First measurements of the index of refraction of gases for lithium atomic waves

We report the first measurements of the index of refraction of gases for lithium waves. Using an atom interferometer, we have measured the real and imaginary parts of the index of refraction n for argon, krypton, and xenon as a function of the gas density for several velocities of the lithium beam. The linear dependence of (n-1) with the gas density is well verified. The total collision cross section deduced from the imaginary part of (n-1) is in very good agreement with traditional measurements of this quantity. Finally, the real and imaginary parts of (n-1) and their ratio rho exhibit glory oscillations, in good agreement with calculations.     

Streuung von 25 keV-Elektronen an Gasen

The differential cross section of neon, argon, krypton, and xenon for the elastic scattering and for the excitation of optical transitions has been measured. For neon and argon the elastic angular distribution can be described by the cross section calculated according toWentzel andLenz. For krypton and xenon there are considerable deviations from the Wentzel-Lenz cross section. In these cases it is better to calculate the elastic differential cross section from Slater eigenfunctions, from Thomas-Fermi-Dirac or from Hartree-Fock electron density distribution. The differential cross sections for the excitation of optical transitions, so far as measured here, obey for?<? _c the dipol approximation, i.e. for angles not to small the inverse square angular dependence is valid.? _c is higher for the heavier rare gases. The oscillator strengths for some transitions have been determined from the scattering measurements in satisfactory agreement with theoretical values.     

Measurements on the glory structure in the total cross section of noble gas systems: III. Ar-Kr,Kr-Kr,Kr-Xe and Xe-Xe; application of the n(x)-6 potential

In a crossed supersonic atomic beam apparatus measurements have been performed on the glory structure in the total cross section of the heavy noble gas systems Kr-Kr, Kr-Xe and Xe-Xe. Refinements in the deconvolution procedures are described and the consistency of the results is tested on newly obtained data for the systems Ar-Kr and Kr-Ar. The overall accuracy of the data for all systems is better than 0.7%. Various potentials, proposed in literature, are tested. Agreement with the measured glory structure is only observed for the n(x)-6 and HFD-C type potentials for Ar-Kr and Kr-Kr. n(x)-6 potentials are constructed not only for Kr-Xe and Xe-Xe, but also for the previously studied Ne-systems and Ar-Xe. The result is that the relative total cross sections for all pairs of noble gas atoms (Ne, Ar, Kr and Xe) within experimental error can be described by a consistent set of n(x)-6 potentials. The obtained values for ? and r_m obey simple combining rules.     

Atom-Atom-Streuexperimente: Geschwindigkeitsabhängigkeit einiger totaler Streuquerschnitte

The velocity dependence of total cross sections for the collision partners Cs-Hg, K-Hg, Xe, Kr, Ar has been measured in crossed beams. Except for Cs-Hg glory scattering oscillations were resolved. Invariably good agreement with theoretical predictions is found for the extrema velocities assumingn-6 potentials with 8≦n≦16 or exp-6 potentials with 10≦α≦18, for the amplitudes of the oscillations no fit is obtained. K-Hg, probably also K-Xe and K-Kr appear to deviate from theν ^?2/5 average velocity dependence expected for dipole-dipole interaction at large distances.     

Weitere Messungen zur Anisotropie der intermolekularen Wechselwirkung durch Streuung von Molekülen in definiertem Quantenzustand

In a previous paper the anisotropy parameter of the attractive part of the intermolecular potential has been determined from total cross sections measured by scattering of TlF-molecules in selected rotational states by rare gases. In this series of papers, further measurements on the systems TlF-He, Ne, Ar, Xe, CH₄, and CsF-He, Ar will be described. In the case of CsF-He, it has been possible to determine the anisotropy parameter of the repulsive part of the potential additionally, by comparing cross sections related to different rotational states over a large velocity range and by using the high energy approximation. The determination of the anisotropy parameter for the repulsive potential requires knowledge of the parameters of the angle averaged potential. Part I describes the determination of these parameters for a Lennard-Jones-potential from measurements of the velocity dependence and the absolute value of the total cross section by scattering of not state selected CsF-molecules by He and Ar. Since these systems show no glory undulations in the experimentally accessible velocity range, they require an evaluation procedure, which is independent of the appearance of such undulations. The procedure described below only uses the velocity dependence of the cross section itself by fitting of quantum mechanically calculated cross sections. The finite resolving power of the apparatus and the influence of velocity distributions are taken into account. The results are communicated, the parallel evaluation of an experiment on K-Ar serves as a test for the procedure described.     

