Download On the Annihilation Cross Section of the Antinucleon and the Nucleon

612
Letters to the Editut
On the Annihilation Cross Section
of the Antinucleon and the Nucleon
){oshio ){anruaguchi
Department of Physics, Osaka City
Uni'l'ersity, Osaka
One can expect that the annihilation
process takes place at the instant that the
proton and the antiproton with the finite
size come into contact. Thus the antiproton with high energies (where the
classical trajectory of motion can be pictured) should have · the annihilation cross
section
O"a ,
February 11, 1957
(3)
We have recently obtained further
informatian1l about the electro-magnetic
structure of nucleons, from the high energy
electron scattering experiments of the
and
(electron-proton
group
Stanford
electron-deuteron scattering experiments)
and the electron-neutron interaction. According to these results, the proton has
the electro-magnetic radius,
r•. v . . rm,v= (0.77 ± 0.10) X 10-13 em,
(1)
while the neutron seems
charge radius
re,n . . 0.
to have the
(2)
The latter requires that, although the
charge dirtribution inside the neutron
should extend intrinsically over a range of
the order of (1), it is essentially neutral
at every local points.
Let us here ask what is expected
from such an electromagnetic size of th:e
nucleon as to the annihilation cross section2),s) of the anti-nucleon and the nucleon.
The most intuitive picture for the antiproton-proton annihilation process may be
the neutralization of the charges. An
argument based on the charge conjugation
proves that the electromagnetic structure
of the antiproton is identical with that of
the proton except for the sign of charge.
and the total cross section 0"1 , including
the diffraction scattering O"d ( ==. O"a, optical
model)
Experimentally it was found thael
0"1 ==-100 mb for high energy (~ 350 Mev)
antiproton on hydrogen.
It is not clear to the author whether
this value of the total cross section is free
from an ambiguity of the diffraction scattering. Considering the present stages of both
experimental and theoretical aspects of this
process, one may conclude that our crude
model is quite promising to predict the
annihilation cross section.
For a low energy antiproton, the
classical approximation adopted above will
break down, and an increase of the cross
section due to the wave mechanic2.l effect
is expected. We shall estimate critical
energy Ec (in lab. sys.), above which the
classical picture should be allowed. Suppose that an antiproton annihilation process
involves partial waves up to the order l
in the incident channel. Then Ec may be
found from the following equati.>n ;
l
0",==.1Z'x}2j(2l'+1),
ltc"'re, 1,;
1'=0
where
9X 10-13/VEc
"'c-"'
A
)
· M eV.
(E cln
(5)
Letters to the Editor
613
distribution inside the physical proton.
we have1l
Using eq. (3), we find
E 0 .::::.34 Mev
for l=O,
(ro,p) 2 = ) dr r2 [Pc (r) + p, (r)],
E0 =136 Mev
for l=l.
(ro,n) 2
and
If the 2ntiproton is captured by the proton
from the p-states beside the s-states, the
wave mechanical increase of the cross section
will be expected for the antiproton with
a kinetic energy smaller than E 0 .::::. 13 6
Mev. Such tendency was clearly seen in
the experimental results.
Finally, let us add a speculation about
the structure of the " physical" nucleon.
Recently, Sakata'> has proposed a new
theory of elementary p2rticles in which the
pion is considered as a composite. system
of the nucleon and the antinucleon. 5>
According to this model, a physical nucleon
is described in terms of (a bare nucleon)
(nucleon pairs). Thus, the diff-erence
of (1) and (2) can easily be understood6>
and it is m.tural to suppose that the annihilation of the 2.ntinucleon and the
nucleon should take place just after the
contact of the rims of the extended
nucleons.
+
1)
2)
3)
4)
D. R. Y ennie, M. M. Levy, and D. G. Ravenhall, Electromagnetic scructure of nucleons, to be
published ; Other references are cited in it.
The author is indebted to Prof. Y ennie for
sending him this preprint.
W. H. Earkas et. al., The antiproton-nucleon
annihilation procrss, to be published ; Other
referencEs are cited in it.
Z. Ko!::a and G. Takeda, to be published ; The
experimental rrsults are quoted in it.
S. Sakata, Prog. Theor. Phys. 16 (1956), 686
(L).
5)
6}
E. Fermi and C. N. Yang, Phys. Rev. 76
(1948)' 1739.
According to a conventional meson theoretical
picture of the physical nucleon, one can proceed
as follows: Let e(Jc (r) and ep.,. (r) be the core
pa" and the pion-cloud pare of the charge
=) drr [p
2
0
Then
(r) -p,(r)].
From the experimental results, eqs (1) and
(2), we can learn that the nucleon-core extends
over the radius=ro,p (';j:>fi/Mc, the nucleon
Compton wave length), which is difficult to
understand from the meson theories, see ref. 1) .