Choice Of Wave Function Research Articles

Combining density functional theory with macroscopic QED for quantum light-matter interactions in 2D materials

A quantitative and predictive theory of quantum light-matter interactions in ultra thin materials involves several fundamental challenges. Any realistic model must simultaneously account for the ultra-confined plasmonic modes and their quantization in the presence of losses, while describing the electronic states from first principles. Herein we develop such a framework by combining density functional theory (DFT) with macroscopic quantum electrodynamics, which we use to show Purcell enhancements reaching 107 for intersubband transitions in few-layer transition metal dichalcogenides sandwiched between graphene and a perfect conductor. The general validity of our methodology allows us to put several common approximation paradigms to quantitative test, namely the dipole-approximation, the use of 1D quantum well model wave functions, and the Fermi’s Golden rule. The analysis shows that the choice of wave functions is of particular importance. Our work lays the foundation for practical ab initio-based quantum treatments of light-matter interactions in realistic nanostructured materials.

Zero modes in electromagnetic form factors of the nucleon in a light-cone diquark model

We use a diquark model of the nucleon to calculate the electromagnetic form factors of the nucleon described as a scalar and axialvector diquark bound state. We provide an analysis of the zero-mode contribution in the diquark model. We find that there are zero-mode contributions to the form factors arising from the instantaneous part of the quark propagator, which cannot be neglected compared with the valence contribution but can be removed by the choice of wavefunction. We also find that the charge, magnetic radii and magnetic moment of the proton can be reproduced, while the magnetic moment of the neutron is too small. The dipole shape of the form factors, GpM(Q2)/μp and GnM(Q2)/μn, can be reproduced. The ratio μGpE/GpM decreases with Q2, but too fast.

Comment on “Improvement of the Davydov theory of bioenergy transport in protein molecular systems”

It is shown that a certain wave function represents a two quanta state of the Davydov-Scott model, contrary to the claims of Pang. Furthermore, Pang's choice of wave function and derivation of equation of motions are criticized. Directions for future work in this area are indicated.

Isgur–Wise function in a relativistic model of constituent quarks

The integral representation for Isgur–Wise function (IWF) is obtained in the framework of instant-form relativistic Hamiltonian dynamics for mesons with one heavy quark. The upper and lower limits are calculated for the slope parameter of IWF ρ 2 by the model independent way. IWF is calculated for different wave functions of quarks in the meson. The difference between the limits of ρ 2 equals 1/3. The constraint on the slope parameter is in a good agreement with experiments. The weak dependence of IWF on the choice of wave functions is found.

Toward an ab Initio Treatment of the Time-Dependent Schrödinger Equation of Molecular Systems

The time-dependent variational principle (TDVP) is employed to produce equations of motion that approximate the time-dependent Schrodinger equation. Choices of wave function and basis sets are discussed. The use of electron translation factors and the electronic and nuclear parts of the molecular wavefunction are put in the context of the electron nuclear dynamics (END) theory. The role of wave function parameters as dynamical variables is discussed, and the use of coherent state parametrization is explored.

Quantum Theory as the Representation Theory of Symmetries

It is proposed that an unconstrained quantum system is completely specified by its configuration space C and its group of symmetries G . It is then shown that the theory of projective unitary representations of G on a certain Hilbert space determined by C and G leads to a definitive resolution of supposed ambiguities relating to superselection rules, choice of wave functions, topological properties of G and C , anomalies, etc. {copyright} {ital 1997} {ital The American Physical Society}

Direct photodesorption of ions from the surface of a crystal

A model of the direct photodesorption of ions from the surface of a crystal, reminiscent of the ionization of an atom in the external photoelectric effect, is studied. The model is based on the concept of a quasiclassical ion, whose motion in a surface potential well is described by a wave packet. The choice of wave function in the form of a packet may be justified by a variational principle, by finding the parameters of the packet. These parameters may also be selected from known experimental data. These methods are standard in solid state physics and make it unnecessary to take into account the form and magnitude of the operator describing the interaction between the ion and the crystal surface.

High-twist contribution to large-p T dilepton production

The high-twist contribution to large-transversemomentum lepton pair production in pion-hadron collisions is investigated. In calculations, various pion model wave functions are used. The high-twist contribution is shown to depend on the choice of wave functions and to exceed the leading one by an order of magnitude in the phase space boundary.

HOW MUCH CAN BE LEARNT ABOUT PION WAVE FUNCTION FROM THE DRELL–YAN PROCESS?

