Nuclear Reactions II: Theory / Kernreaktionen II: Theorie

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

Klappentext

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

Inhalt
Theory of Resonance Reactions and Allied Topics..- A. Introductory survey.- B. Elementary viewpoints and the simpler models.- C. The Wigner development.- D. Phenomenologic treatments and applications.- Acknowledgment.- References.- Coulomb Wave Functions..- A. Fundamental properties and relations.- B. Bessel function expansions.- C. Asymptotic forms and expansions.- D. Approximate expressions.- E. Methods of calculation.- F. Tables of Coulomb functions.- 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).