 .

[27]  G. Temple The Theory of Rayleigh's Principle as Applied to Continuous Systems , 1928 .

[28]  Drake,et al.  Variational calculation for the ground state of lithium and the QED corrections for Li-like ions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[29]  Chung Ionization potential of the lithiumlike 1s22s states from lithium to neon. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[30]  W. Altmann,et al.  I. Lineare Fehlerminimisierung Ein Verfahren zur Eigenwertberechnung bei Schrödinger‐Operatoren , 1976 .

[31]  H. Kleindienst,et al.  The influence of linked correlation terms for the Li ground state , 1989 .

[32]  Bishop,et al.  Accurate variational calculations of energies of the 2 (2)S, 2 (2)P, and 3 (2)D states and the dipole, quadrupole, and dipole-quadrupole polarizabilities and hyperpolarizability of the lithium atom. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[33]  N. Lehmann Optimale Eigenwerteinschließungen , 1963 .

[34]  Sven Larsson,et al.  Calculations on the 2 S Ground State of the Lithium Atom Using Wave Functions of Hylleraas Type , 1968 .

[35]  H. Kleindienst,et al.  I. Linear error minimization. A method for eigenvalue calculation in Schroedinger operators. [Variational principle] , 1976 .

[36]  J. F. Perkins Atomic Integrals Containing r23λ r31μ r12v , 1968 .