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In a recent Letter to the Editor (J Rao, D Delande and K T Taylor 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L391-9) we made a brief first report of our quantal and classical calculations for the hydrogen atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength. A principal point of that communication was our statement that each and every peak in the Fourier transform of the scaled quantum photo-excitation spectrum for scaled energy value = -0.586 538 871 028 43 and scaled electric value = 0.068 537 846 207 618 71 could be identified with a scaled action value of a found and mapped-out closed orbit up to a scaled action of 20. In this follow-up paper, besides presenting full details of our quantum and classical methods, we set out the scaled action values of all 317 closed orbits involved, together with the geometries of many.

We consider n = 20 Rydberg states of the hydrogen atom interacting with a nearby metal surface over an atom - surface distance range of 105 nm - 530 nm. We show that the traditional quadratic approximation to the potential is insufficient to follow the true potential and one needs to include higher order terms to obtain accurate energies for these Rydberg states. We include terms up to eighth order in the electron-proton distance in the potential and demonstrate by means of basis set calculations that the resulting spectra differ significantly from those obtained in the quadratic approximation. We observe an energy spread of the n = 20 manifold which is roughly twice that given by the quadratic approximation. Observed level repulsions are attributed to z-parity symmetry breaking. We compare our results with those from degenerate perturbation theory.

The combined R-matrix, complex-coordinate rotation method is extended, by incorporating a frame transformation, to allow the calculation of the near-threshold spectrum of a simple molecule, para-H2, in the presence of a laboratory strength magnetic field. The below-threshold photoabsorption spectrum obtained is in very good agreement with that from a previous calculation using a different method and the role of excited rotational states of the parent molecular ion in the above-threshold spectrum is identified.

The new method recently presented by Halley et al., combining R-matrix and complex coordinate rotation methods for the calculation of near-threshold resonance dominated spectra, is extended and applied to the calculation of spectra in electric and parallel electric/magnetic fields. Results obtained for the Stark spectra of the sodium atom above the classical ionization threshold are in excellent agreement with experimental findings and those from a previous calculation using a semiclassical method. Results obtained for the sodium atom in the same energy region but in parallel electric and magnetic fields represent the first obtained for any non-hydrogenic atom in such combined fields above the classical ionization threshold.

During an examination of different cell types for CD36 mRNA splice variants, a partial cDNA from HEL cells was isolated and characterized. This CD36 cDNA had a 309-base pair deletion following the region encoding the first putative transmembrane domain of CD36. The open reading frame of the deleted CD36 cDNA was retained and was predicted to yield a protein lacking 103 amino acid residues. The presence of this variant was confirmed in RNA pools from placental tissue by a reverse transcriptase-coupled polymerase chain reaction assay. Comparison of the HEL CD36 cDNA with the genomic sequence revealed that the mRNA represented by this variant CD36 cDNA was produced by a pre-mRNA splicing reaction that excluded exons 4 and 5. Transient expression of the variant CD36 cDNA in COS-1 cells showed that CD36 immunoreactive protein was expressed on the cell surface but lacked an antigenic epitope defined by amino acid residues 41-143. This cell surface glycoprotein (M(r) approximately 57,000) was of identical molecular weight as a CD36 isoform observed on the surface of HEL cells. The exclusion of exons during CD36 pre-mRNA processing appears to be conserved within one other CD36 gene family member, CLA-1.

Full details are presented of the new method of Halley et al. (1992) for the calculation of near-threshold resonance-dominated spectra. This method combines the R-matrix and complex coordinate techniques and has necessitated an extension of quantum defect theory to calculate an appropriate irregular Coulomb function for complex energy and complex radial distance. The method is discussed in particular in its application to the near-threshold photoabsorption spectra of a non-hydrogenic atom in a laboratory strength magnetic field and applied here to the examples of strontium and barium. Excellent agreement is obtained with experimental measurements.

The R-matrix and complex coordinate techniques are combined for the first time and applied to the problem of the positive energy spectrum of a non-hydrogenic atom in a laboratory strength magnetic field. Quantum defect theory is extended to calculate the appropriate irregular Coulomb function at complex energy and complex radial distance. Calculations are carried out for lithium to compare with previous experimental measurements and with a corresponding calculation for hydrogen.

