Unperturbed Wave Functions Research Articles

High harmonic generation spectra for lithium embedded in plasma environment

Effect of plasma on High harmonic generation of Lithium is investigated. Variation of the strength of different harmonics with respect to changes in Debye length is shown. The unperturbed energy eigenvalues and wavefunctions are calculated using the pseudostate summation technique while for the time evolution of wavefunctions the symplectic method is applied. Results for the numerical simulation of High harmonic generation spectra for plasma embedded Lithium are reported.

Generation of quantum vortices in photodetachment: The role of the ground-state wave function

Formation of quantum vortices in laser-induced photodetachment from negative ions is analyzed. The driving laser field consists of a single ultrashort pulse of circular polarization and the unperturbed ground-state wave function of the anion is found in either the $s$ or $p$ state. In particular, numerical illustrations for the photodetachment from ${\mathrm{H}}^{\ensuremath{-}},$ ${\mathrm{O}}^{\ensuremath{-}},$ ${\mathrm{K}}^{\ensuremath{-}},$ and a model ${\mathrm{A}}^{\ensuremath{-}}$ anion are presented. Special attention is paid to the symmetry of the ground-state wave function and ionization potential over the final vortex pattern. It is shown that the two-dimensional spectra of photoelectrons in momentum space comprise three well-defined regions: The low-energy (central) region, multiphotonlike zone, and supercontinuum. While the supercontinuum does not contribute to vorticity and the multiphoton zone depends only on the laser field characteristics, vortices in the low-energy region strongly depend on the bound-state wave function and its ionization potential.

An Electron Propagator Approach Based on a Multiconfigurational Reference State for the Investigation of Negative-Ion Resonances Using a Complex Absorbing Potential Method.

Negative-ion resonances are important metastable states that result from the collision between an electron and a neutral target. The course of many chemical processes in nature is often dictated by how an intermediate resonance state falls apart. This article reports on the development of an electron propagator (EP) based on a Hamiltonian Ĥ perturbed by a complex absorbing potential (CAP) and a multiconfigurational self-consistent field (MCSCF) initial state to study these resonances. Perturbation of Ĥ by a CAP makes the resonances amenable to a bound-state method like MCSCF. Resonances stand out among the non-resonant states as persistent complex eigenvalues of the perturbed Ĥ when the strength (η) of the CAP is varied. The MCSCF method gives a reliable and accurate description of the target states, especially when the non-dynamical correlations are dominant. The resonance energies are obtained from the poles of the EP. We propose three variants of our EP depending on how the effect of the CAP is introduced. We find that the computationally most efficient variant is the one in which the reference state of the EP is an unperturbed MCSCF wavefunction and a non-zero CAP is defined only on the virtual orbital subspace of the reference state. The onset of the CAP is carefully optimized in order to minimize the artifacts due to reflections from the CAP. An extrapolation method (based on a Padé approximant) and a de-perturbation method are adopted in order to account for the limitations of finite basis sets used and determine the resonance energy in the limit of η → 0. 2P Be-, 2Πg N2-, and 2Π CO- shape resonances are investigated. The position and width of these resonances computed in this study agree well with those reported earlier in the literature.

Theoretical derivation of laser-dressed atomic states by using a fractal space

The derivation of approximate wave functions for an electron submitted to both a Coulomb and a time-dependent laser electric fields, the so-called Coulomb-Volkov (CV) state, is addressed. Despite its derivation for continuum states does not exhibit any particular problem within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. Indeed the natural way of translating the unperturbed momentum by the laser vector potential is no longer possible since a bound state does not exhibit a plane wave form explicitly including a momentum. The use of a fractal space permits to naturally define a momentum for a bound wave function. Within this framework, it is shown how the derivation of laser-dressed bound states can be performed. Based on a generalized eikonal approach, a new expression for the laser-dressed states is also derived, fully symmetric relative to the continuum or bound nature of the initial unperturbed wave function. It includes an additional crossed term in the Volkov phase which was not obtained within the standard theory of quantum mechanics. The derivations within this fractal framework have highlighted other possible ways to derive approximate laser-dressed states in QM. After comparing the various obtained wave functions, an application to the prediction of the ionization probability of hydrogen targets by attosecond XUV pulses within the sudden approximation is provided. This approach allows to make predictions in various regimes depending on the laser intensity, going from the non-resonant multiphoton absorption to tunneling and barrier-suppression ionization.

