Semiclassical Cross Sections Research Articles

Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN

Radiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory at high energies. The high energy cross section is overestimated if conventional semiclassical theory is used. The modified semiclassical theory should be valid in general for radiative association transitions from an upper to a lower electronic state. We also implement a quantum dynamical optical potential method with the same type of modification. The rate coefficient is calculated using Breit-Wigner theory and the modified semiclassical formula for the resonance and direct contributions, respectively, for temperatures from 10 K to 20,000 K. A rapid decrease in the rate constant for formation of ground state SiN is observed above 2000 K which was not seen previously.

Energy dependence of scattering ground-state polar molecules

We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on $\mathrm{RbCs}$ and $\mathrm{RbK}$. An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total $M$ to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.

Correspondence Between Quantum and Classical Dynamics in Photodetachment Near Elastic Wall

The photodetachment of H near an elastic wall was investigated and an analytical formula of the cross section was derived. It was found that the cross section is a superposition of a smooth background and sinusoidal oscillation, which depends on the distance between the ion and the elastic wall. The classical dynamics of the photo-detached electron and its quantum correspondence was analyzed. In this model, the semiclassical photodetachment cross section is exactly the same as the quantum result.

Charge transfer betweenS2+and He: A comparative study of quantal and semiclassical approaches

A comparative study of charge transfer in collisions of ground-state ${\mathrm{S}}^{2+}$ ions with He has been performed within fully quantal and semiclassical molecular-orbit close-coupling approaches. The processes for capture into ${\mathrm{S}}^{+}(^{4}S^{0},^{2}D^{0},^{2}P^{0})+{\mathrm{He}}^{+}$ are taken into account. Quantal and semiclassical cross sections were evaluated, respectively, in the diabatic and adiabatic representations and found to be in good agreement. The calculations show that at collision energies below about $40\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$, the charge-transfer processes are dominated by ${\mathrm{S}}^{2+}(^{3}P)+\mathrm{He}\ensuremath{\rightarrow}{\mathrm{S}}^{+}(^{2}D^{0})+{\mathrm{He}}^{+}$, and capture into the $^{2}P^{0}$ and $^{4}S^{0}$ states becomes comparable with that into the $^{2}D^{0}$ state above $40\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$ and $600\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$, respectively. The multireference single- and double-excitation configuration-interaction method was utilized to obtain adiabatic potentials and nonadiabatic coupling matrix elements. A detailed comparison of quantal and semiclassical transition probabilities is discussed. State-selective and total rate coefficients are presented with temperatures between $10\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $5.0\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Quantum production of black holes

We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. Classical solutions describing black hole production resulting from two particle scattering at non-zero impact parameter, combined with our formalism, indicate a geometric cross section for the quantum process. In TeV gravity scenarios these solutions may exhibit large curvatures, but (modulo a mild assumption about quantum gravity) corrections to the semi-classical cross section are small.

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.

Semiclassical photoionization cross section of the hydrogen atom in a magnetic field

We test the accuracy of the semiclassical approximation for a completely chaotic system, the strongly magnetized hydrogen atom. We study a quantity of direct experimental interest, the photoabsorption cross section. The standard semiclassical approximation using periodic orbits is used (without any additional trick to improve convergence) and is shown to agree very well with a fully resolved ab initio quantum ``exact'' calculation. We also study the families of periodic orbits giving the dominant contributions to the spectrum.

Semiclassical inelastic electron-ion collisional excitations in nonideal plasmas

Semiclassical electron-hydrogenic ion collisional excitation cross sections for 1s→2s and 1s→2p0 in nonideal plasmas are obtained. An effective pseudopotential model taking into account the plasma screening and collective effects is applied to describe the electron-ion interaction potential in a classical nonideal plasma. The semiclassical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the total inelastic scattering cross section as a function of the projectile energy, nonideal plasma parameter, and Debye length. It is found that the transition probabilities in ideal plasmas described by the Debye–Hückel potential model are greater than those in nonideal plasmas described by the pseudopotential model. The maximum position of the transition probability gets closer to the target core as the projectile energy increases. It is also found that the scaled cross section decreases when the nonideal plasma parameter (γ) is increased, i.e., the nonideality of plasmas reduces the electron-ion collision cross section.

