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Progress in particle and nuclear physics

A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X12Π3/2 states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core−valence correlation, relativistic effects (scalar and spin−orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 A and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 A, presumably due to an underestimation of molecular spin−orbit coupling effects. Spectroscopic constants for the spin−orbit excited X22Π1/2 states are also reported for each species. The predicted...

http://tyr0.chem.wsu.edu/~kipeters/Pages/pdfs/JPC110.13877.2006.pdf

On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions.

Volume II J. S. R. Chisholm and Rosa M. Morris Amsterdam: North-Holland. 1964 Pp. xviii + 717. Price 72s. This book is a valuable addition to an ever-growing collection of mathematical texts written expressly for the physicist. The authors suggest that the book might also be useful to undergraduates in chemistry and engineering and research workers in other fields, but the content is clearly chosen to meet the needs of modern undergraduate physics.

http://iopscience.iop.org/article/10.1088/0031-9112/16/8/015/pdf

Mathematical Methods in Physics

The theoretical description of the nonlinear photoionization of atoms and ions exposed to high-intensity laser radiation is underlain by the Keldysh theory proposed in 1964. The paper reviews this theory and its further development. The discussion is concerned with the energy and angular photoelectron distributions for the cases of linearly, circularly, and elliptically polarized laser radiation, with the ionization rate of atomic states exposed to a monochromatic electromagnetic wave and to ultrashort laser pulses of various shape, and with momentum and angular photoelectron spectra in these cases. The limiting cases of tunnel (γ 1) and multiphoton (γ 1) ionization are discussed, where c is the adiabaticity parameter, or the Keldysh parameter. The probability of above-barrier ionization is calculated for hydrogen atoms in a low-frequency laser field. The effect of a strong magnetic field on the ionization probability is discussed. The process of Lorentz ionization occurring in the motion of atoms and ions in a constant magnetic field is considered. The properties of an exactly solvable model—the ionization of an s-level bound by zero-range forces in the field of a circularly polarized electromagnetic wave—are described. In connection with this example, the Zel'dovich regularization method in the theory of quasistationary states is discussed. Results of the Keldysh theory are compared with experiment. A brief discussion is made of the relativistic ionization theory applicable when the binding energy of the atomic level is comparable with the electron rest mass (multiply charged ions) and the sub-barrier electron motion can no longer be considered to be nonrelativistic. A similar process of electron-positron pair production from a vacuum by the field of high-power optical or X-ray lasers (the Schwinger effect) is considered. The calculations invoke the method of imaginary time, which provides a convenient and physically clear way of calculating the probability of particle tunneling through time-varying barriers. Discussed in the Appendices are the properties of the asymptotic coefficients of the atomic wave function, the expansions for the Keldysh function, and the so-called 'ADK theory'.

http://iopscience.iop.org/article/10.1070/PU2004v047n09ABEH001812/pdf

Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory)

The divergent Rayleigh-Schrodinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pade approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree. Different branches of the approximants converge to different branches of the function. The success of the high-degree approximants is attributed to their ability to model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter. An efficient recursive algorithm for computing the diagonal approximant sequence is presented.

Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators

Extrapolation methods that accelerate the convergence of coupled-cluster energy sequences toward the full configuration–interaction (FCI) limit are developed and demonstrated for a variety of atoms and small molecules for which FCI energies are available, and the results are compared with those from Moller–Plesset (MP) perturbation theory. For the coupled-cluster sequence SCF, CCSD, CCSD(T), a method based on a continued-fraction formalism is found to be particularly successful. It yields sufficient improvement over conventional CCSD(T) that the results become competitive with, and often better than, results from the MP4-qλ method (MP4 summed with quadratic approximants and λ transformation). The sequence SCF, CCSD, CCSDT can be extrapolated with a quadratic approximant but the results are not appreciably more accurate than those from the CCSD(T) continued fraction. Singularity analysis of the MP perturbation series provides a criterion for estimating the accuracy the CCSD(T) continued fraction.

Extrapolating the coupled-cluster sequence toward the full configuration-interaction limit

An asymptotic expansion for the electronic energy of H 2 + is developed in inverse powers of D, the spatial dimension, and the singularity structure in the D → ∞ limit is elucidated by analysis of the coefficients at large order (∼30 to 45). For the ground state and several excited states, Pade-Borel summation yields on accuracy of eight or more significant figures

Large-order dimensional perturbation theory for H2+

An asymptotic expansion for the electronic energy of two‐electron atoms is developed in powers of δ=1/D, the reciprocal of the Cartesian dimensionality of space. The expansion coefficients are calculated to high order (∼20 to 30) by an efficient recursive procedure. Analysis of the coefficients elucidates the singularity structure in the D→∞ limit, which exhibits aspects of both an essential singularity and a square‐root branch point. Pade–Borel summation incorporating results of the singularity analysis yields highly accurate energies; the quality improves substantially with increase in either D or the nuclear charge Z. For He, we obtain 9 significant figures for the ground state and 11 for the 2p2 3Pe doubly excited state, which is isomorphic with the ground state at D=5 by virtue of interdimensional degeneracy. The maximum accuracy obtainable appears to be limited only by accumulation of roundoff error in the expansion coefficients. The method invites application to systems with many electrons or subje...

Large‐order dimensional perturbation theory for two‐electron atoms

The 1/D expansion, where D is the dimensionality of space, offers a promising new approach for obtaining highly accurate solutions to the Schrodinger equation for atoms and molecules. The method typically employs an asymptotic expansion calculated to rather large order. Computation of the expansion coefficients has been feasible for very small systems, but extending the existing computational techniques to systems with more than three degrees of freedom has proved difficult. We present a new algorithm that greatly facilitates this computation. It yields exact values for expansion coefficients, with less roundoff error than the best alternative method. Our algorithm is formulated completely in terms of tensor arithmetic, which makes it easier to extend to systems with more than three degrees of freedom and to excited states, simplifies the development of computer codes, simplifies memory management, and makes it well suited for implementation on parallel computer architectures. We formulate the algorithm f...

David Z. Goodson

Papers

Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators

Extrapolating the coupled-cluster sequence toward the full configuration-interaction limit

Large-order dimensional perturbation theory for H2+

Large‐order dimensional perturbation theory for two‐electron atoms

A linear algebraic method for exact computation of the coefficients of the 1/D expansion of the Schrödinger equation