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor ( $$D^{\mathrm{SO}})$$ of the axial ZFS parameter D. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of $$\hbox {Mn}^{2+}$$ ion in the host matrix.

Note on predictions for [formula omitted] quarkonia using a three-loop static potential

We extend our treatment of the spectroscopy and decays of the charm-strange quarkonium system to include the effect of using the full three-loop QCD correction to the static short distance potential. As before, our potential model consists of the relativistic kinetic energy term, a scalar linear confining term including its relativistic corrections and the perturbative QCD spin-dependent terms. A set of unperturbed wave functions for the various states is obtained using a variational technique that is further constrained by requiring that the wave functions also satisfy the relativistic virial theorem. These are then used in a perturbative treatment of the potential to fit the mass spectrum of the cs¯ system and calculate the radiative decay widths. Our results accurately describe the Ds spectrum and are compatible with the little data that is available for the radiative decays of the Ds states.

Explicitly correlated coupled-cluster theory for static polarizabilities.

A method of calculation of static polarizabilities with wavefunctions, corresponding to linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. For the proper description of the response of system on applied electric field, modified ansatz is introduced for geminal part of cluster operators. Such extension of CCSD(F12) model provides balanced description of both perturbed and unperturbed wave functions, what leads to the increase of the accuracy of target polarizabilities. As a part of algorithm, explicitly correlated version of coupled-perturbed CCSD equations has also been derived and implemented. Numerical tests conducted for the set of eight molecules show good agreement between static polarizabilities, calculated with developed explicitly correlated approach and corresponding complete basis set results in regular CCSD already at triple-ζ level.

Dalgarno–Lewis perturbation theory for nonlinear optics

We apply the quadrature-based perturbation method of Dalgarno and Lewis to the evaluation of the nonlinear optical response of quantum systems. This general operator method for perturbation theory allows us to derive exact expressions for the first three electronic polarizabilities which require only a good estimate of the ground state wave function, makes no explicit reference to the underlying potential, and avoids complexities arising from excited state degeneracies. We apply this method to simple examples in 1D quantum mechanics for illustration, exploring the sensitivity of this method to variational solutions as well as poor numerical sampling. Finally, to the best of our knowledge, we extend the Dalgarno-Lewis method for for the first time to time-harmonic perturbations, allowing dispersion characteristics to be determined from the unperturbed ground state wave function alone.

Computation of hyperfine energies of hydrogen, deuterium and tritium quantum dots

The hyperfine energies and hyperfine constants of the ground and excited states of hydrogen, deuterium and tritium quantum dots(QDs) are calculated. Quantum genetic algorithm (QGA) and Hartree–Fock–Roothaan (HFR) methods are employed to calculate the unperturbed wave functions and energy eigenvalues. The results show that in the medium and strong confinement regions the hyperfine energy and hyperfine constant are strongly affected by dot radius, impurity charge, electron spin orientation, impurity spin and impurity magnetic moment. Besides, in all dot radii, the hyperfine splitting and hyperfine constant of the confined hydrogen and tritium atoms are approximately equivalent to each other and they are greater than the confined deuterium atom.

Calculation of hyperfine interaction in spherical quantum dot

In this study, we have calculated the unperturbed wavefunctions and energy eigenvalues of the ground and excited states of a spherical quantum dot, GaAs/AlxGa1−xAs, by using quantum genetic algorithm and Hartree–Fock Roothaan method. Hyperfine coupling constant and hyperfine energy of 1s, 2p, 3d and 4f levels are carried out as a function of dot radius. The results show that the hyperfine constant and hyperfine energy varies rapidly in the strong and medium confining regions as dot radius decreases. It is worth pointing out that dot radius, impurity charge and angular momentum have a strong influence on the hyperfine energy. It is also found that hyperfine energy and hyperfine splitting vary with aluminium concentration ratio x.

