41 results on '"Leonard Rosenberg"'
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2. Low-energy scattering by nonspherically symmetric targets
- Author
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Leonard Rosenberg
- Subjects
Elastic scattering ,Physics ,Low energy ,Scattering ,Quantum electrodynamics ,Scattering length ,Scattering theory ,Atomic and Molecular Physics, and Optics - Published
- 1999
- Full Text
- View/download PDF
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3. Absolute determination of zero-energy eigenphase shifts: Applications ton−p,n−d,andp−dscattering
- Author
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Leonard Rosenberg
- Subjects
Physics ,Nuclear and High Energy Physics ,Scattering ,Nuclear Theory ,Zero-point energy ,Scattering length ,Few-body systems ,symbols.namesake ,Pauli exclusion principle ,Quantum mechanics ,Bound state ,symbols ,Tensor ,Scattering theory ,Nuclear Experiment - Abstract
A generalization of Levinson's theorem, relating the phase shift at zero energy to the number of bound states of the system, previously formulated to apply to the single-channel multiparticle scattering of a particle by a neutral system [L. Rosenberg and L. Spruch, Phys. Rev. A 54, 4978 (1996)] is further generalized to allow for multichannel scattering. An application to neutron-proton scattering with tensor forces leads to an extension of the existing version of Levinson's theorem for this system by providing information on each of the eigenphases at zero energy rather than just their sum. The effect of the Pauli principle on the absolute determination of the phase shift is illustrated with applications of the method to the scattering of neutrons and protons by deuterons. more...
- Published
- 1998
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- View/download PDF
4. Multichannel effective-range theory with long-range interactions
- Author
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Leonard Rosenberg
- Subjects
Physics ,Range (particle radiation) ,Quantum electrodynamics ,Crossing ,Scattering length ,Scattering theory ,Inelastic scattering ,Atomic and Molecular Physics, and Optics - Published
- 1998
- Full Text
- View/download PDF
5. On low-energy scattering
- Author
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Leonard Rosenberg and Larry Spruch
- Subjects
Development (topology) ,Classical mechanics ,Low energy ,Scattering ,Computer science ,Thumbnail ,Scattering theory ,Condensed Matter Physics ,Mathematical proof ,Mathematical Physics ,Atomic and Molecular Physics, and Optics ,Sketch - Abstract
Variational bounds have played an important role in the development of low-energy scattering theory. A thumbnail sketch of the development and use of variational bounds on scattering lengths, with emphasis on insights rather than on rigorous proofs and details, is presented here. more...
- Published
- 2006
- Full Text
- View/download PDF
6. Bound-state methods for low-energy electron-ion scattering
- Author
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Leonard Rosenberg
- Subjects
Physics ,Quantum defect ,symbols.namesake ,Scattering ,Quantum mechanics ,Bound state ,symbols ,Electron ,Scattering theory ,Hamiltonian (quantum mechanics) ,Wave function ,Electron scattering ,Atomic and Molecular Physics, and Optics - Abstract
An effective-potential formalism, previously developed for electron scattering by a neutral target, is extended to apply to electron-ion scattering, with the requirement of antisymmetrization now accounted for explicitly. A minimum principle for the effective potential is derived, valid for scattering below the ionization threshold and applicable when, as is usually the case, the target wave functions are imprecisely known. The basis for the minimum principle is the Rayleigh-Ritz property that is satisfied by the modified Hamiltonian in terms of which the effective potential is defined. An analysis of single-channel, zero-energy scattering for a particular partial wave is presented; it is based on the effective-potential formalism and leads to an absolute definition of the zero-energy phase shift \ensuremath{\delta}(0) of the form \ensuremath{\delta}(0)=\ensuremath{\mu}(\ensuremath{\infty})\ensuremath{\pi}, where \ensuremath{\mu}(n) is the quantum defect of the nth energy level. This result may be thought of as an extension of Levinson's theorem for scattering by short-range potentials. \textcopyright{} 1996 The American Physical Society. more...
- Published
- 1996
- Full Text
- View/download PDF
7. Effective-potential method for relativistic electron-ion scattering
- Author
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Leonard Rosenberg
- Subjects
Physics ,Elastic scattering ,Scattering ,Scattering length ,Inelastic scattering ,Mott scattering ,Atomic and Molecular Physics, and Optics ,Scattering amplitude ,symbols.namesake ,Quantum electrodynamics ,Quantum mechanics ,Rydberg formula ,symbols ,Scattering theory - Abstract
The problem of electron scattering by a heavy hydrogenic ion is formulated relativistically by using a simplified version of hole theory in which the effects of virtual-pair creation and exchange of transverse photons are ignored. An effective-potential formalism is developed and a minimum principle for the effective potential is derived, which is valid in a range of energies below the ionization threshold, through a generalization of the projection-operator procedure developed some time ago in the context of the nonrelativistic scattering problem. A version of the minimum principle is shown to hold, even in cases in which an infinite Rydberg series of autoionizing resonances lies below the scattering energy. Concepts derived from quantum-defect theory are used, in conjuction with the effective-potential formalism, to describe the effect of these resonances on the scattering. Positive-energy projection operators appear naturally in the theory. Their presence ensures that ``variational-collapse`` difficulties are avoided, as required for the validity of the minimum principle. Some care is given to the analysis of different features of the scattering theory associated with the appearance of these projection operators. more...
