Quantum and semiclassical dynamics of differential optical collisions

We apply quantum and semiclassical theories to differential optical collisions Na(3²S_1/2) + Kr + Na(3²P_1/2,3/2) + Kr. Our results provide a basis to analyze recent experiments in which for the first time optical collisions were investigated with angular resolution under crossed-beam conditions. A characteristic feature of the differential cross sections is the pronounced oscillatory structure due to interferences of different Condon paths. These Stueckelberg oscillations form an extremely sensitive probe of the collisional dynamics and of the molecular interactions. We demonstrate perspectives to determine geometric properties of the collision complex by excitation with polarized light. By final state analysis nonadiabatic (spin-orbit, rotational) interactions can be studied with complete control of the path. In summary it is shown that the method of differential detection of optical collisions opens a variety of new accesses to atomic and molecular subcollisions. Received: 30 July 1997 / Received in final form: 5 November 1997 / Accepted: 8 January 1998     

Zeeman relaxation of N2 + (2Σ+) in collisions with 3He and 4He

We compare the cross sections for the transitions changing the projection of the total angular momentum of N₂ ⁺(²Σ) in collisions with ³He and ⁴He at very low collision energy. The fundamental states of the two nuclear spin isomers of N₂ ⁺ are considered as well as the two fine structure levels of the first excited para level N=2. It is shown that the two fundamental states of the two nuclear spin isomers behave differently. For the fundamental para level N=0 of N₂ ⁺, the projection changing cross section is always negligible compared to the elastic one for both He isotopes. For the fundamental ortho level N=1 of N₂ ⁺, the spin-rotation interaction couples the different spin levels directly so the spin relaxation becomes a first order process. The associated resonances increase the projection changing cross section which remains smaller but becomes comparable with the elastic one. This is in contrast with the excited rotational levels of N₂ ⁺, which for the rotational deactivation and elastic channels are found to be equal around the resonances for the collisions involving ³He. These two channels are always larger than the projection changing one. We also find that, for transitions involving the fundamental rotational state, the domain of validity of the threshold laws discussed by Krems and Dalgarno [Phys. Rev. A 67, 050704 (2003)] for a potential decreasing faster than 1/r2 is shortened, due to the long range charge induced dipole potential. This effect is illustrated for the collisions of ³He with the fundamental para state of N₂ ⁺.     

Vibrational and rotational energy transfer of CH+ in collisions with 4He and 3He

A quantum mechanical investigation of vibrational and rotational energy transfer in cold and ultra cold collisions of CH⁺ with ³He and ⁴He atoms is presented. Ab initio potential energy calculations are carried out at the BCCD(T) level and a global 3D potential energy surface is obtained using the Reproducing Kernel Hilbert Space (RKHS) method. Close coupling scattering calculations using this surface are performed at collision energy ranging from 10^-6 to 2000 cm^-1. In the very low collision energy limit, the vibrational and rotational quenching cross sections of CH⁺ in collisions with He are found to be of the same order of magnitude. This unusual result is attributed to the large angular anisotropy of the intermolecular potential and to the unusually small equilibrium value of the Jacobi R coordinate of the He–CH⁺ complex. As for the He–N₂ ⁺ collision, we also find a strong isotope effect in the very low collision energy range which is analyzed in terms of scattering length and the differences between these two collisions are also discussed.     

Energy pooling in caesium vapour:

The total rate coefficient k for the energy pooling process has been measured in dependence on the ratio of the number densities of the Cs 6P fine-structure sublevels. The measurements were performed applying the laser fluorescence method. From the set of the obtained data for k, the rate coefficients for the particular collisions were derived. The obtained values for the and collisions at T = 600 K are , and , respectively. The value for k₁ and the estimate for k₃ are consistent with the data previously published by other authors. The rate coefficient k₂ is reported for the first time. Received: 10 June 1997 / Revised: 13 October 1997 / Accepted: 5 January 1998     

