Scattering from non-overlapping potentials. I. General formulation

The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low energy and high energy are considered. Applications to high-energy scattering of elementary particles on nuclei are briefly discussed.     

The fixed scatterer approximation and nucleon deuteron scattering

A method of solving the Schroedinger Equation for the scattering from two fixed local potentials is presented. The solutions are used within the framework of the fixed scatterer approximation to perform model calculations of N-D scattering using both effective range theory potentials and a “semi-realistic” potential with a strong repulsive core. For smooth potentials approximate solutions to the fixed scatterer problem are proposed and found to be quite accurate.Other procedures for calculating elastic scattering were compared with the exact fixed scatterer approximation. The results show that the neglect of longitudinal momentum transfer in the Glauber multiple diffraction theory is a severe effect except in the forward direction. For small angle scattering the Glauber prediction for the double scattering amplitude is quite accurate, and does not depend strongly upon either the extent of potential overlap, or the ratio $\text{V}\text{E}$. Comparisons with the Agassi and Gal results for nonoverlapping potentials indicate that the effects of potential overlap are important, at least for the lowest partial waves. Conclusions about the overall importance of off-energy shell effects in nucleon-deuteron scattering, and about the interference of these effects with the determination of the correlation structure of nuclei are not free from ambiguities.     

Off-shell effects in scattering from the deuteron

A simple model for scattering from a deuteron is studied. Within this model exact coupled channel solutions, including all multiple scattering series terms, are obtained for a fixed separation of the two scattering potentials. These solutions are compared with approximations which involve a spherically averaged or non-overlapping potential. Our results indicate that the non-negligible contributions arising from the overlapping potential region can be adequately reproduced by a combination of simple approximations thereby facilitating calculations of scattering from a more physical deuteron model.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

Variational principle in canonical variables,Weber transformation,and complete set of the local integrals of motion for dissipation-free magnetohydrodynamics

The intriguing problem of the “missing” MHD integrals of motion is solved in this paper; i.e., analogues of the Ertel, helicity, and vorticity invariants are obtained. The two latter have been discussed earlier in the literature only for specific cases, and the Ertel invariant is presented for the first time. The set of ideal MHD invariants obtained appears to be complete: to each hydrodynamic invariant corresponds its MHD generalization. These additional invariants are found by means of the fluid velocity decomposition based on its representation in terms of generalized potentials. This representation follows from the discussed variational principle in Hamiltonian (canonical) variables, and it naturally decomposes the velocity field into the sum of “hydrodynamic” and “ magnetic” parts. The “missing” local invariants are expressed in terms of the “ hydrodynamic” part of the velocity and therefore depend on the (nonunique) velocity decomposition; i.e., they are gauge-dependent. Nevertheless, the corresponding conserved integral quantities can be made decomposition-independent by the appropriate choice of the initial conditions for the generalized potentials. It is also shown that the Weber transformation of MHD equations (partial integration of the MHD equations) leads to the velocity representation coinciding with that following from the variational principle with constraints. The necessity of exploiting the complete form of the velocity representation in order to deal with general-type MHD flows (nonbarotropic, rotational, and with all possible types of breaks as well) in terms of single-valued potentials is also under discussion. The new basic invariants found allow one to widen the set of the local invariants on the basis of the well-known recursion procedure.     

π-Nucleus scattering in the Lee model

The scattering operator of a “pion” on two “nucleons” is evaluated in the Lee model and is shown to be identical to the results of Watson's multiple scattering theory.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Intensities of resonant brillouin scatterings from multicomponent exciton-polaritons

To reduce the arbitrariness in the current analysis of resonant Brillouin scattering (RBS) from multicomponent polaritons, the intensities of scattering peaks are theoretically studied. The interaction among the multicomponent excitons may contain linear and quadratic terms in translational wave vector, electron-hole exchange interaction, and any other terms that retain translational symmetry. As the scattering mechanisms due to TA and LA phonons, we consider various deformation and piezoelectric potentials. In certain cases, this theory leads to a “selection rule”, which can solve the controversy between the two different dispersion curves for CuBr obtained from RBS and two photon resonant Raman scattering, in favor of the latter. The theory also provides a basis to discuss the problem of additional boundary conditions for multicomponent polaritons in terms of the relative intensities of scattering peaks.     

