One and two-photon detachment cross-sections of Ps-

We present detailed calculations for one- and two-photon above-threshold detachment (ATD) cross-sections of the negative positronium ion Ps ^- ( e ⁺ e ^- e ^- ), below the threshold of Ps(n = 2), using a configuration interaction (CI) method on a B splines basis. Both the one- and two-photon detachment cross-sections have a form similar to the corresponding spectra of the H^- ion, scaled accordingly. The peak value of the one-photon cross-section agrees very well with the calculations by Bathia and Drachman [1], while it differs from those by Igarashi et al. [2], which give a value of 15% lower. Two-photon detachment cross-sections are also reported. Received 24 January 2002 / Received in final form 9 April 2002 Published online 19 July 2002     

Helium atom in the monochromatic electromagnetic field

We apply a non-perturbative procedure for the calculation of the total photoionization cross-section of two-electron atomic systems. The procedure is based on the Floquet-Fourier representation of the time-dependent Schr?dinger equation. With the use of the Hylleraas-type basis functions, the total photoionization cross-sections obtained are within the accuracy of a fraction of a percent, which, we believe, is the most accurate estimate for the cross-sections available. The total photoionization cross-sections for neutral helium deviate notably from the benchmark experimental data [J.A.R. Samson et al., J. Phys. B 27, 887 (1994)].     

A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Polarisation effect of laser field in inelastic electron - hydrogen collisions

We study the influence of the laser polarization on the electron impact excitation of atomic hydrogen. Our method takes into account the “dressing” of the target states by including the laser-atom interaction to first order time-dependent perturbation theory, while the interaction of the laser field with the incident electron is treated to all orders by using the non relativist Volkov function. The interaction of the fast projectile with the target atom is treated in the first Born approximation. The calculations are performed via two distinct computations. The first one is based on a direct calculation, the second based on a Sturmian approach. Important differences appear between the angular distributions depending on the polarization chosen. Received : 17 february 1998 / Revised : 20 july 1998 / Accepted : 2 september 1998     

Near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na, K, Rb, Cs; n = 3-6)

The effect of the polarization of the atomic core by the outer electron on near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na-Cs; n=3-6) is investigated. Partial and total cross-sections for photo-ionization of the np-electron were computed utilizing the configuration interaction technique with Pauli-Fock atomic orbitals (CIPF) and including the long range core polarization potential (CP). To calculate the core polarization potential the variational principle is applied. Comparison with previous theoretical results and with available experimental data is made for the total cross-section , for the electron angular distribution parameter , for the ratio of the reduced electric dipole matrix elements and for the phase shift difference , associated with the d-wave and s-wave continua, respectively. In the comparison, new experimental results for , , and , measured for laser-excited, polarized ³⁹K(4p _3/2) atoms, have been included. Received 21 July 1999 and Received in final form 14 October 1999     

Retardation corrections to the angular distributions for the free-bound transitions in H-like atoms

The non-relativistic matrix elements and cross-sections of the radiative recombination for H-like atoms are calculated by considering the retardation corrections up to the first order in . These corrections are evaluated for the transitions to the spherical states using recursion relations which lead to fast and accurate calculations of the cross-sections. Received 4 June 1999     

Temporal coherent control induced by wave packet interferences in one and two photon atomic transitions

The interaction of a sequence of two identical ultrashort laser pulses with an atomic system results in quantum interferences as in Ramsey fringes experiments. These interferences allow achievement of temporal coherent control of the excitation probability. We present the results of a temporal coherent control experiment on two different atomic systems: one-photon absorption in K (4s-4p) and two-photon absorption in Cs (6s-7d). In K, the quantum interferences between the two excitation paths associated with the laser pulses are revealed through rapid oscillations of the excitation probability as a function of the time delay between the two pulses. These oscillations take place at the transition frequency (period T = 2.56 fs). The interferences are modulated by beats (at about 580 fs) resulting from the doublet structure of the excited state (4p (² P _1/2 , ² P _3/2 )). Three complementary interpretations of this experiment are presented: in terms of beats of quantum interferences, of variation in the spectrum intensity, and of wave packet interferences. Whenever the two laser pulses are temporally overlapped, optical interferences are superimposed on to the quantum interferences. The distinction between these two types of interference is clearly revealed in the two-photon excitation scheme performed on Cs (6s-7d (² D _3/2 , ² D _5/2 )) because quantum interferences occur at twice the frequency of the optical interferences. Received: 30 December 1997 / Revised: 28 February 1998 / Accepted: 4 March 1998     

Photoionization cross-sections of the first excited states of sodium and lithium in a magneto-optical trap

A two element magneto-optical trap (MOT) for Na and ⁷Li or ⁶Li is used to cool and trap each of them separately. A fraction of the cold atoms is maintained in the first ²P_3/2 excited state by the cooling laser. These excited state atoms are ionized by laser light in the near-UV region, giving rise to a smaller number of trapped atoms and to different loading parameters. Photoionization cross-sections were derived out of these data. They are in reasonable agreement with data previously obtained using thermal samples and with theoretical predictions. Received 21 March 2001 and Received in final form 3 August 2001     

Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrödinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.     