Three-loop static QCD potential in heavy quarkonia

Abstract We investigate the effects of including the full three-loop QCD correction to the static short distance 1 / r potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full three-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. The perturbed results are compared to the subset of the charmonium and upsilon spectra using a χ 2 test. This approach results in more accurate descriptions of the hyperfine splittings in both the b b ¯ and c c ¯ systems.

Identification of the Keldysh time as a lower limit for the tunneling time

By using first-principles arguments, based on the time-energy uncertainty principle in the form given by Mandelstam and Tamm, we show that the Keldysh time represents a lower limit for the tunnel time. We use the definition of the tunnel time as identified in a recent numerical investigation [C. R. McDonald et al., Phys. Rev. Lett. 111, 090405 (2013)]; it is the time it takes for the unperturbed initial ground-state wave function to evolve into the field-perturbed final eigenstate which is the quasistatic field dressed resonance.

Ionization Process of Atoms by Intense Femtosecond Chirped Laser Pulses

We numerically investigate the ionization mechanism in a real hydrogen atom under intense fem to second chirped laser pulses. The central carrier frequency of the pulses is chosen to be 6.2 eV (λ = 200 nm), which corresponds to the fourth-harmonic of the Ti:Sapphire laser. Our simulation of the laser-atom interaction consists on numerically solving the three-dimensional time-dependent Schrodinger equation with a spectral method. The unperturbed wave functions and electronic energies of the atomic system were found by using an L2 discretization technique based on the expansion of the wave functions on B-spline functions. The presented results of kinetic energy spectra of the emitted electrons show the sensitivity of the ionization process to the chirp parameter. Particular attention is paid to the important role of the excited bound states involved in the ionization paths.

Control of the Atomic Ionization with Short and Intense Chirped Laser Pulses

We investigate a two-photon ionization process in a real hydrogen atom by short and intense chirped laser pulses. Our simulation of the laser-atom interaction consists on numerically solving the three-dimensional time-dependent Schrodinger equation with a spectral method. The unperturbed wave functions and electronic energies of the atomic system were found by using an accurate L2 discretisation technique based on the expansion of the wave functions on B-spline functions. We show the efficiency of chirped laser pulses to control the ionization yield and the transfer of the population to the 2p bound state involved in the ionization path.

Karplus dependence of spin–spin coupling constants revisited theoretically. Part 1: second-order double perturbation theory

A double perturbation theory (DPT) at the second order level of approximation formalism has been applied to examine the dihedral angle dependence of the Fermi-contact (FC) contribution to nuclear spin-spin coupling constants. The unperturbed wave function of the ground state in DPT was approximated by the Hartree-Fock Slater determinant, while the excited states were treated as the single excited determinants. An analytical expression relating the FC term of vicinal proton-proton spin-spin coupling constants across the aliphatic single carbon-carbon bond to the dihedral angle describing inner rotation around the C-C bond in the ten-electron ten-orbital moiety H-C-C-H has been derived and analyzed. In particular, it has been shown that extrema of (3)J(H,H) are observed at φ = πn, n = 0, ±1, ±2,…, which provides a theoretical background of a well-known semiempirical Karplus equation.

New ab initio coupled potential energy surfaces for the Br(2P3/2, 2P1/2) + H2 reaction

The three lowest (1A('), 2A('), and 1A('')) adiabatic potential energy surfaces (PESs) for the Br((2)P) + H(2) reactive system have been computed based on the multi-reference configuration interaction (MRCI) method including the Davidson's correction with a large basis set. These three adiabatic PESs have been transformed to a diabatic representation, leading to four coupling potentials. In addition, the spin-orbit matrix elements were also obtained using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Consequently, six coupling potentials were obtained and their characteristics were extensively discussed. Nonadiabatic quantum dynamics calculations for this system have been realized with these realistic diabatic potentials instead of previous semi-empirical diabatic potentials. Based on two-state model nonadiabatic calculations for the Br((2)P(3∕2), (2)P(1∕2)) + H(2) reaction, the Br((2)P(1∕2)) + H(2) reaction was found to show less reactivity than the Br((2)P(3∕2)) + H(2) reaction at collision energies beyond the threshold of the Br((2)P(3∕2)) + H(2) reaction. Our results are consistent with the previous studies on the XH(2) (X = F, Cl) system, which indicate that the adiabatically forbidden channel is dominant at low energies in the open-shell halogen atom plus H(2) reactions.

