No abstract

Total and Mulholland partial cross sections for the elastic scattering of electrons from the lanthanide atoms lanthanum to lutetium are calculated for the electron impact energy range 0 ഛ E ഛ 1 eV. The recently developed Regge-pole methodology, which naturally embodies the crucial electron correlation effects together with a Thomas-Fermi-type potential incorporating the vital core-polarization interaction are used for the calculations. Dramatically sharp resonances are found to characterize the near-threshold electron elastic scattering total and Mulholland partial cross sections, whose energy positions are identified with the electron affinities ͑EA's͒ of these atoms through a close scrutiny of the imaginary part of the complex angular momentum. The unambiguous extracted EA values of the lanthanide atoms vary from a low value of 0.016 eV for the Tm atom to a high value of 0.631 eV for the Pr atom; none is predicted to have a lower EA value than the former. All the negative ions of the lanthanide atoms can be classified through their binding energies ͑BE's͒ as weakly bound negative ions ͑BE's Ͻ1.0 eV͒, while only three qualify to be classified as tenuously bound ͑BE'Ͻ0.1 eV͒. Ramsauer-Townsend minima, shape resonances, and the Wigner threshold behavior for these lanthanides are also determined. Comparisons of the present calculated EA's with those from various experimental measurements and other theoretical calculations are presented and discussed. In particular, our extracted EA value for the complicated open d-and f-subshell Ce atom agrees excellently with the most recently measured ͓Walter et al., Phys. Rev. A 76, 052702 ͑2007͔͒ and calculated values, while for Nd and Eu the agreement with the latest calculated values of O'Malley and Beck ͓Phys. Rev. A 77, 012505 ͑2008͒; Phys. Rev. A 78, 012510 ͑2008͔͒ is outstanding. These agreements give great credence to the already demonstrated predictive power of the Regge-pole methodology to extract unambiguous and reliable binding energies for tenuously bound and complicated open-shell negative ionic systems, requiring no a priori knowledge of the EA values whatsoever. This new perspective to the EA determination of atoms from low-energy electron elastic scattering resonances promises far-reaching implications for future accurate and reliable theoretical EA values, even for small molecules and clusters.

Resonance effects in the differential cross sections of the Cl+HCl(v,j)→ClH(v′,j′)+Cl reaction are analyzed using Regge pole and complex angular momentum (CAM) techniques. This is the first detailed application of CAM theory to reactive molecular scattering. The rovibrational transitions studied are v=1, j=5→v′=0, j′=15, and v=1, j=5→v′=1, j′=5 at total energies E=0.66, 0.68, 0.70 eV. The CAM theory expresses the scattering amplitude as a background subamplitude plus a pole subamplitude. The uniform (and nonuniform) semiclassical evaluation of the background subamplitude is discussed. It is necessary to include explicitly the resonance Regge pole in the semiclassical theory because it has a small imaginary part. We derive a new generic semiclassical formula, involving the complementary error function for the resonance angular scattering. The position and residue of the resonance Regge pole at each E are extracted numerically from scattering matrix elements calculated by the centrifugal sudden hyperspherical (CSH) quantum scattering method. There is good agreement between the semiclassical CAM and CSH angular distributions. However, the latter involve summing a partial wave (PW) series with a large number of numerically significant terms—as a result the PW computations provide no physical insight. We also show that a simple semiclassical optical model becomes inaccurate when the rotational period of the ClHCl complex is comparable to the resonance lifetime. We derive a new ‘‘sticky’’ optical model which allows for rotation of the complex. All our calculations use the Bondi–Connor–Manz–Römelt semiempirical potential energy surface.

We consider a system trapped in a resonance state, whose decay at zero scattering angle can be related, through the optical theorem, to the total cross section ͑TCS͒. We show that for the resonance to contribute to the TCS a peak structure the resonance conditions must be satisfied: ͑i͒ Several rotations of the complex ͑the Regge trajectory-viz., imaginary part versus the real part of the complex angular momentum-stays close to the real axis͒ and ͑ii͒ coherent addition of forward-scattering subamplitudes ͑the real part of the Regge pole is close to an integer͒. We exploit the recent complex angular momentum approach of Macek et al. ͓Phys. Rev. Lett. 93, 183203 ͑2004͔͒, used to analyze low-energy oscillations observed in the elastic TCS for proton-H scattering, for a detailed analysis of Regge trajectories and their contributions to the TCS in electron-atom scattering for the case of Z = 75 using the model Thomas-Fermi potential. We conclude by demonstrating through comparison with existing theory and measurements that the Thomas-Fermi potential when used with the appropriate parameters captures the essential physics ͑Ramsauer-Townsend minima and the Wigner threshold law͒ in the near-threshold e-Ar and e-Kr elastic scattering.

A quantum transition can be seen as a result of interference between various pathways (e.g.Feynman paths) which can be labelled by a variable f . An attempt to determine the value of f without destroying the coherence between the pathways produces the weak value off . We showf to be an average obtained with amplitude distribution which can, in general, take negative values which, in accordance with the uncertainty principle, need not contain information about the actual range of f which contribute to the transition. It is also demonstrated that the moments of such alternating distributions have a number of unusual properties which may lead to misinterpretation of the weak measurement results. We provide a detailed analysis of weak measurements with and without post-selection. Examples include the double slit diffraction experiment, weak von Neumann and von Neumann-like measurements, traversal time for an elastic collision, the phase time, the local angular momentum (LAM) and the 'three-box case' of Aharonov et al.

We present a semiclassical complex angular momentum (CAM) analysis of the forward scattering peak which occurs at a translational collision energy around 32 meV in the quantum mechanical calculations for the F + H(2)(v = 0, j = 0) --> HF(v' = 2, j' = 0) + H reaction on the Stark-Werner potential energy surface. The semiclassical CAM theory is modified to cover the forward and backward scattering angles. The peak is shown to result from constructive/destructive interference of the two Regge states associated with two resonances, one in the transition state region and the other in the exit channel van der Waals well. In addition, we demonstrate that the oscillations in the energy dependence of the backward differential cross section are caused by the interference between the direct backward scattering and the decay of the two resonance complexes returning to the backward direction after one full rotation.

We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)-->HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.

The interplay between Regge resonances and Ramsauer-Townsend minima in the electron elastic total cross sections for Au and Pd atoms along with their large electron affinities is proposed as the fundamental atomic mechanism responsible for the observed exceptional catalytic properties of Au nanoparticles and to explain why the combination Au-Pd possesses an even higher catalytic activity than Au or Pd separately when catalyzing H 2 O 2 , consistent with recent experiments. The investigation uses the recent complex angular momentum description of electron scattering from neutral atoms and the proposed mechanism in general.