Analysis of multiple scattering for (e, 2e) experiments on thin films

The coincidence rate for (e, 2e) scattering from thin films has significant contributions from multiple collisions in contrast to (e, 2e) experiments on gas targets where the multiple scattering rate is negligible. The most likely multiple scattering events involve one or more small angle collisions in addition to the wide angle (e, 2e) scattering. The total coincidence rate can be written as the convolution of a “smearing function” with the (e, 2e) cross section. The smearing function is an infinite series of multiple order, small-angle scattering events and can be determined from the measured, small-angle cross section of the particular material. The (e, 2e) cross section can be deconvoluted from the smearing function by standard techniques. A general expression for the smearing function is derived in this paper and is evaluated for the specific case of amorphous carbon. As an example in applying this analysis, (e, 2e) data on amorphous carbon are deconvoluted from the smearing function by two different methods.     

Peculiar features of the deuteron scattering potential

Measurements at 52 MeV of elastic scattering of polarized deuterons including the nuclear rainbow region are analyzed “model independently” to yield the underlying scattering potential. The extracted potentials are surprisingly well determined in the nuclear interior. The radial shape of the real parts is found to coincide closely with that observed in nucleon scattering — in contrast to the folding picture, which, however, accounts well for the volume integral of the absorption.     

Folding model potentials from realistic interactions for heavy-ion scattering

The double-folding model, with “realistic” nucleon-nucleon interactions based upon a G-matrix constructed from the Reid potential, is used to calculate the real part of the optical potential for heavy-ion scattering. The resulting potentials are shown to reproduce the observed elastic scattering for a large number of systems with bombarding energies from 5 to 20 MeV per nucleon. Some representative inelastic transitions are also reproduced. Exceptions are the elastic scattering of ⁶Li and ⁹Be for which the folded potentials must be reduced in strength by a factor of about two.The same effective interactions are shown to give a good account of two particular cases of alpha scattering as well as some cases of nucleon-nucleus scattering. Some typical examples of inelastic heavy-ion scattering are also predicted successfully.Some general properties of the folding model are reviewed and its theoretical basis is discussed. An explicit density-dependence is examined for one particular realistic interaction and found not to change the results. Single nucleon exchange is included in an approximate way and its importance is studied.In addition to being a study of the folding model, this work also provides a systematic and comprehensive optical model analysis of heavy-ion elastic scattering in this energy range.     

Effective potential approach to the quantum scattering of solitons

Systems of solitons are approximately described in terms of a finite number of “effective degrees of freedom” interacting via “effective potentials”. These are reconstructed, principally from knowledge of solutions to the classical field equations, by a procedure involving the sometric mapping of a sector of the field theoretical Hilbert space onto the Hilbert space of non-relativistic point particles. The quantum dynamics of solitons is then approximately formulated and solved in terms of ordinary Schrödinger-type equations. As an interesting exercise, our method is applied to an analysis of soliton-antisolotion binding and scattering in the sine-Gordon model. With the exclusion of exceptional values of the coupling constant, corresponding to solutions of an eigenvalue equation, backward scattering is found to occur near threshold and to decay exponentially with the centre-of-mass energy. One of the exceptional, reflectionless sine-Gordon model is, not surprisingly, found to correspond to vanishing coupling in the massive Thirring model.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

Massive lepton pair production as a test of models for particle production on nuclei

The nuclear-size dependence of massive lepton pair production on nuclei is found to provide a selective test of models describing hadron-nucleus interactions. In particular, a clear discrimination is possible between two types of models: the sequential multiple scattering models with energy degradation, and the “parallel” multiple scattering models with a long time scale involved. Both types of models are known to describe equally well the distributions of hadrons produced on nuclei. It is shown, however, that the observedA ¹-dependence of theD-Y process rules out the sequential scattering models as well as some oversimplified versions of the parallel multiple scattering models.     

Resonant surface enhanced Raman scattering by ultra thin Langmuir-Blodgett polydiacetylene polymer films

Using resonant Raman scattering and surface enhanced Raman scattering techniques, changes in the structural and electronic properties of Langmuir-Blodgett (L-B) polydiacetylene films were observed as film thicknesses were increased from one monolayer (or one bilayer) to several bilayers. The L-B films, starting with a single monolayer (or one bilayer) in a disordered “red” phase, were found to change into a mixed phase (ordered “blue” and disordered “red”) as one or more additional bilayers were deposited. This is the first observation of a “disorder to order” transformation in a L-B film. The observed effect is attributed to the ordering brought about by interactions between the initial and subsequent L-B PDA bilayers.     