- Published
- 1995
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8. Infrared radiation by a Dirac electron: First-order correction to the cross-section sum rule
- Author
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Leonard Rosenberg
- Subjects
Physics ,Cross section (physics) ,Dirac electron ,Infrared ,Quantum mechanics ,Quantum electrodynamics ,Scattering theory ,Sum rule in quantum mechanics ,First order ,Atomic and Molecular Physics, and Optics - Published
- 1994
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9. Configuration-space methods for Coulomb scattering in a laser field
- Author
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Fei Zhou and Leonard Rosenberg
- Subjects
Collision theory ,Physics ,Classical mechanics ,Field (physics) ,Projectile ,Plane wave ,Configuration space ,Scattering theory ,Wave function ,Atomic and Molecular Physics, and Optics ,Charged particle - Abstract
The Volkov wave function describing the motion of a charged particle in a laser field serves as a modified plane wave in the formulation of external-field collision theory and is widely used in applications. Exact solutions are unavailable for those cases in which the target, as well as the projectile, carries a net charge. It is shown that this difficulty may be overcome through the adoption of a variational formulation of the theory in configuration space more...
- Published
- 1992
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10. Extended theory of Kapitza-Dirac scattering
- Author
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Leonard Rosenberg
- Subjects
Physics ,Photon ,Scattering ,Quantum mechanics ,Quantum electrodynamics ,Scattering theory ,Electron ,Pauli equation ,Mott scattering ,Spin (physics) ,Atomic and Molecular Physics, and Optics ,S-matrix - Abstract
The standard theoretical treatment of the Kapitza-Dirac effect\char22{}that is, the scattering of an electron passing through a standing-wave laser field\char22{}is extended here through the use of the Pauli equation to account for the interaction of the electron spin with the magnetic field of the standing wave. Prescriptions for determining unitarity-preserving approximations for the transition probabilities for scattering both with and without rotation of the electron spin direction are provided. This formalism is used to develop a perturbation theory for the spin-flip probability which, in the strong-field limit of interest here, reduces to a fairly simple relation between $S$-matrix elements for scattering with and without change in spin orientation, each expressed in terms of a Bessel function. A similar perturbative procedure is applied to estimate corrections to the standard theory for scattering in the absence of spin-flip processes, in which interactions that change the net number of photons in the field are ignored. more...
- Published
- 2004
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11. Reaction theory for three charged clusters
- Author
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Leonard Rosenberg
- Subjects
Physics ,Nuclear and High Energy Physics ,Quantum electrodynamics ,Scattering theory ,Few-body systems ,Mott scattering - Published
- 2002
- Full Text
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12. Electron scattering by nonspherically symmetric atoms: Zero-energy limit
- Author
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Leonard Rosenberg
- Subjects
Physics ,Unitarity ,Quantum mechanics ,Quantum electrodynamics ,Bound state ,Stochastic matrix ,Zero-point energy ,Scattering theory ,Perturbation theory ,Multipole expansion ,Threshold energy ,Atomic and Molecular Physics, and Optics - Abstract
A modified perturbation theory, previously introduced for the construction of asymptotic states accounting for a general class of long-range angle-dependent multipole potentials is developed in further detail. The threshold behavior of these states is presented in explicit form and these results are used, with the aid of a modified effective-range formulation, to determine the threshold energy dependence of the multichannel transition matrix. Unitarity properties are established formally and verified in the low-energy limit. A variational procedure for determining the parameters appearing in the modified effective-range expansion is described. The same procedure accounts for the presence of zero-energy bound states leading to resonant behavior that alters the threshold energy dependence. more...
