Nuclear Reactions II: Theory / Kernreaktionen II: Theorie

ISBN-13: 9783642459252 / Angielski / Miękka / 2012 / 580 str.

Opis

449 one finds that for y = Fo (e) C=: n; V3 Po (2'Yj) 3 -kjF(i) ] (2'Yj) Fd (2'Yj) 3 -ijF (-m, } 1 ( 14.17) C2 =: n; - (2'Yj) Fd (2'Yj) 3 -ijF(i) ] Fo (2'Yj) 3 -;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G (2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob- tained from (14.8). 1 J. K. TYSON has employed the modified Hankel functions of order one- third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n (x) = (12) e-;/6 A;{- x) - iB;(-x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4). His results give re- presentations of FL(e), Gde) in the vicinity of e=2'Yj whereas (14.11), (14.12) converge near e=eLJ when L

Spis treści

Theory of Resonance Reactions and Allied Topics..- A. Introductory survey.- 1. Introductory survey.- B. Elementary viewpoints and the simpler models.- I. Resonances for central field scattering.- 2. Real energy treatment.- 3. Complex energy treatment.- 4. Partial extension to reactions.- II. Channels and scattering matrix.- 5. Formulation of method.- 6. Resonances by the method of complex energies.- 7. Specialization to one channel.- 8. Specialization to two channels.- III. Schematic model of many-channel reactions.- 9. General formulation.- 10. Expansion of schematic model reaction amplitude.- IV. Effect of ?-ray emission.- 11. Quantum treatment of radiation.- 12. The equivalent classical quantity.- 13. Calculation of ?? for dipole emission.- V. Many-particle features.- 14. The spherical shell model.- 15. Construction of Green’s functions.- 16. General plan for applications of Green’s functions.- 17. Green’s functions for the many-dimensional separable case.- 18. Schematic illustrations by means of Green’s functions.- 19. Correspondence principle connections.- 20. Connection with the Hamilton-Jacobi partial differential equation.- C. The Wigner development.- 21. Introductory remarks and an example.- 22. The ? matrix in the many-channel case.- 23. Time reversal requirements and relation of ?-matrix to scattering matrix.- 24. Reaction cross sections.- 25. Resonance forms.- 26. Parameters of the resonance formulas.- 27. Illustrations of level systems.- 28. The occurrence of G2 + F2 in single-level one-channel formulas.- 29. Role played by ?-matrix. Origin of factorization.- 30. Employment of different boundary conditions l6l.- 31. Closed channels. The reduced ?-matrix and connection with the scattering matrix.- 32. Resonance formulas in terms of the reduced ?-matrix.- 33. The sum rules.- 34. The Weisskopf approach to the second sum rule.- 35. The statistical ?-matrix.- 36. Comparison with experiment.- 37. Penetration factors.- 38. Direct measurements of strength function.- 39. One-level formula for two channels with application to H3 (d, n) He4 and He3(d, p) He4.- D. Phenomenologic treatments and applications.- 40. The optical model.- 41. The giant resonance interpretation of the potential well representation.- 42. Cross sections near thresholds.- 43. Angular distributions of reaction products.- 44. High-energy deuteron stripping and electric disintegration of the deuteron.- 45. General theory of pick-up and stripping.- 46. Mathematical transformations for preceding section.- 47. Theory of alpha-particle decay and lower limit of energy variation of phase shifts.- 48. Heavy particle reactions.- Acknowledgment.- References.- Coulomb Wave Functions..- A. Fundamental properties and relations.- 1. Introduction.- 2. Normalization and asymptotic forms of the Coulomb wave functions.- 3. Power series expansions for FL and GL.- 4. Integral representations.- 5. Recurrence relations.- B. Bessel function expansions.- 6. Expansion for FL (?) useful for low energies.- 7. Expansion for GL (?) useful for low positive energies.- 8. Asymptotic expansion of GL (?) useful for low positive energies.- 9. Expansions for large ?, E< 0.- 10. Expansions for Fl(?), Gl(?) for small ?.- 11. Expansion of the regular solution for small ?.- C. Asymptotic forms and expansions.- 12. The phase and amplitude functions.- 13. Asymptotic expressions, any ?.- 14. Asymptotic expressions and expansions useful near the classical turning point.- D. Approximate expressions.- 15. Introduction.- 16. The JWKB approximation.- 17. Extensions of the JWKB method.- 18. Steepest descents approximation.- E. Methods of calculation.- 19. Introduction.- 20. Numerical integration.- 21. Riccati equation.- 22. Calculation of the irregular function by quadrature.- 23. Miscellaneous formulas.- F. Tables of Coulomb functions.- 24. List and description of tables.- Polarization of Nucleons Scattered by Nuclei..- 1. Introduction.- 2. Basic relations.- 3. Polarization of particles with spin ½ scattered by spinless target.- 4. Polarization produced in scattering from complex potential well.- References.- Coulomb Excitation..- 1. Introduction.- 2. Correspondence principle considerations.- 3. Semi-classical first-order theory.- 4. Quantum-mechanical first-order theory.- 5. Radial matrix elements.- 6. Dipole excitation.- 7. Comparison of quantum and semi-classical theories.- 8. Higher order effects.- 9. Limitations of the theory.- References.- Sachverzeichnis (Deutsch/Englisch).- Subject Index (English/German).