Abstract
The study of the angular distribution and correlation of nuclear radiations is applied to two broad classes of phenomena. The first of these, to which the term “angular correlation” is normally applied, concerns the decay, by the emission of successive radiationsl, of radioactive nuclei, and of nuclei which have been produced in unstable excited states. These radiations may be detected at particular directions with respect to the decaying nuclei and the relative probability of detection of the cascade is then a function, inter alia, of these directions. In addition to this directional correlation, which refers to directions of emission only, other angle variables may be involved, e.g. if the efficiency of the detectors of radiation depends also on the state of polarisation of the radiations, and in such cases the appropriate correlation functions are more complex functions of several angles. Furthermore, if the original system of decaying nuclei is not isotropic, in a statistical sense, or if the cascade of radiation occurs in the presence of some anisotropic disturbance, such as an extra-nuclear electromagnetic field, then the correlation function will involve angles relating the directions of emission and of polarisation to those characterising the original or external anisotropies, as well as angles characteristic of the relative directions of emission and polarisation themselves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliography
General references, survey articles and reviews
Wigner, E. P.: Gruppentheorie. Braunschweig 1931.
Coxnon, E. U., and G. H. Shortley: Theory of Atomic Spectra. Cambridge 1935.
Racah, G.: Theory of Complex Spectra. Phys. Rev. 62, 438; 63, 367 (1942) (transformation theory used for the analysis of complex spectra).
Spiers, J. A.: Directional Effects in Radioactivity. Nat. Res. Council Canada, Publ. No. 1925, 90 pp., 1949 (extensive discussion of properties of angular-momentum states with application to radioactive emissions).
Deutsch, M.: Angular Correlations in Nuclear Reactions. Rep. Progr. Phys. (Physical Society London) 14, 196–226 (1950) (early survey of experiments involving angular correlations, including an account of elementary theory and a description of experimental technique).
Blatt, J. M., and L. C. Biedenharn: The Angular Distribution of Scattering and Reaction Cross-Sections. Rev. Mod. Phys. 24, 258–272 (1952) (theory of reactions with unpolarised particles. Racah algebra and S-matrix formalism is used).
Biedenharn, L. C., J. M. Blatt and M. E. Rose: Some Properties of Racah and Associated Coefficients. Rev. Mod. Phys. 24, 249–257 (1952).
Fano, U.: Statistical Matrix Techniques and Their Applications to the Direction Correlation of Radiations. Nat. Bur. Standards Report NBS 1214. Phys. Rev. 90, 577 (1952, 1953) (detailed formal development of the statistical-tensor and efficiency-tensor methods).
Biedenharn, L. C., and M. E. Rose: Theory of Angular Correlation of Nuclear Radiations. Rev. Mod. Phys. 25, 729–777 (1953) (comprehensive exposition of theory of correlations in cascade radiations, involving a, ß and y radiations and conversionelectrons—using Racah formalism mainly
Frauenfelder, H.: Angular Correlation of Nuclear Radiation. Ann. Rev. Nucl. Sci. 2, 129–162 (1953) Stanford (early survey of experiments and dealing mainly with cascade correlations).
Coester, F.: Gamma-Gamma Angular Correlations. Argonne Nat. Lab. Report ANL 5316, 29 pp., 1954 (concise presentation of statistical-tensor and efficiency-tensor method).
Jahn, H. A., and J. Hope: Symmetry Properties of the Wigner 9-j Symbol. Phys. Rev. 93, 318 (1954).
Huby, R.: Stripping Reactions. Progr. Nucl. Phys. 3, 177 (1953) London (survey of theoretical and experimental investigations, including results of deuteron-stripping reactions and some allied processes).
Siegbahn, K., editor: Beta-and Gamma-Ray Spectroscopy. Amsterdam 1955.
Frauenfelder, L.: Angular Correlations, Chap. XIX, pp. 531–599 (general survey of cascade correlations including the effects of extra-nuclear perturbations—mainly experimental).
Steffen, R. M.: Extra-nuclear Effects on Angular Correlations of Nuclear Radiations. Adv. Physics (Phil. Mag.) 4, No. 15, 293-362 (1955) (elementary theory and comprehensive survey of experiments).
Satchler, G. R.: Some Aspects of Nuclear Structure being Some Applications of the Group-Theoretic Properties of Angular Momentum Eigenstates. Thesis Oxford University 1955 (theory of angular correlations using statistical tensors).