Experimental and theoretical data for energy levels and radiative transitions in Fe VIII and Fe VII are very scarce. The authors' study is a first attempt to present a comprehensive set of data, using an ab initio target representation. The close coupling approximation is used in LS coupling, including the first 9 and 31 terms of Fe8+ and Fe7+ respectively. This detailed and systematic approach generates a sound basis for future experimental and more accurate theoretical investigations. The results demonstrate the importance of electron correlation and core excitation effects in these ions.

Multiphoton detachment rates have been obtained for Na− using the R-matrix Floquet (RMF) approach. In the low intensity limit agreement has been found with recent theoretical calculations of the total photodetachment cross section. At intensities of 1010 W cm−2 two-photon above threshold detachment rates are presented and similarities with earlier calculations in Li− are discussed. Also at this intensity, three-photon rates are investigated for energies ranging from below the 3p 2P° threshold to the 4p 2P° threshold.

The Multiphoton and Electron Collisions Consortium is formed from groups of scientists working at problems demanding High Performance Computing resource at the following institutions: The Queen’s University of Belfast Durham University Imperial College London Oxford University University College London CLRC Rutherford Appleton and Daresbury Laboratories

While both diamagnetic and Stark spectra of hydrogen can be analyzed accurately in terms of classical orbits, in nonhydrogenic atoms the multielectron core induces additional spectral modulations that cannot be analyzed reliably in terms of standard periodic orbit-type theories. However, by extending closed-orbit theory to include core-scattered waves consistently, both diamagnetic and Stark photoabsorption spectra of nonhydrogenic Rydberg atoms at constant scaled energy can be analyzed semiclassically using only the closed orbits of the corresponding hydrogenic systems. Frequencies and amplitudes of the core-scattered modulations, as well as corrected amplitudes for contributions from repetitions of primitive hydrogenic orbits, are found to be in excellent agreement with quantum results. We consider whether these nonhydrogenic systems correspond to quantum chaos. \textcopyright{} 1996 The American Physical Society.

We study the behaviour of hydrogen and helium atoms in intense two-colour linearly-polarised laser fields. Two cases are considered - the case where both fields act with parallel axes of polarisation and the case where the polarisation axes are perpendicular. We report extensions of the HELIUM code and a related hydrogen code to study these two cases of the two-colour problem. The impact of the second laser pulse on the harmonic spectrum is explored.

The spectrum of hydrogen in a magnetic field is a paradigm of quantum chaos and may be analyzed accurately by periodic-orbit-type theories. In nonhydrogenic atoms, the core induces pure quantum effects, especially additional spectral modulations, which cannot be analyzed reliably in terms of classical orbits and their stability parameters. Provided core-scattered waves are included consistently, core-scattered modulations as well as corrected amplitudes for primitive orbits are in excellent agreement with quantum results. We consider whether these systems correspond to quantum chaos.

During an examination of different cell types for CD36 mRNA splice variants, a partial cDNA from HEL cells was isolated and characterized. This CD36 cDNA had a 309-base pair deletion following the region encoding the first putative transmembrane domain of CD36. The open reading frame of the deleted CD36 cDNA was retained and was predicted to yield a protein lacking 103 amino acid residues. The presence of this variant was confirmed in RNA pools from placental tissue by a reverse transcriptase-coupled polymerase chain reaction assay. Comparison of the HEL CD36 cDNA with the genomic sequence revealed that the mRNA represented by this variant CD36 cDNA was produced by a pre-mRNA splicing reaction that excluded exons 4 and 5. Transient expression of the variant CD36 cDNA in COS-1 cells showed that CD36 immunoreactive protein was expressed on the cell surface but lacked an antigenic epitope defined by amino acid residues 41-143. This cell surface glycoprotein (M(r) approximately 57,000) was of identical molecular weight as a CD36 isoform observed on the surface of HEL cells. The exclusion of exons during CD36 pre-mRNA processing appears to be conserved within one other CD36 gene family member, CLA-1.