- Published
- 2001
- Full Text
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13. Distorted-wave reaction theory with long-range multipole potentials
- Author
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Leonard Rosenberg
- Subjects
Elastic scattering ,Scattering amplitude ,Physics ,Quantum electrodynamics ,Crossing ,Scattering length ,Scattering theory ,Multipole expansion ,Electron scattering ,Atomic and Molecular Physics, and Optics ,S-matrix - Published
- 2001
- Full Text
- View/download PDF
14. Absolute determination of zero-energy phase shifts for multiparticle single-channel scattering: Generalized Levinson theorem
- Author
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Leonard Rosenberg and Larry Spruch
- Subjects
Physics ,Scattering amplitude ,Scattering ,Computer Science::Information Retrieval ,Quantum mechanics ,Bound state ,Zero (complex analysis) ,Scattering length ,Scattering theory ,Wave function ,Ground state ,Atomic and Molecular Physics, and Optics ,Mathematical physics - Abstract
Levinson{close_quote}s theorem relates the zero-energy phase shift {delta} for potential scattering in a given partial wave {ital l}, by a spherically symmetric potential that falls off sufficiently rapidly, to the number of bound states of that {ital l} supported by the potential. An extension of this theorem is presented that applies to single-channel scattering by a compound system initially in its ground state. As suggested by Swan [Proc. R. Soc. London Ser. A {bold 228}, 10 (1955)], the extended theorem differs from that derived for potential scattering; even in the absence of composite bound states {delta} may differ from zero as a consequence of the Pauli principle. The derivation given here is based on the introduction of a continuous auxiliary {open_quote}{open_quote}length phase{close_quote}{close_quote} {eta}, defined modulo {pi} for {ital l}=0 by expressing the scattering length as {ital A}={ital a}cot{eta}, where {ital a} is a characteristic length of the target. Application of the minimum principle for the scattering length determines the branch of the cotangent curve on which {eta} lies and, by relating {eta} to {delta}, an absolute determination of {delta} is made. The theorem is applicable, in principle, to single-channel scattering in any partial wave for {ital e}{sup {plus_minus}}-atom and nucleon-nucleusmore » systems. In addition to a knowledge of the number of composite bound states, information (which can be rather incomplete) concerning the structure of the target ground-state wave function is required for an explicit, absolute, determination of the phase shift {delta}. As for Levinson{close_quote}s original theorem for potential scattering, {ital no} {ital additional} {ital information} {ital concerning} {ital the} {ital scattering} {ital wave} {ital function} {ital or} {ital scattering} {ital dynamics} {ital is} {ital required}. {copyright} {ital 1996 The American Physical Society.}« less more...
- Published
- 1996
15. Generalized Levinson theorem: Applications to electron-atom scattering
- Author
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Leonard Rosenberg and Larry Spruch
- Subjects
Physics ,Angular momentum ,Scattering ,Computer Science::Information Retrieval ,Scattering length ,Type (model theory) ,Atomic and Molecular Physics, and Optics ,symbols.namesake ,Pauli exclusion principle ,Atom ,Bound state ,symbols ,Scattering theory ,Atomic physics - Abstract
A recent formulation provides an absolute definition of the zero-energy phase shift {delta} for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave {ital l}. This formulation, along with the minimum principle for the scattering length, leads to a determination of {delta} that represents a generalization of Levinson`s theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates {delta}/{pi} to the number of bound states of that {ital l}. The generalized Levinson theorem relates {delta}/{pi} for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum {ital +} a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1{ital s}){sup 2}(2{ital s}){sup 2}(2{ital p}){sup 6}3{ital s} configuration and with one {ital L}=0 singlet composite bound state, {delta} would be {pi}+2{pi} for {ital s}-wave singlet scattering, 0+3{pi} for {ital s}-wave triplet scattering, and 0+{pi} for both triplet and singlet {ital p}-wave scattering; the Pauli contribution has been listed first. The methodmore » is applicable to a number of {ital e}{sup {+-}}-atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for {ital e}{sup {minus}}-H and {ital e}{sup {minus}}-He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five {ital p} electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations. {copyright} {ital 1996 The American Physical Society.}« less more...
- Published
- 1996
16. Levinson-Seaton theorem for potentials with an attractive Coulomb tail
- Author
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Leonard Rosenberg
- Subjects
Physics ,Statistics::Theory ,Statistics::Applications ,Atomic and Molecular Physics, and Optics ,Quantum defect ,Integer ,Quantum mechanics ,Bound state ,Coulomb ,Continuum (set theory) ,Scattering theory ,Wave function ,Energy (signal processing) ,Mathematical physics - Abstract
The zero-energy scattering in a particular partial wave by a potential V=${\mathit{V}}_{\mathit{s}}$+${\mathit{V}}_{\mathit{c}}$ that is a superposition of short range and attractive Coulomb components is characterized by the additional phase shift ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$(0), due to ${\mathit{V}}_{\mathit{s}}$. It has been known for many years that ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$(0)(mod\ensuremath{\pi})=\ensuremath{\mu}(\ensuremath{\infty})\ensuremath{\pi}, where \ensuremath{\mu}(n) is the quantum defect of the nth energy level. In analogy with Levinson's theorem for short-range potentials, one might expect that a more precise statement, based on an absolute definition of the phase shift, would be ${\mathrm{\ensuremath{\delta}}}_{\mathit{s}}$(0)=\ensuremath{\mu}(\ensuremath{\infty})\ensuremath{\pi}, with the value of the largest integer contained in \ensuremath{\mu}(\ensuremath{\infty}) representing the number of additional bound states due to ${\mathit{V}}_{\mathit{s}}$. A simple derivation of this relation is presented here, based on variational principles for the binding energies and phase shifts, and on the property (fundamental to quantum-defect theory) that appropriately normalized bound-state wave functions for n\ensuremath{\rightarrow}\ensuremath{\infty} merge smoothly into the energy-normalized regular continuum solutions at the continuum threshold. more...