Edmonds, A. R.: Angular Momentum in Quantum Mechanics. CERN 55–26 Copenhagen 1955 (detailed presentation of definitions and mathematical relationships involving functions of angular-momentum variables).
Rose, M. E.: Multipole Fields, 99 pp. New York 1955 (description of the electromagnetic field with particular emphasis given to internal conversion and emission of radiation using the transformation properties of the multipole fields).
Feenberg, E., and G. E. Pake: Notes on the Quantum Theory of Angular Momenta, 54 pp. Cambridge, Mass. 1953 (contains a discussion of angular-momentum transformations together with applications to nuclear moments).
Hamilton, D. R.: On Directional Correlation of Successive Quanta. Phys. Rev. 58, 122 (1940) (first treatment of y-y correlations, using time-dependent perturbation theory).
Goertzel, G.: Angular Correlation of y-Rays. Phys. Rev. 70, 897 (1946) (extension of the treatment in [20],including the first investigation into the effects of external fields on the angular correlation).
Yang, C. N.: On the Angular Distribution in Nuclear Reactions and Coincidence Measurements. Phys. Rev. 74, 764 (1948) (some general theorems concerning angular distributions, using group-theoretical methods).
Gardner, J. W.: Directional Correlation between Successive Internal-Conversion Electrons. Proc. Phys. Soc. Lond. A 62, 763 (1949).
Fierz, M.: Zur Theorie der Multipolstrahlung. Heiv. phys. Acta 22, 489 (1949).
Falkoff, D. L., and G. E. Uhlenbeck: On the Directional Correlation of Successive Nuclear Radiations. Phys. Rev. 79, 323 (1950) (extension of early theory to arbitrary radiations).
Spiers, J. A.: On the Directional Correlation of Successive Nuclear Radiations. Letter in Phys. Rev. 80, 491 (1950) (generalisation of treatment of [25],using only the properties of angular momentum—a summary of the theory developed in [4]).
Racah, G.: Directional Correlation of Successive Nuclear Radiations. Phys. Rev. 84, 910 (1951) (formalism of the tensor parameters of radiation).
Lloyd, S. P.: The Angular Correlation of Two Successive Nuclear Radiations. Phys. Rev. 85, 904 (1952) (general formulation by means of group-theoretical methods, summarising the author’s previous work).
Coester, F., and J. M. Jauch: Theory of Angular Correlations. Hell,. phys. Acta 26, 3 (1953) (formalism of statistical and efficiency tensors).
Satchler, G. R.: The Angular Correlation of Three Nuclear Radiations. Phys. Rev. 94, 1304 (1954).
Myers, R. D.: The Angular Distribution of Resonance Disintegration Products. Phys. Rev. 54, 361 (1938) (early use of symmetry arguments with regard to nuclear reactions involving isolated resonance levels).
Breit, G., and B. T. Darling: Note on Calculation of Angular Distributions in Resonance Reactions. Phys. Rev. 71, 402 (1947) (two general theorems concerning properties of angular-momentum transformation coefficients).
Eisner, E., and R. Sachs: Note on Angular Distributions in Nuclear Reactions. Phys. Rev. 72, 680 (1947) (general theorem with regard to complexity of angular distributions).
Wigner, E. P., and L. Eisenbud: Higher Angular Momenta and Long-Range Interaction in Resonance Reactions. Phys. Rev. 72, 29 (1947) (formal theory of reactions and scattering in terms of the compound nucleus).
Blatt, J. M., and V. F. Weisskopff: Theoretical Nuclear Physics, Chap. VIII, IX and X, p. 311— 564. New York 1952 (nuclear reactions).
Coester, F.: The Symmetry of the S-Matrix. Phys. Rev. 89, 619 (1953).
Konopinski, E. J., and G. E. Uhlenbeck: On the Fermi Theory of ß-Radioactivity. Phys. Rev. 60, 308 (1941) (early presentation of the theory).
Falkoff, D. L., and G. E. Uhlenbeck: On the Beta-Gamma Angular Correlation. Phys. Rev. 79, 334 (1950).
Groot, S. R. DE, and H. A. Tolhoek: On the Theory of Beta-Radioactivity. Physica, Haag 16, 456 (1950) (one of the early treatments of the beta-neutrino angular correlation).
