E. Bonderup

On the concept of temperature for a small isolated system

The microcanonical temperature is shown to be a useful concept in calculations of the decay of a small isolated system with well defined energy. A simpler and more transparent description is obtained than in Klots’ formulation of finite-heat-bath theory, where the system is represented by a canonical ensemble. As a further illustration of the utility of the microcanonical temperature concept, we discuss a formula derived by Dunbar for the probabilities for excitation of a single oscillator in a collection of harmonic oscillators with well defined total energy. This formula expresses the excitation probabilities in terms of the temperature for a canonical ensemble with mean energy equal to the energy of the system. However, a much improved accuracy is obtained if the canonical temperature and heat capacity are replaced by their microcanonical values. We justify this replacement through a modified derivation, in which the microcanonical temperature appears as the canonical temperature of a fictitious system...

Thermionic emission from clusters

We discuss the interpretation of delayed electron emission from excited clusters as a statistical process analogous to thermionic emission from a hot filament. We argue that transition state theory is not a good theoretical framework for electron emission. Instead the calculation of emission rates may be based on detailed balance and theoretical or experimental cross sections for electron capture, but there can be large uncertainties in theoretical estimates of cross sections. We emphasize the conceptual simplicity obtained with the introduction of the microcanonical temperature. In experiments, the energy distribution is often so broad that it is essential to account for its modification by depletion, which for a very broad distribution leads to a decay rate inversely proportional to time. Another complication is photon emission, and we present estimates of the radiation intensity based on a simple model of a cluster as a sphere containing a gas of free electrons. In the analysis of experiments, we first discuss the information about cluster dynamics obtained from studies of photoelectron spectra. However, we focus mainly on a detailed analysis of measurement of the rate of delayed electron emission and its dependence on the cluster excitation. Often the parameters of a statistical description, derived from fits to measurements, have appeared to be inconsistent with estimates from theory or from independent experiments. We analyse a measurement of laser-induced electron emission from small Nb clusters and find that inclusion of anharmonic effects in the heat capacity and, even more important, of the competition by radiative decay leads to more reasonable parameters in the statistical description than obtained from the original analysis. The most detailed studies have been performed for fullerene anions. For most of the measurements, radiative cooling is not significant, but it is important to take into account the finite width of the energy distribution, deriving from the initial heating in an oven. Measured cross sections for electron attachment can be applied in lifetime calculations, and an improved analysis leads to the conclusion that the experiments are consistent with the interpretation of electron emission as thermionic emission.

A Bethe theory for the directional dependence of stopping by molecules

Abstract We derive a Bethe formula for the stopping of swift ions by target molecules oriented with respect to the beam. The theory is characterized by a directional mean excitation energy formed from transition energies and dipole matrix elements. The expression for the mean excitation energy is similar to the one for an isotropic sample but the dipole matrix elements corresponding to the various transition moment directions carry unequal weights which depend on the orientation of the molecule with respect to the beam. For a large class of molecules, the logarithm of the mean excitation energy is linear in sin2 θ, where θ denotes the angle between the beam and the principal molecular axis. We illustrate the properties of the theory in the simple case of a diatomic molecule.

Momentum diffusion of atoms moving in laser fields

The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.

Near-infrared photoabsorption by C 60 dianions in a storage ring

We present a detailed study of the electronic structure and the stability of C(60) dianions in the gas phase. Monoanions were extracted from a plasma source and converted to dianions by electron transfer in a Na vapor cell. The dianions were then stored in an electrostatic ring, and their near-infrared absorption spectrum was measured by observation of laser induced electron detachment. From the time dependence of the detachment after photon absorption, we conclude that the reaction has contributions from both direct electron tunneling to the continuum and vibrationally assisted tunneling after internal conversion. This implies that the height of the Coulomb barrier confining the attached electrons is at least approximately 1.5 eV. For C(60)(2-) ions in solution electron spin resonance measurements have indicated a singlet ground state, and from the similarity of the absorption spectra we conclude that also the ground state of isolated C(60)(2-) ions is singlet. The observed spectrum corresponds to an electronic transition from a t(1u) lowest unoccupied molecular orbital (LUMO) of C(60) to the t(1g) LUMO+1 level. The electronic levels of the dianion are split due to Jahn-Teller coupling to quadrupole deformations of the molecule, and a main absorption band at 10,723 cm(-1) corresponds to a transition between the Jahn-Teller ground states. Also transitions from pseudorotational states with 200 cm(-1) and (probably) 420 cm(-1) excitation are observed. We argue that a very broad absorption band from about 11,500 cm(-1) to 13,500 cm(-1) consists of transitions to so-called cone states, which are Jahn-Teller states on a higher potential-energy surface, stabilized by a pseudorotational angular momentum barrier. A previously observed, high-lying absorption band for C(60)(-) may also be a transition to a cone state.

Forces on atoms in laser fields with multidimensional periodicity

A description is given of a method for calculating forces on atoms from periodic laser fields in an arbitrary number of dimensions. A crucial approximation is the introduction of an average force which depends on the magnitude and direction of the particle velocity but not on position. A simple two-dimensional example is studied and a strong force component perpendicular to the two-dimensional atomic velocity is found. It may become of interest for the construction of well collimated atomic beams of high intensity. Fluctuations are not included but results from simulations at high laser intensity indicate that average forces alone serve as useful guides in the prediction of modifications of velocity distributions.

Coherence Lengths for Emission of Classical Channeling Radiation

The spectrum of bremsstrahlung emitted by electrons or positrons penetrating a solid is strongly modified when the particles are channeled.1 This paper is concerned with the theoretical treatment of channeling radiation from particles in the GeV region, where the description may be based on classical electrodynamics.1

The influence of multiple scattering on channeling radiation from gev positrons

Abstract Classical calculations of the intensity of channeling radiation from GeV positrons moving in continuum potentials agree reasonably well with experimental data. However, generally, the peaks of the experimental spectrum appear at 5–10% lower frequencies, and they are broader. Since multiple scattering was expected to cause such changes, the classical formula for the intensity has been extended to include this effect. While the calculated broadening is of the right order, it appears that multiple scattering is not the major cause of the shift.

Scattering of neutral atoms by the evanescent field around an optical fibre

We present quantum mechanical and classical calculations for the scattering of atoms by an azimuthally symmetric evanescent field around an optical fibre. For the mode studied, the electric field points in the azimuthal direction. In atoms with degenerate lower states, the scattering leads to a coherent transfer among these states and we show that associated oscillatory structures in the quantal differential cross sections may be described quantitatively as interference between Feynman path integrals along alternative classical trajectories.