We present a new method for computing the spectrum of one-electron Rydberg states of non-hydrogenic atoms in a magnetic field, at constant scaled energy. It is based on a variant of the R-matrix method allowing the computation of many energy levels in a single diagonalization. The results are compared with recently obtained high-resolution experimental spectra of the helium atom. The relation between peaks observed in the Fourier transform of scaled spectra and classical closed orbits is discussed. We show the existence of 'ghost' peaks not corresponding to any closed orbit, and also of peaks existing only in non-hydrogenic spectra, due the scattering of the electron by the ionic core. © 1994 IOP Publishing Ltd.

This paper will be concerned with the quantum mechanical theory and associated calculations developed to treat atoms in strong laboratory strength (1–5 tesla) magnetic fields. These developments began in the early seventies in attempts to understand spectra of the alkaline earths obtained in the pioneering measurements by Garton and Tomkins [1], but, (together with those in classical theory), have been greatly stimulated over the last few years by the high resolution measurements on atomic hydrogen, made by the Bielefeld group [2].

A number of ‘large‐scale’ calculations using supercomputers are discussed including the generation of atomic data in the Opacity Project; the diagonalisation of large matrices on the CRAY X‐MP/48, and application in state‐of‐the‐art calculations on electron‐helium scattering; the novel topic of Rydberg states of diatomic molecules in a magnetic field. The use of linked arrays of transputers is considered, not only in relation to large existing FORTRAN codes but also with new codes employing extremely advantageous algorithms.

The R-matrix theory of photoionization described by Burke and Taylor (1975) is used to obtain cross sections for the photoionization of ground-state carbon and oxygen atoms. The calculations are the first to couple systematically all channels corresponding to the 2s22p1, 2s2pq+1 and 2p1+2 configurations of the residual ion. The results are in good agreement with experiment where comparison is possible.

The programming of the R-matrix method recently used to calculate total and partial atomic photoionisation cross sections has been extended to enable photoelectron angular-distribution beta parameters to be studied for a general atomic system. The program has been used to calculate the beta -parameters for photoelectrons ejected from the outer p subshell of both neon and argon atoms. Good agreement with absolute experiments has been obtained in non-resonant regions. In resonant regions the results are the first to be obtained and have been parametrised according to the prescription of Kabachnik and Sazhina (1976).

The asymmetry parameter beta of photoelectrons ejected from the 2s shell of carbon have been calculated for three carbon ionic states, 4Pe, 2De and 2Se. The large departures from the Cooper-Zare value of 2 in each case can be understood systematically in the angular momentum transfer theory of Dill and Fano.

The authors have calculated the 3p photoionisation cross section of K2+ (isoelectronic series of Cl, with ground-state configuration 3p5) using R-matrix theory. The results of two calculations, one involving a 3d pseudo-orbital, are compared with the authors' previous ones beyond the 3p4 1Se threshold, and, for the first time, various families of autoionisation resonances are pointed out and analysed in terms of Fano's parameters and quantum defects. This analysis concerns Rydberg series converging on the 1De and 1Se thresholds, since they describe the residual ion K3+ (3p4) from its lowest three terms: 3Pe, 1De and 1Se.

A method has been developed to calculate the spectrum over the $l$- and $n$-mixing regimes of an arbitrary nonhydrogenic system in an external laboratory-strength magnetic field. The original experimental results on Sr and Ba are explained in detail for the first time. The importance of quadratic Zeeman spectroscopy in the quantitative study of atomic structure is made clear.

For pt.VI, see ibid., vol.20, p.6447-56 (1987). Energy levels, f values and photoionisation cross sections are calculated for He-like ions using methods described in paper II of this series. The 'target' states included in the close-coupling expansions are 1s, 2s, 2p, 1p and 1d, where 1p and 1d allow for dipole and quadrupole polarisation, respectively, of 1s. The calculations are made for all bound states 1snl with n

The authors have analysed the linear Zeeman effect (LZE) for Rydberg states of the H2 molecule. Three distinct angular momentum coupling schemes are found to be appropriate for different regions of the molecular wavefunction. Using quantum defect theory the authors have calculated energy level positions and line intensities for n>5 for photoabsorption from the 1 Sigma g+ ( nu =0, J=0) ground state of H2. The authors find that: (i) whereas in the absence of a magnetic field the dipole selection rule restricts upper states to be pure J=1, the removal of J conservation by the field means that transitions to states dominated by J=2, 3, 4, 5, . . . also become accessible in the range B=1-30 T; (ii) The M degeneracy is removed by the field. There are wide variations in behaviour between corresponding lines for different M.

