Showing papers in "Physica Scripta in 1980"
TL;DR: In this paper, a density matrix formulation of the super-C I and Newton-Raphson methods in complete active space SCF (CASSCF) calculations is presented.
Abstract: A density matrix formulation is presented of the super-C I and Newton-Raphson methods in complete active space SCF (CASSCF) calculations. The CASSCF method is a special form of the MC-SCF method, where the C I wave function is assumed to be complete in a subset of the orbital space (the active space), leaving the remaining orbitals doubly occupied in all configurations. Explicit formulas are given for all matrix elements in the super-C I method and the first and second derivatives in the Newton-Raphson formulation. The similarities between the two methods are pointed out and the differences in the detailed formulations are discussed. Especially interesting is the fact, that while the second derivatives can be expressed in terms of first and second order density matrices, the matrix elements between the super-C I states involve also the third order density matrix in some cases.
560 citations
TL;DR: A series of molecular applications of many-body perturbation theory (MBPT) and the coupled-cluster doubles (CCD) model are described in this paper, including correlation energies, including contributions from single, double, and quadruple excitations diagrams in fourth-and higher-order; dissociation energies; potential energy surfaces; and molecular polarizabilities and hyperpolarizabilities.
Abstract: A series of molecular applications of many-body perturbation theory (MBPT) and the coupled-cluster doubles (CCD) model are described. Even though these methods have been available for sometime, only recently have large scale, MBPT molecular calculations become available. In the case of CCD, the results presented here are among the first obtained from a general purpose ab initio program. The intention of this paper is to present an overview of the current state of the many-body approach to ground state properties of molecules. The properties studied are correlation energies, including contributions from single, double, and quadruple excitations diagrams in fourth-and higher-order; dissociation energies; potential energy surfaces; and molecular polarizabilities and hyperpolarizabilities. Examples are taken from studies of a variety of molecules including HF, H2O, HCO, C6H6, B2H6, CO2, and N2. In many cases, it is found that quantitatively accurate dissociation energies, geometries, and force constants can be obtained. In an illustration of the X1Σg+ potential energy curve of N2, it is shown that a single UHF or RHF reference function MBPT/CCD approach is inadequate at some internuclear separation.
322 citations
TL;DR: In this article, the authors analyse the effect of the alignment of individual particles in the deformed potential on the rotational band structure of real bosons and compare with the coupling scheme based on the alignment.
Abstract: The interacting boson model is first analysed at the level of real bosons with a view to establishing the conditions for the occurrence of rotational band structure. The conditions on the effective interactions are much less restrictive than those required for the occurrence of SU (3) symmetry. The wave functions for the aligned bosons are analysed from the microscopic point of view in order to compare with the coupling scheme based on the alignment of individual particles in the deformed potential. In general, these two coupling schemes, both of which yield rotational band structure, lead to major differences in the nuclear properties. The region of validity of the boson coupling scheme is studied in terms of the effective interactions between the nucleons. Only for rather small deformations, is it justified to truncate the boson space to J = 0 and 2.
155 citations
TL;DR: The spectrum of initial cosmological perturbations posited by Zel'dovich and co-workers for the pancake theory of galaxy formation has been shown to follow from grand unified gauge theories as mentioned in this paper.
Abstract: The spectrum of initial cosmological perturbations posited by Zel'dovich and co-workers for the pancake theory of galaxy formation has (i) adiabatic perturbations only, and (ii) constant perturbation amplitude on all scales at their respective horizon times. Assumption (i) has recently been shown to follow from grand unified gauge theories. This paper shows that assumption (ii) may also be a consequence of spontaneous symmetry-breaking at sufficiently high temperatures. In this case the Universe may have been exactly Friedmannian originally. In a classical, U(1) Abelian Higgs model, the scale-independent dimensionless size of perturbations is here calculated to be ?T00/T00 ~ (8?/3)(Tc/m*)2 where m* is the Planck mass (1019 GeV) and Tc is the critical temperature of spontaneous symmetry-breaking, related to the mass of the gauge boson of the symmetry group. For the pancake model, one needs Tc ~ 1017 GeV.