Spiers, J. A., and R. J. Blin-Stoyle: A Formulation of Beta-decay Theory for Forbidden Transitions of Arbitrary Order. Proc. Phys. Soc. Lond. A 65, 801, 809 (1952) (formulation using a representation characterising the electron-plus-neutrino angular momenta).
Kofoed-Hansen, O.: Theoretical Angular Correlations in Allowed Beta Transitions. Dan. Mat.-Fys. Medd. 28 No. 9, 19 pp. (1954) (transformation of fl-neutrino angular correlation into functions of the recoil particle).
Rose, M. E.: The Theory of Allowed ß-Decay, Chap. IX, pp. 273–292. 1955.
Konopinski, E.: The Theory of Forbidden ß-Decay, Chap. X, pp. 292–314. 1955.
Kofoed-Hansen, O.: Neutrino Recoil Experiments, Chap. XI, pp. 357–373. 1955.
Morita, M.: Explicit Formulae of Beta-Gamma Directional Correlation. Progr. Theor. Phys. 14, 27 (1955)(generalisation of earlier work of
Hauser, I.: Directional Correlation of i4-Rays, 97 pp. 1956. Thesis State University of Iowa
Alder, K.: Contribution to the Theory of Directional Correlation. Rely. phys. Acta 25, 235 (1952) (early treatment of perturbations due to external fields, using Racah algebra).
Abragam, A., and R. V. Pound: Influence of Electric and Magnetic Fields on Angular Correlations. Phys. Rev. 92, 943 (1953) (contains generalisations of earlier treatments in [21] and [60] and deals with specific examples).
Alder, K., H. Albers-Schönberg, E. Heer and T. B. Novey: The Measurement of Nuclear Moments of Excited States by Angular Correlation Methods. Hely. phys. Acta 26, 761 (1953) (particular discussion is given of experimental arrangements).
Coester, F.: Influence of Extranuclear Fields on Angular Correlations. Phys. Rev. 93, 1304 (1954) (external fields using density matrices).
Frankel, S.: The Effect of Scattering on Angular Correlation Measurements. Phys. Rev. 83, 673 (1951) (corrections for finite solid angles of detectors and multiple scattering in source).
Rose, M. E.: The Analysis of Angular Correlation and Angular Distribution Data. Phys. Rev. 91, 610 (1953) (corrections for finite solid angles of detectors and discussion of counting rates and errors).
Breitenberg, E.: Remarks on the Least-Square Reductions of Angular Correlations Data. Proc. Phys. Soc. Lond. A 69, 489 (1956).
Mitchell, A. C. G.: The Coincidence Method, Chap. VII, pp. 201–223. 1955.
Bell, R. E.: Measurement by Delayed Coincidences. Comparison Methods, Chap. XVIII, pp. 494–520. 1955.
Wolfenstein, L.: Theory of Proposed Reactions Involving Polarised Protons. Phys. Rev. 75, 1664 (1949).
Fano, U.: Remarks on the Classical and Quantum-Mechanical Treatment of Partial Polarization. J. Opt. Soc. Amer. 39, 859 (1949) (on the use of STOKES’ parameters in the treatment of y-radiation).
Blin-Stoyle, R. J.: Polarised Nuclear Reactions. Proc. Phys. Soc. Lond. A 64, 700 (1951).
Dalitz, R. H.: On Polarised Particle Beams. Proc. Phys. Soc. Lond. A 65, 175 (1952) (use of statistical tensors in the designation of polarisation).
Simon, A., and T. A. Welton: Production of Polarized Particles in Nuclear Reactions. Phys. Rev. 90, 1036 (1953).
Simon, A.: Theory of Polarized Particles and y-Rays in Nuclear Reactions. Phys. Rev. 92, 1050 (1953) ([84],extended to include polarised initial beams).
Lakin, W.: Spin Polarization of the Deuteron. Phys. Rev. 98, 139 (1955).
Satchler, G. R.: Polarisation in Nuclear Reactions. Proc. Phys. Soc. Lond. A 68, 1041 (1955) (results for polarisation in the L-representation).
Tolhoee, H. A.: Electron Polarization, Theory and Experiment. Rev. Mod. Phys. 28, 277 (1956) (description of polarisation using density matrices, being a summary of previous work by author—represents a survey of theory and experiment involving electron polarisation).
