Letters to the Editor
On the Correlation between Yukawa
Particle and Meson.
T. Inouc and S. Ogawa.
mstitute , for Chemical Research,
Kyoto University.
In stitute of Theoretical Physics,
Nagoya University.
June 30, 1948
Previously(1) one of the present authors put forward a new meson theory which modified the original Vukawa theory in
discyiminating the mesotron (m±,light or cosmic-ray meson, Fermi-particle)from the Yukawa Particle(Y±, heavy or nuclear
meson, Buse-particle). This scheme had been proposed to resolve the descrepancies between theory and experiment which until that time had been seriously manifested, principally on the decay and nuclear scat-tering of the meson. This scheme is in-deed a sort of two-meson hypotheses which have been developed by several authors(2) in connection with recent experimental works by the Bristol group.(3) Thus it is desirable that recent experimental results on mesons should be investigated basing upon the above hypotheses.
Of course, two-meson theory itself al-lows several alternative models (e. g. clas-sification of spin value or type of wave field between two kinds of meson). We adopt the above model and consequently introduce the following, interaction schemes
where y, y';γ arc the coupling constants
of interactions (A), (B) and (C) respecti-vely.
The consequences of investigation are as follows.
(1)Thc nuclear force and the β-decay of the nucleus are due to the Yukawa particle (pseudoscalar field) with.the fol-lowing coupling constants; g2/hc∼10-1
(nuclear force), g'2/hc∼10-13 (β-decay).
The mass of Yukawa particle (300-400 m) is taken from the recent experimental data on the nuclear force-range.
(2) The Yukawa particle decays into the mesotron through the process (C). We have the following decay-probability,
where x=myc/h,μ=muc/h,ν=mnc/h(my,
mμ and mn are masses of the Yukawa particle, charged-mesotron and neutral mesotron). This process corresponds to the μ-decay of π-meson discovered by
Lattes et al.(3) According to their experi-mental results, we take the mass of the Yukawa particle (π-meson), the charged mesotron(μ-meson)and the neutral meso-trop (the neutral decay product of π-me-son), as 400m,200m and 180m(m is one electron mass). Putting γ2/hc≠10-12∼ 10-14, we have 10-10∼10-8 sec. for the decay-lifetime of the Yukawa particle. (3) Capture of the charged mesotron by
the nucleons occurs through thc following process.
(P:Proton, N:Neutron,m±:mox: charged and neutral mesotron)
We have the following capture probability;
Letters to the Editor
where a=an/Z. an is the Bohr radius of the mesotron. Z is the nuclear charge.
W is the binding energy of nuclei. M is
￨∫Ψ
σΨdv￨(Ψ,Ψ represent wave functions
of nucleons). This process corresponds to the capture of the cosmic-ray meson in the matter investigated by the Rome group or others.(4) Taking the numerical value determined from (1) and (2), we have Wcap as depends on Z4 and takes the value 106 for Z=10. These results are in ac-cordance with the experimental results.(4) Furthermore, by this process, meson cap-ture is accompanied by the emission of neutral mesons of 180m mass, so the
ex-perimental fact that the "stars" are rarely found in meson capture, is explained.(5)
(4)The β-disintegration or cosmic-ray mesen occurs through the combined pro-ccs of(B)and(C).The lifetime
calcu-lated in this way with coupling constanis determined above is too long to explain the observed data 10-6 sec. But, as
sug-gested by Anderson's recent observation,(6) the cosmic-ray meson decay may be ex-plained by assuming a direct process in
which a charged mesotron (Fermi particle) decays into one electron and two neutrinos. Assuming this process besides the above, an explanation of the cosmic-ray is possible with no contradiction to experiments up to now.
(1)S.Sakala & T.Inone:Prog. Theor.
Phys. 1 (1946), 143.
(2) R.E. Marshak & H. A. Bethe: Phys. Rev. 72 (1947), 506. Y. Tanikawa: Prog. Theor. Phys. 2 (1947), 220.
(3) C. M. G. Latces, C. P. S. Occhialini and O. E. Powell, Nature, 160 (1947), 453, 486. (4) M. Conversi, E. Pancini and O. ni, Phys. Rev. 71 (1947), 209 H. Ticho & M.Shein, Phys. Rev,73(1948), Sl. (5)O.Piccioni,Phys. Rev.75(1948),411. (6)C.V.Anderson,&R. V. Adams, Phys. Rev.72 (1947),724.
