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Notes: Using symplectic integrator schemes, we calculate the classical trajectory of a Rydberg electron in external electric and magnetic fields. We also solve the equation of motion obtained by taking the mean values over one revolution of the electron in the undisturbed motion. The resulting secular motion is periodic. When only an electric field F is applied, as long as the modulation period in the orbital angular momentum l is longer than the revolution period, the motion agrees with the secular one and the duration for which l is much larger than its low initial value is stretched. The residence time (RT), namely, the probability of finding the electron at the distance r, is hence smaller than that at F=0. In crossed electric and magnetic fields, the secular motion predicts that an additional time stretching due to a magnetic field occurs up to the critical value of magnetic field strength, Bc=33nF (n is the principal action). In the actual simulations, the RT near the core is smaller than that at B=0 even beyond Bc, regardless of the magnitude of the non-Coulombic interaction C2/r2. Slow modulations in l are generated by transitions to secular motions that maintain high l, in addition to the fast modulation originating from the secular motion. When the magnetic field is so strong as to induce chaotic motion (∼4000 G for the energy of −5 cm−1), the RT is one order of magnitude as large as those in weak field cases around 40 G. In the intermediate region (〉 a few hundred Gauss), without a non-Coulombic interaction, the RT monotonically increases as B increases. In the presence of C2/r2, transitions from low l states to high l states occur: the RT decreases. The motions in high l states can be explained by the well-known model in which an electron bound to the core by a harmonic force moves in a magnetic field. © 1999 American Institute of Physics.

Notes: A dual transformation technique that can deal with awkward Coulomb potentials is developed for electronic wave packet dynamics. The technique consists of the variable transformation of the Hamiltonian and the transformation of the wave function with a normalization constraint. The time evolution is carried out by the alternating-direction implicit method. The operation of the transformed Hamiltonian on the wave function is implemented by using three- and five-point finite difference formulas. We apply it to the H atom and a realistic three-dimensional (3D) model of H2+. The cylindrical coordinates ρ and z are transformed as ρ=f(ξ) and z=g(ζ), where ξ and ζ are scaled cylindrical coordinates. Efficient time evolution schemes are provided by imposing the variable transformations on the following requirements: The transformed wave function is zero and analytic at the nuclei; the equal spacings in the scaled coordinates correspond to grid spacings in the cylindrical coordinates that are small near the nuclei (to cope with relatively high momentum components near the nuclei) and are large at larger distances thereafter. No modifications of the Coulomb potentials are introduced. We propose the form f(ξ)=ξ[ξn/(ξn+αn)]ν. The parameter α designates the ρ-range where the Coulomb potentials are steep. The n=1 and ν=〈fraction SHAPE="CASE"〉12 transformation provides most accurate results when the grid spacing Δξ is sufficiently small or the number of grid points, Nξ, is large enough. For small Nξ, the n=〈fraction SHAPE="CASE"〉12 and ν=1 transformation is superior to the n=1 and ν=〈fraction SHAPE="CASE"〉12 one. The two transformations are also applied to the dissociation dynamics in the 3D model of H2+. For the n=〈fraction SHAPE="CASE"〉12 and ν=1 transformation, the main features of the dynamics are well simulated even with moderate numbers of grid points. The validity of the two transformations is also enforced by the fact that the missing volume in phase space decreases with decreasing Δξ. © 1999 American Institute of Physics.

Notes: We investigate the quantal dynamics of the electronic and nuclear wave packet of H2+ in strong femtosecond pulses (≥1014 W/cm2). A highly accurate method which employs a generalized cylindrical coordinate system is developed to solve the time-dependent Schrödinger equation for a realistic three-dimensional (3D) model Hamiltonian of H2+. The nuclear motion is restricted to the polarization direction z of the laser electric field E(t). Two electronic coordinates z and ρ and the internuclear distance R are treated quantum mechanically without using the Born-Oppenheimer approximation. As the 3D packet pumped onto 1σu moves toward larger internuclear distances, the response to an intense laser field switches from the adiabatic one to the diabatic one; i.e., electron density transfers from a well associated with a nucleus to the other well every half optical cycle, following which interwell electron transfer is suppressed. As a result, the electron density is asymmetrically distributed between the two wells. Correlations between the electronic and nuclear motions extracted from the dynamics starting from 1σu can be clearly visualized on the time-dependent "effective" 2D surface obtained by fixing ρ in the total potential. The 2D potential has an ascending and descending valley along z=±R/2 which change places with each other every half cycle. In the adiabatic regime, the packet starting from 1σu stays in the ascending valley, which results in the slowdown of dissociative motion. In the diabatic regime, the dissociating packet localized in a valley gains almost no extra kinetic energy because it moves on the descending and ascending valleys alternately. Results of the 3D simulation are also analyzed by using the phase-adiabatic states |1〉 and |2〉 that are adiabatically connected with the two states 1σg and 1σu as E(t) changes. The states |1〉 and |2〉 are nearly localized in the descending and the ascending valley, respectively. In the intermediate regime, both |1〉 and |2〉 are populated because of nonadiabatic transitions. The interference between them can occur not only at adiabatic energy crossing points but also near a local maximum or minimum of E(t). The latter type of interference results in ultrafast interwell electron transfer within a half cycle. By projecting the wave packet onto |1〉 and |2〉, we obtain the populations of |1〉 and |2〉, P1 and P2, which undergo losses due to ionization. The two-state picture is validated by the fact that all the intermediates in other adiabatic states than |1〉 and |2〉 are eventually ionized. While E(t) is near a local maximum, P2 decreases but P1 is nearly constant. We prove from this type of reduction in P2 that ionization occurs mainly from the upper state |2〉 (the ascending well). Ionization is enhanced irrespective of the dissociative motion, whenever P2 is large and the barriers are low enough for the electron to tunnel from the ascending well. The effects of the packet's width and speed on ionization are discussed. © 1999 American Institute of Physics.

