Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space

The rich phenomenology of crossings and anticrossings of energies and widths, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of the topological properties of the energy hypersurfaces close to the degeneracy point. The hypersurface representing the complex resonance eigenvalues, as functions of the control parameters, has an algebraic branch point of rank one, and branch cuts in its real and imaginary parts, in parameter space. Associated with this singularity in parameter space, the scattering matrix, S _ℓ (E), and the Green’s function, G _ℓ ⁽⁺⁾(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of any degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.     

Resonances: Calculations and Observables

Methods to calculate resonances energies, decay widths, and corresponding wave functions, are discussed in realistic problems. Proton radioactivity from deformed drip-line nuclei described as decay of a resonant state of the proton in the field of the daughter nucleus, is used to test the models and to show that all experimental data currently available can be consistently described.     

Interaction of Wannier–Stark levels in a wide well superlattice

We have investigated the energy spectrum of a superlattice with wide quantum wells under the bias of an electric field perpendicular to the superlattice layers. By using photocurrent spectroscopy, transitions of Wannier–Stark levels for the various electron and hole states are observed, and at low fields, further structures corresponding to miniband edge transitions are found. Various anticrossings could be observed at higher and lower electric fields. The anticrossings at high electric fields are due to energy alignment of different electronic sublevels in adjacent wells. The anticrossing structures at low fields could be interpreted as resonances between intrawell and interwell excitonic Wannier–Stark states with equal sublevel states, where the anticrossing is caused by differences in exciton binding energy. Fitting of transitions and anticrossings was done by using a semi-empirical model and we have extracted relevant fitting parameters like the quantum-confined Stark coefficient, binding energies for the excitonic Wannier–Stark levels and the resonant coupling strength for states involved in the various anticrossing transitions. Finally, insight into the excitonic influences on the coupling of the WS states could be obtained by comparing the fitted parameters for the various transitions.     

Effective couplings between quantum resonances: application to the resonant dissociation of the <Superscript>6</Superscript>Li<Superscript>7</Superscript>Li molecule

The theory of line profiles in spectroscopy is investigated by means of effective Hamiltonians describing simultaneously the resonances (long-lived states) and the relevant part of the continuum (short-lived states). The energies, widths and wave functions of the resonances are derived by perturbing the resonances by the continuum. Resulting simple analytical expressions allow to study the energy dependence of the dissipation rates. When this dependence is strong, for instance for interacting resonances, the physics is conveniently described by a hierarchy of weakly energy-dependent effective Hamiltonians. The resonant predissociation induced by ungerade-gerade symmetry breaking in the ⁶Li⁷Li molecule is revisited.Dedicated to Prof. Jií Horáek in honor of his 60th birthday.     

Unnatural parity resonance states in positron-excited hydrogen scattering

<正>The coupled-channels optical method for positron scattering has been applied to investigate resonance states with unnatural parities in a positron-excited hydrogen system.The positronium formation channels and continuum channel are included via a complex equivalent local potential.Resonance states with angular momenta L = 1 to L = 2 and parities（—1）^L+1 are calculated.Resonance energies and widths are reported and compared with other theoretical calculations.We found that the opening positronium formation channels play an important role in forming nondipole Feshbach resonances.     

Dynamically generated resonances from the vector octet-baryon decuplet interaction and their radiative decays into γ-baryon decuplet

The dynamically generated resonances from vector meson-baryon decuplet are studied using La-grangians of the hidden gauge theory for vector interactions. One shows that some of the generated states can be associated with some known baryon resonances in the PDG data, while others are predictions for new states. Furthermore, we calculate the radiative decay widths of these resonances into a photon and a baryon decuplet.     

Effect of interdiffusion and magnetic field on two-electron states in Gaussian-shaped double quantum rings

The effects of interdiffusion and electrons' Coulomb interaction on the energy spectrum in Gaussian-shaped single and double quantum rings in the presence of magnetic field has been considered in the framework of exact diagonalization method. The one-electron energies as functions of magnetic field for different values of diffusion parameter have been obtained. The two-electron energies and electron probability density distributions are obtained as well. It is shown that the energy oscillations which are more pronounced for a single quantum ring, smooth out due to the interdiffusion. The Coulomb interaction transforms the crossings of the two-electron levels to anticrossings and can lead to the appearance of an additional level between the anticrossing levels.     