Cross sections for symmetric resonance charge transferin one-electron ion-ion collisions

Differential cross sections for charge transfer in4He+-3He2+collisions for centre-of-mass energies 0.5 ⩽ E ⩽ 13.6 keV werecalculated in the perturbed stationary states approximation usingaccurate potentials.The semiclassical differential cross sections were found to bein excellent accord with fully quantal calculations of Falcón.Good agreement with the experiment and calculations ofKrüdener et al was found.Total cross sections for this and isoelectronic systems werefound to agree with the simple formula of Bates and Boydto within 5%.A similar agreement with the approximate calculations ofTharamel et al was also found.

Absorption of dilaton partial waves by D3-branes

We calculate the leading term in the low-energy absorption cross section for an arbitrary partial wave of the dilaton field by a stack of many coincident D3-branes. We find that it precisely reproduces the semiclassical absorption cross section of a 3-brane geometry, including all numerical factors. The crucial ingredient in making the correspondence is the identification of the precise operators on the D3-brane world-volume which couple to the dilaton field and all its derivatives. The needed operators are related through T-duality and the IIA/M-theory correspondence to the recently determined M(atrix) theory expressions for multiple moments of the 11D supercurrent. These operators have a characteristic symmetrized trace structure which plays a key combinatorial role in the analysis for the higher partial waves. The results presented here give new evidence for an infinite family of non-renormalization theorems which are believed to exist for two-point functions in N=4 gauge theory in four dimensions.

Quantal and semiclassical calculations of charge transfer cross sections in + H collisions for impact energies of

Total and n-partial cross sections for charge transfer in collisions are calculated for collision energies between and . A molecular expansion is employed, and semiclassical and quantal calculations are carried out including a common translation factor and a common reaction coordinate, respectively. The comparison between quantal and semiclassical cross sections and transition probabilities is discussed.

Can the effective string see higher partial waves?

The semiclassical cross sections for arbitrary partial waves of ordinary scalars to fall into certain five-dimensional black holes have a form that seems capable of explanation in terms of the effective string model. The kinematics of these processes is analyzed in detail on the effective string and is shown to reproduce the correct functional form of the semiclassical cross sections. But it is necessary to choose a peculiar value of the effective string tension to obtain the correct scaling properties. Furthermore, the assumptions of locality and statistics combine to forbid the effective string from absorbing more than a finite number of partial waves. The relation of this limitation to cosmic censorship is discussed.

Symmetrisation in the semiclassical theory of Coulomb excitation

Corrections to the Alder and Winther semiclassical cross section for first order Coulomb excitation are considered through the Sukumar and Brink systematic expansion of the propagator in inverse powers of Sommerfeld's parameter, η. The zeroth order term is that provided by unsymmetrised Alder-Winther theory and it is shown that to order 1 η the only type of correction is one corresponding to energy symmetrisation.

Testing effective string models of black holes with fixed scalars

We solve the problem of mixing between the fixed scalar and metric fluctuations. First, we derive the decoupled fixed scalar equation for the four-dimensional black hole with two different charges. We proceed to the five-dimensional black hole with different electric (one-brane) and magnetic (five-brane) charges, and derive two decoupled equations satisfied by appropriate mixtures of the original fixed scalar fields. The resulting greybody factors are proportional to those that follow from coupling to dimension (2,2) operators on the effective string. In general, however, the string action also contains couplings to chiral operators of dimension (1,3) and (3,1), which cause disagreements with the semiclassical absorption cross sections. Implications of this for the effective string models are discussed.

Plasma-screening effects on direct 1s→2p± electron–ion collisional excitation rates in dense plasmas

Plasma-screening effects are investigated on the 1s→2p− (m=−1) and 1s→2p+ (m=+1) electron–ion collisional excitation rates in dense plasmas. The excitation rates are calculated using the semiclassical excitation cross sections obtained by the classical straight-line trajectory approximation with the nonspherical Debye–Hückel potential. The results show that the ratio of the 1s→2p+ to 1s→2p− excitation rates is found to be a slowly varying function of the temperature. Including the plasma-screening effects for hydrogenic ions, the ratio is found to be a monotonically increasing function of the parameter (Z2Ry/kT)1/2. However, without the plasma-screening effects, the ratio becomes a monotonically decreasing function. The plasma-screening effects appreciably enhance the 1s→2p− excitation rates and reduce the 1s→2p+ excitation rates.