A New Way of Looking at Nuclear Resonant Scattering

A new model for nuclear-resonant scattering of gamma radiation from resonant matter has been developed and is summarized here. This “coherent-path” model has lead to closed-form, finite-sum solutions for radiation scattered in the forward direction. The solution provides a unified microscopic picture of nuclear-resonant scattering processes. The resonant absorber or scatterer is modeled as a one-dimensional chain of “effective” nuclei or “effective” planes. The solution is interpreted as showing that the resonant radiation undergoes sequential scattering from one absorber “nucleus” or “plane” to another before reaching the detector. For recoil-free processes the various “paths” to the detector contribute coherently. The solution for this case gives calculated results that are indistinguishable from those using the classical optical model approach, although the forms of the solutions are completely different. The coherent-path model shows that the “speed-up” and “dynamical beating” effects are primarily a consequence of the fact that the single “effective” nuclear scattering processes are 180° out of phase with the incident radiation while the double nuclear scattering processes are in phase with the incident radiation. All multiple scattering paths are, and must be, included. The model can also treat the incoherent processes, i.e., processes involving gamma emission with recoil or conversion-electron emission. The source of the resonant gamma radiation can be from a radioactive source or from synchrotron radiation: both cases are treated. The model is used to explain and understand the results when each of the following experimental procedures is applied: time-differential Mössbauer spectroscopy, time-differential synchrotron radiation spectroscopy, enhanced-resolution resonant-detector Mössbauer spectroscopy, and the “gamma echo”.     

Scattering of low energy pions by 12C, 40Ca, 58,60,64Ni and the anomaly in pionic atoms

Several cases of anomalously small level shifts and widths are known in pionic atoms. These lead to pion-nucleus potentials which are different from those describing all other “normal” pionic atoms. Data on the elastic scattering of 19.5 MeV π^± by ¹²C and ⁴⁰Ca and 30 MeV π^± by ^58,60,64Ni is in very good agreement with predictions made with normal potentials and clearly rule-out potentials obtained from the “anomalous” cases.     

To the theory of I–V characteristics of the superlattices

The influence of inelastic scattering on the I–V characteristics of “dirty” and “pure” superlattices (SL) in the quasielastic limit is studied. It is shown that the form of the I–V characteristics of “dirty” SL is determined solely by the frequency of elastic scattering in a wide range of parameters and that the electron-phonon interaction in “pure” SL leads to the formation of two regions with negative differential conductivity (NDC) on the I–V characteristics.     

Real‐Time and Broadband Terahertz Wave Scattering Manipulation via Polarization‐Insensitive Conformal Graphene‐Based Coding Metasurfaces

Here, for the first time, the real‐time and broadband manipulation of terahertz (THz) waves are acquired by introducing a multifunctional graphene‐based coding metasurface (GBCM). The designed structure consists of subwavelength patterned graphene units whose operational statuses can be dynamically switched between two digital states of “0” and “1”. By engineering the spatial distribution of chemical potentials across the GBCM, various scattering patterns having single, two, four, and numerous reflection beams are elaborately achieved just within one planar structure. To compute the far‐field pattern of GBCM, an inverse discrete Fourier transform (IDFT) is established, providing a fast and efficient design method. The proposed GBCM provides a low reflection bellow ?10 dB over a broad frequency band ranging from 1 THz to 1.9 THz. In addition, the metasurface retains its low reflection behavior in a wide range of incident wave angles for both TE and TM polarizations. According to conformal invariance of graphene sheets, the stealth property of GBCM is well preserved while wrapping around a curved object. The proposed technique of real‐time scattering manipulation leads to multifunctional THz devices, opening new routes contributing to numerous applications such as imaging and stealth technology.     

一种基于多重散射的光学Hash函数

本文提出了一种基于光与多重散射介质相互作用的光学Hash函数构造方法.该方法创新性地利用多重散射介质对相干调制光的天然随机散射作用,实现了对调制光的"混淆"和"扩散",从而满足了Hash函数的核心功能要求:高安全强度的单向编码/加密.所设计的光电混合系统能有效地模拟Hash函数中的"压缩函数",结合具有特征提取功能的S...