Serber, R.: The Production of High-Energy Neutrons by Stripping. Phys. Rev. 72, 1008 (1947).
Nuclear Reactions. Proc. Roy. Soc. Lond., Ser. A 208, 559 (1951).
Bhatia, A. B., K. Huang, R. Huby and H. C. Newns: Angular Distribution in (d,p) and (d, n) Reactions. Phil. Mag. 43, 485 (1952) (Born-approximation calculations).
Satchler, G. R., and J. A. Sriers: Angular Distribution of y-Radiation following a Deuteron-Stripping Reaction. Proc. Phys. Soc. Lond. A 65, 980 (1952).
Huby, R.: Theory of the Deuteron-Stripping Reaction. Proc. Roy. Soc. Lond., Ser. A 215, 385 (1952).
Dalitz, R. H.: Some Features of the Deuteron-Stripping Process. Proc. Phys. Soc. Lond. A 66, 28 (1953).
Grant, I. P.: Theory of (d, p) and (d, n) Reactions. Proc. Phys. Soc. Lond. A 67, 981; A 68, 244 ( 1954, 1955 ).
Horowitz, J., and A. M. L. Messiah: Sur les Reactions (d, p) et (d, n). J. Phys. Radium 14, 695 (1955).
Tobocman, W., and M. H. Kalos: Numerical Calculation of (d, p) Angular Distributions. Phys. Rev. 97, 132 (1955)
Austern, N., S. T. Butler and H. Mcmanus: Angular Distributions from (n, p) Nuclear Reactions. Phys. Rev. 92, 350 (1953) (treatment in terms of direct nucleon-nucleon interaction).
Satchler, G. R.: Gamma-Radiation following Surface Scattering of Nucleons. Proc. Phys. Soc. Lond. A 68, 1037 (1955).
Brink, D. M.: Inelastic Scattering of Neutrons by Deformed Nuclei. Proc. Phys. Soc. Lond. A 68, 994 (1955).
Hayakawa, S., and S. Yoshida: Inelastic Scattering of Neutrons by Rotational Excitation. Progr. Theor. Phys. 14, 1 (1955).
Yoshida, S.: The Inelastic Scattering of Nucleons by the Surface Interaction. Proc. Phys. Soc. Lond. A 69, 668 (1956).
Jaeger, J. C., and H. R. Hulme: The Internal Conversion of y-Rays with the Production of Electrons and Positrons. Proc. Roy. Soc. Lond., Ser. A 148, 708 (1935) (calculation of electric dipole and quadrupole coefficients using Dirac hydrogen-like wave functions for Z = 84).
Rose, M. E.: Internal Pair Formation. Phys. Rev. 76, 678 (1949) (Born-approximation calculation for radiation of arbitrary multipole type).
Dalitz, R. H.: On Radiative Corrections to the Angular Correlation in Internal Pair Creaton. Proc. Roy. Soc. Lond., Ser. A 206, 521 (1951) (detailed calculation for monopole transition).
g]Wilson, R.: Internal Pair Formation, Chap. XX, p. 636–649 1955 (survey of theory and experiment).
Ter-Martirosyan, K. A.: The Excitation of Nuclei by the Coulomb Field of Charged Particles. J. exp. theor. Phys. USSR. 22, 284 (1952) (in Russian) (semi-classical treatment for dipole excitation).
Bohr, A., and B. R. Mottelson: Collective and Individual Particle Aspects of Nuclear Structure, Appendix VI. Dans. Mat.-Fys. Medd. 27, No. 16 (1953) (contains a summary of the above calculation).
Alder, K., and A. Winther: The Theory of Coulomb Excitation of Nuclei. Letters in Phys. Rev. 91, 1578; 96, 237 (1953, 1954) (application of [103] to correlation with y-rays following Coulomb excitation).
Breit, G., M. E. Ebel and J. E. Russell: Gamma-Ray Angular Distribution in Coulomb Excitation. Phys. Rev. 101, 1504 (1956) (quantum mechanical calculation for quadrupole excitation).
Biedenharn, L. C., J. L. Mchale, R. M. Thaler and M. GOLDSTEIN: Quantum Calculation of Coulomb Excitation. Phys. Rev. 100, 376; 101, 662; 102, 1567 ( 1955. 1956 ).
Breit, G., R. L. Gluckstern and J. E. Russell: Reorientation Effect in Coulomb Excitation. Phys. Rev. 103, 727 (1956).