- Published
- 1995
17. Resonant contributions to bound-state Compton scattering
- Author
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Leonard Rosenberg
- Subjects
Physics ,Quasielastic scattering ,X-ray Raman scattering ,Scattering ,Compton scattering ,Scattering length ,Scattering theory ,Atomic physics ,Inelastic scattering ,Mott scattering ,Atomic and Molecular Physics, and Optics - Published
- 1995
18. Bremsstrahlung near reaction thresholds
- Author
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Leonard Rosenberg
- Subjects
Physics ,Scattering amplitude ,Singularity ,Mathematical model ,Quantum electrodynamics ,Bremsstrahlung ,Scattering length ,Scattering theory ,Electromagnetic radiation ,Electron scattering ,Atomic and Molecular Physics, and Optics - Published
- 1994
19. Minimum principle for Dirac scattering lengths
- Author
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Leonard Rosenberg
- Subjects
Physics ,Scattering length ,Atomic and Molecular Physics, and Optics ,symbols.namesake ,Dirac equation ,Quantum mechanics ,symbols ,Two-body Dirac equations ,Relativistic wave equations ,Scattering theory ,Wave function ,Dirac sea ,Eigenvalues and eigenvectors ,Mathematical physics - Abstract
A minimum principle for the nonrelativistic scattering length was derived some years ago under the assumption that only a finite number of discrete states exist below the scattering threshold. The variational bound is applicable even when the bound-state wave functions are imprecisely known\char21{}they need only be accurate enough to give binding in a Rayleigh-Ritz calculation. The method is generalized here to apply to potential scattering described by the Dirac equation. An apparent difficulty associated with the existence of a continuum of negative-energy states, that is, the problem of ``variational collapse,'' is removed through the inclusion of second-order terms in the variational expression involving matrix elements of the square of the Dirac Hamiltonian. In the course of the derivation a relativistic version of the Hylleraas-Undheim theorem is developed. Applications of this theorem are described that provide a sufficient condition for the existence of a given number of bound states, lower bounds on the energy eigenvalues, and a systematic procedure for improving the accuracy of trial bound-state wave functions. A very simple model calculation was performed to illustrate the minimum property and the stability of the numerical procedure. more...
- Published
- 1994
20. Bremsstrahlung in laser-assisted scattering
- Author
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Leonard Rosenberg and Fei Zhou
- Subjects
Physics ,Scattering amplitude ,Amplitude ,Field (physics) ,Scattering ,Bremsstrahlung ,Scattering theory ,Atomic physics ,Electron scattering ,Resonance (particle physics) ,Atomic and Molecular Physics, and Optics - Abstract
The process of spontaneous radiation accompanying the scattering of a charged particle by a center of force is studied under conditions in which the scattering takes place in an intense, low-frequency laser field. Approximations are developed which provide expressions for both the amplitude and the total rate for spontaneous bremsstrahlung in the presence of the external field, given in terms of the physical (onshell) amplitude for bremsstrahlung in the absence of the field. Of particular interest is the effect of the external field on the radiation probability when there is a narrow resonance in the field-free scattering more...
- Published
- 1993
21. Generalized Volkov wave functions: Application to laser-assisted scattering
- Author
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Leonard Rosenberg and Fei Zhou
- Subjects
Physics ,Field (physics) ,Scattering ,Wave packet ,Type (model theory) ,Wave equation ,Atomic and Molecular Physics, and Optics ,Schrödinger equation ,symbols.namesake ,Quantum mechanics ,Quantum electrodynamics ,symbols ,Physics::Atomic Physics ,Scattering theory ,Wave function - Abstract
Wave equations---nonrelativistic and relativistic---describing the motion of a charged particle in a multimode laser field are considered and solutions are derived that may serve as asymptotic wave functions in the evaluation of amplitudes for laser-assisted scattering and multiphoton ionization. Unlike the well-known Volkov solutions that can be used only for fields of the plane-wave type, the wave functions obtained here are appropriate for the wider class of fields for which the different modes need not all have the same direction of propagation. This generalization allows in principle for the construction of wave packets, fields that are localized in space as well as time and hence capable of providing a more realistic description. The treatment of the nonrelativistic case is essentially exact, in the sense that errors introduced, of order (v/c${)}^{2}$, are comparable to those inherent in the nonrelativistic approximation. As an illustration, a low-frequency approximation for potential scattering in a multimode field is derived based on the use of the generalized Volkov solutions as asymptotic wave functions. Generalized Volkov solutions of the Klein-Gordon and Dirac equations are derived as well, though here in an approximation requiring a limitation on the strength of the external field. more...
- Published
- 1993
22. Relativistic scattering in a multimode external field
- Author
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Leonard Rosenberg and Fei Zhou
- Subjects
Physics ,Field (physics) ,Scattering ,Atomic and Molecular Physics, and Optics ,Scattering amplitude ,symbols.namesake ,Classical mechanics ,Variational principle ,Quantum electrodynamics ,Dirac equation ,symbols ,Scattering theory ,Wave function ,Klein–Gordon equation - Abstract
A variational principle is applied to the study of the relativistic scattering of a charged particle from a center of force in the presence of a strong, slowly varying external electromagnetic field. The analysis is first given in terms of a spin-zero wave equation and then modified to describe the scattering of a Dirac particle. In contrast to previous treatments of problems of this nature, the field is not assumed to be of the plane-wave type. More realistically, it is modeled as a superposition of modes, each with a different frequency and direction of propagation. Exact solutions of the wave equation describing the asymptotic motion of the particle in the presence of the field are not available for fields of this type. Nevertheless, the variational principle allows for a formulation of the scattering problem and, by a suitable choice of trial functions, generates a gauge-invariant low-frequency approximation for the transition amplitude. The error introduced by the inaccuracy in the asymptotic wave function is compensated for by the inclusion of a variational correction term which properly accounts for the effect of stimulated Compton scattering in initial and final states. It is verified that previously derived low-frequency approximations for one- and two-photon spontaneous bremsstrahlung are reproduced by taking the weak-field limit of the approximate stimulated-bremsstrahlung amplitude. more...
