442
Letters to the Editor
Zero-zero Transition and ElectronNeutron Interaction
Y. Yamaguchi
D parlment of Physics, Osalca City Unive'l"sity
June 14, 1951
As is well known, the zerO-zero transitions can be explained in two different
manrwrs I); (i) the ordinary electro-magnetic
interaction between protons and eiecJrons and
( ii) the hypothesis of direct coupling between
nucleons and electrons. As for ot016, the
energy spectrum,2) the angular correlation of
the positron with respect to the electron 3) and
the life time4 ) are all in good agreement with
calculation based on (1). It seems, however,
to be of some interest to discuss the· assumption (ii) in connection with the electron
neutron interaction established by the excellent
experiment of Rabi et al.")
Let us assume the direct coupling of the
type ' )")
(1)
where !Jf and ¢ are the nucleon and electron
wave functions, respectively, analogous to
the interaction responsible to (1~decay. This
type of the interactions was extensively
examined by Nomoto. 6 ) According to him,
Letters to tlte Editor
the first forbidden transition of axial vector
coupling (0=((1, r5» with only the nuclear
matrix element Sr5 and the allowed transition
of pseudo-scalar coupling (0=r5, nuclear
matrix element J/h 5 ~ Jr 5) give the desired
energy spectrum 2) and all other cases are
rejected. (In the allowed transitions of scalar
and vector cases the nuclear matrix elements
J{j and J1 vanish in contrast to the correspoIJ.ding cases of (j-decay.) Nuclear matrix
element Sr5 changes the parity of the nucleus,
while the nuclear matrix element Sqr u* E r2qr •
all protOllS
(which we shall write briefly as Sr2 hereafter) in the ordinary electro-magnetic case
does not change the parity.
The parity change of the nucleus is the
most direct check of two explanations (i)
and (ii) .1) But there is no definite experimental evidence concerning parity change of
zero-zero transition.
The current nuclear
model favours to parity change "no" though
it is not decisive.
The angular correlation is as follows 7l :
1+0.95 cos () for electro-magnetic case,
1 + 0.91 cos () for axial vector case, (2)
and
1-0.91 cos () for pseudo-scalar case;
where () means the angle between electron
and positron. In these calculations we use
the plane wave for electron and positron wave
functions. Comparing the above results with
experimental one 1+0.85 cos (},S) we can
reject the pseudo-scalar case. If we assume
1Jr51 2 - 10- 2, as in the case of {j-decay, the
axial vector coupling constant must be the
following order of magnitude
g - 5 me~(e2/me2)S, m=electron mass, (3)
in order to fit the observed life time of "0 16
((7 ±0.7) 10- 11 ).4)
On the other hand we can explain. the
electron-neutron scattering on the basis of
phenomenological direct interaction of the
type (1). If we adopt the axial vector type,
the coupling constant is determined by the
443
electron-neutron scattering5) as follows:
(4)
Since (4) is quite small compared with (3),
we must give up to explain the zero-zero
transitions on. the assumption of direct
electron-nucleon coupling, unless the direct
(non-electro-magnetic) interaction between
electrons and protons is unreasonably greater
than the one between electrons and neutrons.
Therefore we may safely conclude that the
assumption (ii) mui!t be abandoned and only
the more reasonable explanation (i) remains.
Thus the parity change in zero-zero tranbition
is "no" and the parity of, e.g., "'0 16 must
be even.
As is discussed above the zero-zero transition is certainly caused by the ordinary electromagnetic interaction. Then we· can detemline
the values of nuclear matrix element Jr2
from the observed life times and the exact
expression for zero-zero transition probability:
1S1,212=
2.3 (2e2
1
.)4 for Ge72,
me-
3.7"
for 0
(m=electron mass).
(5)
16,
Thus the matrix element S1.2 seems to be
nearly independent of mass number A, which
is contrast with the expectation (J r 2ocR2oc
A"I., R=nuclear radius) 8) •
However the
similar situation occurs in the nuclear matrix
element of a-type transition of the first forbidden (j-decay ; i.e., the corresponding matrix
element B li , which is expected to be proportional to A'ia, is in fact known to be
nearly independent of A from the analysis
of the so-called ft-values. 9 ) And these facts
must be explained in parallel way.
Finally we want to add some considerations about SS2. It is very likely that the
positron!;! accompanying to the (j-decay of PS2
is originated from the zero-zero transition of
S32 as was pointed out by Nakano. IO ) Assuming the 1.38 MeV level of S82-nucleus
with zero spin and even parity, and using
Letters to the Editor
444
the value of nuclear matrix element:
8)
the mean life time of pair emission is estimated as
1.4""" 2.2 x 10- 6 sec.
According to Nakano/D) the ratio of electronpositron pair emission to orbital electron
Furthermore the
ejection is 38.0: 28.6.
angular correlation is
1+1.1cos8,
if we use the plane wave for electron and
positron wave functions. Since the estimated
life time for pair emission of S32 is rather
long, it must easily be measured. We hope
that these predictions about the zero-zero
transition of S32 will be soon checked experimentally.
I am deeply indebted to 1\'11'. Nakano
for several numerical calculations. The author
wishes to thank Professor Tanikawa and
Professor Nambu for their kind discussions.
R. Oppenheimer and J. Schwinger, Phys.
Rev. 56 (1939), 1066.
H. Vukawa and S. Sakata, Proc. Phys.-Math.
Soc. Japan 17 (1935), 397.
2) M. Kojima, Proc. Imp. Acad. Tokyo, 19
(1943), 282.
Rasmussen, Hornyak, and Lauritsen, Phys.
Rev. 77 t(195U), 617.
3) S. Devons and G. R. Lindsey, Nature 164
(1949), 539.
4) S. Devons, H. G. Hereward and G. R. Lindsey,
Nature 164 (1949), 586.
Also the life time of Ge72 has been measured
by J. C. Bowe et al. (Phys. Rev. 73 (1948),
1219 (A)).
5) W. W. Havens, L. J. Rainwater and I. I. Rabi,
Phys. Rev. 82 (1951), 34-5 (A).
6) M. Nomoto, Sci. Rep. Tohoku Univ., series I.
Vol. XXXIII, No.3 (1949), 157.
7) J. R. Oppenheimer, Phys. Rev. 60 (1941),164
(A).
These calculations are essentially the same as
the ones of electron-neutrino angular correlation in fl-deca y.
1)
J.
9)
10)
This conclusion is not in agreement with the
result of S. D. Drell (Phys. Rev. 81 (1951),
656 (A)). The differenee seems to come from
the following reason: while Drell used the
approximate formula (derived by Oppenheimer
and Schwinger, ref. 1)) valid at very large'
excitation energy (~mc2) and neglected the
Coulomb effect on the electron and positron
wave function, we have used the el<act expressio. valid for any value of excitation energy
and used the relativistic Coulomb wave functions for electron and positron when we
calculaled the nuclear matrix element (5) from
the observed life times.
J. P. Davidson, Phys. Rev. 82 (1951), 43.
T. Nakano, Prog. Thear. Phys. 6 (1951), in
press.