148 citations
TL;DR: Coupled Clustered Clustering (CCL) as discussed by the authors is a coupled cluster approach to the many-electron correlation problem for both closed and open shell systems.
Abstract: A brief overview concerning the motivations and the development of the coupled cluster approach to the many-electron correlation problem for both closed and open shell systems is given. The basic characteristics and applications of this approach are briefly summarized as well as its relationship to other approaches.
145 citations
TL;DR: The density functional formalism as discussed by the authors provides a framework for including exchange and correlation effects in the calculation of ground state properties of many-electron systems, which leads to important numerical advantages over other ab initio methods of incorporating correlation effects.
Abstract: The density functional formalism provides a framework for including exchange and correlation effects in the calculation of ground state properties of many-electron systems. The reduction of the problem to the solution of single-particle equations leads to important numerical advantages over other ab initio methods of incorporating correlation effects. The essential features of the scheme are outlined and results obtained for atomic and molecular systems are surveyed. The local spin density (LSD) approximation gives generally good results for systems where the bonding involves s and p electrons, but results are less satisfactory for d-bonded systems. Non-local modifications to the LSD approximation have been tested on atomic systems yielding much improved total energies.
142 citations
TL;DR: In this paper, a simple and efficient algorithm for the calculation of two-electron matrix elements of spin-independent Hamiltonians needed in the unitary group configuration interaction (shell model) approach is presented.
Abstract: The various existing approaches for the evaluation of matrix elements of unitary group generators and their products with respect to the basis of electronic Gelfand states or the corresponding Yamanouchi-Kotani states are interrelated, and their desirable features combined, yielding a direct algorithm for the evaluation of matrix elements of products of two generators and, consequently, a simple and efficient algorithm for the calculation of two-electron matrix elements of spin-independent Hamiltonians needed in the unitary group configuration interaction (shell model) approach. Moreover, this algorithm is compatible with the efficient generation and representation scheme for electronic Gelfand states based on the distinct row table concept. Diagrammatic techniques based on the time-independent Wick theorem and graphical methods of spin algebras are used to derive the required factors for both one and two-generator (or electron) matrix elements for three different phase conventions and several possible simplifications in the evaluation of the two-electron part of the Hamiltonian matrix are outlined.
118 citations
TL;DR: In this article, numerical perturbation calculations on Be and C2+ were performed starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s 22p2.
Abstract: We report here numerical perturbation calculations on Be and C2+ starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s22p2. We use numerically represented radial pair functions which are solutions of a system of coupled differential equations obtained by a finite difference method. By iterating the system of pair equations the most important correlation effects are included to all orders. This is demonstrated for C2+, where excitation energies for the 2p2 levels are obtained with an accuracy better than 1% or 0.2 eV. For Be only second-order results are reported. Here the iterative scheme does not converge, probably due to the presence of intruder states of the type 2sns 1S, which lie between the two 1S states originating from the model space. The second-order calculation with the two-configurational model space and orbitals generated in the 1s2 Hertree-Fock core yields 93.6% of the correlation energy, compared to 80.9% for a similar calculation using a model space with only the ground-state configuration 1s22s2 and orbitals generated in the Hartree-Fock potential of that configuration.
116 citations
TL;DR: The graphical unitary group approach (UGA) has been cast into an extraordinarily powerful form by restructuring the Hamiltonian in terms of loop types as discussed by the authors, which allows the adoption of the loop-driven formulation which illuminates vast numbers of previously unappreciated relationships between distinct Hamiltonian matrix elements.