- Published
- 1992
23. Low-frequency expansions for laser-assisted collisions
- Author
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Leonard Rosenberg and Fei Zhou
- Subjects
Elastic scattering ,Physics ,Amplitude ,Scattering ,Linear polarization ,Quantum electrodynamics ,Quantum mechanics ,Sum rule in quantum mechanics ,Scattering theory ,Inelastic scattering ,Electromagnetic radiation ,Atomic and Molecular Physics, and Optics - Abstract
A variational approach to the problem of scattering in a low-frequency laser field is adopted, with trial functions chosen to be of the type originally introduced by Kroll and Watson (Phys. Rev. A 8, 804 (1973)), who used them nonvariationally. The variational calculation leads to a low-frequency approximation that includes higher-order correction terms of a relatively simple form. This provides the basis for an analysis of the accuracy of the approximation as the strength of the external field varies over a wide range of values. The cross-section sum rule is shown, for the case of a linearly polarized monochromatic field of moderate intensity, to be more accurate than had previously been realized by virtue of the cancellation of higher-order correction terms in the transition amplitude. The approach is shown to be applicable to elastic and inelastic electron-atom scattering in a multimode laser field with arbitrary polarization properties; it represents a natural generalization of the standard Kohn-type variational procedure frequently employed for field-free scattering problems, reducing to it in the absence of the field. The dressing of the target by the field, an effect which is known to have a significant influence on the scattering cross section in certain circumstances, ismore » not accounted for in the construction of the trial function, but is properly included as part of the variational correction.« less more...
- Published
- 1991
24. Second-order correction to the Bloch-Nordsieck sum rule
- Author
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Leonard Rosenberg
- Subjects
Scattering amplitude ,Physics ,Unitarity ,Quantum mechanics ,Order (ring theory) ,Optical theorem ,Context (language use) ,Sum rule in quantum mechanics ,Scattering theory ,Atomic and Molecular Physics, and Optics ,Energy (signal processing) - Abstract
As shown many years ago by Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)] and Nordsieck [Phys. Rev. 52, 59 (1937)], the cross section for scattering with the emission of an arbitrary number of soft photons is finite and can be expressed in terms of the cross section for scattering in the absence of the radiation field. The model used by Bloch and Nordsieck included only soft-photon modes of the field, with maximum frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$. They argued that corrections to their sum rule would be expressed in terms of two small parameters, ${\mathit{r}}_{0}$${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$/c and \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$/\ensuremath{\nu}, where ${\mathit{r}}_{0}$ is the classical electron radius and \ensuremath{\nu} is the scattering energy. Corrections of first order were obtained previously by the author [Phys. Rev. A 21, 1939 (1980)], in the context of a nonrelativistic formulation of the scattering problem. Here all corrections of second order are derived. As in the earlier versions, the corrected cross section for scattering in the radiation field, summed over final states of the field, is determined from a knowledge of the field-free cross section. Use of the unitarity property (the optical theorem) is found to be a simplifying technical device for this calculation, as indicated by the cancellation of divergences in the scattering amplitude in the forward direction. It is shown that in the dipole approximation the term in the electron-field interaction that is quadratic in the vector potential, while contributing to an energy-level shift, has no effect, to second order, on the final form of the sum rule. more...
- Published
- 1991
25. Second-order correction to the low-frequency approximation for scattering in a laser field
- Author
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Leonard Rosenberg
- Subjects
Physics ,Scattering amplitude ,Elastic scattering ,Cross section (physics) ,Amplitude ,Scattering ,Quantum mechanics ,Sum rule in quantum mechanics ,Scattering theory ,S-matrix - Abstract
It has been known for some time how to construct an approximation to the amplitude for non- relativistic potential scattering in a low-frequency laser field that is correct to first order in the frequency and that depends only on the on-shell field-free scattering amplitude. The next term in the expansion, of second order in the frequency, is determined here. In addition to the physical field-free scattering amplitude, a knowledge of the single-photon spontaneous bremsstrahlung amplitude (up to terms of first order in the frequency) is required. The improved low-frequency approximation obtained here is used to derive an improved sum rule. It is found that when the cross section (correct to second order) is summed over final photon states, the result depends only on the physical field-free cross section in a form which is identical to that obtained from a classical description of the motion of the particle in the field, with the collision taking place instantaneously and without influence from the field. A relativistic version of this sum rule was given earlier by Brown and Goble (Phys. Rev. 173, 1505 (1968)), who based their analysis on general field-theoretic considerations. more...