Relativistic R-matrix close-coupling calculations for photoionization of Ne-like Al IV

We present relativistic close-coupling photoionization calculations of Al IV using the Breit-Pauli R-matrix method to obtain photoionization cross-section of Al IV from the ground state and the lowest two J=0 (even) excited states. A multi-configuration eigenfunctions expansion of the core Al V is employed with spectroscopic configurations 2s²2p⁵, 2s2p⁶, 2s²2p⁴3s, 2s²2p⁴3p, 2s²2p⁴3d and 2s²2p⁴4s. We have included, for the first time, the lowest 68 level target states of Al V in the photoionization calculations of Al IV. Extensive configuration interaction wavefunctions are used to describe both the initial Al IV states and the final Al V states. Cross-sections are compared from three level calculations including only 2s² 2p^{5 2}P^o _3/2, _1/2 and 2s 2p^{6 2}S_1/2 levels of Al V. The present calculation using the lowest 68 target levels of Al V are presented for the first time and should provide reasonably complete database for practical application for photoionization cross-section for Al IV, where high-energy cross-sections along with near-threshold photoionization cross-section is required.     

Interaction of frequency modulated light pulses with rubidium atoms in a magneto-optical trap

The spatial displacement of the ⁸⁵Rb atoms in a Magneto-Optical Trap (MOT) under the influence of series of frequency modulated light pulse pairs propagating opposite to each other is measured as a function of the time elapsed after the start of the pulse train, and compared with the results of simulations. Adiabatic excitation and consecutive de-excitation take place between the ground 5²S_1/2 (F=3) and the 5²P_3/2 (F'=2, 3, 4) excited levels as the result of the interaction. The displacement of the ⁸⁵Rb atoms is calculated as the solution of simple equation of motion where the expelling force is that arising from the action of the frequency modulated light pulses. The restoring and friction forces of the MOT are taken into account also. The system of Bloch equations for the density matrix elements is solved numerically for transitions between six working hyperfine levels of the atom interacting with the sequence of the frequency modulated laser pulses. According to these simulations, the momentum transferred by one pulse pair is always smaller than the expected 2ħk, (1) where ħ is the Plank constant and k=2π/λ where λ is the wavelength, (2) having a maximum value in a restricted region of variation of the laser pulse peak intensity and the chirp.     

Electron angular distributions in double photoionization: Use of effective Sommerfeld parameters

We present calculations of the fivefold differential cross-section (FDCS) for double photoionization of helium at excess energies of 6 and 20 eV above threshold. Our results are obtained using for the final double-continuum state a product of three Coulomb wave functions, with the Sommerfeld parameters modified to describe the strength of interaction of any two particles affected by the third particle. Our calculations are compared with recent absolute measurements by D?rner et al. (Phys. Rev. A 57, 1074 (1998)), both in coplanar and non-coplanar geometries. Very good agreement is obtained for the shape of the angular distributions, and differences in the absolute magnitude exist in comparison with the standard choice of Sommerfeld parameters. Received: 17 July 1998 / Received in final form and Accepted: 23 October 1998     

Acceleration of cold Rb atoms by frequency modulated light pulses

The displacement of Rb atoms in a magneto-optical trap (MOT) caused by the force of a finite time series of counter-propagating frequency modulated light pulse pairs is measured as a function of the chirp of the pulses. The frequency modulated light pulses induced ⁸⁵Rb 5²S_1/2 F=3 ↔ ⁸⁵Rb 5²P_3/2 F'=2, 3, 4 excitation and de-excitation of the atoms. The result of this excitation de-excitation process is a force causing the acceleration and, consequently, the displacement of the maximum of the spatial distribution of the trap atoms. The time dependence of the populations of the levels of the atom are calculated — including also the ⁸⁵Rb 5²S_1/2 F=2 and F'=1 states — as the result of the interaction with the finite train of counter propagating frequency modulated light pulses by the solution of the Bloch equations. As the result of the measurement the interval of the chirp of the frequency modulated light of given intensity where the transitions take place, are determined. The results of the experiment and the expectation on the basis of model calculations are in qualitative agreement.     

