Prog. Theor. Phys. Vol. 6 No. 5 (1951) pp. 849-890

[ Full Text PDF : FREE ACCESS (3701K) ]

Production of Charged π-Meson by γ-Ray

— Higher Order Corrections —

Ziro Koba, Tsuneyuki Kotani and Shinzo Nakai

Department of Physics, Faculty of Science, Osaka University

(Received August 25, 1951)

Abstract:

The effective cross section for the production of charged π-meson by γ-ray is calculated by the Lorentz-covariant perturbation method, including the effects of order e² f⁴ (e² g⁴). The pseudoscalar meson field with both pseudoscalar and pseudovector coupling has been employed. Virtual mesons in intermediate states can be either charged or neutral.
The procedure of the renormalization of mass and mesic charge (f, g) is sufficient to determine unambiguously the finite fourth order matrix element except only one term to be interpreted as “electric charge of neutron,” which we have struck out.
The general requirement of gauge invariance restricts the possible interaction of nucleon and meson with photon to only four types; consequently we have divided numerious Dyson diagrams into certain gauge invariant classes and then reduced them according to Dyson's general program, to obtain ultimately those four types.
In our second approximation the anomalous magnetic moment of the nucleon plays an essential part; consequently the lack of any correct analysis for the latter complicates our results considerably. Moreover, in our γ-π process the behaviour of the magnetic corrections, dependent on the incident energy of photon, are comparable with the static effects.
Three provisional measures have been taken with regard to the anomalous moments and the resulting values for the various combinations and couplings of meson fields are compared and discussed. Though the results depend upon the choice of these possibilities, it is shown, in general, that the fourth order contributions turn out for the energy region of the present experiments (incident X-ray being about 330 Mev.), not so large compared with the second order in the case of the symmetrical combination, while they are of the same order of magnitude with the second order in the case of the “charged plus pure neutral” combination.
Finally some qualitative aspects of the γ-π process are discussed, which might be valid independently of the order of approximation.

URL : http://ptp.ipap.jp/link?PTP/6/849/
DOI : 10.1143/PTP.6.849

References:

E. M. McMillan and J. M. Peterson, Science 109 (1949), 438
E. M. McMillan, J. M. Peterson and R. S. White, Science 110 (1949), 579
J. M. Peterson, W. S. Gilbert and R. S. White, Phys. Rev. 81 (1951), 1003[APS].
G. Araki, Sci. Pap. I. P. C. R. 39 (1941), 14; Prog. Theor. Phys. 5 (1950), 641[PTP]; Phys. Rev. 82 (1951), 959[APS].
A more detailed lists of the theoretical papers concerning this problem have been given in these works.
P. Urban, Acta Physica Austrica 1 (1948), 55; ibid. 1 (1948), 167.
O. Halpern, Phys. Rev. 78 (1950), 69[APS].
K. A. Brueckner and M. L. Goldberger, Phys. Rev. 76 (1949), 1725[APS].
P. B. Benoist-Guental, J. Prentki et J. Ratier, Comp. Rend. 230 (1950), 1146; J. de Phys. et Rad. 11 (1950), 553.
J. Steinberger and A. S. Bishop, Phys. Rev. 78 (1950), 494[APS].
J. Steinberger, W. K. H. Panofsky and J. Steller, Phys. Rev. 78 (1950), 802[APS].
A. S. Bishop, J. Steinberger and L. J. Cook, Phys. Rev. 80 (1950), 291[APS].
R. F. Mozley, Phys. Rev. 80 (1950), 493[APS].
R. M. Littauer and D. Walker, Phys. Rev. 82 (1951), 746[APS].
J. R. Oppenheimer, H. Snyder and R. Serber, Phys. Rev. 57 (1940), 75[APS].
E. Fermi, “Nuclear Physics,” (Lecture at the University of Chicago) (1949), 137.
J. M. Luttinger, Helv. Phys. Acta 21 (1948), 483; Phys. Rev. 75 (1949), 309[APS]; ibid. 75 (1949), 1277[APS].
K. M. Case, Phys. Rev. 74 (1948), 1884[APS]; ibid. 76 (1949), 1[APS].
M. Slotonick and W. Heitler, Phys. Rev. 75 (1949), 1645[APS].
S. M. Dancoff and S. D. Drell, Phys. Rev. 76 (1949), 205[APS];
S. D. Drell, Phys. Rev. 76 (1949), 427[APS].
S. Borowitz and W. Kohn, Phys. Rev. 76 (1949), 818[APS].
K. Sawada, Prog. Theor. Phys. 4 (1949), 383[PTP]; ibid. 4 (1949), 532[PTP];
S. Hori and K. Sawada, Prog. Theor. Phys. 5 (1950), 333[PTP].
E. Yamada, Prog. Theor. Phys. 5 (1950), 312[PTP].
H. Miyazawa, Soryushiron Kenkyu 2 (1950), No. 4, 37, (in Japanese).
K. A. Brueckner, Phys. Rev. 79 (1950), 641[APS].
K. A. Brueckner and K. M. Watson, Phys. Rev. 79 (1950), 187[APS].
K. M. Watson and E. W. Hart, Phys. Rev. 79 (1950), 918[APS].
Y. Fujimoto, K. Nishijima, T. Okabayashi, K. Takayanagi and Y. Yamaguchi, Prog. Theor. Phys. 5 (1950), 870[PTP].
R. E. Marshak, Phys. Rev. 78 (1950), 346[APS].
Y. Fujimoto and H. Miyazawa, Prog. Theor. Phys. 5 (1950), 1053[PTP].
K. Aidzu, Y. Fujimoto and H. Fukuda, Prog. Theor. Phys. 6 (1951), 193[PTP].
M. F. Kaplon, Phys. Rev. 82 (1951), 324[APS]; Phys. Rev. 83 (1951), 712[APS].
Z. Koba and S. Minami, Soryushiron Kenkyu 3 (1951), No. 1, 143, (in Japanese); ibid. 3 (1951), No. 3, 71; Prog. Theor. Phys. 6 (1951), 895[PTP].
T. Tati and S. Tomonaga, Prog. Theor. Phys. 3 (1948), 391[PTP].
J. Schwinger, Phys. Rev. 75 (1949), 651[APS].
R. E. Marshak, “Meson Physics,” Chapter for Nuclear Science Reviews of 1950.
A more detailed list concerning these problems has been given in this work.
F. J. Dyson, Phys. Rev. 75 (1949), 1736[APS].
Z. Koba, N. Mugibayashi and S. Nakai, Prog. Theor. Phys. 6 (1951), 322[PTP].
W. Pauli and F. Villars, Rev. Mod. Phys. 21 (1949), 433[APS].
Y. Katayama, Prog. Theor. Phys. 5 (1950), 272[PTP].
H. Fukuda and T. Kinoshita, Prog. Theor. Phys. 5 (1950), 1024[PTP].
P. T. Matthews, Phys. Rev. 76 (1949), 684[APS]; ibid. 76 (1949), 1419[APS].
Z. Koba, Prog. Theor. Phys. 5 (1950), 139[PTP]; ibid. 5 (1950), 696[PTP].
K. Nishijima, Prog. Theor. Phys. 5 (1950), 405[PTP].
F. Rohrlich, Phys. Rev. 80 (1950), 666[APS].
H. Fukuda and G. Takeda, Prog. Theor. Phys. 5 (1950), 800[PTP].
R. P. Feynman, Phys. Rev. 76 (1949), 769[APS].
R. Karplus and N. M. Kroll, Phys. Rev. 77 (1950), 536[APS].
R. G. Sachs and L. L. Foldy, Phys. Rev. 80 (1950), 824[APS].
M. N. Rosenbluth, Phys. Rev. 79 (1950), 615[APS].
K. Nakabayasi and I. Sato, Prog. Theor. Phys. 6 (1951), 252[PTP]; Sci. Rep. Tohoku Univ. Series I, XXXIV (1950), 169.
K. M. Case, Phys. Rev. 76 (1949), 14[APS].
L. Rosenfeld, “Nuclear Forces”, (1948), Chap. XVI, §16.4.
A detailed list concerning mixed theories has been given in this work.

