Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

Elastic scattering 2H(d,d)2H below 360 keV: (II). Theory

The elastic d-d scattering near threshold is calculated with a resonating group method using exact deuteron wave functions evaluated from the Malfliet-Tjon two-nucleon potential. There is agreement with a recent experiment, where no evidence for a resonance near threshold has been found. This is supported also theoretically.     

Variational calculations for the hydrogen-antihydrogen system with a mass-scaled Born-Oppenheimer potential

The problem of proton-antiproton motion in the H- $\bar H$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This improved treatment of the interaction includes the nondivergent part of the otherwise divergent adiabatic correction and shows the correct threshold behaviour. Using this potential we calculate the vibrational energy levels with angular momentum 0 and 1 and the corresponding nuclear wave functions, as well as the S-wave scattering length. We obtain a full set of all bound states together with a large number of discretized continuum states that might be utilized in variational four-body calculations. The results of our calculations gives an indication of resonance states in the hydrogen-antihydrogen system.     

Electron-acceptor luminescence from a non-Maxwellian distribution of photoexcited electrons in GaAs

Distribution functions are calculated for photoexcited electrons in GaAs, under conditions of continuous, monochromatic excitation. The lattice temperature is taken to be 1.2 K and the excitation intensity such that the density of photoexcited carriers is insufficient for the distribution to be affected by intercarrier scattering. A Boltzmann equation approach is used to take account of the effects of, injection of electrons into the conduction band, at an energy below the threshold for longitudinal optical phonon emission, scattering by acoustic phonons, via the deformation potential and piezoelectric interactions, and recombination. The equation is solved numerically using an iterative technique and the distribution functions are found to differ significantly from a Maxwellian form. Emission spectra due to conduction band to neutral acceptor transitions are derived from the computed distribution functions and are compared with recent experimental results.     

Near-barrier fusion, breakup and scattering for the Be + Sm system

Fusion, breakup and scattering for the ⁹Be + ¹⁴⁴Sm system at near barrier energies are investigated by different approaches. We show that at energies above the barrier there is a small complete fusion suppression when compared with predictions from a double folding potential and with a similar tightly bound system. At sub-barrier energies there is no significant deviation from the predictions using coupled channel calculations that do not include the breakup channel. The energy dependence of the optical potential does not show the usual threshold anomaly found in tightly bound systems. From a simultaneous analysis of fusion and scattering data we estimate the distance where breakup starts to occur.     

Mechanisms of photo double ionization of helium by 530 eV photons

We have measured fully differential cross sections for photo double ionization of helium 450 eV above the threshold. We have found an extremely asymmetric energy sharing between the photoelectrons and an angular asymmetry parameter beta approximately 2 and beta approximately 0 for the fast and slow electrons, respectively. The electron angular distributions show a dominance of the shakeoff for 2 eV electrons and clear evidence of an inelastic electron-electron scattering at an electron energy of 30 eV. The data are in excellent agreement with convergent close-coupling calculations.     

Analytical solution for the one-dimensional scattering problem

We introduce the scattering problem in the case of one-dimensional space. The transmission factor is calculated for the whole domain of the potential energy. Connection with a field in interaction with a two-level quantum system is established for which the coupling parameter is considered to be explicitly time-dependent.     

Realization of a resonant Fermi gas with a large effective range

We have measured the interaction energy and three-body recombination rate for a two-component Fermi gas near a narrow Feshbach resonance and found both to be strongly energy dependent. Even for de Broglie wavelengths greatly exceeding the van der Waals length scale, the behavior of the interaction energy as a function of temperature cannot be described by atoms interacting via a contact potential. Rather, energy-dependent corrections beyond the scattering length approximation are required, indicating a resonance with an anomalously large effective range. For fields where the molecular state is above threshold, the rate of three-body recombination is enhanced by a sharp, two-body resonance arising from the closed-channel molecular state which can be magnetically tuned through the continuum. This narrow resonance can be used to study strongly correlated Fermi gases that simultaneously have a sizable effective range and a large scattering length.     

Operation of the Faddeev Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.     

Most probable and average energy losses of the beam of monoenergetic charge particles with average and low energies at multiple scattering

The results of statistical modeling of the discrete process of multiple inelastic scattering are presented. This process is modeled to find the most probable and average energy losses of a beam of charged particles (electrons and protons) passing through a material layer with a given thickness. The proposed approach is based on determining the most probable energy loss at single small-angle scattering, on including the effect of the statistical probability on this quantity at multiple scattering, and on determining the average number of inelastic interactions for particles in a film with a known thickness. The dependence of the particle energy lost during interaction with atomic electrons on their relative motion is taken into account for low-energy particles. A new interpretation is offered for the parameter J in the logarithmic term in the formulas for the average and most probable energy losses of charged particles. A computational scheme for this parameter as an average potential energy of atomic electrons is given.     

Crossings and Anticrossings of Unbound States

We investigate the characteristic crossings and anticrossings of energies and widths of a doublet of resonances, observed in the vicinity of, and at a degeneracy of unbound states, when the control parameters of the system are varied. This characteristic behavior is explained in terms of the local, topological structure of the surfaces that represent the complex energy eigenvalues in parameter space in the vicinity of a degeneracy point. In the simple but illustrative case of the scattering of a beam of particles by a double barrier potential well with two regions of trapping, we solved numerically the implicit, transcendental equation that defines the eigenwave numbers of a degenerate isolated doublet of resonances as functions of the real, control parameters of the system. We found that, at a degeneracy of unbound states, the surface representing the resonance eigenwave numbers as functions of the control parameters has an algebraic branch point of rank one. Unfolding the degeneracy point, crossings and anticrossings of energies and widths are obtained as projections of sections of the eigenwave number surfaces.     