Measurement of the pp cross sections in the momentum range 0.9–2.0 GeV/c

The pp total, elastic, and all the inelastic cross sections were measured at 11 momenta in the range 0.9–2.0 GeV/c. No clear structure was observed in their momentum dependences. The momentum dependence of the total cross section agrees quite well with the result of a phase-shift analysis by Arndt. Our measurement of the ppπ⁰ and pnπ⁺ cross sections served to normalize the earlier systematic but relative and extrapolated measurements of these cross sections over a narrower momentum range. Calculations by König and Kroll based on a pion exchange model including the effect of an I = 1 dibaryon did not fit the single-pion production cross sections.     

Radiative quenching and excitation of metastable states upon differential scattering of atoms: II. The He(1<Superscript>1</Superscript><Emphasis Type="Italic">S</Emphasis>–2<Superscript>1</Superscript><Emphasis Type="Italic">S</Emphasis>)-Ne molecule

The differential cross sections of radiative-collisional quenching (absorption) of a metastable state of a colliding atom are calculated for the first time. As a particular example, the reaction of quenching (excitation) of the metastable state He(2¹S) in collisions with Ne atoms in the ground state is considered. The calculations are performed for the thermal collisional energy E = 10^?3 au for a wide range of radiation frequencies, including both wings and the center of the line of a forbidden atomic transition, and are based on the uniform quasi-classical approximation, which generalizes the Franck-Condon approximation to the case of an exponential dependence of the transition dipole moment on the internuclear distance, as well as to the case of nonintersecting terms. The calculated differential cross sections have an oscillating structure, which, for the blue wing of the forbidden spectral line, is interpreted as Stückelberg oscillations. At a radiation frequency close to the frequency of the forbidden atomic transition, a sharp maximum in the differential cross section—the giant glory effect—is observed in the range of small scattering angles. This effect is shown to occur as a result of superimposition of the rainbowlike feature of the differential cross section on the glory feature.     

Multiple scattering effects for quasifree scattering in 3He(d,dd)1H breakup reaction

The differential cross sections for the ³He(d, dd)¹H breakup reaction have been measured in the kinematical region corresponding to quasifree scattering (QFS). The angular dependence of the cross section at the minimum laboratory energy of the unobserved proton has been obtained. The shapes of energy spectra are approximately reproduced by a calculation in the plane-wave impulse approximation (PWIA). As for the angular dependence of the cross section and for the absolute values, the calculation fails to reproduce the experimental results. A calculation with multiple scattering effects reproduces the experimental data well, not only for the shape of the energy spectra but also for the angular dependence. For the absolute cross sections, the ratio of the experimental values to the calculated ones with multiple scattering effects is 0.7 and this value is improved compared with the value of 0.3 obtained by the PWIA calculation.     

Experimental and theoretical study of the elastic break-up of the alpha particle on58Ni nuclei atE α=172.5 MeV

The triton-proton angular correlation function has been measured for the⁵⁸Ni(α, t p)⁵⁸Ni reaction leading to the ground state of the target nucleus. The obtained experimental data have been interpreted in terms of the direct break-up (fragmentation) of the alpha particle on the target nucleus potential. It is shown that the main features of the measured double differential cross section are well predicted by the DWBA theory of the break-up. The dependence of the elastic and inclusive break-up cross sections upon the fragment-target interaction potentials is discussed.     