Contribution of the high twist Feynman diagrams to the dilepton production cross section in pion–hadron collisions is investigated. In calculations the asymptotic, Chernyak–Zhitnitsky and two other pion model wave functions P2, P3 are used. It is shown that this contribution depends on the choice of wave functions and for large dilepton transverse momentum pT and invariant mass Q in the limit [Formula: see text] exceeds the leading one by an order of magnitude. Perspectives of the Drell–Yan process in the context of the pion wave function investigation are discussed.

Chiral electron pairs from double photoionization

Double photoionization of a randomly oriented free atom by circularly polarized light produces photoelectron pairs with the ability to distinguish a right-handed coordinate frame from a left-handed one. This chirality, a new manifestation of electronic correlation, causes a circular dichroism in multiply differential cross sections. Necessary kinematical conditions for the observability of a finite chirality of a photoelectron pair are worked out and discussed. Results of numerical calculations for He and H- show the amount of circular dichroism to depend strongly: (i) on the choice of wavefunctions used, especially on the description of correlation, (ii) on the energy distribution of the photoelectrons, and (iii) on the light frequency. In particular, the authors have found a critical frequency where the dichroism changes sign. The threshold behaviour has been analysed within the frame of the Wannier-Peterkop-Rau theory.

The multiple scattering contribution to fixed-angle elastic hadron-hadron scattering

Using the factorized form of the leading behavior (in powers of Q) of fixed-angle elastic hadron-hadron scattering given by Botts and Sterman, the leading perturbative QCD contribution to d σ/d t ( ϑ = π/2) for pions and protons is numerically evaluated. Various models of the long-distance, nonperturbative hadronic wave functions are used and the different soft cutoff prescriptions made explicit. For the proton case, it is found that the size of the Landshoff contribution is of the same order as the observed data, though in that energy range the resulting cross sections are strongly dependent on momenta cutoffs, choice of wave function and the small ξ contribution. The onset of asymptopia, defined to be where soft effects become negligible, is found to occur at ln( s/1 GeV 2) ≈ 4 for pions and ln( s/1 GeV 2) ≈ 8 for protons. Logarithmic effects swamp out the power-law predictions of Botts and Sterman and Mueller, d σ/d t| ππ αs −5.83 and d σ/d t| pp α s −9.59, until ln( s/1 GeV 2) ≈ 20.

M-subshell ionization of U by light-ion bombardment

M X-rays of U were produced by proton, deuteron and alpha-particle bombardment in the energy range of 0.20–1.00 MeV/u. N 6,7 → M 5 (M α ), N 6 → M 4 (M β ), N 5 → M 3 (M γ ), N 4 → M 2 and N 2 → M 1 line yields were obtained from a least-squares fit to the spectra and used to convert M X-ray production into M-subshell ionization cross sections. The uncertainty induced by the atomic parameters (X-ray fluorescence yields, Coster-Kronig and radiative transition rates) used in the conversion is discussed. The subshell ionization cross sections are then compared to PWBA values corrected for Coulomb deflection and energy loss according to Brandt and Lapicki, to the semiclassical theoretical values of Kocbach and to relativistic PWBA results, corrected for Coulomb and binding effects, of Chen et al. Intrashell transitions induced by the projectile and multiple ionization are suggested as causes of disagreement between theory and experiment, especially for alpha-particles. It is concluded that theory must go beyond the simple picture of the first-order perturbation approximation to explain M-subshell results and that care must be taken in the choice of wave functions.

Study of the [formula omitted] reaction

We evaluate the cross section for the p d→π - p reaction, by assuming p̄N annihilation into two pions or one pion and a ρ-meson, with one pion or the ρ-meson in a virtual state being absorbed by a second nucleon. This is a meson-exchange mechanism for the p̄-annihilation involving two nucleons. The results are evaluated with the Paris and two Bonn deuteron wave functions and depend strongly on the choice of wave function. Within the theoretical uncertainties the results are in qualitative agreement with experiment.

Wavefunction effects in the calculation of cross sections for electron impact ionisation of helium at high energy

Triple differential cross sections for the ionisation of helium by fast (8 keV) electrons are calculated using the first Born approximation. Generalised oscillator strengths are also obtained, as a function of momentum transfer, for ejected electron angles of 0 and 180' with respect to the momentum transfer direction. Comparison is made with experiment and with previous theoretical calculations. The results are very sensitive to the choice of wavefunctions for the initial and final target states.

Fusion Characteristics in Exotic Catalyzed Systems

Muon catalyzed fusion represents a potential long-term approach to fusion power. The sensitivity of the fusion properties of muomolecules to the choice of wave function describing the system is studied. The need for an improved understanding of the problem and correct evaluation of nonadiabatic effects is stressed, and the discrepancy between fusion rates from Born-Oppenheimer- and Hylleraas-type wave functions is pointed out.

