Application of a new variational functional for electron-molecule collisions: an extension of the Schwinger variational principle

Discusses a variational functional for scattering theory which has been recently proposed by Takatsuka and McKoy (1980). It is shown that this functional can provide results with a purely discrete set of functions which are approximately equivalent to those obtained by Lucchese et al. (1980) from the first iteration of the iterative Schwinger method. Applications to the scattering of electrons by systems including CO+ and LiH illustrate this relationship and other features of the method

Efficient semiclassical quantization methods : Combination of the AFC-II theory and cellularized dynamics(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました。本研究では、AFC-II理論とセル化の手続きを組み合わせて効率的な半古典量子化の方法を導入する。この方法で得られたスペクトルを古典トラジェクトリーに基づき解析する。さらに、AFC-IIの公式はセル化の手続きによっても導くことが可能であることを示す。この証明によって、AFC-II理論を初期運動量を持つトラジェクトリーにまで拡張することが可能である。また、異なる初期運動量を持つトラジェクトリー間の干渉の効果を議論する。We propose new efficient semiclassical quantization methods, which are combinations of the amplitudefree correlation function II(AFC-II) theory and cellularized dynamics. We analyze the semiclassical spectra obtained here by using the classical trajectory. In addition, we show that the AFC-II formulation can be derived by the celluarization procedure. Using this derivation, we can extend the AFC-II theory straightforwardly in order to quantize the non-zero initial momentum trajectories. We demonstrate that the extended AFC-II quantization is successful. We also discuss the effect of the interference between the different, initial momentum traifectories

Theory of electronically inelastic scattering of electrons by molecules

We discuss a multichannel formulation of the Schwinger and a related variational principle (of one order higher than the Schwinger principle) in a form suitable for application to the scattering of low-energy electrons by both linear and nonlinear molecules. The theory includes the effects of polarization straightforwardly and should be particularly useful for obtaining electronically inelastic cross sections. An expansion of the trial scattering wave function in a discrete basis is possible. With certain choices for these basis functions this feature can be particularly advantageous

Time-resolved photoelectron spectroscopy of wavepackets through a conical intersection in NO_2

We report the results of theoretical studies of the time-resolved femtosecond photoelectron spectroscopy of quantum wavepackets through the conical intersection between the first two ^2A′ states of NO_2. The Hamiltonian explicitly includes the pump-pulse interaction, the nonadiabatic coupling due to the conical intersection between the neutral states, and the probe interaction between the neutral states and discretized photoelectron continua. Geometry- and energy-dependent photoionization matrix elements are explicitly incorporated in these studies. Photoelectron angular distributions are seen to provide a clearer picture of the ionization channels and underlying wavepacket dynamics around the conical intersection than energy-resolved spectra. Time-resolved photoelectron velocity map images are also presented

Extension of the Schwinger variational principle beyond the static-exchange approximation

We propose a new vairational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below k^2=0.64 demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open- and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostates) is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our 1s-2s―-2p― calculation are comparable to those of 1s-2s-2p-3p―-3d― calculation of Matese and Oberoi [Phys. Rev. A 4, 569 (1971)], which are very close to the exact values. Several aspects of the convergence characteristics are also discussed

Variational scattering theory using a functional of fractional form. I. General theory

We propose a variational method for scattering in which the functional is of a fractional form as for the Schwinger variational principle. However, our functional does not involve the Green's function, but the Hamiltonian and the potential function. This method shows features of both the Schwinger-type variational principles and the Kohn-type standard variational principles. As a result, our method can derive distinct advantages from both of these approaches. The resultant K matrix is symmetric and anomaly-free. Some other properties, including a minimum principle, which is useful in the selection of an optimum basis for the expansion of the scattering functions are also discussed

Energy- and angle-resolved pump–probe femtosecond photoelectron spectroscopy: Molecular rotation

We have incorporated a classical treatment of molecular rotation into our formulation of energy- and angle-resolved pump–probe photoelectron spectroscopy. This classical treatment provides a useful approach to extracting the photoelectron signal primarily associated with vibrational dynamics in cases where rotational motion is slow and the coupling between rotational and vibrational motion is weak. We illustrate its applicability with pump–probe photoelectron spectra for wave packets on the ^1Σ^+_u double-minimum state of Na_2

Time-resolved photoelectron spectroscopy of proton transfer in the ground state of chloromalonaldehyde: Wave-packet dynamics on effective potential surfaces of reduced dimensionality

We report on a simple but widely useful method for obtaining time-independent potential surfaces of reduced dimensionality wherein the coupling between reaction and substrate modes is embedded by averaging over an ensemble of classical trajectories. While these classically averaged potentials with their reduced dimensionality should be useful whenever a separation between reaction and substrate modes is meaningful, their use brings about significant simplification in studies of time-resolved photoelectron spectra in polyatomic systems where full-dimensional studies of skeletal and photoelectron dynamics can be prohibitive. Here we report on the use of these effective potentials in the studies of dump-probe photoelectron spectra of intramolecular proton transfer in chloromalonaldehyde. In these applications the effective potentials should provide a more realistic description of proton-substrate couplings than the sudden or adiabatic approximations commonly employed in studies of proton transfer. The resulting time-dependent photoelectron signals, obtained here assuming a constant value of the photoelectron matrix element for ionization of the wave packet, are seen to track the proton transfer

Variational scattering theory using a functional of fractional form. II. An L2 approach

An L2 approach to our variational method which is based on a functional of fractional form is proposed. As in the R-matrix theory, configuration space is divided into two parts. However, unlike the R-matrix theory, the associated wave function is always smooth. The resulting K matrix is anomaly-free and symmetric (and hence the S matrix is unitary). Application of this method to an exactly soluble two-channel model problem shows that our new approach gives much better results than the other standard variational principles