- Published
- 1989
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26. Extension of the Bloch-Nordsieck model
- Author
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Leonard Rosenberg
- Subjects
Scattering amplitude ,Elastic scattering ,Physics ,symbols.namesake ,Scattering ,Quantum mechanics ,Quantum electrodynamics ,symbols ,Scattering length ,Scattering theory ,Inelastic scattering ,Mott scattering ,Rayleigh scattering - Abstract
An analysis of infrared radiation in the potential scattering of a Dirac electron was presented by Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)], in their now classic work, to illustrate how divergence difficulties are removed by nonperturbative treatment of the radiation of soft photons. It is shown here how an improved low-frequency approximation can be obtained which provides a small correction to the Bloch-Nordsieck sum rule for the scattering cross section, while still requiring as input only physical (on-shell) values of the amplitude for scattering in the absence of the radiation field. The calculation is based on a variational determination of the radiative amplitude with trial functions chosen in accordance with the Bloch-Nordsieck approximation. An extension of the model scattering problem is introduced which allows for potentials with a Coulomb tail. The applicability of the approximation procedure to the analogous problem of relativistic scattering in a low-frequency external field is pointed out. more...
- Published
- 1985
- Full Text
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27. Gauge-invariant approximations for scattering in a strong external field
- Author
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Leonard Rosenberg
- Subjects
Electromagnetic field ,Physics ,Classical mechanics ,Amplitude ,Scattering ,Time evolution ,Scattering theory ,Gauge theory ,Invariant (physics) ,Wave function - Abstract
While the exact amplitude for scattering in the presence of an external electromagnetic field is invariant under a change of gauge, the invariance property will not necessarily be preserved in approximations, and this may lead to inaccuracies and ambiguities in the results of numerical calculations. A method for removing this undesirable feature through a reformulation of the scattering problem is proposed here. The equations which determine the time evolution of the system are rewritten in a form which involves not the (gauge-dependent) vector and scalar potentials associated with the external field but rather effective potentials which are gauge independent; this allows for the introduction of gauge-invariant approximations in a systematic way. To focus on the essential features the method is described in the context of the relatively simple problem of nonrelativistic potential scattering but greater generality is possible. As an illustration of the method the problem of scattering in a slowly varying external field is considered and an approximation of the ''low-frequency'' type is obtained. The result, whose gauge invariance is verified explicitly, represents an improvement over earlier versions, having been obtained through a more accurate treatment of the interaction of the projectile with the external field in intermediate statesmore » of the scattering process.« less more...
- Published
- 1986
- Full Text
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28. Two-photon bremsstrahlung in low-frequency approximation
- Author
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Leonard Rosenberg
- Subjects
Physics ,Two-photon excitation microscopy ,Quantum mechanics ,Quantum electrodynamics ,Bremsstrahlung ,Scattering theory ,Low frequency ,Electron scattering - Published
- 1987
- Full Text
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29. Final-state interactions in multiphoton-ionization theory
- Author
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Leonard Rosenberg
- Subjects
Physics ,Work (thermodynamics) ,Classical mechanics ,Amplitude ,Unitarity ,Field (physics) ,Quantum electrodynamics ,Ionization ,Scattering theory ,Integral equation ,S-matrix - Abstract
In the final state of a multiphoton-ionization process the ejected electron may interact simultaneously with the external laser field and with the residual atomic system. A procedure for calculating transition probabilities for such processes is described which incorporates the effects of resonances in the final continuum states of the atom. By using standard methods of scattering theory, it is shown how these resonant states may be separated out leaving a "background" amplitude which is a smooth function of the energy, and which therefore lends itself more readily to numerical evaluation. Such an evaluation may be based on the generalized Lippmann-Schwinger integral equation presented here. The constraint imposed by unitarity on the background amplitude is derived, and it is pointed out how approximations may be set up which satisfy unitarity automatically. A simplified model is described in order to illustrate this and other features of the theory and to make contact with some earlier work on this subject. Finally, a low-frequency approximation is developed in which final-state interaction effects are accounted for in a relatively simple analytical form. more...
- Published
- 1984
- Full Text
- View/download PDF
30. Three-cluster states in reaction theory
- Author
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Leonard Rosenberg
- Subjects
Physics ,Scattering amplitude ,Nuclear and High Energy Physics ,Faddeev equations ,Classical mechanics ,Scattering ,Optical theorem ,Scattering length ,Scattering theory ,Wave function ,Integral equation - Abstract
In recent work it was shown how a rigorous subsidiary minimum principle of the Rayleigh-Ritz type could be used as an aid in the construction of the closed-channel part of the scattering wave function, thereby making available a potentially powerful new tool in the variational approach to multiparticle scattering problems. The earlier discussion, which was restricted to scattering below the threshold for target breakup, is generalized here to the case where both two-body and three-body channels are open. The scattering problem is formally reduced to an equivalent three-body problem. Effective two-body and three-body potentials are defined explicitly (without the use of projection operators) and integral equations of the Faddeev type are derived. This analysis, which suggests a variety of cluster approximations, is used here as the basis for a decomposition of the wave function into an open-channel part, which contains the two-body and three-body outgoing scattered waves, and a decaying closed-channel part. The closed-channel part is shown to satisfy a minimum principle whose rigor can be maintained even when the target bound-state wave functions are imprecisely known. A calculational procedure which combines this minimum principle with the Kohn variational construction of the scattering amplitude is described.NUCLEAR REACTIONS Scattering theory. Effective three-body formulation. Derivation of extremum principle for the wave function. more...
