Amplitudes of two-channel scattering by a two-dimensional potential barrier with a constant height

The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t ₁, t ₂, r ₁, and r ₂ are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k ₂ → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

The potential barrier height for a Jahn-Teller center

The EPR spectrum of the Cu²⁺ ion in a ZnSiF₆·6H₂O crystal is studied in the temperature range T=5?300K. It is shown that the EPR spectrum can be represented in the form of a superposition of three contributions with essentially different properties. The first contribution is characterized by the maximal intensity at low temperatures and is described by a spin Hamiltonian with a large anisotropy of parameters. The second contribution has the maximal intensity at high temperatures and is described by a spin Hamiltonian with a low anisotropy of parameters. The third contribution cannot be described by a spin Hamiltonian and has the form of a partly orientationally averaged EPR spectrum. The reason for the emergence of these contributions is substantiated along with the form of the temperature dependence of their intensities on the basis of variation of the populations of vibronic states upon a change in temperature. The height (E₀=4±1cm_?1) of the potential barrier separating three equivalent Jahn-Teller potential wells of the Cu²⁺ ion is determined from analysis of the temperature dependence of the integrated intensity of the EPR spectrum. The obtained value of the barrier height substantially differs from the estimate (100 cm^?1) obtained earlier [2, 3] for the Cu²⁺ ion in ZnSiF₆·6H₂O on the basis of the tunneling model. It is shown that the forms of the temperature dependences of the linewidth of the low-and high-temperature EPR spectra are essentially different. This difference indicates that the contributions of the low-and high-temperature EPR spectra are associated with quantum-mechanical transitions between these states. It is proposed that the low-and high temperature contributions to the EPR spectrum are associated with the filling of under-the-barrier and above-the-barrier vibronic states, respectively.     

Particle tunneling and scattering in a three-dimensional potential with a barrier

The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.      

A multichannel quasi-separable potential approach to nucleon-nucleus scattering

A quasi-separable potential model for two-body multichannel scattering is developed. Spin and Coulomb effects are taken into account. By a suitable choice of the separable nuclear interactions we arrive at simple analytic expressions for the transition amplitudes. Our model is applied to the study of the n-¹²C and p-¹²C scattering processes. Effects arising from the excitation of the target nucleus are well reproduced.     

Electron scattering by a short-range potential in a constant homogeneous magnetic field

The scattering of spin-oriented electrons, moving in a constant homogeneous magnetic field, by a short-range potential is analyzed. The change in the electron spin orientation is calculated using the Born approximation.     

Quantization on a two-dimensional phase space with a constant curvature tensor

Some properties of the star product of the Weyl type (i.e., associated with the Weyl ordering) are proved. Fedosov construction of the *-product on a two-dimensional phase space with a constant curvature tensor is presented. Eigenvalue equations for momentum p and position q on a two-dimensional phase space with constant curvature tensors are solved.     

Reflection at a complex potential barrier in the semiclassical theory of scattering

The reflection of spherical waves at a complex potential barrier is discussed in the semiclassical approximation. We study the complex WKB method and the Uniform Approximation in the special case of weakly absorptive barriers, typical of surface transparent optical potentials used in heavy-ion reactions. It is found that the complex WKB results lead to a very accuratecross- section despite their inaccuracy in the most importantphase shifts. Thereby, the amazing stamina of the WKB has been confirmed once more. One of us (Y.A.) spent the summer of 1976 at the Max-Planck Institute at Heidelberg where the present work has been done. He would like to thank J. Hüfner and H. Weidenmüller for the hospitality extended to him.     

Exactly soluble multichannel scattering problems with Coulomb interactions

A general separable potential approach to elastic and inelastic scattering processes is developed which takes account of Coulomb interactions in an exact way. Effective nuclear interactions are used that are separable in the channel relative motion variables and take explicit account of the coupled-channel nature of the problem. After solving the coupled-channel integral equations by means of both matrix inversion techniques and a suitable channel-decoupling procedure, we arrive at exact manageable expressions of the Coulomb-corrected nuclear transition amplitudes.     

