\ Herring Archive A313 - Scattering

Herring References

Prof. Robert B. Laughlin
Department of Physics, Stanford University
Stanford, CA 94305

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A313 - Scattering

Theory of Heisenberg's S-Matrix
W. Heisenberg, "Die 'beobachtbaren' Grössen in der Theorie der Elementarteilchen. I," Z. Phys. 120, 513 (1943).
W. Heisenberg, "Die 'beobachtbaren' Grössen in der Theorie der Elementarteilchen," Z. Phys. 120, 513, 673 (1943).
C Møller, "General Properties of the Characteristic Matrix in the Theory of Elementary Particles," D. Kgl. Danske Vidensk. Selsk. Mat.-Fys. Medd. 23, No. 1 (1945).
C Møller, D. Kgl. Danske Vidensk. Selsk. Mat.-Fys. Medd. 23, No. 19 (1946).
W. Heisenberg, "Der methematischen Rahmen der Quantertheorie der Elementarteilchen," Z. Naturforschung 1, 608 (1946).
W. Heitler and N. Hu, "Interpretation of Complex Roots of the S-Matrix," Nature 159, 776 (1947).
W. Pauli, Meson Theory of Nuclear Forces (Interscience, 1946).
M. L. Goldberger, "Causality Conditions and Dispersion Relations. I. Boson Fields," Phys. Rev. 99, 979 (1955).
B. S. DeWitt, "State-Vector Normalization in Formal Scattering Theory," Phys. Rev. 100, 905 (1956).
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955).
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 57, 3 (1955).
N. N. Bogoliubov and D. V. Shirkov, "Probleme der Quantenfeldtheorie der Felder," Fortschr. Phys. 3, 439 (1955).
N. N. Bogoliubov and D. V. Shirkov, "Probleme der Quantenfeldtheorie," Fortschr. Phys. 4, 438 (1956).
H. Ekstein, "Theory of Time-Dependent Scattering for Multichannel Processes," Phys. Rev. 101, 880 (1956).
N. G. van Kampen, Physica 23, 157 (1957).
N. Hu, "On the Application of Heisenberg's Theory of S-Matrix to the Problems of Resonance Scattering and Reactions in Nuclear Physics," Phys. Rev. 74, 131 (1948).
R. Josts, "Über die falschen Nullstellen der S-Matrix," Helv. Phys. Acta 20, 256 (1947).
W. Schützer and J. Tiomno, "On the Connection of the Scattering and Derivative Matrices with Causality," Phys. Rev. 83, 249 (1951).
E. P. Wigner, Revista Mexicana de Fisica 1, 9 (1952).
F. Coester, "The Symmetry of the S Matrix," Phys. Rev. 89, 619 (1953).
N. G. van Kampen, Physica 20, 115 (1954).
N. G. van Kampen, Physica 21, 579 (1955).
N. G. van Kampen, Physica 21, 127 (1955).
J. C. Polkinghorne, "An Identity for the S Matrix for a Finite Time Interval," Phys. Rev. 93, 228 (1954).
S. Nakai, "Bound States and S-Matrix in Quantum Field Theory," Prog. Theor. Phys. 11, 179 (1954).
Y. Fujii, "Validity of Phase-Shift Representations," Phys. Rev. 139, B472 (1965).
G. F. Chew, Physics 1, 77 (1964).
J. R. Taylor, "Place of Hilbert Space in S-Matrix Theory," Phys. Rev. 140, B187 (1965).

General Theory of Single Scattering
E. A. Hylleraas, "Calculation of a Perturbing Central Field of Force from the Elastic Scattering Phase Shift," Phys. Rev. 74, 48 (1948).
C. N. Yang, "On the Angular Distribution in Nuclear Reactions and Coincidence Measurements," Phys. Rev. 74, 764 (1948).
G. Wentzel, Helv. Phys. Acta 21, 49 (1948).
E. Feenberg, "Theory of Scattering Processes," Phys. Rev. 74, 664 (1948).
W. Heitler and H. W. Peng, "The Influence of Radiation Damping on the Scattering of Light and Mesons by Free Particles. II," Proc. Camb. Phil. Soc. 38, 296 (1942).
W. Heitler, "Bermerkungen über eine Erweiterung der Borsche Näherung für Stossprobleme," Acta Phys. Austriaca 1, 110 (1947).