- Published
- 1976
- Full Text
- View/download PDF
31. Long-range interactions in free-free transitions
- Author
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Leonard Rosenberg
- Subjects
Physics ,Photon ,Field (physics) ,Scattering ,Quantum mechanics ,Quantum electrodynamics ,Bremsstrahlung ,Coulomb ,Configuration space ,Scattering theory ,Mott scattering - Abstract
The soft-photon approximation for bremsstrahlung derived some time ago by Low and extended by Feshbach and Yennie to allow for resonances is further generalized, in the framework of nonrelativistic scattering theory, to apply to the case where the scattering potential has a long-range Coulomb tail. The derivation is based on an asymptotic evaluation of the matrix element in configuration space in which electric-dipole, magnetic-dipole, and electric-quadrupole components of the particle-field interaction are accounted for. The $M1$ and $E2$ contributions give rise to retardation corrections, of order $\frac{v}{c}$, to the leading $E1$ term. The Coulomb tail has the effect of introducing certain factors into the approximate bremsstrahlung amplitude which depend logarithmically on the photon frequency. The result obtained here has an immediate application to the problem of Coulomb scattering in a low-frequency laser field and provides a generalization of earlier work based on the electric-dipole approximation. more...
- Published
- 1983
- Full Text
- View/download PDF
32. Variational Methods in Charged-Particle Collision Theory
- Author
-
Leonard Rosenberg
- Subjects
Physics ,Collision theory ,symbols.namesake ,Classical mechanics ,Scattering ,Variational principle ,Wave packet ,symbols ,Scattering theory ,Charged particle ,Schrödinger equation ,S-matrix - Abstract
A variational principle of the Kohn type is formulated for the scattering of three charged particles, with particular attention given to the breakup process. In addition, an effective-potential theory, which also allows for variational formulation, is derived for the three-body system with long-ranged Coulomb interactions properly accounted for. These results generalize previous work done for systems with short-ranged interactions; the difference lies, essentially, in the use of Coulomb-modified plane waves to describe the asymptotic states. To establish the physical justification for this modified version of scattering theory a section is included containing a time-dependent description of the collision process in which the wave packets follow classical, Coulomb-modified, trajectories in the initial and final states. more...
- Published
- 1973
- Full Text
- View/download PDF
33. Generalized Faddeev Integral Equations for Multiparticle Scattering Amplitudes
- Author
-
Leonard Rosenberg
- Subjects
Physics ,Scattering amplitude ,Inverse scattering transform ,Scattering ,Integro-differential equation ,Differential equation ,Quantum electrodynamics ,General Physics and Astronomy ,Scattering theory ,Summation equation ,Integral equation - Published
- 1965
- Full Text
- View/download PDF
34. Minimum Principle for Multi-Channel Scattering
- Author
-
Larry Spruch and Leonard Rosenberg
- Subjects
Physics ,symbols.namesake ,Matrix (mathematics) ,Classical mechanics ,Pauli exclusion principle ,Variational method ,Scattering ,Bound state ,symbols ,General Physics and Astronomy ,Scattering theory ,Linear combination ,Upper and lower bounds - Abstract
The usual variational principles of scattering theory are simply stationary principles. In a recent series of papers, all restricted to single- channel scattering, conditions have been established under which variational principles can be found which are much more powerful in that the functional that represents the variational estimate is not simply stationary in the neighborhood of the cxact scattering solution but is rather an extremum. A lower bound has been obtained on the single real parameter, tann/sub c/, which charactertzes the scattering in the (uncoupled) channel c. The conditions previously established allowed for composite bound states, for the Pauli principle, for arbitrary angular momenta, and for long-range and in particular Coulomb potentials; at nonzero energies, the various potentials had to be truncated. The present paper deals with the extension to multi-channel scattering in which each of the open channels contains only two systems. The bounds are now on linear combinations of the elements of the reactance matrix or of the derivative matrix. The potentials must be truncated in a fashion very similar to that used in WignerEisenbud theory. (auth) more...
- Published
- 1962
- Full Text
- View/download PDF
35. Upper Bounds on Scattering Lengths for Compound Systems:n−DQuartet Scattering
- Author
-
Leonard Rosenberg and Larry Spruch
- Subjects
Physics ,Scattering amplitude ,Elastic scattering ,Scattering ,Quantum mechanics ,Bound state ,Center (category theory) ,General Physics and Astronomy ,Scattering length ,Scattering theory ,Upper and lower bounds - Abstract
In the zero-energy scattering of a particle by a compound system under the conditions that (1) only one exit channel is open (elastic scattering) and (2) no composite bound state exists for the particle and the scattering system in the state of given total angular momentum, the Kohn variational principle gives an upper bound on the scattering length. This is one of several results given previously for the case of scattering by a center of force which may be taken over directly, provided conditions (1) and (2) are satisfied. As a particular application of these results, several previous calculations of the $n\ensuremath{-}D$ quartet scattering length, ${A}_{Q}$, based on the Kohn principle (the method of Verde and the static approximation of Buckingham and Massey are included) are reanalyzed using the rigorous criterion that the best result is the one giving the lowest value. Further, some calculations of ${A}_{Q}$ based on the Rubinow formulation, which do not necessarily provide a bound, are converted to the Kohn form, thereby obtaining, in addition to a bound, an improved approximation to the scattering length. Some limitations and possible extensions of the method are discussed. more...