Citing Article(s) :

Progress of Theoretical Physics Vol. 6 No. 3 (1951) pp. 322-341 :
On Gauge Invariance and Equivalence Theorems

Ziro Koba, Nobumichi Mugibayashi and Shinzô Nakai
Progress of Theoretical Physics Vol. 6 No. 5 (1951) pp. 772-787 :
The Phenomenological Analyses of Mesonic Processes

Yoshio Yamaguchi
Progress of Theoretical Physics Vol. 6 No. 5 (1951) pp. 788-800 :
Nuclear Interaction of µ-Meson

Hiroshi Fukuda, Yoichi Fujimoto and Masatoshi Koshiba
Progress of Theoretical Physics Vol. 6 No. 5 (1951) pp. 895-896 :
π⁰-Meson Production by Gamma-Ray

S. Minami
Progress of Theoretical Physics Vol. 6 No. 6 (1951) pp. 1007-1012 :
On the Mesonic Correction to the β-Decay

Tsuneyuki Kotani, Shigeru Machida, Seitaro Nakamura, Hisao Takebe, Minoru Umezawa and Tets Yoshimura
Progress of Theoretical Physics Vol. 7 No. 1 (1952) pp. 69-92 :
Neutral-Meson Production by Gamma-Ray

Shigeo Minami
Progress of Theoretical Physics Vol. 8 No. 1 (1952) pp. 53-76 :
The S Matrix Method in Pion Reactions

Tadao Nakano and Kazuhiko Nishijima
Progress of Theoretical Physics Vol. 8 No. 2 (1952) pp. 212-220 :
Some Consequences of Gauge Invariance

Masaaki Kawaguchi and Nobumichi Mugibayashi
Progress of Theoretical Physics Vol. 8 No. 5 (1952) pp. 531-548 :
Pion Reactions in One Nucleon System and Nucleon Isobars

Shigeo Minami, Tadao Nakano, Kazuhiko Nishijima, Hisaichiro Okonogi and Eiji Yamada
Progress of Theoretical Physics Vol. 12 No. 6 (1954) pp. 758-766 :
Kinematical Investigation of the S-matrix

Masaaki Kawaguchi
Progress of Theoretical Physics Vol. 31 No. 6 (1964) pp. 1026-1043 :
Feasible Complete Experiments of Pion Photoproduction

Masaaki Kawaguchi, Hiroo Shimoida, Yoshio Sumi and Tamotsu Ueda