Flux enhancement model for cold cesium fine-structure changing collisions

The measurements of fine-structure changing collisions in a cesium magneto-optical trap, reported in a previous work [A. Fioretti et al., Phys. Rev. A 55, R3999 (1997)], are reanalyzed within a model based on the flux enhancement effect, which takes place in cold atomic collisions. In the present analysis, we consider the cooperative effect of the long-range and the shorter-range excitation by the strong trap laser. We evidence also the important role of the hyperfine structure of the Cs₂ molecular levels asymptotically connected to the ground-state and excited-state dissociation limits. Received 22 July 1999 and Received in final form 4 May 2000     

Rotational excitation of NH<Subscript>3</Subscript> and ND<Subscript>3</Subscript> due to He atom collisions

Quantum close-coupling and coupled-states approximation scattering calculations for rotational energy transfer of rotationally excited NH₃ and ND₃ due to collisions with He are presented. Calculations were performed for collision energies between 10^-5 and 10 000 cm^-1 using the NH₃-He potential of Hodges and Wheatley [J. Chem. Phys. 114, 8836 (2001)]. State-to-state and total quenching cross sections from some selected initial states are presented. Rate coefficients for ortho-NH₃ for the quenching 10+→00+ transition were obtained on potentials scaled to reproduce measurements of second virial coefficients with the results showing strong sensitivity to the potential, especially at low temperatures. Significant isotope effects are found in quenching cross sections in the cold to ultracold regime particularly in the region dominated by quasi-bound resonances, ~0.1 to 10 cm^-1. As ammonia has been translationally cooled via Stark deceleration methods, it is a good candidate for experimental study of such effects at cold temperatures. Comparison of rate coefficients with available theoretical results are also presented.     

A comparative nearside-farside analysis of the He–N2 + and He–N2 inelastic collisions

A comparative study of the inelastic scattering of ¹⁴N₂ ⁺ and ¹⁴N₂ in collision with ³He atoms is presented. The unrestricted nearside-farside (NF) method proposed by Connor [J. Chem. Phys. 104, 2297 (1995)] is applied to analyse the Close Coupling rotationally state selected angular distributions for four kinetic energies. These four energies illustrate different regimes of the dynamics. The relationships between the structures of the calculated differential cross-sections (DCS) and the different regions of the potential energy surfaces involved which can be extracted from semi classical models are here easily obtained from a simple reading of the (NF) figures. At the higher energy far-off the wells (1000 cm^-1) the shape of the DCS are quite similar for the two systems and their nearside-farside components also, showing that the inelastic process is controlled by the short range repulsive part of the potential which is essentially the same for these two collisions. When the energy is decreased the differences between the two wells associated with the He–N₂ ⁺ and He–N₂ complexes are responsible for the differences between the DCS for the two systems. The farside component associated with the well become more and more prominent for the elastic scattering while inelastic scattering remains controlled by the repulsive core in a large angular interval. The nearside farside analysis gives also a new picture of a resonance which is regarded as an equilibrium between the repulsive and the attractive parts of the potential.     

Binary stopping theory for swift heavy ions

The Bohr theory treats charged-particle stopping as a sequence of interactions with classical target electrons bound harmonically to their equilibrium positions. We demonstrate that equivalent results can be derived on the assumption of free binary collisions governed by a suitable effective potential. This kind of mapping is rigorous in the limits of distant and close collisions and therefore provides a tool to evaluate energy losses via binary-scattering theory. This model was developed with the aim of calculating stopping forces for heavy ions at moderately high velocities, where a classical-orbital calculation is typically superior to the Born approximation. The effective potential employed holds equally well for dressed as for stripped ions. Unlike the Bohr theory, the present evaluation avoids a formal division into regimes of close and distant collisions that do not necessarily join smoothly. Moreover, no perturbation expansion is necessary. For these reasons the overall accuracy as well as the range of validity of the Bohr model are significantly enhanced. Extensive tests have been performed, including comparisons with rigorous evaluations of the Z ₁ ³ effect, with excellent agreement even where such was not necessarily expected. Moreover, credible results have been obtained under conditions where the perturbation expansion shows poor convergence. A comparison with experimental data on O–Al is encouraging, even though shell corrections and projectile excitation/ionization have not yet been incorporated and input has not yet been optimized. Received 21 April 2000 and Received in final form 16 June 2000 An erratum to this article is available at .     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