- Published
- 1960
- Full Text
- View/download PDF
36. N-Body Relativistic Scattering Theory
- Author
-
Leonard Rosenberg
- Subjects
Physics ,Scattering amplitude ,Quantum mechanics ,Quantum electrodynamics ,Crossing ,General Physics and Astronomy ,Quantum gravity ,Scattering length ,Scattering theory ,Liouville field theory ,Unified field theory ,S-matrix - Published
- 1966
- Full Text
- View/download PDF
37. Approximation Techniques in Three-Body Scattering Theory
- Author
-
Leonard Rosenberg
- Subjects
Physics ,Classical mechanics ,Codes for electromagnetic scattering by spheres ,Scattering ,Quantum mechanics ,High frequency approximation ,General Physics and Astronomy ,Scattering length ,Scattering theory ,Born approximation ,X-ray scattering techniques ,S-matrix - Published
- 1964
- Full Text
- View/download PDF
38. Kohn-Type Variational Principle for Three-Body Breakup Processes
- Author
-
M. Lieber, Leonard Rosenberg, and Larry Spruch
- Subjects
Many-body problem ,Scattering amplitude ,Physics ,Classical mechanics ,Variational method ,Variational principle ,Luke's variational principle ,Scattering theory ,Breakup ,Wave function - Abstract
A Kohn-type variational principle normally requires knowledge of the asymptotic form of the time-reversed final-state wave function. For the breakup collision of a bound pair of particles by a third particle, the time-reversed final state is a state in which three free particles are incident, and the asymptotic form of the associated wave function is only incompletely understood. We have nevertheless been able to obtain a Kohn-type variational principle for the breakup scattering amplitude (for short-range potentials). The final expression involves only well-defined integrals, though in the course of the derivation we are forced to separate finite integrals into separately divergent components. These divergences, which also occur elsewhere in scattering theory, are handled by a redefinition of the integrals which is the analog for integrals of Ces\`aro summation. more...
- Published
- 1972
- Full Text
- View/download PDF
39. Note on the Brown-Goble soft-photon approximation
- Author
-
Leonard Rosenberg
- Subjects
Elastic scattering ,Scattering amplitude ,Physics ,Soft photon ,Scattering ,Quantum electrodynamics ,Quantum mechanics ,Optical theorem ,Scattering length ,Scattering theory ,Classical limit - Abstract
Some time ago Brown and Goble analyzed the problem of charged-particle scattering in a low-frequency external radiation field in order to establish the correspondence with the classical limit. The underlying soft-photon approximation developed in that work is used here to examine the structure of the scattering amplitude in somewhat greater detail. An explicit expression for the scattering amplitude is given in terms of the on-shell amplitude for scattering in the absence of the field. This result is used to obtain a modified sum rule for the cross section which takes into account the presence of an isolated resonance. more...
- Published
- 1980
- Full Text
- View/download PDF
40. Variational Bounds on Scattering Amplitudes for Unphysical Energies
- Author
-
Leonard Rosenberg
- Subjects
Scattering amplitude ,Physics ,Quantum electrodynamics ,Quantum mechanics ,Scattering length ,Scattering theory - Published
- 1970
- Full Text
- View/download PDF
41. Modified perturbation theory for scattering in a laser field
- Author
-
Leonard Rosenberg
- Subjects
Physics ,Matrix (mathematics) ,Amplitude ,Field (physics) ,Scattering ,Quantum mechanics ,Strong interaction ,Coulomb ,Scattering theory ,Perturbation theory - Abstract
A variation-iteration procedure is described for determining the amplitude for scattering in the presence of a laser field. The essential limitation of the method lies in the requirement that the interaction of the charged projectile with the external field be sufficiently weak, relative to its interaction with the target, to justify use of perturbation theory to account for the effect of the field in intermediate states of the collision process. This still allows for fields which are strong enough to significantly affect the motion of the projectile in initial and final states (leading, for example, to multiphoton transitions) and this strong interaction is treated nonperturbatively. The first two terms in the modified perturbation expansion are analyzed in detail. They are expressed in terms of those matrix elements which describe one- and two-photon free-free transitions in the absence of an external field. The method is not restricted to a consideration of fields of low frequency but the first-order amplitude obtained here does reduce, in that limit, to the known form of low-frequency approximation and the second-order amplitude provides a correction. The theory is described in the context of nonrelativistic potential scattering. A discussion is included of some of the special features of the second-order amplitude associated with potentials having a long-range Coulomb tail. more...
- Published
- 1986
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