Multichannel Quantum Defect Methods Research Articles

Precision spectroscopy of high rotational states in H2investigated by Doppler-free two-photon laser spectroscopy in theEF 1Σg+–X 1Σg+system

Recently a high precision spectroscopic investigation of the EF^1\Sigma_g^+ - X^1\Sigma_g^+ system of molecular hydrogen was reported yielding information on QED and relativistic effects in a sequence of rotational quantum states in the X^1\Sigma^+_g$ ground state of the H_2 molecule [E.J. Salumbides et al., Phys. Rev. Lett. 107, 043005 (2011)]. The present paper presents a more detailed description of the methods and results. Furthermore, the paper serves as a stepping stone towards a continuation of the previous study by extending the known level structure of the EF^1\Sigma^+_g state to highly excited rovibrational levels through Doppler-free two photon spectroscopy. Based on combination differences between vibrational levels in the ground state, and between three rotational branches (O, Q and S branches) assignments of excited EF^1\Sigma^+_g levels, involving high vibrational and rotational quantum numbers, can be unambiguously made. For the higher EF^1\Sigma^+_g levels, where no combination differences are available, calculations were performed using the multi-channel quantum defect method, for a broad class of vibrational and rotational levels up to J=19. These predictions were used for assigning high-J EF-levels and are found to be accurate within 5 cm^-1.

Time-dependent wave-packet study of the direct low-energy dissociative recombination ofHD+

Wave-packet methods involving the numerical solution of the time-dependent Schr\"odinger equation have been used with great success in the calculation of cross sections for dissociative recombination of molecular ions by electron impact in the high energy region where the ``boomerang'' model [L. Dube and A. Herzenberg, Phys. Rev. A 11, 1314 (1975)] is valid. We extend this method to study low-energy dissociative recombination where this approximation is no longer appropriate. We apply the method to the ``direct'' low-energy dissociative recombination of ${\mathrm{HD}}^{+}.$ Our results are in excellent agreement with calculations using the multichannel quantum defect method.

Photoionization of the hydrogen atom in strong magnetic fields of White Dwarfs

The photoionization cross-sections of the hydrogen atom in strong magnetic fields of magnetic White Dwarf stars were calculated with a direct numerical integration method using the Landau basis as a high field approach. The validity regime of these solutions overlap with those of the spherical symmetry and complement other recently developed methods. An important result is the relation between the density of states and the normalization for the more than one open channel regime leading to additional coupling terms not taken into account by multi channel quantum defect methods.

Universal and nonuniversal statistical properties of levels and intensities for chaotic Rydberg molecules.

We study Rydberg molecules taking into account the interaction between the rotational motion of the nuclei and the radial motion of the electron. This situation can be treated to a good approximation in quantum mechanics by the multichannel quantum-defect method which in turn has a well-defined classical limit. We are able to calculate very long sequences of levels and the corresponding amplitudes of wave packets. This allows us to study the statistical properties of both in detail. Our interest focuses on aspects of quantum chaos'' that can be particularly well understood in this case. Our main result is that, in a completely chaotic classical situation, where statistics of quantum-level spacings follow the expected universal Gaussian-orthogonal-ensemble behavior, and statistics of line intensities display the expected universal Porter-Thomas behavior, nonuniversal properties are explicitly contained in correlations between intensities and spacings, determined by the time needed for the classical system to mix on a length scale given by the quantum wavelength.

The perturbed even-parity J = 1e, 2e autoionizing spectra of strontium below the 4d5/2 threshold: observation and theoretical analysis

The even-parity J = 1e, 2e autoionizing spectra of neutral strontium are investigated below the 4d5/2 threshold in a two-step laser experiment via the 4d5p 1P1 level in a strontium atomic beam. The produced Sr+ ions are analysed by a time-of-flight microchannel plate detector. The J final level assignment is obtained by comparing the line intensity dependence from two recorded spectra with pi pi and pi sigma polarizations of the two lasers. More than 400 new resonance lines are measured with an accuracy of +or-0.2 cm-1 for the narrow ones using standard laser calibration procedures. They are assigned to fifteen autoionizing Rydberg series 4dns, 4dn d and 4dng and many perturbers belonging to the 5p6p configuration. Interpretation is made by a combination of the eigenchannel R-matrix and multichannel quantum defect methods (MQDT).

