Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

复标度方法对原子核单粒子共振态的研究

在相对论平均场理论框架下, 利用复标度方法研究了 Zr 同位素的单粒子共振问题. 以 ¹²²Zr 为例, 演示了复标度方法确定共振态的具体步骤, 确定了 ¹²²Zr 所有可能共振态的能量和宽度, 以及相应共振态的复标度波函数, 并与耦合常数的解析延拓方法进行了比较.在此基础上, 进一步系统研究了 Zr 同位素的共振问题, 获得了与散射相移方法一致的结果.     

Optical absorption in asymmetric double quantum wells driven by two intense terahertz fields

Optical absorption is investigated for asymmetric double quantum wells driven by a resonant terahertz field and a varied terahertz field both polarized along the growth direction. Rich nonlinear dynamics of the replica peak and the Autler-Townes splitting of various dressed states are systematically studied in undoped asymmetric double quantum wells by taking account of multiple factors, such as the frequency of the varied terahertz field and the strength of the resonant terahertz field. Each electron subband splits into two dressed states when the resonant terahertz field is applied in the absence of the varied terahertz field, the optical absorption spectrum shows the first order Autler-Townes splitting of the electron subbands. When a varied terahertz field is added into the resonant system, the replica peak and the second order Autler-Townes splitting of the dressed states near the band edge respectively emerge when the varied terahertz field is non-resonant and resonant with these dressed states. When the strength of the resonant terahertz field is increased, the first order Autler-Townes double peaks and the replica peak in the optical absorption spectrum shift with the shifts of the dressed states. The presented results have potential applications in electro-optical devices.     

Relativistic wave functions for single-proton resonant states

With the relativistic boundary condition, single-proton resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean-field (RMF) theory. In this scheme, we investigate the wave functions for l≠ 0 proton resonant states close to the continuum threshold in the stable nuclide ¹²⁰Sn for the first time. Some hints for pseudospin symmetry in the resonant states of nuclei are mentioned as well.     

Double resonance mechanism of ferromagnetism and magnetotransport in (Ga-Mn)As

We calculate the electronic states of the Mn-doped semiconductors and show that resonant states are formed at the top of the down spin valence band due to magnetic impurities and that they give rise to a strong and long-ranged ferromagnetic coupling between Mn moments. We propose that the coupling of the resonant states, in addition to the intra-atomic exchange interaction between the resonant and nonbonding states, is the origin of the ferromagnetism of (Ga-Mn)As. The mechanism is thus called "double resonance." The resonant states bring about the spin-dependent resistivity to produce magnetoresistive properties in (Ga-Mn)As and their junctions.     

Highly asymmetric atom-lead coupling in nanowires for resonance regime

Concerning quantum transport at resonant states in a one-atom nanowire (nanoconstriction), for the first time, a theoretical study is presented upon strongly asymmetric coupling between the atom at the nanoconstriction and the involved leads. Under these conditions, an approximate relationship for the conductance at resonance in a single-atom wire is considered and an expression for the number of resonant states is derived and discussed. In addition, the density of resonant electronic states is determined under a quantum-box approach by which the conduction electrons are assumed to behave as quantum harmonic oscillators confined in a potential well transverse to the wire.     

Transmission resonance via quantum bound states in confined arrays of antidots

We have studied the transmission resonances for a confined array of antidots, using the lattice Green's function method. Two kinds of resonant peaks via quasibound states are found. One kind of resonant peak corresponds to the split quasibound states. The split states originate from the superposition of quasibound states respectively localized in different (T or crossed) junctions, while the number of quasibound states in each junction is associated with the arm-width of the junction. Electrons in these split states are mainly localized in the junctions. The other kind of resonant peaks correspond to the high quasibound states which exist in (transverse and longitude) multi-period confined arrays of antidots. It is interesting to note that electrons in some of the high quasibound states are mainly localized in the intersection of the junctions rather than in the junctions themselves.     

Resonant acceptor states in uniaxially strained semiconductors

A new approach to calculating the parameters of resonant states is proposed, which also makes it possible to determine the probabilities of the resonant scattering and capture probabilities at the resonant state. This approach is based on the application of the method of configuration interaction, which was proposed for the first time by Fano for an analysis of field ionization of the helium atom. Following Fano, use is made of two different Hamiltonians of the initial approximation for the states of continuum and the initial local state. Following Dirac, the wave functions are constructed in the same way as in the general theory of scattering. A detailed analysis and specific calculations are made for resonant acceptor states in uniaxially strained germanium under a pressure directed along the [001] and [111] axes.     

Resonant Continuum in the Relativistic Mean-Field Theory

Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.     

Probabilistic interpretation of resonant states

We provide probabilistic interpretation of resonant states. We do this by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space. On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area. This momentum leakage is also the reason for the spatial exponential divergence of resonant state. It is by combining the opposite temporal and spatial behaviours of resonant states that we arrive at our probabilistic interpretation of these states. The physical need to normalize resonant wave functions over an expanding spatial domain arises because particles leak out of the region which contains the potential range and escape to infinity, and one has to include them in the total count of particles.     