Structure Dependence of Excitonic Effects in Chiral Graphene Nanoribbons

We explore the excitonic effects in chiral graphene nanoribbons(cGNRs), whose edges are composed alternatively of armchair-edged and zigzag-edged segments. For cGNRs dominated by armchair edges, their energy gaps and exciton energies decrease with increasing chirality angles, and they, as functions of widths, oscillate with the period of three, while the exciton binding energies do not have such distinct oscillation. On the other hand,for cGNRs dominated by zigzag edges, all the energy gaps, exciton energies, and exciton binding energies show oscillation properties with their widths, due to the interactions between the edge states localized at the opposite zigzag edges. In addition, the triplet excitons are energy degenerate when the electrons are spin-unpolarized,while the degeneracy split when the electrons are spin-polarized. All the studied cGNRs show strong excitonic effects with the exciton binding energies of hundreds of meV.     

On the variational calculation of energies and widths of resonances

An approximation, based on a direct method of the calculus of variations, is applied in order to compute energies and widths of resonances (and energies of bound states).     

A full numerical calculation of the Franz--Keldysh effect on magnetoexcitons in a bulk semiconductor

We have performed a full numerical calculation of the Franz--Keldysh (FK) effect on magnetoexcitons in a bulk GaAs semiconductor. By employing an initial value method in combination with the application of a perfect matched layer, the numerical effort and storage size are dramatically reduced due to a significant reduction in both computed domain and number of base functions. In the absence of an electric field, the higher magnetoexcitonic peaks show distinct Fano lineshape due to the degeneracy with continuum states of the lower Landau levels. The magnetoexcitons that belong to the zeroth Landau level remain in bound states and lead to Lorentzian lineshape, because they are not degenerated with continuum states. In the presence of an electric field, the FK effect on each magnetoexcitonic resonance can be identified for high magnetic fields. However, for low magnetic fields, the FK oscillations dominate the spectrum structure in the vicinity of the bandgap edge and the magnetoexcitonic resonances dominate the spectrum structure of higher energies. In the moderate electric fields, the interplay of FK effect and magnetoexcitonic resonance leads to a complex and rich structure in the absorption spectrum.     

Single-particle subband properties of quantum cables

We proposed a new kind of coupled coaxial cylindrical quantum wires structure - quantum cable, and calculated its single-electron energy subband spectrum for the varying structure parameters, in order to investigate its subband motion in the structure parameter space. It is shown that quantum cable has unique subband spectrum, which differs either from the (solid and hollow) cylindrical quantum wire or from the usual coupled double quantum wires (CDQWs) structure. Aside from the two-fold degeneracy induced by the cylindrical symmetry, crossings (accidental degeneracies) and anticrossings (repulsions) of quantum cable subbands with different azimuthal and radial quantum numbers are observed as one of the cable structure parameters varies. This introduces the dependence of the subband ladder on the structure parameters of the quantum cable structure. However, the subband with the lowest azimuthal and radial quantum numbers remains the lowest subband and never crosses with the other subbands irrespective of the value of structure parameters. As the coupling barrier is broadening (coupling becoming weak), some subbands bundling toward another subband is seen before the extreme isolating limit achieved. Moreover, the separation between neighboring subbands exhibits non-monotonous evolution as one changes the thickness of one of the cylindrical quantum wires, with a minimum existing in the separation between some two adjacent subbands. Interesting optical and transport phenomena arising from these unique subband properties of the quantum cable structure are also predicted. Received 22 March 2000 and Received in final form 6 June 2000     

Performance characteristics of an energy selective electron refrigerator with double resonances

This paper establishes the energy selective electron (ESE) engine with double resonances as a refrigerator in one dimensional (1D) system. It consists of two infinitely large electron reservoirs with different temperatures and chemical potentials, and they are perfectly thermally insulated from each other and interaction only via a double `idealized energy filter' whose widths are all finite. Taking advantage of the density of state and Fermi distribution in the 1D system, the heat flux into each reservoir may then be calculated. Moreover, the coefficient of performance may be derived from the expressions for the heat flux into the hot and cold reservoirs. The performance characteristic curves are plotted by numerical analysis. The influences of the resonances widths, the energy position of resonance and the space of two resonances on performance of the ESE refrigerator are discussed. The results obtained here have theoretical significance for the understanding of thermodynamic performance of the micro--nano devices.     