The 5dnp and 5dnf J=1 autoionizing series of Ba in one-photon laser excitation from the 6s2 1S0 ground state

The 5dnp, nf J=1 series of barium converging to both the 5d3/2 and 5d5/2 limits were studied in a heat-pipe system in a one-step pulsed UV laser excitation from the atomic ground state. Strong interseries and continuum interactions were observed and experimental evidence of interaction with 6p7s J=1 levels was found. A comparison of the observed spectra with spectra calculated using an eigenchannel R-matrix multichannel quantum-defect method is presented. The agreement is satisfactory in view of the complexity of the calculations.

Convergence of cross sections to their peripheral (Born) limit.

The electron-ion complex formed in a collision is treated by eigenchannel {ital R} matrix and multichannel quantum defect methods. Convergence of the results to the limit of peripheral collisions where the Born approximation holds is displayed. Cascade effects are included quantitatively. Extensive results of electron collisions with alkaline earth ions are illustrated here by the prototype {ital e}+Mg{sup +}.

The (5d3/2,5/2; np and nf) J=1 series in atomic barium

The authors report results, obtained by a multi-step laser excitation technique, on the (5d3/2,5/2; np and nf) J=1 autoionizing states in barium. The observed series exhibit noticeable electronic channel interactions. The agreement between these results and a theoretical approach that combines eigenchannel R-matrix and multichannel quantum defect methods gives further support to this approach.

Multichannel Rydberg spectra of the rare gas dimers

Rydberg levels of several heteronuclear rare gas dimers are treated theoretically by combining multichannel quantum defect methods with a nonperturbative Fermi-type analysis. Calculations confirm many major spectral features observed in experiments by Dehmer and Pratt, and permit the first detailed interpretation and classification of some of the observed spectra. The dimer spectra closely resemble atomic spectra in many cases, while others show dramatic molecular effects.

Near-threshold associative ionisation reactions of atoms

The quantum approach to the theory of endoergic associative ionisation reactions of atoms within the framework of the multichannel quantum defect method taking account of configurational interaction between the Rydberg and valence dissociative states is developed. It has been shown that the total cross section of the AI reaction near the ionisation threshold is proportional to the energy E measured from the ionisation threshold ( sigma AI approximately E). The effect of the resonant quasidiscrete valence states on the ionisation spectrum is studied. As an example, the AI cross section for the reaction N+O to NO++e- is calculated. The temperature dependence of the AI thermal rate coefficients over a broad temperature range has been considered. The effect of a strong monochromatic radiation field on the AI reactions has been discussed.

Photoionization of the E F excited state of H2: Calculation of vibrational branching ratios and photoelectron angular distributions

Vibrational branching ratios and photoelectron angular distributions have been calculated for photoionization from the lowest vibrational levels of the EF state in H2. The Rydberg-continuum dipole transition moments have been evaluated in the Coulomb approximation and the oscillator strengths have been calculated with the multichannel quantum defect method. Rovibronic coupling between continuum final-state channels has been included and rotational/vibrational preionization is also accounted for where it arises. Only minor deviations from the Franck–Condon principle are predicted, primarily related to the promotion of the pσu Rydberg (continuum) orbital. This result disagrees somewhat with the (2+1) REMPI experiment of Anderson, Kubiak, and Zare (1984) near 18.5 eV. On the other hand, the results obtained in a (4+1) REMPI experiment by Cornaggia et al. (1986) at 15.7 eV are correctly reproduced. The possible influence of doubly excited configurations on the photoelectron distributions in various REMPI experiments in H2 is discussed.