Abstract: The graphical unitary group approach (UGA) has been cast into an extraordinarily powerful form by restructuring the Hamiltonian in terms of loop types. This allows the adoption of the loop-driven formulation which illuminates vast numbers of previously unappreciated relationships between otherwise distinct Hamiltonian matrix elements. Several new developments are presented and discussed. Among these developments are the use of new segment coefficients, improvements in the loop-driven algorithm, implicit generation of loops wholly within the external space adopted within the framework of the loop-driven methodology, and comparisons of the diagonalization tape method to the direct method. It is also shown how it is possible to implement the GUGA method without the time-consuming full (m5) four-index transformation. A particularly promising new direction involves the use of the graphical UGA methodology to obtain one-electron and two-electron density matrices. Once these are known, analytical gradients (first derivatives) of the CI potential energy can be easily obtained. Several calculations have been performed and times are compared with our preliminary implementation [J. Chem Phys. 70, 5092, (1979)] of the method. Also included is a calculation on the asymmetric 21A' state of SO2 with 23 613 configurations to demonstrate methods for the diagonalization of very large matrices on a minicomputer.
113 citations
TL;DR: The relativistic random phase approximation (RRPA) as discussed by the authors was developed from linearized time-dependent Hartree-Fock theory and applied to determine excitation energies and oscillator strengths along the He, Be, Mg, Zn and Ne isoelectronic sequences.
Abstract: The relativistic random phase approximation RRPA is developed from linearized time-dependent Hartree-Fock theory. Applications of the resulting relativistic many-body equations to determine excitation energies and oscillator strengths along the He, Be, Mg, Zn and Ne isoelectronic sequences are discussed and compared with other recent experimental and theoretical work. The multi-channel RRPA treatment of photoionization is described and applications are given to total cross sections, branching ratios, angular distributions and to autoionizing resonances.
111 citations
TL;DR: In this paper, the spectral function of ionization is discussed for the whole energy range, and it is found that different energy regions are likely to exhibit different types of many-body effects.
Abstract: The spectral function of ionization is discussed for the whole energy range. It is found that different energy regions are likely to exhibit different types of many-body effects. For the ionization out of an outer valence orbital most of the intensity appears in one main line. The many-body effects explain the additional satellite lines and, in addition, can lead to an ordering of main lines which is different from the ordering determined from one-particle calculations. For the ionization out of an inner valence orbital the intensity may be distributed over several lines and in many cases it is not possible to identify any of these lines as the main line representing the orbital. Such a breakdown of the quasiparticle picture of ionization is stressed to be a common phenomenon. Ionization of core orbitals can usually be viewed within a quasiparticle picture, i.e., the process leads to a main line accompanied by satellite lines. In cases, however, where the creation of the core hole leads to a strong charge transfer, the shake-up energies can become small or even negative and the quasiparticle picture may break down. The origin of the above effects is discussed and typical examples are presented.
TL;DR: In this paper, the authors used tensorial techniques with particular reference to octahedral complexes to calculate the contribution of vibronic lines in the absorption spectra of rare earth or actinide ions to the neighboring ligands.
Abstract: The intensities of certain lines in the absorption spectra of rare-earth or actinide ions are very sensitive to the neighboring ligands. The contributions to these intensities coming from vibronic transitions (combined electronic and vibrational transitions) are calculated by tensorial techniques with particular reference to octahedral complexes. The expansions that are used possess leading terms that indicate that the strongest vibronic lines should be associated with electronic transitions that satisfy the selection rules on J (the total angular momentum) that are identical to those for quadrupole radiation. General agreement is obtained with the recent work of Faulkner and Richardson on the transition 7F0 → 5D2 of Eu3+, though some of the approximations and assumptions, as well as much of the mathematics, are different.
TL;DR: In this paper, a diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented, where the necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided.
Abstract: A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He2 excited Σg+ states) is demonstrated.
TL;DR: In this article, a coupled-cluster procedure for closed-shell as well as open-shell atoms is described, and results from calculations on the closedshell atoms Be and Ne are presented.
