Letters to the Editor
220
+ (1/3)p(g2/477:) (e-x/x)
X (1+ (3/x) + (3/x 2»
X [1 +3aT (e-"'/ x) +3bT (e- x/ X)2JS12
+p.GLS(e- x / x) [aLAe-x/x)
+bis(e- z /x)2](L·S) ,
A Proton-Proton Potential
Tetsuo Hamada
The Daily Telegraph Theoretical
Department, School of Physics
University of Sydney
Sydney, N. S. W., Australia
A search has been going on for the
energy independent potential which is
consistent with the available pop scattering data. We report here on the
preliminary results.
Based on the belief that the potential
must have the one·pion-exchange tail,
we have assumed the following type
of potentials:
V+ (x) = - p. (g2/477:) (e-'"/ x)
X [1+1ao+ (e--"/x)
+ Ib&(e--"/x) 2] ,
= (1/3)p.(g2/477:) (e-"'/x)
X [1 +3ao (e- c/ x) +3bo (e- z / x) 2]
1
V ~ (x) Q12= - 0.0054p (e- x/ x 3) Q12,
Q12=1/2·[(L·Ul) (L'U2)
+ (L'U2) (L'UI)]'
There is some pion theoretical evidence
for a weak, although long ranged, QpotentiaP) We did not find such a
force useful for the triplet odd potential
(2).
The best over-all fit so far to the
experimental data has been attained for
the following values of parameters:
(t/477:) =0.08, Ixt=0.343, 3xo =0.32,
(1)
3V-(X)
wherep=pion mass,x=pr, and (g2/477:)
=effective pion-ncleon coupling constant. We have also assumed a hard
core of radius lXd and 3X I; for (1) and
(2), respectively.
The singlet even potential (1) with
the parameters given in (4) can reproduce the zero energy scattering parameters and at the same time ISO phase
shift of MacGregor et al.'s solution 1
(MMS 1) at 310 Mev. l ) This potential,
however, gives too large ID2 phase
shifts above 100 Mev. The difficulty
has been overcome by adding to (1)
a weak quadratic spin-orbit potential
(Q-potential)
where*
April 28, 1960
1
(2)
la~=10,
Ib6=9, 3ao =-9, 3bo =5,
* Q12=-l(l+l)
for the singlet states.
Letters to the Editor
sa;=-1.2, sb;=0.35, G.iS=-0.1474,
a£s= -0.75, bLS =7.9.
6
(4)
0----
,,I
,,
,
0-
:
\~oc!-;'_:_
In.
f
••
-o-_Q
~/
145Mev
95Mev
-L •
0
0
0
••
0
-- __________ ~_.:' __o__
.?_
Fig. 1.
As an illustration we show in Figs. 1 to
4 the observable quantities calculated
from (1) to (4) at 95 and 145 Mev.
Experimental points are taken from
Palmieri et al.,S) Hwang et al.,4) and
Bird et al. 5) At lower energies the fit
to the experimental data is quite satisfactory. At 310 Mev, on the other
hand, the phase shifts calculated from
the proposed potential are close to MMS
1 as shown in Table I.
Table I. Phase shifts at 310 Mev.
Entries are the nuclear Blatt·Biedenharn
phase shifts in radians.
0.3
P
0.2
I the calculated
from
I
potential (1) to (4)
0.1
0
-0.1
0---_
!
0-
-0.2 0
60
30
lSo
145Mev
95Mev
8
1D2
1G4
90
Fig. 2.
0;5 r--.--r---,--~-,--r_-r--~_,
D
/-J----t----y---------r----/'
t-
0~~_7,'~',L~~~--~~~~~~
o Harvard} 145Mev
o Harwell
---- 145Mev
95Mev
3Q
60
:0
90
Fig. 3.
0·---- 145Mev
R
221
-
116
sPo
sP1
sFs
sH5
sP2
sF2
E2
sF4
sH4
E4
sH6
sK6
Eo
-0.158
0.244
0.026
0.007
-0.198
-0.459
-0.069
-0.022
0.309
0.007
-0.101
0.080
0.001
-0.367
0.015
-0.006
-0.739
MMS 1
-0.156
0.207
0.013
-0.197
-0.480
-0.062
-0.020
0.291
0;020
-0.051
0.056
0.006.
-0.215
0.004
A full account, with some possible
refinements, will be published shortly.
95Mev
O~--------------------_--~--~~-{
Fig. 4,
1) M. H. MacGregor, M. J. Moravcsik and H.
P. Stapp, Phys. Rev. 116 (1959). 1248.
2) S. Okubo and R. E. Marshak, Ann. Phys.
4 (1958), 166.
3) J. N. Palmieri, A. M. Cormack, N. F. Ramsey
and R. Wilson, Ann. Phys. 5 (1958), 299.
222
4)
5)
Letters to the Editor
C. F. Hwang, T. R. Cphel, E. H. Thorndike,
R. Wilson and N. F. Ramsey, Phys. Rev.
Letters 2 (1959), 310.
L. Bird, D. N. Edwards, B. Rose, A. E.
Taylor and E. Wood, Phys. Rev. Letters
<l (1960), 302.