V. Bargmann, "On the Connection Between Phase Shifts and Scattering Potential," Rev. Mod. Phys. 21, 488 (1949).
M. Lax, "On a Well-Known Cross-Section Theorem," Phys. Rev. 78, 306 (1950).
B. A. Lippmann and J. Schwinger, "Variational Principles for Scattering Processes. I," Phys. Rev. 79, 469 (1950).
G. J. Kynch, Proc. Roy. Soc. A 65, 83 (1952).
G. J. Kynch, Proc. Roy. Soc. A 65, 94 (1952).
W. Kohn, "The Validity of Born Expansions," Phys. Rev. 87, 539 (1952).
N. Levinson, Danske Vid. Selsk. Mat.-Fys. Medd. 25, No. 9 (1949).
I. M. Gelfand and B. M. Levitan, "On the Determination of a Differential Equation from Its Spectral Function," Izv. Akad. Nauk SSSR 15, 309 (1951).
N. Levinson, "Certain Explicit Relationships Between Phase Shift and Scattering Potential," Phys. Rev. 87, 755 (1953).
J. R. Oppenheimer, "On the Quantum Theory of Electron Impacts," Phys. Rev. 32, 361 (1928).
K. Wildermuth, "Das analytische Verhalten der asymptotischen Wellenfunktion und die S- bzw. N-Matrix für mehrere Teilchen. I," Z. Phys. 127, 92 (1949).
S. Altshuler, "The Binary Rearrangement Collision," Phys. Rev. 92, 1159 (1953).
B. Roth, "Two-Body Scattering at Low Energy," Phys. Rev. 92, 1250 (1953).
G. Breit and H. A. Bethe, "Ingoing Waves of Final State of Scattering Problems," Phys. Rev. 93, 888 (1954).
L. I. Schiff, Prog. Theor. Phys. 11, 288 (1954).
M. Gell-Mann and M. L. Goldberger, "The Formal Theory of Scattering," Phys. Rev. 91, 398 (1953).
A. Morita Prog. Theor. Phys. 11, 609 (1954).
T. Kikuta, Prog. Theor. Phys. 12, 225 (1954).
T. Kikuta, "Upper and Lower Bounds of Born Approximation. II," Prog. Theor. Phys. 12, 234 (1954).
P. Swan, Proc. Roy. Soc. A 228, 10 (1955).
E. P. Wigner, "Lower Limit for the Energy Derivative of the Scattering Phase Shift," Phys. Rev. 98, 145 (1955).
D. S. Jones, "On the Scattering Cross-Section of an Obstacle," Phil. Mag. 46, 957 (1955).
W. Pauli, Meson Theory of Nuclear Forces (Interscience, 1946).
R. Jost and W. Kohn, Kgl. Danska Videnskab. Selsab. Mat. Fys. Medd. 27, No. 9 (1953).
H. Rollnik, Z. Phys. 145, 639 (1956).
D. Park, Indianr. J. Theor. Phys. 3, 83 (1955).
S. Borowitz and B. Friedman, "Variational Principles for Three-Body Scatering Problems," Phys. Rev. 89, 441 (1953).
M. Burnat, "On the solution of a Problem for the Schrödinger Equation in the Infinite 3-Dimensional space," Dokl. Akad. Nauk. SSSR 112, 224 (1957).