Hofstadter, R.: Electron Scattering and Nuclear Structure. Rev. Mod. Phys. 28, 214 (1956).
Condon, E. U., and G. H. Shortley: Theory of Atomic Spectra, Tables 13, 2, 33, 43 Cambridge (1935) [algebraic tables of (a α b ß|c γ)b=1\2, 1, 3\2,2)
Biedenharn, L. C., J. M. BLATT and M. E. ROSE: Some Properties of the Racah and Associated Coefficients. Rev. Mod. Phys. 24, 249 (1952) [algebraic tables of W(1L1’L’ s k) for s= 1\2, 1, 3\2, 2].
Alder, K.: Contribution to the Theory of Directional Correlation. HeIv. phys. Acta 25, 253 (1952) (general formulae); pp. 254–257 (algebraic table of Racah coefficients).
Yamada, M., and M. Morita: On the fl-Ray Angular Correlation. Prog. Theor. Phys. 8, 444 (1952) [algebraic table of (aα, 3ß| cγ.)
Biedenharn, L. C.: Tables of the Racah Coefficients. Oak Ridge Nat. Laboratory, ORNL 1098, 1952 [algebraic tables of W(lLl’L’ sk) for s= 1\2, 1, 3\2, 2, and numerical tabels for s = 0 to 3 in half-integral steps and k= 0, 1, 2,?, 8).
Biedenharn, L. C.: Revised Z-Tables of the Racah Coefficients. ORNL 1501, 1953 (numerical tables of Z(1L1’L’ sk) for same values of parameters as in [5]).
Simon, A., J. H. Van Der Sluis and L. C. Biedenharn: Tables of the Racah Coefficients. ORNL 1679, 1952.
Simon, A.: Numerical Table of the Clebsch-Gordan Coefficients. ORNL 1718, 1952.
Ferentz, M., and N. Rosenzweig: Table of F-Coefficients. Argonne Nat. Laboratory, ANL 5234, 1953 [numerical tables of F(LL’j) for integral and half-integral values of j1 and j from 0 to 12).
Sharp, W. T., J. M. Kennedy, B. J. Sears and M. G. Hoyle: Tables of Coefficients for Angular Distribution Analysis. Atomic Energy of Canada, Limited, AECL 97, 1953 [includes numerical tables of Z(1L1’L’ sk), Z 1 (LjL’j 1k) (related to the F-coefficients)\(W(lLlL;sk)W(j{j_1}j{j_1};Lk),\left( {\begin{array}{*{20}{c}} {abc} \\ {{a^,}bc} \\ {ghk} \end{array}} \right),\left( {\begin{array}{*{20}{c}} {abc} \\ {aef} \\ {kk1} \end{array}} \right),(lo,{l^,}o|ko),and(Ll,L' - 1|KO)\)
Kennedy, K. M., B. J. Sears and W. T. Sharp: Tables of X-Coefficients, AECL 106, 1954 (numerical tables of the 9-j symbol).
Arima, A., H. Horie and Y. Tanabe: Generalised Racah Coefficient and its Applications. Progr. Theor. Phys. 11, 143 (1954) (definitions and useful formulae involving the 9-j symbol).
Sato, M.: Tables of W(abcd; ef) for e=3, 7\2, 4 and 2. Progr. Theor. Phys. 13, 405 (1955).
Kennedy, L. M., and M. J. Cliff: Transformation Coefficients Between LS and j-j I / lI z 11 coupling. AECL 224, 1955 (numerical tables of \(\hat L\hat S{\hat j_1}{\hat j_2}\left( {\begin{array}{*{20}{c}} {{l_1}\frac{1}{2}{j_1}} \\ {{l_2}\frac{1}{2}{j_2}} \\ {LSJ} \end{array}} \right)\),for l1 and l2 not exceeding 5.
Rights and permissions
Copyright information
© 1957 Springer-Verlag OHG. Berlin · Göttingen · Heidelberg
About this chapter
Cite this chapter
Devons, S., Goldfarb, L.J.B. (1957). Angular Correlations. In: Kernreaktionen III / Nuclear Reactions III. Handbuch der Physik / Encyclopedia of Physics, vol 8 / 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45878-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-45878-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45880-4
Online ISBN: 978-3-642-45878-1
eBook Packages: Springer Book Archive