Highly excited spin-1 states in 88Sr by the (γ, γ) reaction

The resonant scattering of bremsstrahlung γ-rays by a SrCO₃ target has been studied for γ-ray energies of 5–11 MeV. Six γ-transitions of energies between 6–8 MeV, which indicate six resonant states in ⁸⁸Sr, were observed. The relative intensities of the resonantly scattered γ-rays at 125 and 150° were found to be compatible only with the assignment of spin 1 to the six states. Radiative widths of the resonant states were deduced. The possibility that these states are components of the giant M1 resonance in ⁸⁸Sr is discussed.     

Effect of resonant continuum on pairing correlations in the relativistic approach

A proper treatment of the resonant continuum is to take account of not only the energy of the resonant state, but also its width. The effect of resonant states on pairing correlations is presented in the framework of the relativistic mean-field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The study is performed in an effective Lagrangian with the parameter set NL3 for neutron-rich even-even Ni isotopes. Results show that the contribution of the proper treatment of the resonant continuum to pairing correlations for those nuclei close to the neutron drip line is important. The pairing gaps, Fermi energies, pairing correlation energies, and binding energies are considerably affected by a proper consideration of the width of resonant states. The problem of unphysical particle gas, which may appear in the calculation of the traditional mean field plus BCS method for nuclei in the vicinity of the drip line could be well overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.PACS: 21.60.-n Nuclear-structure models and methods - 24.10.Jv Relativistic modelsZhong-Yu Ma: Also at Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, PRC and Institute of Theoretical Physics, Beijing 100080, PRC.     

Resonant transmission in three-terminal triangle graphene nanojunctions with zigzag edges

Three-terminal nanojunctions based on triangle zigzag edged graphene flakes are proposed and their transport properties are studied. In the solid and hollow triangle graphene junctions, there exist different resonant transmissions due to the different electronic states in the two structures. The quasi-bound states in the solid junction are confined in the inner of the triangle flake, while those in the hollow junction are confined at the zigzag edges. In addition, these states are tightly associated with the size of the triangle flake, thus the resonant transmissions in the triangle graphene junctions can be tuned by the structural size and geometry.     

Resonant breather states in Josephson coupled systems

A review of diverse resonant effects appearing in weakly dissipative Josephson coupled systems in the presence of inhomogeneous dynamic localized state (discrete breather) is given. As particular examples I discuss the resonant interaction of breather states with linear electromagnetic excitations (EEs) in dc driven Josephson junction ladders and a single plaquette containing three Josephson junctions. Such resonant interaction manifests itself by resonant steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the resonant interaction leads to an increase of breather dynamical complexity, e.g., enlargement of the breather core, low symmetry or quasiperiodic breather states. I show that the application of an external magnetic field allows to tune the resonant interaction, and correspondingly to increase (or decrease) the height of the resonant steps, to change the stability of the breather states.     

引入量子干涉的双光子共振非简并四波混频

研究了级联四能级系统中双光子共振非简并四波混频(NFWM)由于加入耦合光场而产生的量子干涉效应，发现在强耦合场作用下NFWM频谱呈现AT劈裂，它反映的是两个缀饰态的能级.量子干涉还使NFWM信号被抑制或增强.此方法牵涉到三光子共振，因此可以成为研究原子或分子高激发态的有效光谱学工具. 关键词： 四波混频 量子干涉     

Resonant Continuum in Extended RMF Plus BCS Approximation

The contribution of the resonant continuum to pairing correlations is investigated in the relativistic mean field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The resonance states with their widths in the continuum are considered explicitly. The numerical study is performed in an effective Lagrangian with the parameter set NLSH for neutron-rich nucleus ⁸⁴Ni. The results show that the effect of the proper treatment of the resonant continuum on pairing correlations for nucleus close to neutron drip line is important. It is found that the problem of an unphysical particle gas could be overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.     

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the weakly bound nucleus ~(66)Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.     

Impurity absorption of light involving resonant states of shallow donors in quantum wells

The energy spectrum of localized and resonant states of shallow donors in heterostructures GaAs/Al_xGa_1?xAs with quantum wells is calculated. The widths of the resonant states belonging to the second size quantization subband are determined. It is shown that the width of a resonance level is mainly determined by the interaction with optical phonons. The spectrum of impurity absorption of light due to electron transitions from the ground state of the donor to the resonant states belonging to the second size quantization subband is calculated.     

Inter-Well Coupling and Resonant Tunneling Modes of MultipleGraphene Quantum Wells

We investigate the inter-well coupling of multiple graphene quantum well structures consisting of graphene superlattices with different periodic potentials. The general form of the eigenlevel equation for the bound states of the quantum well is expressed in terms of the transfer matrix elements. It is found that the electronic transmission exhibits resonant tunneling peaks at the eigenlevels of the bound states and shifts to the higher energy with increasing the incident angle. If there are N coupled quantum wells, the resonant modes have N-fold splitting. The peaks of resonant tunneling can be controlled by modulating the graphene barriers.