Sisyphus cooling of rubidium atoms on the line: The role of the neighbouring transitions

We study one-dimensional Sisyphus cooling on the transition of ⁸⁷ Rb atoms in the electric field created by two counter-propagating linearly polarized laser beams with an angle of between the polarization directions. The neighbouring F '=0 and F '=2 excited states are found to play an important role in the cooling mechanism, e.g., by inhibiting a significant population of the velocity-selective dark state. Our experimental data, such as temperatures and probe absorption coefficients, agree well with the results of quantum Monte-Carlo wavefunction simulations. Received 26 November 1998 and Received in final form 20 April 1999     

Cold inelastic collisions between lithium and cesium in a two-species magneto-optical trap

We investigate collisional properties of lithium and cesium which are simultaneously confined in a combined magneto-optical trap. Trap-loss collisions between the two species are comprehensively studied. Different inelastic collision channels are identified, and inter-species rate coefficients as well as cross-sections are determined. It is found that loss rates are independent of the optical excitation of Li, as a consequence of the repulsive Li^*-Cs interaction. Li and Cs loss by inelastic inter-species collisions can completely be attributed to processes involving optically excited cesium (fine-structure changing collisions and radiative escape). By lowering the trap depth for Li, an additional loss channel of Li is observed which results from ground-state Li-Cs collisions changing the hyperfine state of cesium. Received 28 December 1998 and Received in final form 16 February 1999     

Reflection of thermal atoms by a pulsed standing wave

Reflection of thermal atoms by a pulsed standing wave with a duration in the nanosecond range is studied. The momentum distribution of the reflected atoms is determined by calculations based on the adiabatic atom-photon interactions. It is shown that with a proper choice of the field intensity and the pulse duration the standing-wave pattern functions as a row of independent atom mirrors. At an optimum choice of the parameter values, the fraction of the elastically reflected atoms is more than 20%. Furthermore, we show that the pulsed standing-wave mirror can be used to manipulate their final momentum distribution. When using laser pulses with an intensity of several tens of MW/cm², tens of thousands of atoms can be reflected by a single laser pulse. Received 3 December 1999 and Received in final form 25 April 2000     

Effect of electron correlation on positronium formation in positron-helium scattering

A three-parameter correlated wave function for the helium ground state is used to study the scattering reaction , where Ps stands for positronium atom. An exact analytical expression is constructed for the first Born scattering amplitude for Ps formation from helium. Based on this numerical results are presented for both differential and total cross-sections. It is demonstrated that the inner electronic correlation of the target atom plays a crucial role in explaining the discrepency between theory and experiment. Received: 9 April 1998 / Revised: 29 September 1998 / Accepted: 19 October 1998     

Measurement of total M shell photoionization cross sections for Au,Pb, Th and U in the energy region 6–12 keV

The total M shell relative photoionization cross-sections for Au, Pb, Th and U have been measured in the energy region 6–12 keV. External conversion K X-rays of suitable elements has been employed as incident photons to photo ionize the total M shell of elements under investigation. The method provides relative cross-sections therefore does not make use of theoretically calculated average M shell fluorescence yields which involve uncertainties of the order of 20%. No evidence of deviation from calculated values of cross-sections have been observed within experimental errors for all incident photon energies.     

Photoionization cross-section measurements from the 2p, 3d and 3s excited states of lithium

The photoionization cross-sections from the 2p²P_{1/2, 3/2}, 3d²D_{3/2, 5/2} and 3s²S_1/2 excited states of lithium have been measured at different ionizing laser wavelengths, above the first ionization threshold. The experiments are performed by using a thermionic diode working in the space charge limited mode and the cross-sections are measured by employing the saturation technique. By changing the ionization photon energy, a smooth frequency dependence of the cross-sections has been observed for the 2p and 3d states. The cross-section from the 3s excited state has been measured at a single photon energy. The measured values of the photoionization cross are compared with the available data.     

Buffer-gas loaded magnetic traps for atoms and molecules: A primer

Over the past three years we have developed the technique of buffer-gas cooling and loading of atoms and molecules into magnetic traps. Buffer-gas cooling relies solely on elastic collisions (thermalization) of the species-to-be-trapped with a cryogenically cooled helium gas and so is independent of any particular energy level pattern. This makes the cooling technique general and potentially applicable to any species trappable at the temperature of the buffer gas (as low as 240 mK). Using buffer-gas loading, paramagnetic atoms (europium and chromium) as well as a molecule (calcium monohydride) were trapped at temperatures around 300 mK. The numbers of the trapped atoms and molecules were respectively about 10¹² and 10⁸. The atoms and molecules were produced by laser ablation of suitable solid precursors. In conjunction with evaporative cooling, buffer-gas loaded magnetic traps offer the means to further lower the temperature and increase the density of the trapped ensemble to study a large variety of both static (spectra) and dynamic (collisional cross-sections) properties of many atoms and molecules at ultra-low temperatures. In this article we survey our main results obtained on Cr, Eu, and CaH and outline prospects for future work. Received 2 November 1998 and Received in final form 19 February 1999