Multiple collisions in molecular beam scattering experiments

Due to the forward peaked differential cross section for elastic atom—atom scattering the effect of multiple collisions has to be considered in the analysis of crossed beam measurements of the total cross section and especially of the small angle differential cross section at large values of the beam attenuation. At angles θ ≈ θ₀, with θ₀ the quantum mechanical scaling angle of the elastic differential cross section, the correction for the latter case amounts to 20% at beam attenuations I/I₀ = exp(?1). Firstly, a careful analysis of the probabilities for single and multiple scattering is given, resulting in an expression for the measured beam signals which is correct for all values of the beam attenuation. The probability for multiple scattering is then calculated for an inverse power potential V(r) = ?C_sr^?s, with s = 4 through s = 7, which include both the case of ion—atom scattering (s = 4) and atom—atom scattering (s = 6). The results are given as effective differential cross sections σ_n(θ) for n-fold scattering. They are described by a single, simple analytical function with four free parameters that have been determined for n = 2, 3 and 4 by a least squares method. The σ_n(θ) are normalised to the total cross section Q.     

Monte Carlo calculation of angular transmission functions for small angle scattering

We define an angular transmission function η in the center of mass system. The convolution of the differential cross section σ with η yields the signal in the laboratory system. For the case of elastic small angle scattering by spherically symmetric potentials we calculate η by a Monte Carlo method. Random positions are taken in the beam defining collimators, resulting in a trajectory with a deflection angle at the scattering centre. These deflection angles are transformed to the c.m. system with the small angle tranformation formulae. From the distribution we calculate η as a histogram and the central moments of η. The function η depends on the velocity ratio and on the mass ratio of the scattering partners. We store the results in such a way that the central moments can be calculated afterwards for all mass and velocity ratios. By using the central moments the convolution integral can be reduced to a simple weighted sum of σ-values at different scattering angles. The r.m.s. deviations of the central moments scale with N^{$\text{1}\text{2}$}, with N the number of Monte Carlo trajectories. A typical deviation is 1% in the second order moment for N = 2 × 10⁴, increasing slightly with increasing order of the moments. This method of calculation gives a large degree of freedom for optimisation of the collimation geometry. The use of an angular transmission function defined in the center of mass system gives a good insight in the experimental reflection of the physical events. As an example we apply the method to the case of small angle scattering of Ar as a primary beam by Kr as a secondary beam and the inverse configuration of Kr by Ar.     

High-power broad-area diode lasers for laser cooling

Received: 1 April 1996/Revised version: 24 September 1996     

Laser frequency stabilization using an Fe-Ar hollow cathode discharge cell

Polarization spectroscopy of an Fe-Ar hollow cathode discharge cell was used to lock a frequency-doubled Ti:sapphire laser to the 372-nm⁵D₄⁵F₅ transition of ⁵⁶Fe. The discharge cell produced a density of 10¹⁸ m^-3 ground-state ⁵⁶Fe atoms at a temperature of 650 K, this density being comparable to a conventional oven at 1500 K. Saturated absorption spectroscopy and two schemes of polarization spectroscopy were compared with respect to signal-to-background ratio and the effect of velocity-changing collisions. The laser was locked within 0.2 MHz for hours by feedback of the dispersive polarization spectroscopy signal. PACS 33.55.Ad; 42.62.Fi; 52.25.Ya     

Grating feedback in a 810 nm broad-area diode laser

Narrow linewidth, single spectral mode operation has been obtained in a high power, 810 nm broad-area diode laser in an extended cavity configuration with a grating as external reflector (grating feedback). For stable operation it was necessary to misalign the feedback slightly in the plane of the laser junction. Characteristics of the thus obtained laser system are a linewidth below 5 MHz, an output intensity of about 50% of the free running power, a large-scale tuning range of 15 nm and continuous scanning over 4 GHz. In the spatial domain, the laser remains multimode and astigmatic. To show the practical applicability of this system, saturated absorption of a krypton line is demonstrated.     

Bright thermal atomic beams by laser cooling: A 1400-fold gain in beam flux

Using a three-step transverse laser cooling scheme, a strongly diverging flow of metastable Ne(3s ³ P ₂] atoms is compressed into a well-collimated, small diameter atomic beam (e.g., 1.4 mrad HWHM divergence at 3.6 mm beam diameter) with an unmodified axial velocity distribution centered at 580 m/s. The maximum increase in beam flux 1.04 m downstream of the source is a factor 1400; the maximum increase in phase space density, i.e., brightness, is a factor 160. The laser power used is only 140 mW. The scheme is extendable to a large variety of atomic species and enables the application of bright atomic beams in many areas of physics.     

Lifetimes of the Ne 2p fine structure states by measurements of linewidths of the laser induced flourescence of an atomic beam

The laser induced fluorescence signal of a crossed atomic beam-photon beam is used to measure the natural lifetimes of six of the 2p fine structure states of Ne I. The excitation profiles are analysed with a model function consisting of an unbroadened lorentzian lineshape with the full-width at half-maximum Δν (natural lineshape) as a free parameter, which is then fully convoluted with the experimental conditions as Doppler effect, Zeeman splitting and saturation. The broadening due to these effects is typically 3 MHz. To avoid strong correlations of the value of Δν with an incorrect shape of the model function, we only use the datapoints that are most sensitive to Δν, i.e. at the maximum and at half height. The resulting lifetimes lie all within the 1 σ error bound (5%) from other experimental results. Our results add as independent set of data to these well investigated lifetimes.