On the direct inversion of total scattering cross sections beyond the glory region

A method is described for directly inverting measurements of the total scattering cross section at velocities beyond the glory undulations to determine the intermolecular potential, without the use of specific mathematical models for the potential. The only parameter needed is a quantity describing the potential well area, which is accurately obtained from the spacing of the glory undulations. A second quantity obtained from the glory spacings allows the use of relative rather than absolute cross sections. The method is illustrated with simulated cross section data. The results of this paper and the preceding one show that virtually the entire potential curve can in principle be obtained from only relative measurements of the total cross section, without the use of specific models.     

On the direct inversion of total scattering cross sections in the glory region

The total scattering cross section as a function of velocity in the glory region can be accurately described semiclassically as the sum of an average part and an undulating part. In practice the velocity dependence of the average cross section is complicated because of contributions from different dispersion terms in the attractive part of the potential and eventually from repulsive terms as well. It is shown that the average cross section can be accurately retrieved from the data, without the assumption of a mathematical model for the potential, and that the retrieved values can be directly inverted to numerical values of the potential tail. The separated results for the undulating part yield numerical values for five of the usual glory parameters. The procedure is tested on simulated total cross section data showing several full glory oscillations, and the glory parameters and potential tail are reproduced to accuracies consistent with the graphical-numerical methods employed.     

Light atom scattering from adsorbates at low coverage

A multiple scattering theory is developed for the scattering of light atoms from a disordered adsorbate on a smooth surface. Using gas phase potentials for adatom potentials, excellent agreement is found with data for He scattering from adsorbed Xe and surprisingly good agreement with the extensive data for He scattering from adsorbed CO. The attractive adatom potential must be included in the calculation if quantitative comparison with experimental data is to be made. An important contribution to the total cross section of an adatom are quantum mechanical oscillations similar to glory oscillations in gas phase scattering. The dependence of the total cross section on the incident angle is strongly influenced by the varying number of adatoms seen by the probe.     

Totale effektive Streuquerschnitte für die Streuung von He,HD und D2 an verschiedenen Molekülen

The measured velocity dependence of the total scattering cross section for the scattering of He, HD, and D₂ by the molecules CH₄, N₂, O₂, NO, CO, HD, and D₂ can be described relatively well by a Lennard-Jones-(12.6)-potential. Only for the systems with a CO₂ target are large deviations from the L. J.(12,6) predictions found: the measured glory amplitudes are considerably smaller. The deformation of the spherically symmetric potential which must be made in order to fit the CO₂ glory pattern is given. Furthermore, the CO₂ systems were calculated using an angle-dependent L.J.(12.6)-potential, taking into account only elastic processes. The agreement with the measurements is good.     

Cross section measurements for the 9Be+9Be System at subbarrier energies

The total reaction cross section and the characteristic y-ray cross sections have been measured for the ⁹Be+ ⁹Be reaction in the energy range E_cm = 1.4–3.4 MeV, detecting the prompt γ-rays emitted by the various residual nuclei with two Nal detectors in nearly 4π geometry and with a germanium detector, respectively. The differential elastic cross sections for the same system have also been measured at e_c.m.= 2.2, 2.7 and 3.2 MeV. The cross sections calculated with the “standard” and the proximity optical model potentials, which describe well the total reaction cross sections of the light nuclei, agree with the ⁹Be + ⁹Be elastic-scattering data, but underpredict the total reaction cross section by a factor of 2 to 3. The characteristic γ-ray measurements show that all two-particle emission channels, nα ¹³C, nn¹⁶O, np¹⁶N and αα¹⁰Be are enhanced by about that factor, while the single-particle emission channel, p¹⁷N, is not enhanced.     

Calculation of the cross sections for the photoionization of H2 and D2 into different vibrational states of the ion

The dependence of the electronic transition moment on the internuclear distance is explicitly taken into account in the calculation of the photoionization cross section. Thus, the partial ionization cross sections for producing different vibrational states of the residual ion are obtained without invoking the Franck-Condon factor approximation. The exact electrostatic potential of H₂⁺, as well as the two-center Coulomb field, is used in the evaluation of the continuum wave function. The result can explain fairly well the ratios of the partial cross sections measured at 584 Å. The effect of the polarization of H₂⁺ due to the departing photoelectron is also studied and found to be small as far as the relative cross section is concerned. The total photoionization cross sections of H₂ and D₂ are compared with previous results obtained by other authors.     