Electron multiplicity in slow collisions of Ar ions with C

Electron capture by Ar⁸⁺ in collisions with C₆₀ fullerene has been investigated using coincident measurements of the number n of ejected electrons, the mass and charge of multicharged Cr+ ₆₀ recoil ions and their fragments Ci+ m and the final charge state of outgoing projectiles Ar(8-s)+ (). The number of captured electrons r is the sum of the numbers of stabilized and emitted electrons: r = n + s. The ratio n / s decreases by a factor three with s increasing from 1 to 7 showing that the multiply excited states populated by capture of a large number of electrons are rather stable against auto-ionisation. Each kinetic energy spectrum of Ar⁺ and Ar²⁺ projectiles is composed of two peaks which we attribute to collisions “inside” and “outside” the C₆₀ cage. The measured energy shift of the projectile keV is consistent with the corresponding energy loss keV in a carbon foil with an equivalent thickness. Inside collisions are characterized by a strong dissociation of recoil ions into light monocharged fragments and by a high multiplicity of ejected electrons. Received: 25 March 1998 / Received in final form and Accepted: 9 June 1998     

Measurement of vibrational energy transfer of OH (A2Σ+,v′=1→0) in low-pressure flames

2 Σ⁺) was measured in a low-pressure H₂/O₂ flame for three rotational levels of OH (v^′=1). Rate coefficients for collisions with H₂O and N₂ were determined. At 1600 K, k_VET (N₂) is (in 10^-11 cm³s^-1) 10.1±2, 6.1±1.8, and 3.8±1.3 for N^′=0, 5, and 13, respectively. The k_VET (H₂O) is <1.1±1.8. The k_Q (N₂) is <2.4±8 for both vibrational levels. The k_Q (H₂O) in v^′=1 is 59.1±6.5, 54.7±6.4, and 54.9±6.6 for N^′=0, 5, and 13, respectively, and, determined indirectly, 74.6±10.4, 70.6±10.3, and 63.4±7.3 for N^′=0, 5, and 13 in v^′=0. A multi-level model of OH population dynamics, which is being developed for the quantitative simulation of experimental LIF spectra, was extended to include VET. It was attempted to simulate state-to-state-specific VET coefficients for N₂ collisions. From these simulations it appears that angular momentum conservation does not determine the N dependence of the vibrational relaxation step. Received: 9 September 1996/Revised version: 6 January 1997     

Optimizing the production of metastable calcium atoms in a magneto-optical trap

We investigate the production of long-lived metastable (4³ P ₂ ) calcium atoms in a magneto-optical trap (MOT) operating on the 4¹ S ₀ ?4¹ P ₁ transition at 423 nm. For excited 4¹ P ₁ atoms a weak decay channel into the triplet states 4³ P ₂ and 4³ P ₁ exists via the 3¹ D ₂ state. The undesired 4³ P ₁ atoms decay back to the ground state within 0.4 ms and can be fully recaptured if the illuminated trap volume is sufficientlylarge. We obtain a flux of above 10¹⁰ atoms/s into the 4³ P ₂ state. We find that our MOT lifetime of 23 ms is mainly limited by this loss channel, and thus the 4³ P ₂ production is not hampered by inelastic collisions. If we close the loss channel by repumping the 3¹ D ₂ atoms with a 671 nm laser back into the MOT cycling transition, a non-exponential 72 ms trap decay is observed, indicating the presence of inelastic two-body collisions between 4¹ S ₀ and 4¹ P ₁ atoms. Received: 10 July 2001 / Revised version: 22 October 2001 / Published online: 23 November 2001     

Direct measurement of fine structure changing collisional losses in cold trapped 85Rb

Using a technique that consists in ionizing atoms out of the 5P _1/2 fragments originated in the cold collision process, we have measured the contribution of the fine structure changing collision (FS) to the total trap loss rate of cold ⁸⁵Rb. Our results show that FS contribution is responsible for about 4% of the total trap loss. This result should stimulate new theoretical discussions involving exoergic cold collisions. Received 26 October 1998 and Received in final form 2 February 1999     

Large-scale collisional energy transfer in laser-pumped metastable Ca atoms: Excitation of resonance states of Ca II