L. I. Schiff, "Approximation Method for High-Energy Potential Scattering," Phys. Rev. 103, 443 (1956).
B. A. Lippmann, Ann. Phys. 1, 113 (1957).
J. M. Jauch, Helv. Phys. Acta 30, 143 (1957).
J. M. Jauch, Helv. Phys. Acta 31, 127 (1958).
J. M. Jauch, Helv. Phys. Acta 31, 661 (1958).
T. Imamura, Prog. Theor. Phys. 18, 51 (1957).
D. Park Proc. Phys. Soc. A 70, 905 (1957).
E. Gerjuoy, "Time-Independent Nonrelativistic Collision Theory," Ann. Phys. (N.Y.) 5, 58 (1958).
B. W. Lee, "Dispersion Relation for Nonrelativistic Potential Scattering," Phys. Rev. 112, 2122 (1958).
M. H. Mittleman and K. M. Watson, "Scattering of Charged Particles by Neutral Atoms," Phys. Rev. 113, 198 (1959).
K. W. Ford and J. A. Wheeler, "Semiclassical Description of Scattering," Ann. Phys. (N.Y.) 7, 259 (1959).
P. L. Kapur and R. E. Peierls, "The Dispersion Formula for Nuclear Reactions," Proc. Roy. Soc. A 166, 277 (1938).
R. E. Peierls, Proc. Roy. Soc. A 253, 16 (1959).
L. Spruch and L. Rosenberg, "Upper Bounds on Scattering Lengths for Static Potentials," Phys. Rev. 116, 1034 (1959).
A. Weinmann, "Bounds for Elastic and Inelastic Scattering," Proc. Phys. Soc. 75, 510 (1960).
F. T. Smith, "Lifetime Matrix in Collision Theory," Phys. Rev. 118, 349 (1960).
R. J. Eden, "Analytic Structure of Collision Amplitudes in Perturbation Theory," Phys. Rev. 119, 1763 (1960).
B. Bosco and J. Sucher, Nuovo Cimento 19, 1183 (1961).
B. A. Lippmann, M. H. Mittleman and K. M. Watson, "Scattering of Electrons by Neutral Atoms," Phys. Rev. 116, 920 (1959).
M. H. Mittleman, Ann. Phys. (N.Y.) 14, 94 (1961).
R. A. Mapleton, "Characteristic Coulomb Green's Function and Its Eigenfunction Expansion," J. Math. Phys. 2, 478 (1961).
V. S. Buslaev, "Trace Formulas for the Schrödinger Operator in a Three-Dimensional Space," Dokl. Akad. Nauk SSSR 143, 1067 (1962) [Sov. Phys. Dokl. 7, 295 (1963)].
M. Froissart, M. L. Goldberger and K. M. Watson, "Spatial Separation of Events in S-Matrix Theory," Phys. Rev. 131, 2820 (1963).
L. L. Faddeyev and B. Seckler, "The Inverse Problem in the Quantum Theory of Scattering," J. Math. Phys. 4, 72 (1963).
L. L. Faddeyev, "The Inverse Problem in the Quantum Theory of Scattering," Usp. Matern. Nauk 14, 57 (1959).
R. F. Dashen, "New Approach to Low-Energy Potential Scattering," J. Math. Phys. 4, 388 (1963).
F. Cologero, "A Novel Approach to Elementary Scattering Theory," Nuovo Cimento 27, 261 (1963).
J. M. Cook, "Convergence to the Møller Wave-Matrix," J. Math. and Phys. 36, 82 (1957).
M. N. Hack, Nuovo Cimento 9, 731 (1958).
J. M. Jauch and I. I. Zinnes, "The Asymptotic Condition for Simple Scattering Systems," Nuovo Cimento 11, 553 (1959).
W. Hunziker, "Potential Scattering at High Energies," Helv. Phys. Acta 36, 838 (1963).
N. Limic, "On the Existence of the Scattering Operator," Nuovo Cimento 28, 1066 (1963).
S. Weinberg, "Quasiparticles and the Born Series," Phys. Rev. 131, 440 (1963).
B. A. Lippmann, "Ehrenfest's Theorem and Scattering Theory," Phys. Rev. Lett. 15, 11 (1965).
B. L. Moiseiwitsch, "Lower Bound to the Reciprocal of the Scattering Length," Proc. Phys. Soc. 86, 363 (1965).
S. Tani, "Padé Approximant in Potential Scattering," Phys. Rev. 139, B1011 (1965).
M. Bosterli and J. MacKenzie, Physics 2, 141 (1965).
E. Gerjuoy, "Momentum Transfer Cross-Section Theorem," J. Math. Phys. 6, 993 (1965).
E. Gerjuoy, "Momentum Transfer Cross-Section Theorem for Inelastic Processes," J. Math. Phys. 6, 1396 (1965).
E. Gerjuoy, "Extensions of the Momentum Transfer Theorem," Phys. Rev. Lett. 16, 132 (1966).
T. T. Wu, "Born Approximation and Large-Momentum-Transfer Processes in Potential Scattering," Phys. Rev. 143, 1110 (1966).
P. Swan and W. A. Pearce, Nucl. Phys. 79, 77 (1966).
B. A. Lippmann, "Operator for Time Delay Induced by Scattering," Phys. Rev. 151, 1023 (1966).
J. M. Jauch and J.-P. Marchand, "The Delay Time Operator for Simple Scattering Systems," Helv. Phys. Acta 40, 217 (1967).
P. Pechukas, "Time-Dependent Semi-Classical Scattering Theory. I. Potential Scattering," Phys. Rev. 181, 166 (1969).
P. Pechukas, "Time-Dependent Semi-Classical Scattering Theory. I. Atomic Collisions," Phys. Rev. 181, 174 (1969).
H. Ekstein, "Scattering Without Scattering Operators," Ann. Phys. (N.Y.) 74, 303 (1972).
A. P. Penner and R. Wallace, "Semiclassical Collision Theory Within the Feynman Path-Integral Formalism," Phys. Rev. A 7, 1007 (1973).