Fusion probability of symmetric heavy,nuclear systems determined from evaporation-residue cross sections

Cross sections were measured for the formation of evaporation residues in ⁴⁸Ca-, ⁸⁶Kr- and ¹²⁴ Sn-induced reactions with Yb, Sb and Zr isotopes. For the nearly symmetric systems, the energy dependence of the fusion probability in central collisions was determined. The fusion probability at the expected fusion barrier as calculated from a one-dimensional heavy-ion potential was found to be reduced by several orders of magnitude. The fusion cross sections increase gradually, and only at energies appreciably above the expected fusion barrier the major part of the cross section of central collisions leads to fusion. The observed hindrance of the fusion process is compared with model predictions.     

A fast and accurate semiclassical calculation of the total elastic cross section in the glory energy range

A method for the semiclassical calculation of the total cross section in atomic and molecular elastic collisions, for the glory energy range, is reported. The parameters needed for the calculation of the glory undulatory component of the cross section are obtained from a few JWKB phase shifts for impact parameters near the glory impact parameter. The smooth component of the cross section is obtained from JB phase shifts for the long range attraction. The procedure, suitable for every potential model, is accurate and much faster than a full JWKB calculation. A discussion of some typical results is reported and an analysis of the information obtainable from experimental absolute cross sections is also given.     

A theoretical study of the non-adiabatic charge transfer process Ar2+ (3 P) + He(1 S) → Ar+(2 P) + He+(2 S)

CI calculation with a large basis have been used to calculate the two lowest ³Π adiabatic potential energy curves for the title reaction. These potentials have been transformed to diabatic potentials by employing a recipe based on the CI coefficients. Quantum mechanical close coupling calculations in the diabatic basis have produced total and differential cross sections which are in good agreement with experimental data. Full quantum mechanical and Landau-Zener calculations of the total cross section are in fair agreement with recent experimental measures and by small changes to the diabatic potentials can be brought into essentially exact agreement.     

Reaction cross section measurements of the neutron-rich isotopes8,9,11Li at 80 MeV/nucleon

Total interaction cross sections have been measured for⁸Li on C and Pb targets, for⁹Li on C, Al, Cu, Sn and Pb targets as well as for¹¹Li on C, Sn and Pb targets. For each beam, we also used a plastic scintillator as target. The measurements with the scintillator targets are used to extract reduced nuclear radii of the lithium isotopes. These radii are then used for the calculation of the nuclear part of the total cross section for the other targets. The total electromagnetic-dissociation (EMD) cross sections have been deduced and are compared to different models. A strong target-charge-dependent EMD cross section is measured for¹¹Li reaching 2.96 _–0.82 ^+0.84 b for the Pb target. In the⁹Li case, a large EMD cross section for high-Z targets has been observed which amounts to 0.75 ± 0.45 b for the Pb target. The EMD cross sections of both,⁹Li and¹¹Li, may be understood by the giantdipole-resonance model.This work forms part of the PhD Thesis of B. Blank     

Temperature dependence of the disorientation cross section σ 1 2/(1) in rubidium-rare gas collisions

The cross sections for the collision induced transfer²P_1/2m_j=1/2 → m_j = ?1/2 optically polarized Rb-vapour has been measured for collisions with He, Kr and Xe in the temperature range 30 °C → ～ 400 °C. The measurements were done by observing the degree of polarization in the fluorescent light emitted by the Rb-vapour. To avoid hyperfine structure effects, the nuclear spin was decoupled with a magnetic field. Calculations are presented in the temperature range 20 K → 1000 K using a semiclassical treatment and the Pascale Vandeplanque potentials. In the case of helium theoretical and experimental results are at variance, whereas for krypton and xenon satisfactory agreement is obtained. For the heavy rare gases the importance of trajectory effects, notably orbiting, becomes apparent.