Photodetachment of He- in the vicinity of the two-electron escape threshold

Recording the yield of He(1snl(3)L) Rydberg states for n=11-14, we measure the photodetachment cross sections of metastable He-(1s2s2p(4)P(o)) ions in the vicinity of the two-electron escape threshold. We observe a large number of double Rydberg He- quartet state resonances and report energies and widths of intrashell states in the n=13-15 manifolds. Sharp thresholds are measured at He((3)P(o)) and He((3)D(e)) Rydberg states with preference for population of the former, whereas the He((3)S(e)) states are not populated, in agreement with qualitative theoretical arguments.     

The determinantal method for bound states and resonances of three-particle systems

Bound state energies, positions and widths of resonances of two-particle systems may be calculated as zeros of an analytic function of the energy, the modified Fredholm determinant of the Lippmann-Schwinger equation. This generates degenerate perturbation theory particularly easily. The method is generalized to the threebody problem. Here too, the bound states and resonances appear as zeros of an analytic function of the energy, the modified Fredholm determinant of a square-integrable kernel. It is proved that the multiplicity of a zero equals the degeneracy of the corresponding eigenvalue.Invited talk at the symposium Theory of lightest nuclei, Liblice, Czechoslovakia, May 1974.Work supported in part by the National Science Foundation.     

Long-range molecular resonances in a cold Rydberg gas

We present evidence for molecular resonances in a cold dense gas of rubidium Rydberg atoms. Single UV photon excitation from the 5s ground state to np Rydberg states (n=50-90) reveals resonances at energies corresponding to excited atom pairs (n-1)d+ns. We attribute these normally forbidden transitions to avoided crossings between the long-range molecular potentials of two Rydberg atoms. These strong van der Waals interactions result in avoided crossings at extremely long range, e.g., approximately 58 000 times the Bohr radius (a(0)) for n=70.     

Positions and Widths of Anticrossings for Potassium Rydberg Stark States

The B-spline expansion technique is applied to study the anticrossings for potassium Rydberg states in a static electric field. The results of our calculation indicate that the antierossings are caused mainly by the core interaction or by the fine structure interaction. Our results for the positions and the widths of the anticrossings are in good agreement with experimental data.     

Doubly Excited <Superscript>1,3</Superscript><Emphasis Type="Italic">P</Emphasis><Superscript>e</Superscript> Resonance States of the Positronium Negative Ion with Coulomb and Screened Coulomb Potentials

We have investigated the doubly excited ^1,3 P ^e resonance states of positronium negative ion with Coulomb and screened Coulomb potentials using highly accurate correlated exponential wavefunctions. For Coulomb interaction, the stabilization and the complex-rotation methods are employed to extract resonance parameters (resonance positions and widths). We have obtained two ¹ P ^e resonances and three ³ P ^e resonances below the n = 3 Ps threshold. In addition to Feshbach resonances lying below n = 3 Ps threshold, we have calculated one ³ P ^e shape resonances lying above the Ps (n = 2) threshold. For screened Coulomb (Yukawa) interaction, we employ the stabilization method to extract resonance parameters as functions screening parameter. The resonance energies and widths for ^1,3 P ^e resonance states of Ps⁻ below the n = 3 Ps threshold for different screening parameters ranging from infinity (Coulomb case) to small values are reported, along with the Ps(3S) and Ps(3P) threshold energies. The screened Coulomb results for the ^1,3 P ^e resonance states are reported for the first time in the literature.     

Exact finite-range DWBA treatment of heavy-ion-induced reactions to unbound residual states

We show that when one considers heavy-ion-induced direct nuclear reactions, the narrowly localized reaction surface makes a traditional approximation used in analysis of light-ion reactions to particle-unbound states a very poor one. Even for unbound states having single-particle widths 10^?5 of their resonance energies, quite different heavy-ion angular distributions are predicted using weakly-bound states versus more realistic complex-energy eigenstates (Gamow states).     

过渡金属离子Pt+和甲烷气相反应的势能面研究

采用密度泛函理论（DFT）中的B3LYP方法研究了二重态和四重态Pt+与甲烷反应的机理。通过几何构型优化和频率计算,分别获得三个过渡态,并利用内禀反应坐标（IRC）计算进行了验证。在更高的基组水平上计算了单点能,并详细讨论了二重态和四重态的势能面。结果表明在二重态势能面上的反应具有比较低的能垒,是一个放热反应,所以该反应更易于在二重态上进行。氧化加成生成中间体HPt(CH3)+的步骤需要克服一个小小的能垒。