One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/205/pdf

Applications of B-splines in atomic and molecular physics

The interaction of an atom with an ultra-intense radiation field is characterized by the involvement of many photons in absorptions and emissions. Of course the word 'intense' has to be compared with some atomic reference: if the induced transition coupling between bound states exceeds inherent widths, then the dressed atom Rabi oscillations which dominate the atomic evolution are typical intense field effects, even though laser intensities may actually be quite modest. When laser intensities exceed IOi3 Wcm-', and infrared frequencies are employed, tben free electrons are dressed by interaction energies which exceed the photon energies. Non-perturbative continuum processes such as above- threshold ionization then occur, combined with the emission of very high order harmonics ofthe pump laser frequency. At higher laser intensities, the optical electric field can exceed the Coulombic binding electric field and allow aver-the-barrier ionization. which defines a new regime of high intensity physics. In this region (or at higher intensities) the atomic electron charge cloud oscillates in the laser field with large amplitude excursions from the nucleus, during which time it is unable to absorb further photons. This stabilization regime is predicted to persist until the electron dressing energy approaches the restmass energy when wholly unexplored regions remain 10 be investigated. In this topical review, we examine theorelied models of atoms dressed by intense fields. We review the breakdown of lowest-order perturbation theory and those 'essential states' methods adopted to include Rabi frequencies, Stark shifts, induced widths and continuum dressing. Newer methods more suitable for super-svong fields are described, such as Floquet and Valkov methods and the direct numerical integration ofthe Schr6dinger equation. Such methods are used to provide completely non-perturbative strong field descriptions of atomic dynamics. We conclude with a brief examination of the relativistic effects expected to be important when new high intensity ultrashort pulse lasers currently under development are employed in strong field physics.

/pdf/atoms-in-ultra-intense-laser-fields-41msu3cq5z.pdf

Atoms in ultra-intense laser fields

We present a quantitative study of radiation amplification without population inversion based on models recently proposed by Harris (Phys. Rev. Lett. 62, 1033 (1989)). We discuss both two-level and three-level arrangements in terms of the density matrix. Our calculations, which are fully time dependent, incorporate an incoherent pumping mechanism that is essential for amplification. We discuss in detail the range of and conditions on atomic parameters for which amplification is possible. Its feasibility is demonstrated through the direct calculation of the change of the intensity of a probe beam interacting with the atom.

Radiation amplification through autoionizing resonances without population inversion.

Two-photon ionization of atomic helium has been measured by combining femtosecond extreme-ultraviolet pulses from the free-electron laser in Hamburg (FLASH at DESY) with intense light pulses from a synchronized neodymium-doped yttrium lithium fluoride laser. Sidebands appear in the photoelectron spectra when the two laser pulses overlap in both space and time. Their intensity exhibits a characteristic dependence on the relative time delay between the ionizing and the dressing pulses and provides an inherent time marker for time-resolved pump-probe experiments. The measurements of the sidebands are in good agreement with theoretical predictions and allow for a direct analysis of two-photon ionization, free from processes related to interference between multiple quantum paths.

/pdf/two-color-photoionization-in-xuv-free-electron-and-visible-3ef0mknmws.pdf

Two-color photoionization in xuv free-electron and visible laser fields

We report the first observation of an asymmetric autoionizinglike line shape in the ionization of atomic Na due to laser-induced continuum structure. The results are in very good agreement with a theoretical time-dependent analysis employing independently calculated atomic parameters combined with the instrumental parameters of the experiment.

Observation of laser-induced continuum structure in ionization of sodium

We apply multichannel-quantum-defect theory (MQDT) to multiphoton ionization of rare gases in lowest-order perturbation theory. We determine MQDT parameters of J = 1,3 odd-parity states, J = 0,2 even-parity states in xenon and krypton by fitting experimental energy levels and constructing Lu-Fano plots. We present calculations of two- and three-photon ionization of xenon and krypton in the autoionization region between the two thresholds. We compare autoionization spectra and also photoelectron angular distributions to experimental data (S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Phys. Rev. A 35, 3793 (1986); J. L. Dehmer, S. T. Pratt, and P. M. Dehmer, ibid. $fat 36: , 4494 (1987)). Agreement between theory and experiment is reasonable, especially for krypton.

Multiphoton ionization of rare gases using multichannel-quantum-defect theory.

We present a theoretical analysis of a recent experiment [ J. Opt. Soc. Am. B6, 1513 ( 1989)] on two-color three-photon ionization of Xe through resonant even-parity Rydberg states. We calculate second-order ac-Stark shifts, two-photon Rabi frequencies, and ionization widths by using wave functions obtained from a multichannel quantum-defect-theory analysis of the Rydberg series in Xe. We perform a detailed description of the experiment, using the density-matrix formalism, accounting for the temporal and spatial distributions of the laser fields. The agreement with the experiment is good except for the ac-Stark shift of the Rydberg states, which, in our calculation is close to the ponderomotive energy, whereas in the experiment it is measured to be half of this value.

Theoretical aspects of three-photon two-color ionization of xenon through ac-stark-shifted resonant Rydberg states

A Comment on the Letter by M. H. R. Hutchinson, and K. M. M. Ness, Phys. Rev. Lett. 60, 105 (1988).

Comment on "Laser-induced continuum structure in xenon"

We present a theoretical interpretation of the experimental results on three-photon-resonant four-photon ionization of Kr reported by Landen, Perry, and Campbell [Phys. Rev. Lett. 59, 2558 (1987)] and Perry and Landen [Phys. Rev. A 38, 2815 (1988)]. Our calculations are based on multichannel quantum-defect theory combined with a density-matrix formalism describing the spatiotemporal development of the process. We obtain good agreement with the data, which even at intensities as high as ${10}^{14}$ W/${\mathrm{cm}}^{2}$ show the imprint of the underlying atomic structure.

Theory of resonant multiphoton ionization of krypton by intense ultraviolet laser radiation.

Using complex scaling and a correlated basis constructed in terms of B splines, we calculate the ${\mathrm{Li}}^{+}$ photoion yield in the presence of a laser-induced coupling between the triply excited ${2s}^{2}{2p(}^{2}{P}^{o})$ and ${2s2p}^{2}{(}^{2}{D}^{e})$ resonances in lithium, the first of which is assumed to be excited by synchrotron radiation from the ground state. The laser coupling between the triply excited states is shown to lead to a significant and readily measurable modification of the line profile which provides a unique probe of the dipole strength between highly correlated triply excited states. We also present results for some higher-lying triply excited states of ${}^{2}{P}^{o}$ symmetry.

/pdf/laser-induced-transitions-between-triply-excited-hollow-m2gzjezab3.pdf

Laser-induced transitions between triply excited hollow states

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