ISGUR–WISE FUNCTION IN A QCD POTENTIAL MODEL WITH COULOMBIC POTENTIAL AS PERTURBATION

We study heavy light mesons in a QCD inspired quark model with the Cornell potential [Formula: see text]. Here we consider the linear term br as the parent and [Formula: see text], i.e. the Coloumbic part as the perturbation. The linear parent leads to Airy function as the unperturbed wave function. We then use the Dalgarno method of perturbation theory to obtain the total wave function corrected up to first order with Coulombic piece as the perturbation. With these wave functions, we study the Isgur–Wise function and calculate its slope and curvature.

Absorption effects in halo-nucleus core or nucleon stripping reactions

Inclusive halo-nucleus core or nucleon stripping reactions are considered on the basis of a potential three-body model using the eikonal and adiabatic approximations. Clear analytical expressions for the cross sections of these reactions are obtained, and numerical calculations for 11Be halo nucleus are performed. Constituent absorption by the target nucleus substantially influences the integral and differential (with respect to longitudinal momentum) nucleon stripping cross section. It is demonstrated that the differential core stripping cross section contains more complete information on the unperturbed wave function of the halo nucleus.

New ab initio potential energy surface for BrH2 and rate constants for the H + HBr → H2 + Br abstraction reaction

A global potential energy surface (PES) for the electronic ground state of the BrH(2) system was constructed based on the multireference configuration interaction (MRCI) method including the Davidson's correction using a large basis set. In addition, the spin-orbit correction were computed using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Adding the correction to the ground state potential, the lowest spin-orbit correlated adiabatic potential was obtained. The characters of the new potential are discussed. Accurate initial state specified rate constants for the H + HBr → H(2) + Br abstraction reaction were calculated using a time-dependent wave packet method. The predicted rate constants were found to be in excellent agreement with the available experimental values and much better than those obtained from a previous PES.

Verification of structural and electrostatic properties obtained by the use of different pseudoatom databases

The existing pseudoatom databases (ELMAM, Invariom, UBDB and ELMAM2) enable structure refinement to be performed with the use of aspherical scattering factors computed from the transferable aspherical atom model (TAAM) as an alternative to independent atom model refinement. In addition, electrostatic properties can be estimated with the help of the databases. The quality of the structural and electrostatic properties obtained from the individual databases was tested. On the basis of a 100 K high-resolution single-crystal X-ray diffraction experiment on L-His-L-Ala dihydrate and 23 K high-resolution data for L-Ala [Destro & Marsh (1988). J. Phys. Chem. 92, 966-973], the structural properties, electron-density distributions and molecular electrostatic potentials obtained from different TAAMs were compared to each other and to reference models. Experimental multipolar models and theoretical models refined against theoretical structure factors computed from periodic density functional theory (DFT) calculations were compared to the TAAMs in order to determine which model best describes the crystal-field effect. Unperturbed wavefunctions based on the MP2 and DFT calculations and properties obtained directly from these were used as a reference to judge how properly the databases reproduce the properties of isolated molecules. For Gly-L-His dihydrate, D,L-His and the above-mentioned two crystal structures, deviations of the molecular dipole moments and Coulombic intermolecular interaction energies from the reference values were examined. Root-mean-square deviations (RMSDs) and correlation coefficients were used as a quantitative measure of the quality of the analysed properties. TAAM refinements reproduce X-H bond lengths optimized in theoretical periodic calculations. Structural properties obtained from different database models are similar to each other. The anisotropic displacement parameters from TAAMs are similar to the results of experimental multipolar refinement; differences are about 0.5 and 2.5% for high-resolution and low-resolution data, respectively. Differences in dipole-moment magnitudes calculated from database models are about 5%, and directions differ by up to 30°. The values of electrostatic interaction energies estimated from the individual TAAMs differ greatly from each other and from the reference values. RMSDs are about 9-15 and 22-33 kJ mol(-1) for UBDB and the other database models, respectively.