Adiabatic inner-shell ionization by light ions.

For very slow collisions, the ionization cross section depends on the projectile kinematics in the combined field of the nucleus and atomic electrons, on the time evolution of the electron wave function, and on the recoil of the nucleus. First-order semiclassical cross sections in the united-atom limit were calculated for the Thomas-Fermi and Hartree-Fock screening potentials. The time evolution of the wave function was considered by the model of a perturbed harmonic oscillator and by a simplified atomic model involving only a few lowest states. Theoretical K-shell ionization cross sections were compared with the mean experimental data calculated for groups of atoms with neighboring atomic numbers. It was pointed out that the averaging process, also employing theoretical data, depends essentially on the projectile kinematics in the screened atomic field. Taking this into account, good agreement between mean experimental and theoretical cross sections was obtained. \textcopyright{} 1996 The American Physical Society.

L-resolved intercombination transitions in Rydberg atoms in collisions with electrons.

A systematic study of semiclassical and quantum cross sections of l-resolved intercombination transitions in Rydberg atoms due to collisions with fast electrons is performed in the Ochkur approximation for principal quantum numbers n\ensuremath{\le}15 and all possible orbital numbers l and changes \ensuremath{\Delta}l. The semiclassical approach provides reasonable estimates for cross sections over the angular-momentum range up to l\ensuremath{\sim}n/2. Intercombination transitions are shown to obey the ``Bethe rule'': at large l the transitions with n and l changing in the same direction dominate transitions with changes in opposite directions. It is also demonstrated that the more deeply inelastic the collision is, the higher the multipoles \ensuremath{\Delta}l that prevail in the total cross section. The semiclassical approach makes it possible to derive simple analytic formulas for cross sections with an explicit dependence on principal and orbital quantum numbers.

K shell ionization cross sections of Au, Pb and Bi induced by low energy proton impact

K X-ray production cross sections induced by proton impact were measured on thick targets of Au, Pb and Bi in the energy range 0.5 < E 0 < 1.7 MeV. The yields of characteristic X-rays were normalised to the yields of backscattered protons. For proton energies E 0 > 0.8 MeV, the deduced K shell ionization cross sections are uncertain by 12%, these uncertainties being smaller than those of the data published before. Our experimental results are compared with the semiclassical cross sections calculated within the united atom binding procedure. Experimental values agree well with theoretical ones, their difference being generally smaller than our experimental errors. The ionization cross sections measured for E 0 < 0.8 MeV are too large to be explained by proton induced direct ionization. We showed that for thick targets and proton energies smaller than E 0 < 0.8 MeV, the K-shell ionization is produced notably by fluorescence on account of bremsstrahlung photons emitted in the collisions between protons and target nuclei.

First-order theories for adiabatic L-shell ionization by protons.

[ital L]-shell ionization cross sections, evaluated as mean values of the experimental data, were compared with the first-order theoretical values obtained by the plane-wave Born and semiclassical method. Hydrogenic Dirac wave functions in the united-atom limit were employed in the calculation. The plane-wave Born approximation cross sections with Dirac-Hartree-Slater wave functions were obtained from the tables of Chen and Crasemann [At. Data Nucl. Data Tables 33, 217 (1985); 41, 257 (1989)]. The agreement between the experimental and semiclassical cross sections was generally better than 20%, except for the [ital L][sub 1] subshell of heavy elements and for the very adiabatic region of [ital L][sub 2,3] subshells. The differences between both sets of data were largely reproduced by a simplified coupled-channel calculation performed nonrelativistically for a single final state. The calculation also suggests that, due to the uncertainties of the fluorescence yields, the ionization cross sections deduced from the measured data are overestimated by 10%.

Monte Carlo simulation of keV electron transport in solid media

Transport of 1–10 keV electrons in solid media is investigated by means of a single scattering Monte Carlo scheme. Interaction of the incident electron with the target is modeled using bound atom elastic scattering cross sections, together with inelastic collision cross sections and excitation functions, for the weakly bound outer electrons, obtained from dielectric theory with a model dielectric function. Inelastic collisions of the incident particle with the tightly bound inner shell electrons of the target are sampled using semiclassical ionization cross sections. Representative backscattering and transmission calculations are presented and compared with experimental data.