Abstract: A coupled-cluster procedure, applicable to closed-shell as well as open-shell atoms, is described, and results from calculations on the closed-shell atoms Be and Ne are presented. The procedure is based on numerical solution of coupled radial pair equations, which can be iterated to self-consistency. The coupling between different pair excitations is considered in two steps. The first step, called intra-shell coupling, includes the interaction between excitations differing in the final states as well as in the mlms values of the electrons being excited. In the second step, the inter-shell coupling, also the residual interaction between excitations involving different nl shells is considered. While the former coupling is quite important, it has been found that the latter contributes only about 1% to the correlation energy. Single and triple excitations are neglected in the present work, but quadrupole excitations are included by means of the exponential ansatz of the coupled-cluster procedure. According to our results for Be, 98.6% of the experimental correlation energy is obtained with complete pair-pair coupling, which is consistent with the estimated value of about 1.5% for the contribution of single and triple excitations. With only intra-shell coupling the result is in almost exact agreement with the experimental value due to cancellations between single/triple excitations and inter-shell couplings. Similar results are obtained for Ne. The results of the present work are compared and discussed in relation to earlier many-body calculations on these systems.
TL;DR: In this paper, the decay of autoionizing and inner-shell vacancy states is studied in a multichannel scattering theory. But the decay is not considered in this paper.
Abstract: The time-independent multichannel scattering theory is formulated in a way which makes it appropriate for the study of the decay of autoionizing and inner-shell vacancy states. A general interpretation of the parameters in the Fano profile is given and the concept of decay is introduced for both autoionizing and inner-shell vacancy states in a transparent manner. The theory is applied to a study of the influence of photon-electron coupling effects on the radiative and nonradiative decay probabilities. A generalization which includes post-collision interactions in inner-shell ionization is also presented.
TL;DR: In this article, the electron structure of hexagonal GaN has been investigated by means of ESCA, in particular the valence region has been studied and the value of an ionicity parameter for GaN is derived from the electron spectrum.
Abstract: The electron structure of hexagonal GaN has been investigated by means of ESCA. In particular the valence region has been studied. Comparisons with existing pseudopotential band structures are made. The value of an ionicity parameter for GaN is derived from the electron spectrum.
TL;DR: In this paper, existing observations of transitions 2s22pk-2s2pk+1-2 pk+2 in F I-, O I- and Be I-like spectra are collected and examined as to their isoelectronic consistency by plotting against Z appropriate functions of selected intervals.
Abstract: Existing observations of transitions 2s22pk-2s2pk+1 and 2s2pk+1-2pk+2 in F I-, O I- and Be I-like spectra are collected and examined as to their isoelectronic consistency by plotting against Z appropriate functions of selected intervals. The functions are then expressed by polynomials of the fourth to the sixth degree, derived by a weighted least-squares fitting over a range of about twenty Z-values, up to Z = 33, 32 and 28 in the F I, O I and Be I sequences, respectively. In the case of the Be I sequence, a previous investigation is now extended with the aid of new observations by Lawson and Peacock for Z = 24-28. For all three sequences the results of the examination are presented in tables of recommended level values and recalculated wavelengths.
TL;DR: In this paper, an infinite summation method is used to obtain the intrinsic photoemission spectrum of a conduction electron in the sudden limit, and it is predicted that an electron at the bottom of the conduction band should have an asymmetry index comparable to that of a core electron.
Abstract: An infinite summation method is used to obtain the intrinsic photoemission spectrum of a conduction electron in the sudden limit. It is predicted that an electron at the bottom of the conduction band should have an asymmetry index comparable to that of a core electron and that the strengths of its plasmon satellites should be similar to those of a core electron. The width of their plasmon satellites, however, should become smaller under the influence of recoil. In essence, our results show that the exchange-correlation hole left after a photoemitted conduction electron has a very similar effect as the core hole left after a photoemitted core electron. Use of synchrotron radiation gives high enough a resolution to make possible the verification of these effects.
TL;DR: In this article, the authors extended previous beam-foil lifetime studies in the EUV range to cover all n = 2 states of Si VII and Si IX, and the lifetime values obtained agree with theoretical data of Nicolaides and Beck.
Abstract: Previous beam-foil lifetime studies in the EUV range are extended to cover all n = 2 states of Si VII and Si IX. The lifetime values obtained agree with theoretical data of Nicolaides and Beck. For some states of Si X and Si XI information about initial population ratios of singly and doubly excited states is obtained. After foil excitation, the contribution of cascades from doubly excited states in the n = 2 shell to the intensities of decays from singly excited to ground states amounts to 20-40%.