Notes: The magnetic quenching of fluorescence in intermediate case molecules is modeled by including two triplet manifolds {||bj〉} and {||cj〉} mutually shifted by the zero-field splitting Egap (though a triplet has three spin sublevels); the {||bj〉} are coupled to a bright singlet state ||s〉 by intramolecular interaction V and the two manifolds are coupled by a magnetic field. For the two manifold Bixon–Jortner model where the level spacings and the couplings to ||s〉 are constant and no spin–vibration interactions exist (the Zeeman interaction connects only the spin sublevels of the same rovibronic level j), there are two sets of field dressed eigenstates, {||bˆj〉} and {||cˆj〉}, of the background Hamiltonian H−V. ||bˆj〉 and ||cˆj〉 are liner combinations of ||bj〉 and ||cj〉. We call the energy structure "eclipsed (E)'' when the two sets of dressed states overlap in energy and call it "staggered (S)'' when every ||bˆ〉 state is just between two adjacent ||cˆ〉 states.The E and S structures alternatively appear with increasing Zeeman energy hZ. As hZ increases, the number of effectively coupled background levels, Neff, increases for the S structure but remains unchanged for the E structure. The S structure is in accord with the experimental result that the quantum yield is reduced to 1/3 at anomalously low fields (hz/Egap(very-much-less-than)1): in the far wing regions of the absorption band the mixing between the manifolds is determined by the ratio hZ/Egap, but near the band center the intermanifold mixing is enhanced by the presence of ||s〉. Using a random matrix approach where H is constructed of the rotation–vibration Hamiltonians HB and HC arising from the manifolds {||bj〉} and {||cj〉}, we show that an S structure can be formed in real molecules by nonzero ΔHBC≡HB−HC−Egap (Egap is the zero-field splitting at the equilibrium nuclear configuration). Indirect spin–vibration interactions lead to ΔHBC≠0; the vibrational ΔHBC caused by spin–spin and vibronic interactions and the rotational ΔHBC caused by spin–rotation and rotation–vibration interactions. The matrix elements of H are written down in terms of the eigenfunctions {||j〉} of the average Hamiltonian (HB+HC)/2. If the vibrational modes are strongly coupled (the energies of levels are given by a Wigner distribution and the coupling strengths are given by a Gaussian distribution), the vibrational 〈j||ΔHBC||j′〉 for wave functions of roughly the same energy are Gaussian random.As the rms of 〈j||ΔHBC||j′〉 approaches the average level spacing (on excitation into higher vibrational levels), the efficiency of magnetic quenching becomes as high as in the S case. Nonzero 〈j||ΔHBC||j′〉 let isoenergetic levels belonging to different manifolds vibrationally overlap: the ΔHBC, together with the magnetic field, causes level repulsion leading to the S structure and opens up isoenergetic paths between the manifolds. The efficient magnetic quenching in pyrazine can be explained by the vibrational ΔHBC, since the S1–T1 separation is as large as 4500 cm−1. If Coriolis couplings cause K scrambling considerably, the rotational ΔHBC mixes {||j〉}. This mechanism explains the rotational dependence of magnetic quenching in s-triazine of which S1–T1 separation is only ∼1000 cm−1. © 1995 American Institute of Physics.

Notes: We have developed an efficient grid method that can accurately deal with the electronic wave packet dynamics of two-electron systems in three-dimensional (3D) space. By using the dual transformation technique, we remove the numerical difficulties arising from the singularity of the attractive Coulomb potential. Electron–electron repulsion is incorporated into the wave packet propagation scheme without introducing any approximations. The exact electronic dynamics of H2 is simulated for the first time. At small internuclear distances (e.g., R=4 a.u.), an ionic component characterized by the structure H+H− is created in an intense laser field E(t) (intensity〉1013 W/cm2 and λ(approximate)720 nm) because an electron is transferred from the nucleus around which the dipole interaction energy for the electron becomes higher with increasing |E(t)|. The localized ionic structure is identified with the H− anion at the nucleus around which the dipole interaction energy becomes lower. Tunneling ionization proceeds via the formation of such a localized ionic structure, and direct ionization from the covalent structure is much smaller; the localized ionic structure plays the dominant doorway state to ionization of H2. © 2000 American Institute of Physics.