Donald R. Beck

The variational calculation of energies and widths of resonances

Abstract It is shown that the “difficulties” which Bransden recently associated with the variational calculation of resonance parameters are nonexistent, provided the norm of the Gamow functions is defined appropriately and consistently.

Approach to the calculation of the important many-body effects on photoabsorption oscillator strengths

Abstract By a combination of selection rules for dipole transitions and notions from variation-perturbation theory, we develop a first-order theory of oscillator strengths (FOTOS) whereby the important correlations for an accurate treatment of electric dipole processes in atoms and molecules can be easily understood, formally derived and calculated. FOTOS is applied here to certain one- and two-electron transitions in Li I, N I and N II. The calculation of the corresponding oscillator strengths present considerable theoretical problems. Our results resolve the existing discrepancy between lifetime experiments and previous many-body calculations.

On the length, velocity and acceleration expressions for the calculation of accurate oscillator strengths in many-electron systems

Abstract The problem of deciding which of three equivalent forms of electric dipole transition probabilities is the most “proper” or “accurate” to use, has been discussed in recent papers from various points of view. Here we examine this question and also certain conditions which have to be satisfied for the three forms to give the same results. Regarding the question of accuracy, we suggest that, on the whole, arguments based on the importance of regions of configuration space are still the most convincing, in spite of recent attempts to select only one form as the proper one. A number of many-body calculations are carried out for transitions in BI, CII, OI, OIV and SiX. For the CII, OIV 1s 2 2s 2 2p 2 p 0 → 1s 2 2s2p 2 2 D oscillator strengths, good agreement between all three expressions is obtained for the first time.

AB INITIO POTENTIALS AND PRESSURE SECOND VIRIAL COEFFICIENTS FOR CH4-H2O AND CH4-H2S

Ab initio Hartree–Fock (HF) and second‐order many‐body perturbation theory (E2) were used to generate data for pair potentials of the mixtures CH4–H2S and CH4–H2O. The points were fit with site–site functions consisting of terms for interactions of the following types: exponential repulsion and R−6 and electrostatic attraction. The basis sets of Gaussian functions were developed by systematically adding polarization functions to maximize the zeroth‐order dipole polarizability; the counterpoise method was used to correct basis set superposition error. The best well depths calculated for CH4–H2S and CH4–H2O were −0.0227 and −0.0215 eV, respectively (with no experimental results available for comparison). The potentials were evaluated by examining errors in the dipole polarizabilities and pressure second virial coefficients.

Lower bounds to static polarizabilities

Abstract We suggest that the oscillator strength formula for polarizabilities together with only a few accurate values for oscillator strenths can yield very good lower bounds for a number of ground and excited states. Better lower bounds are obtained for states in Li, Be and CIII for which the Weinhold formula has recently been applied by Sims and co-workers. Application to a number of states whose polarizabilities were recently calculated by very large Cl (Li, Mg, K, Ca) or measured experimentally (Na), has yielded lower bounds which fall above the results of the direct calculations and measurement.

A variational method for calculating the energies and widths of resonances

Abstract We present a variational method which employs complex wave-functions and yields both the energy and the width of resonances.

Obtaining accurate pressure second virial coefficients for methane from an ab initio pair potential

The pressure second virial coefficients, including fourth‐order many‐body effects, have been calculated for methane and are found to agree with the experiment on the average, to 2.8% over the temperature range 110–623 K using the basis set of Sadlej. This is a major improvement over the usual 30%–40% accuracy of ab initio potentials and also has been attained by us for H2O. Monte Carlo simulations have also been performed with the potential and a C–C radial distribution function and the internal energy is obtained. The latter (−0.0757 eV/molecule) is in good agreement with experiment (−0.0738 eV/molecule).

Electronic structure and oscillator strengths of highly excited states: Resonances in He−, Li, and Be

The calculation of energy levels and widths of certain highly excited states in atoms and molecules is an interesting theoretical problem. This is due primarily to peculiarities of their wavefunctions which result from the (near) degeneracies of such states with Rydberg and continuum series. In this paper we: (a) discuss certain aspects of this problem related to the computation of compact excited‐state wavefunctions. The BeI″1s22p2″ 1S and NI 1s22s2p4 4P states serve as examples; (b) present results of a variational treatment of the positions of the 2s22p and ″2p3″ 2P0 resonances in He−(57.3 eV, 60.5 eV) and Li (141.7 eV, 148.5 eV) and an estimate for the He−″2s2p3d″ 2P0 resonances {[(2s2p)  3P03d] 2P0: 61.9 eV, [(2s2p)  1P03d] 2P0: 63.1 eV}. The 2s22p 2P0 levels are in good agreement with recent experimental values (57.2 eV, ∼141.5 eV). A many‐body calculation of the Li 1s22s 2S→2P0 two and three electron excitation oscillator strengths yields f2s22p=0.00018, f2p 3=0.0007. These calculations were carrie...

High spin and mixed states in BI and BII

Abstract We present theoretical oscillator strengths and wavelengths for transitions between high spin states in BI and BII (e.g. BI 1s2s2p23s6P - 1s2s2p3 6S0), recently observed for the first time in Beam-Foil Spectroscopy, and between the ground state 2P0 and the 2S mixed (valence-Rydberg) excited states in BI.

On the theory of KLL auger energies

Abstract Accurate KL 1 L 1 Auger energies are calculated for atomic carbon and oxygen. They are: = 460.5 eV and = 243.6 eV. These values can serve as standards for the evaluation of experimental uncertainties present in various spectroscopic measurements. In this paper they have also served as standards for the appraisal of various one-particle approximations dealing with the calculation of Auger energies.