D. C. Mattis, "Solution of Multiple Scattering by Finite Iteration," Phys. Rev. Lett. 40, 210 (1978).
R. G. Newton, "New Result on the Inverse Scattering Problem in Three Dimensions," Phys. Rev. Lett. 43, 541 (1979).
V. Enss and B. Simon, "Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods," Phys. Rev. Lett. 44, 319 (1980).
T. A. Osborn, R. G. Froese and S. F. Howes, "Sum-Rule Dynamics," Phys. Rev. Lett. 45, 1987 (1980).
E. Pollak and W. H. Miller, "New Physical Interpretation for Time in Scattering Theory," Phys. Rev. Lett. 53, 115 (1984).
R. G. Newton, "Representation of the Potential in the Schrödinger Equation," Phys. Rev. Lett. 53, 1863 (1984).
D. Bollé and F. Gesztesy, "Scattering Observables in Arbitrary Dimension n ≥ 2," Phys. Rev. A. 30, 1279 (1984).
T. Maniv and M. H. Cohen, "Collisions in the Classical Limit: the Vanishing-Potential Theorem," Phys. Rev. Lett. 54, 611 (1985).
Y. Alhassid and R. D. Levine, "Formal Scattering Theory by an Algebraic Approach," Phys. Rev. Lett. 54, 739 (1985).
D. Bollé, F. Gesztesy, C. Danneels and S. F. J. Wilk, "Threshold Behavior and Levinson's Theorem for Two-Dimensional Scattering Systems: A Surprise," Phys. Rev. Lett. 56, 900 (1986).
B. Gazdy and J. M. Bowman, "Novel Decomposition of the Multichannel Scattering Matrix at Resonances," Phys. Rev. Lett. 59, 3 (1987).

General Theory of Multiple Scattering
M. Lax, "Multiple Scattering of Waves," Rev. Mod. Phys. 23, 287 (1951).
M. Lax, "Multiple Scattering of Waves. II. Effective Field in Dense Systems," Phys. Rev. 85, 621 (1952).
G. Vinyard, "Geometrical Optics and the Theory of Multiple Small Angle Scattering," Phys. Rev. 85, 633 (1952).
L. L. Foldy, "The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers," Phys. Rev. 67, 107 (1945).
H. Ekstein, "Scattering by Many-Body Systems in Terms of Two-Body Collision Parameters," Phys. Rev. 87, 31 (1952).
H. Ekstein, "Multiple Elastic Scattering and Radiation Damping. I," Phys. Rev. 83, 721 (1951).
H. Ekstein, "Multiple Elastic Scattering and Radiation Damping. II," Phys. Rev. 89, 490 (1952).
G. F. Chew and C. C. Wick, "The Impulse Approximation," Phys. Rev. 87, 778 (1952).
K. M. Watson, "Multiple Scattering and the Many-Body Problem - Applications to Photomeson Production in Complex Nuclei," Phys. Rev. 89, 575 (1953).
G. Molière, "Theorie der Streuung schneller geladener Teilchen. II. Mehrfach und Vielfachstreuung," Z. Naturforschung 3a, 78 (1948).
H. S. Snyder and W. T. Scott, "Multiple Scattering of Fast Charged Particles," Phys. Rev. 76, 220 (1949).
W. T. Scott, "Mean-Value Calculations for Projected Multiple Scattering," Phys. Rev. 85, 245 (1952).
S. Goudschmit and J. L. Saunderson, "Multiple Scattering of Electrons," Phys. Rev. 57, 24 (1940).
S. Goudschmit and J. L. Saunderson, "Multiple Scattering of Electrons. II," Phys. Rev. 58, 36 (1940).
H. W. Lewis, "Multiple Scattering in an Infinite Medium," Phys. Rev. 78, 526 (1950).
H. A. Bethe, "Molière's Theory of Multiple Scattering," Phys. Rev. 89, 1256 (1953).
K. M. Watson, "Quantum Mechanical Transport Theory. I. Incoherent Processes," Phys. Rev. 118, 886 (1960).
P. C. Waterman and R. Truell, "Multiple Scattering of Waves," J. Math. Phys. 2, 512 (1961).
B. J. Uscinski, Phil. Trans. Roy. Soc. A 262, 609 (1968).
D. C. Mattis, "Solution of Multiple Scattering by Finite Iteration," Phys. Rev. Lett. 40, 210 (1978).