TL;DR: The transition potential model for the transition from one to two holes in the silicon core has been developed to take into account the difference between the 1s and 2p binding energy shifts as discussed by the authors.
Abstract: The silicon KL2, 3L2, 3(1D2) Auger energies and the silicon 2p3/2 binding energies have been measured for more than twenty organic silicon compounds in the gas phase. The group shift model has been applied to the Auger energy data as well as the binding energy data. Approximate proportionality between these two types of chemical shifts was found for some sub-series of the type SiR4-nTn. The transition potential model for the transition from one to two holes in the silicon core has been developed to take into account the difference between the 1s and 2p binding energy shifts. Semi-empirical calculations have been performed for most of the compounds, CNDO/2 and EWMO (a modified iterative extended Huckel method, briefly presented in the text). It was found that EWMO provides a more satisfactory description of the valence charge densities and their changes upon core ionization than does CNDO/2. The correlation with the experimental data was also found to be better applying the transition potential models to the EWMO calculated charges than to the CNDO/2 charges.
TL;DR: The pion brems-strahlung, a chunk of nuclear matter, is decelerated along a straight path, the deceleration being parametrized by the "stopping time" τ as mentioned in this paper.
Abstract: The production of pions in relativistic heavy ion collisions may be regarded as classical radiation process. The source of this "pion brems-strahlung", a chunk of nuclear matter, is decelerated along a straight path, the deceleration being parametrized by the "stopping time" τ. The collective character of the source causes measureable pion production cross-sections even below the single nucleon threshold energy. The emitted pions appear as a strongly forward peaked beam with high kinetic energy.
TL;DR: In this article, a review of the available literature on electron impact ionization of ions of charge + 3 or greater is presented, and several easily used formulae are presented-the classical result, the Lotz formula, and a scaled Coulomb-Born prescription.
Abstract: The available literature on electron impact ionization of ions of charge + 3 or greater is reviewed. Several easily used formulae are presented-the classical result, the Lotz formula, and a scaled Coulomb-Born prescription. The available experimental cross-sections, which now include a few good quality crossed-beams measurements, are compared with the cross-sections obtained from the formulae and, where available, with true Coulomb-Born calculations. The Lotz formula is overall found to be closest to the experimental results. However, this result is fortuitous since much of the experimental data are found to contain measurable contribution from the excitation-autoionization process not included in any of the formulae. It appears to be more important to include estimates of the excitation-autoionization contribution to ionization cross-sections than to improve the models of the direct ionization process.
TL;DR: In this paper, the beam-foil technique has been used for lifetime measurements for doubly-excited states in Li. Decay curves for almost every transition known to belong to the doublyexcited system have been recorded.
Abstract: Lifetime measurements using the beam-foil technique have been performed for doubly-excited states in lithium. Decay curves for almost every transition known to belong to the doubly-excited system have been recorded. The measurements confirm the assignments of transitions from the 2p3s 4P0, 2p3d 4D0 and 2p4d 4D0 levels. To determine the lifetime for the 2s3s 4S level it was necessary to perform a cascade subtraction, since it was found that the exponential corresponding to the primary decay was cancelled due to the cascading. The lifetimes obtained for the low-lying levels 2s3s 4S, 2p2 4P and 2s3d 4D are in very good agreement with theory. The lifetime measurements are used for discussion of assignments of transitions in the quartet and doublet level scheme of Li I.
TL;DR: In this article, the 4p core hole was shown to break down due to very strong dynamical dipolar fluctuations and associated decay processes of the 4 p core hole, and the theory presented agrees well with experimental data.
Abstract: Many-electron interactions within one atomic shell can cause a breakdown of the quasi-particle picture of a core hole by causing strong fluctuations. Typical examples are 4s and 4p XPS spectra and Lγ2,3(L1N2,3) X-ray emission spectra of the elements 46Pd to 54Xe. In these cases quasiparticle picture of 4p core hole breaks down due to very strong dynamical dipolar fluctuations and associated decay processes of the 4p core hole. The theory presented agrees well with experimental data.