Accurate results for the photoionisation of the Si+ (3s23p 2P0) ground state are reported for the photon energy region between the first two ionisation thresholds, Si2+ (3s2 1Se, 3s3p 3P0), at 750 and 540 AA. The cross section is dominated by the autoionised 3P0 np, nf (n>or=4) Rydberg series, whose shapes and oscillator strengths are drastically perturbed by the 1P0 4p 2Se, 2De interlopers. These results are the first outcome of an elaborate calculation, based on a consistent LS multichannel description of the initial bound state and the final continua. The ejection of one valence electron is allowed for, together with flexible relaxation within the remaining valence shell, and possible monoexcitation into a near-spectroscopic orbital (3d, 4s, 4p). This extensive calculation (12 ionic states, up to 22 channels) is the first application of a new numerical approach combining the advantages of the R-matrix and the multichannel quantum defect (MQDT) theories.

Dynamic dipole polarisabilities for neon and argon have been calculated using the R-matrix approach presented and discussed in a previous paper. The dynamic dipole polarisabilities are calculated for the ground states of the atoms for photon frequencies ranging from zero up to at least the first pole. A comparison is made between the results of calculations which omit and include the R-matrix surface contributions and values derived for the oscillator strengths for transitions from the ground state of each atom are presented.

The authors describe a method of calculating highly excited states of hydrogen in uniform magnetic fields of moderate strength ( approximately 5T). Results for Balmer emission lines and an approximate photoabsorption spectrum for Cs are presented. The authors comment on the use of adiabatic approximations and the role of the spin-orbit interaction.

For pt.II. see ibid., vol.20, p.6379-97 (1987). The close-coupling methods described in paper II are used to calculate oscillator strengths, f, for all transitions between energy levels of C II having effective quantum numbers V

The R-matrix method is used to calculate the photoionization cross section of ground state aluminium atoms Al(2P0), leaving the residual ions in their ground Al+(1Se) or first two excited states Al+(3P0,1P0). The initial bound state Al(2P0) as well as the three possible final continuum states (Al++e-)(2Se,2Pe, 2De) are represented consistently by R-matrix expansions in terms of three lowest states of the ion Al+(1Se,3P0,1P0). These ionic states are in turn described by accurate configuration-interaction wavefunctions. Good agreement is obtained with recent experiments by Kohl and Parkinson (1975) and by Esteva (1974) and results probably accurate to better than 15% are given from 2070 AA to 570 AA.

The R-matrix method described by Burke and Taylor (1975) is used to calculate photoionisation cross sections of carbon atoms from 1s22s22p2 3Pe, 1De and 1Se states. Configuration-interaction wavefunctions are used both for the initial and final states involving all terms of the 1s22s22p, 1s22s2p2 and 1s22p3 configurations of the singly ionised carbon-ion core. Total and partial cross sections are obtained from threshold down to below 350 AA and are presented in the form of figures. Tables of the results have been prepared and are available from the authors.

The authors present the oscillator strengths for dipole transitions to high Rydberg states for hydrogen in a magnetic field of 47 kG. The complex spectra can be largely understood in terms of independent, weakly interacting series.

A quantum mechanical study of a simple two-dimensional problem identifies lines in coordinate space about which the probability densities are localised. These lines in general do not correspond to extrema in the system's static potential energy surface. The subject of this study has been the hydrogen atom in externally applied parallel electric and magnetic and magnetic fields. Probability density plots of eigenstates, in which the electron experiences comparable influences from all three fields: Coulomb, electric and magnetic, are each found to display a localisation at a polar angle related to an invariant previously obtained in a classical study of the problem. The line about which localisation occurs is found to vary with energy and is in coincidence with a periodic trajectory found within a classical framework.