The continued fraction method in the theory of slow electron scattering by molecules and molecular ions

Analytical possibilities of the continued fraction method are demonstrated by solving two problems connected with a description of slow electron resonance scattering by positive molecular ions. Using the rotation adiabatic approximation, exact solutions of the multiquantum vibrational transition problem have been found for the fractional-linear approximation of the vibrational adiabatic K matrix. The equivalence of different formulations of the multichannel quantum defect method has been shown. The existence of autoionization states with anomalously small decay widths has been established. The role of simultaneous rotational-vibrational transitions in molecular Rydberg spectra and autoionization is analyzed.

Transitions between Rydberg states of diatomic molecules in slow collisions with atoms

A close analytic representation has been found for the Green function of highly excited diatomic molecule in the framework of the multichannel quantum defect method. This expression has been used to describe the potential energy surfaces of the quasi-molecule X 2 * +A. The specific behaviour of the terms of this system has been studied as a function of the angular orientation of the moleculeX2 and of the distanceR between the molecule and atomA. The terms have been found to have quasi-crossings responsible for the transitions when particles suffer collision. Some terms located near the continuous spectrum boundary, when the distance varies, cross the spectrum boundary and pass into auto-ionization state. Calculations have been made for the system H 2 * +B, whereB is an inert gas atom. Cross-sections of the vibrational transitions occurring under slow atom-molecule collisions have been evaluated.

The absorption spectrum resonance structure of diatomic molecules near the ionization threshold

The problem of the near-threshold photoionization of the non-symmetrical molecules XY is formulated in connection with the problem of scattering of the emitted electrons by molecular ions using the integral multichannel quantum defect methods and results of the adiabatic approximation. In addition to the general theory, analytical formulae are obtained describing the simplest two-channel cases which demonstrate specific features of interference structure of absorption spectra as well as the role of various factors in the formation of the line profile

Rovibronic interactions in the photoabsorption spectrum of molecular hydrogen and deuterium: An application of multichannel quantum defect methods

Multichannel quantum defect theory (MQDT) is applied to the treatment of electron motion in molecular Rydberg states and its coupling to the vibrational and rotational motions of the nuclei. The full rovibronic Hamiltonian is taken into account and the theory formulated in terms of parameters which relate to the standard Born–Oppenheimer (BO) theory. The development is an extension of Seaton’s quantum defect theory and relies on Fano’s frame transformation method. MQDT is not restricted to the BO approximation, but includes the so-called adiabatic corrections and nonadiabatic effects (i.e., vibronic coupling and rotational l uncoupling), however strong, without requiring the explicit evaluation of the interactions between individual levels. The general formalism can be simplified for the H2 and D2 molecules in the range below or near the ionization threshold and for vibrational excitation well below the dissociation energy. The only input data required are the potential energy curve of the ion core in its ground state and the ionization potential (both of which are accurately known), plus two BO potential functions of Σ and Π symmetry, respectively. The theory has been tested in detail using recent experimental and theoretical data on the first five Rydberg absorption transitions of H2 and D2. Theoretical rovibronic levels have been obtained for the B and C states over an extended range of vibrational and rotational quantum numbers on the basis of the best ab initio potential functions currently available. They are found to agree with the experimental levels to within a few cm−1 in all cases, and represent a considerable improvement over previous calculations carried out in the BO and adiabatic approximations with the same potential curves. Conversely, MQDT has been employed to extract BO curves of comparable accuracy for the B′, D, and B″ states directly from the observed levels, without prior evaluation of molecular constants. The higher vibrational levels of the B″ and D states are subject to numerous perturbations by levels belonging to higher Rydberg states: the MQD calculation accounts for these as well, and predicts accurately all Rydberg levels with their manifold interactions, up to the ionization limit. The detailed discussion of these results is deferred, along with the extension to other molecules and to higher energies, into ranges where rotational, vibrational, or electronic preionization, predissociation, or dissociative ionization become important.

Quantum Defect Theory oflUncoupling inH2as an Example of Channel-Interaction Treatment

Formulas are developed which account for the details of the high-resolution photoabsorption spectrum of ${\mathrm{H}}_{2}$ near threshold observed by Herzberg. The treatment illustrates the application of Seaton's multichannel quantum defect method under schematic conditions, and might serve as a basis for further developments.