We report the first experimental observation of the excitation of the 4p ² P _{3/2, 1/2} resonance states of Ca II (located at 74 720.4 and 74 497.5 cm^–1 above the ground state of Ca I) following pulsed-laser pumping of the 4s ^{2 1} S _O–4s4p ³P₁ intercombination transition of Ca I (E _ex = 15 210 cm^–1). Large scale collisional transfer of energy between the laser-excited atoms is believed to be responsible for this. This is possibly because sufficient time is available (_rad of the 4s4p ³ P ₁ state is approximately 350 µs) for collisions to build such a high level of excitation. Some interesting additional features of the fluorescence spectra of the laser-pumped Ca vapor, such as temperature dependence of the fluorescence intensities and evolution in time of some selected states, are also presented.     

Investigation of magneto-optical effect in transverse magnetic field in He

The non-linear Voigt effect has been studied in He discharge under resonance laser interaction with the He transition. The range of non-linear signal existence was determined. The contribution of the lower and upper states to the overall signal was analyzed. The cross-section for depolarizing collisions with ground state He atoms was estimated for the 3³ D _2,3 He state. Received: 16 June 1998 / Received in final form: 14 December 1998     

Measurement of helium-3 and deuterium stopping power ratio for negative muons

The measurement method and results measuring of the stopping power ratio of helium-3 and deuterium atoms for muons slowed down in the D/³He mixture are presented. Measurements were performed at four values of pure ³He gas target densities, ϕ_He = 0.0337, 0.0355, 0.0359, 0.0363 (normalized to the liquid hydrogen density) and at a density 0.0585 of the D/³He mixture. The experiment was carried out at PSI muon beam μE4 with the momentum Pμ= 34.0 MeV/c. The measured value of the mean stopping ratio S$_{3^He/D}$ is 1.66±0.04.     

High energy collisions of protonated water clusters

We have measured attenuation cross sections and fragmentation cross sections for protonated water clusters H(H₂O)_n ⁺ (n = 1 to 100) colliding with noble gas atoms (He and Xe) at a laboratory energy of 50 keV. In collisions with He, a transparency effect in the attenuation cross section was observed. For the case of fragmentation in collisions with Xe, a strong enhancement of small clusters was observed which we attribute to multifragmentation. Received 30 November 2000     

Rotational excitation of CH<Subscript>4</Subscript> by He atoms

Quantum close-coupling and coupled-state approximation scattering calculations for rotational energy transfer of rotationally excited CH₄ due to collisions with He are presented for collision energies between 10⁻⁷ and 3000 cm⁻¹ using the MP4 potential of Calderoni et al. [J. Chem. Phys. 121, 8261 (2004)]. State-to-state cross sections and rate coefficients from selected initial rotational states of CH₄ in symmetries A, E, and F are studied from the ultra-cold to the thermal regime. Comparison of the cross sections with available theoretical results and experimental data show good agreement. Applications to astrophysics and cold laboratory environments are briefly addressed.     

Electron detachment and fragmentation in collisions between 1.25 keV/carbon and clusters and

The destruction cross-section for 22.5 and 50 keV C^1- , for 10 and 50 keV C₈ ^1- and for 50 and 75 keV C₆₀ ^1- clusters in collisions with H₂ has been measured by an attenuation method. The destruction of the cluster anions is dominated by electron detachment rather than fragmentation and is of the order of the geometric cross-section. The cross-sections vary little with bombarding energy. Received: 16 September 1998 / Received in final form: 23 February 1999     

Energy dependence of the Penning ionization electron spectrum of Ne* (3P2,0)+Kr

A crossed beam experiment is carried out to measure the energy of electrons emitted in Penning ionization processes by Ne^*(³P_2,0)–Kr collisions. The electron energy spectra have been measured at four different collision energies: 0.050, 0.140, 0.190, 0.460 eV. The analysis of the results allows the separation of spin orbit contributions both in the entrance and in the exit channels providing the related cross-section ratios. Some theoretical considerations have been made to clarify nature and role of interatomic potentials driving the collisions and some general features about the role of atomic fine structure in the Penning ionization processes.