TL;DR: In this article, the beamfoil method has been used to measure lifetimes for six levels in Si I. The results were compared with emission data and theoretical values, and improved experimental values were also given for a number of previously measured levels of Si II-Si IV.
Abstract: The beam-foil method has been used to measure lifetimes for six levels in Si I. The results are compared with emission data and theoretical values. Improved experimental values are also given for a number of previously measured levels in Si II-Si IV.
TL;DR: In this paper, the beam-foil excitation technique was applied to populate the doubly excited states in the triplet spectrum of the Be III in the wavelength region of 75-5000 A in order to test the validity of the theoretical term values reported by Lipsky et al.
Abstract: The triplet spectrum of doubly excited Be III has been studied in the wavelength region of 75-5000 A in order to test the validity of the theoretical term values reported by Lipsky et al. The beam-foil excitation technique was applied to effectively populate the doubly excited states. The identified lower-lying, doubly excited states 2p2 3P, 2pnp 3P, or 3D, and 2pnd 3P, or 3D (n = 3, 4) show that the theoretical term values should be slightly modified.
TL;DR: In this paper, it was shown that one-particle calculations of X-ray spectra in simple metals give very different results depending on whether the core hole is taken into account or not.
Abstract: The authors have previously shown that one-particle calculations of X-ray spectra in simple metals give very different results depending on whether the core hole is taken into account or not. Guided by experiment and the dynamical theory of X-ray spectra developed by Nozieres and DeDominicis (ND) (1969) the authors have, however, also established the rule that rather realistic spectra can be obtained from a one-particle calculation provided final state wavefunctions are used in the transition matrix elements. They report on direct numerical evaluations of the dynamical ND theory for several different cases including the case where a bound state appears. In all cases the results support their final state rule. They also give arguments in support of the procedure used to extract threshold exponents and asymmetry indices from X-ray absorption and emission spectra and X-ray photoemission spectra.(18 refs) (Less)
TL;DR: In this article, the anomalous atomic scattering factor has been studied in terms of threshold resonances and damping effects, with an overview of recent experimental and theoretical work and a discussion of the very strong anomalous dispersion recently observed near the L3 edge in a cesium complex.
Abstract: The availability of tunable synchrotron radiation has made it possible to perform systematic X-ray diffraction studies in regions of anomalous scattering near absorption edges, e.g., in order to derive phase information for crystal structure determination. We give an overview of recent experimental and theoretical work and discuss the properties of the anomalous atomic scattering factor, with emphasis on threshold resonances and damping effects. The results are applied to a discussion of the very strong anomalous dispersion recently observed near the L3 edge in a cesium complex [11]. We also discuss briefly other systems where similar behaviour can be expected. Finally, we discuss the influence of solid state and chemical effects on the absorption edge structure.
TL;DR: In this paper, semi-empirical values for the lifetimes, transition probabilities and oscillator strengths have been computed for all n = 4, n = 5 and some n ≤ 9 Rydberg transitions for ions in the Cu I isoelectronic sequence through In XXI.
Abstract: Semi-empirical values for the lifetimes, transition probabilities and oscillator strengths have been computed for all n = 4, n = 5 and some n ≤ 9 Rydberg transitions for ions in the Cu I isoelectronic sequence through In XXI. Extrapolation and interpolation techniques were utilised to obtain a set of estimated term values and ionisation potentials which, although crude by spectroscopic standards, are of sufficient accuracy to serve as inputs for transition probability calculations by the numerical Coulomb approximation.
TL;DR: In this article, the L-shell soft-X-ray emission spectra of Cu, Zn, Ga, As, Br, Rb and Sr from laser-produced plasma sources were recorded with a convex-crystal spectrograph.
Abstract: The L-shell soft-X-ray emission spectra of Cu, Zn, Ga, As, Br, Rb and Sr from laser-produced plasma sources were recorded with a convex-crystal spectrograph. The spectrograms were measured to provide wavelengths accurate to ± 2 mA for neon-like and 2p5-2p43s, 3d fluorine-like transitions. Theoretical wavelengths and oscillator strengths were computed to aid the classification of the experimental spectra.