强子物质中的介子-介子散射(英文)

建立了一个夸克交换模型和提出了一个夸克-反夸克湮灭模型来研究介子-介子散射。从量子色动力学我们得到一个依赖于温度的夸克作用势。从微扰量子色动力学推导对应于夸克-反夸克湮灭和产生的跃迁势。模型给出基态介子质量的实验值,并且在玻恩近似下能说明真空中阈能附近的π-π弹性散射相移的实验值。从S矩阵元出发,推导散射的跃迁振幅和截面公式。计算出涉及π,ρ,K,K*的反应的非极化截面。发现这些截面具有强烈的温度依赖性。We have established a quark-interchange model and have proposed a quark-antiquark annihilation model to study meson-meson scattering. From QCD we obtain a temperature-dependent quark potential. The transition potential corresponding to quark-antiquark annihilation and creation is derived in perturbative QCD. The experimental ground-state meson masses are reproduced and the experimental data of elastic phase shifts for ππ scattering near the threshold energy in vacuum can be accounted for in the Born approximation. Starting from S-matrix element, we derive the transition amplitude and the cross section for the scattering. Unpolarised cross sections for reactions involving π, ρ, K and K* are calculated. Remarkable temperature dependence of the cross sections is found.     

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.     

Low density expansion of the nucleon-nucleus optical-model potential

The optical-model potential for nucleon-nucleus scattering is studied within the framework of the Green function approach to the many-body problem. The optical potential is identified with the self-energy, for which an expansion in terms of irreducible graphs exists. We propose to group the diagrams of this expansion according to the number of independent hole lines and to sum the graphs within each class. This procedure essentially amounts to an expansion in powers of the density and is closely related to the Bethe-Brueckner expansion for the binding energy of nuclear matter. We show that the same convergence parameter appears in both expansions. The one-and two-hole line contributions are studied in detail, numerical estimates are provided and compared with experiment. At low energy, our expansion can be related to the calculation of the optical potential within the framework of nuclear reactions (e.g., using doorway states). At high energy one is led in a natural way to the expressions derived from multiple scattering theory. Thus the hole-line expansion ties together the low and high energy domains of the optical potential. Hole line expansions for the momentum distribution and the total energy are derived from the expansion of the self-energy. The self-consistency requirement is discussed. The present study is restricted to nuclear matter but most results apply to finite nuclei as well.     

Semi-exact Solutions of Konwent Potential

In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).     

Medium corrections to the reaction cross section for low energy pion4He scattering

We investigate the effects of the Pauli principle and the nucleon binding on the reactive content of the single scattering optical potential. The binding and exclusion principle effects are calculated for low energy pion-⁴He scattering. A careful treatment of the Pauli principle enables us to determine a pion nucleon energy shift representing binding effects from the requirement that the reaction channel opens at the correct threshold energy. We find that binding and Pauli effects lead to a reduction of the reaction cross section by about 30–50% and (expect for very low energies) to a slight increase of the elastic cross section by 5–10%.     

蒙特卡罗法计算无序激光器的阈值

提出了计算无序激光器阈值增益的模型,提出了已知平均自由程和散射强度分布得到分布函数及相应的随机变量的方法.对各向同性的光散射,导出了各分布函数,并在每次散射中得到相应的随机变量.运用蒙特卡罗法模拟光子在无序介质中的随机行走,得到了无序激光器的阈值.讨论了阈值增益与光子平均自由程、增益区半径、增益区深度、非增益区光吸收系数的关系,提出了降低阈值的方法.理论结果与实验数据是符合的. 关键词： 激光物理 阈值 蒙特卡罗 散射     

Scaling and decay in periodically driven scattering systems

We investigate irregular scattering in a periodically driven Hamiltonian system of one degree of freedom. The potential is asymptotically attracting, so there exist parabolically escaping scattering orbits, i.e. orbits with asymptotic energy E(out)=0. The scattering functions (i.e. the asymptotic out-variables as functions of an asymptotic in-variable) show a characteristic algebraic scaling in the vicinity of these orbits. This behavior is explained by asymptotic properties of the interaction. As a consequence, the number N(Deltat) of temporarily bound particles decays algebraically with the delay time Deltat, although no KAM scenario can be found in phase space. On the other hand, we find the number N(n) of temporarily bound particles to decay exponentially with the number n of zeros of x(t).     

库仑程函近似下非弹性散射振幅角分布的广义函数分析

在库仑程函近似框架下,引进实参量(时间扫描参数)积分,将能壳上跃迁矩阵元分为靶的结构因子和弹的扭曲因子,导出了非分波扭曲因子的主项表达式和结构因子的解析表达式,利用广义函数方法分析了电子与类氢离子的非弹性散射角分布.     

Barrier penetration effects for electrons in quantum wells: screening,mobility, and shallow impurity states

A two-dimensional electron gas in a quantum well confined by finite barriers is considered. We present analytical expressions for the finite confinement effects of a square-well potential and calculate the electron-electron interaction potential, the electron-impurity interaction potential, the interface-roughness scattering potential and the alloy-disorder scattering potential. The dielectric function of the interacting electron gas, the mobility (for charged-impurity scattering, for interface-roughness scattering, and for alloy-disorder scattering), and the binding energy of hydrogenic impurities (screened and unscreened) are discussed.