On two-sided estimates of the particle scattering amplitude by a potential and the amplitudes of multichannel processes

Functions permitting two-sided estimates to be obtained for the real and imaginary parts of the particle scattering amplitude by a nonspherical potential and for the amplitudes of multichannel processes are considered. To diminish the interval between the two estimates it is proposed to use Schwinger iteration of the test functions, whose multiparticle generalization permits estimation of the error in the approximation of P-coupled channels and the approximate assignment of the wave functions and the energy of the internal motion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 78–83, July, 1973.The author is deeply grateful to his colleagues m the Theoretical Physics Laboratory of the Joint Institute of Nuclear Research, Lkhagva Oido-Vyn' and Doctor B. N. Zakhar'ev, for formulating the problem and for useful comments which made this research realizable.     

一维势垒散射中粒子的概率分布

利用数值计算方法研究了E>U0、0相似文献   

Magnetic barrier in a two-dimensional hole gas

Transport properties of a magnetic barrier in a Ga_xAl_1−xAs based two-dimensional hole gas are reported. A ferromagnetic cobalt film, separated by an AlO_x layer from the semiconductor in order to prevent leakage currents, is magnetized in-plane, such that the fringe field generates a localized perpendicular magnetic field acting as a magnetic barrier. The resistance as a function of the in-plane magnetic field shows a characteristic minimum at the coercive field of the ferromagnetic film. Semiclassical simulations based on the Landauer–Büttiker formalism show good agreement with the experiment.     

Relationship between torsional frequency and potential barrier height forAB n type molecular system

A relationship between the torsional frequency (v ₁₀) and the potential barrier (V _n) has been determined forAB _n type molecular system havingn-fold symmetry axis. It is found thatv ₁₀ varies prominently asV _n ^1/2 ,V _n andV _n ² in certain ranges. TheV _n value computed fromv ₁₀ andI* _r has been compared with that obtained from other experimental data for someAB _n units in different molecular-crystalline systems. Although there is in general a good agreement, in some cases the values differ significantly, perhaps due to the erroneous assignment of torsional mode and/or the large errors in theV _n value obtained from other experimental data.     

Definition and existence of multichannel scattering states

The field theoretical formulation of quantum mechanics is used to consider the nonrelativistic multichannel scattering theory. With the help of appropriately constructed time dependent creation operators, Hilbert vectors are formed whose limits in time can be defined as multichannel scattering states in the usual sense. The existence of these states is proved under certain assumptions for the potential, by showing the convergence of the above mentioned operators. The commutation relations for the limits of these operators are given.     

Tunable multichannel drop filters based on the two-dimensional photonic crystal with oval defects

Light propagation through the channel filter based on the two-dimensional photonic crystals with oval-rod defects is studied by the finite-difference time-domain method. In addition to the traditional size tuning, shape alteration of the defects from the usual circle to the ellipse offers a powerful approach to tune the resonant frequency of channel-drop filters based on two-dimensional photonic crystals. It is found that the resonant frequency can be flexibly adjusted only by changing the orientation angle of the oval defects. The sensitivity of the resonant frequency to the alteration of the oval rods’ rotation angle is systematically studied. Because the rotation angles of the ellipse can be continuously adjusted, so the channel drop filter based on this kind of defects with different rotation angles is more suitable to the occasion where a large number of output channel filters is need.     

双模压缩真空态和纠缠相干态的一维势垒散射

分析了双模压缩真空态和纠缠相干态的一维势垒散射问题,结果表明,两种散射态的纠缠度都随势垒的透射系数呈类抛物线关系,且抛物线谷底对应半反半透势垒.前者的纠缠度还随入射压缩因子呈类抛物线关系,后者随入射纠缠呈线性关系.两种散射的保真度都可以由透射系数的增加而得到提高,但前者还会随入射压缩因子的增大而降低,后者随入射相干态模的增加而降低.     

Tunnelling across a potential barrier

Generalized expressions for the tunnelling probability spectrum and the tunnelling time are derived for a potential barrier of arbitrary shape independent of the use of the perturbation theory. A method to obtain the tunnelling current density by solving the continuity equation in the barrier region is proposed.     

High-energy scattering in a two-dimensional gauge theory

We study high-energy scattering in two-dimensional quantum chromodynamics in the 1/N_colour expansion. To first order, high-energy forward scattering amplitudes are power-behaved with the factorization, signature and exchange degeneracy properties found in dual Regge models. Backward scattering has deviations from naive quark power-counting rules which are related to the form factor and “Regge” behaviours. In the second order of 1/N_colour vacuum exchange diagrams do not give a new Pomeron singularity, but do break exchange degeneracy.