Comparative studies on a maximum bond order principle

A recently proposed maximum bond order principle is studied with respect to choice of basis orbitals, choice of wavefunction and compared with other methods. Results for bond orders support the choice of Schmidt orthogonalized AO's with subsequent Lowdin orthogonalization. Differences between semiempirical andab initio wavefunctions in minimal basis sets usually have only minor effects on bond order values. For hydrocarbons bond order values are quite similar for Cohen's and this method. Finally, the dependence of bond orders on internal rotation and vibration is investigated in a few simple cases.

Dissociative Excitation of Water Molecule by Electron Impacts. I. General Survey and the Born Approximation

Emission cross sections are evaluated in the Born approximation for the dissociative excitation processes of H 2 O by electron impacts, accompanied by the OH violet band, or the Lyman-α emission. Wave functions are from the Hatano-Nomura-Tanaka basis set as well as the Lin-Duncan set. The choice of wave functions strongly affects the magnitude of the cross section, but hardly affects its dependence on the incident electron energy. For the OH band, main contribution comes from the transition 3 a 1 →4 a 1 , and the electron exchange collision should be considered. For the Lyman-α emission, to which a number of superexcited states may correlate, it is found that the contribution of the transition 1 b 2 →6 a 1 (=4 s a 1 ) is dominant, while ones 1 b 2 →3 d a 1 , 3 d a 2 and 3 d b 2 the next. The calculated cross section is different from the experimental one at low energies of the incident electron, but is in accord with the experimental one at high energies. Alternative comparison is made on the optical and ...

High order correlation effects in intermolecular forces

A new approach to the calculation of intermolecular forces is presented. The total hamiltonian is used and no arbitrary separation into “orders” is made. The approach allows the interaction to be calculated, including intraatomic electron correction, to various degrees of approximation, the ultimate being full configuration interaction. The approximations are guided by the choice of wave function and the partitioning of the variational form. In this paper the method is applied to the long range interactions of helium, and in more approximate forms to HHe and LiHe. For He 2, studies are made of two- and three-electron excitations. Three-electron excitations contribute almost 9% to the value of the C 6 coefficient. Our final C 6 coefficient is 1.457 (in atomic units) versus the best semi-empirical value of 1.4618 ≠ 0.0004. The results are compared with other calculations in a formal way so as to demonstrate the value of our alternative expressions.

Embedding of the Brueckner Approximation in the Extended Jastrow Scheme

A nonperturbative derivation of the Brueckner approximation to the ground-state energy of nuclear matter (with standard choice of hole and particle energies) is given within the framework of the method of correlated basis functions. The structure of the factor-cluster (FIY) expansion of the expectation value of the Hamiltonian with respect to a trial function incorporating short-range correlations in a general fashion, is analyzed for a uniform extended medium of fermions. With a special choice of correlated wave function, the Brueckner approximation is extracted from the FIY expansion by selective summation of two-body combination terms to all orders in the smallness parameter $\ensuremath{\kappa}$ associated, in this case, with both Brueckner-Bethe-Goldstone and FIY energy expansions. A reexamination of the numerical comparison of conventional Brueckner and Jastrow methods carried out earlier for two simple models of nuclear matter leads to the conclusion that it is inadvisable, at least in a Jastrow calculation satisfying the average Pauli condition, to incorporate the $O(\ensuremath{\kappa})$ contribution of the analog of the dispersion correction of reaction-matrix theory without at the same time including the $O(\ensuremath{\kappa})$ contribution of the analog of the Bethe-Faddeev term. For the uniform extended medium for the Jastrow choice of wave function, there is a formal cancellation of these two three-body contributions, the scale of this cancellation being governed by the size of $\ensuremath{\kappa}$. In the numerical example considered, $\ensuremath{\kappa}$ is about 0.22 and the cancellation goes something like +14 MeV-15 MeV=-1 MeV. These findings, when juxtaposed with the standard Brueckner results for the simple models in question, suggest that a departure from the standard prescription of hole and particle energies in reaction-matrix theory may be necessary when $\ensuremath{\kappa}$ is sizeable-as in liquid $^{3}\mathrm{He}$ and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.

Compton profiles for the first and second row atoms

Calculations of the atomic Compton profile and various 'moments of the momentum distributions' have shown that these physical properties are very sensitive to the choice of wavefunctions used to characterize the scattering system. The Compton profile and (pn) for n equal to -1, 1, 2 are studied for atoms in their ground state described by approximate HF GTO (Hartree-Fock Gaussian type orbitals) by Huzinaga. The results are compared with those obtained by a HF STO (Hartree-Fock Slater type orbitals) Clementi basis set. It appears that the calculated values are very similar for the two types of wavefunctions.