An extension of the R-matrix theory of atomic photoionisation of Burke and Taylor (1975) to allow calculations within a pair-coupling scheme is reported. An application to the calculation of the photoionisation cross section and asymmetry parameter in the region of the Beutler-Fano resonances in argon is presented. The origins of phenomena not previously ascribable to any particular relativistic term in the Hamiltonian are accounted for.

The R-matrix method, which has been used recently to calculate electron-atom and ion collision cross sections and atomic polarizabilities is extended to enable atomic photoionization processes to be studied. Both the initial atomic bound state and the final atomic continuum state are expanded in terms of R-matrix bases. The method is programmed for a general atomic system and then used to calculate the photoionization cross sections of ground state neon and argon atoms leaving the residual ions in their ground or first excited states. Good agreement is obtained with recent experiments using synchrotron radiation both in resonant and non-resonant regions, showing that the method has a wide range of applicability.

The field desorption spectra of [(L)M(CO) 3 ] + BF 4 − [M = Fe, L = cyclo-C 6 H 7 , cyclo-C 7 H 9 , cyclo-C 10 H 11 , 2-MeO-cyclo-C 6 H 7 ; M = W, L = cyclo-C 7 H 7 ], [(Ar)Fe(C 5 H 5 )] + PF 6 − [Ar = C 6 H 6 , CH 3 C 6 H 5 , (CH 3 ) 3 C 6 H 3 ], [(cyclo-C 8 H 11 )Co(C 5 H 5 )] + BF 4 − and [(C 6 H 6 )Cr(CO) 3 ] have been obtained. In all cases molecular or quasi-molecular ions for the cations were present, usually as the base peaks in the spectra. Fragment ions corresponding to metal—ligand cleavages were also found in most cases.

The authors obtain a classification of the 'b' and 'c' resonances in electron scattering by neon, which supports previous conjectures made on the basis of the grandparent model.

A new set of periodic orbits is found in the irregular region for the hydrogen atom in a magnetic field. The quantisation of these orbits is discussed and new level spacings near the zero-field threshold are predicted.

Initial results are presented on the elastic scattering of electrons by argon atoms in the neighbourhood of the well known ((3p5)3/2,1/2(4s)2) resonances. An R-matrix calculation is employed to investigate how the resonance characteristics change as the spin-orbit interaction is switched on.

The authors examine the 2F spectrum of caesium in the presence of a 70 kG magnetic field. The effect on the photoabsorption of the small quantum defect of the f wave (about 0.03), due to the long-range polarisation field, is highlighted by investigating both the inter-l and inter-n mixing regimes.

Zimmerman, Kash and Kleppner1 have recently posulated the existence of a ‘hidden’ symmetry in atomic hydrogen in a uniform magnetic field. We have drawn similar conclusions from independent work2. Here, we show that the quasi-constant of the motion in this system can be related in a simple way to the asymptotic form of the quantum mechanical wavefunction. This development is consistent with the broad outline drawn by Fano3,4 who has emphasized the role of this particular problem as a member of a large and important class of dynamical systems characterized by the existence of motion along a ‘ridge’ of a potential surface.

There have been many new developments in the analysis of the quadratic Zeeman effect, both in theory and experiment since the last meeting (Nayfeh and Clark.1New high resolution experiments on hydrogen have revealed a dense series of sharp lines near and above the ionization threshold by Holle et al.,2 and Main et al.3 showing that the lower resolution quasi-Landau modulations of Garton and Tomkins4 are full of structure. A Fourier transform of the absorbtion spectrum also revealed new modulations. Theoretically the large basis set calcultions for hydrogen by Clark and Taylor5 harve been taken higher in energy towards threshold by Wintgen and Freidrich,6 Delande and Gay,7 and Wunner et al.8 There has followed a parallel development in the semi-classical treatment of the problem by Al-Laithy et al.,9 and Wintgen and Freidrich.10 The quadratic Zeeman effect for atoms has proved to be a physically realizable quantum system whose classical Hamiltonian exhibits chaotic motion. The consequences of this will be discussed in detail in Section 3, but initially in Section 2 we will describe a new approach which extends the basis set methods to non-hydrogenic systems O’Mahony and Taylor.11