Nuclear Physics A382 (1982) 242-254
© North-Holland Publishing Company
ANALYZING POWERS AND CROSS SECTIONS
IN ELASTIC p~ SCATTERING AT 65 MeV
H. SHIMIZU, K. IMAI', N. TAMURA and K. NISIMURA
Department o/Physics, Kyoto University, Kyoto 606, Japan
K. HATANAKA and T. SAITO
Research Center for Nuclear Physics, Osaka University, Osaka 565, Japan
and
Y. KOIKE and Y. TANIGUCHI
Depurtnaent of Nuclear Engineering, Kyoto Universitti~, Kyoto 606, Japan
Received 30 December 1981
Abstract : Analyzing powers and differential cross sections for ß-d elastic scattering have been measwed at
64 .8 MeV. The angular distributions cover center-of-mass angles between 8° and 169° . The relative
uncertainties of the analyzing power measurement are typically ±0 .005 at c.m . angles less than
80° and are in general ±0 .015 at the remaining angles . The absolute scale of the analyzing power
measurement has an uncertainty of f 0.013 . The data are compared with three-body calculations
based on the Faddeev theory. In contrast with the differential cross sections, the analyzing powers
could not be reproduced without the D-wave nucleon-nucleon interactions .
E
NUCLEAR REACTIONS ZH(polarized p, p), E = 64.8 MeV; measured A(B), Q(B) . Threenucleon Faddeev theory .
I . IIItCOduCtIOu
The goal ofstudies of the p-d system is to obtain the detailed information about the
NN interaction. In the last two decades the p-d system has recEived much attention
from both theorists and experimentalists and a great deal of work on the system
have been performed. Especially, in cooperation with the development of polarized
ion sources, there has been acquired a lot of polarization data of the p-d system at
energies below 50 MeV. The present work has intended to extend the analyzing
power data of p-d elastic scattering up to 65 MeV. Based on the success of three-body
calculations at lower energies, the present data will be useful in extending the calculations so as to include the effect ofhigher partial waves. The Coulomb effect is expected
" Present address: High Energy Physics Division, Argonne National Laboratory, Argonne, USA.
242
H. Shimiru et al . / Analvzing poss~ers
2q3
to be negligibly small at 65 MeV. This is one of the merits of this experiment in comparing the data with three-body calculations .
It is difficult to solve the Faddeev equations with a realistic local potential including higher partial wave two-nucleon interactions . The use of separable interactions makes the calculation considerably easy though it is difficult to construct a
"realistic" separable potential, or to make a reasonable separable approximation to
a realistic t-matrix . We estimate the role of higher partial waves of the NN interaction
assuming simple Yamaguchi-type separable potentials and compare results of the
calculation with the present data at 65 MeV.
2. Experiment
The experiment was performed with a polarized proton beam from the AVF
cyclotron at Research Center for Nuclear Physics, Osaka. The polarized proton
beam from the AVF cyclotron was transported to an experimental area and focused
onto a deuterium gas target cell . The beam spot at the target position was about
2 mm in diameter. After passing through the target, the beam was refocused onto
the second target of a 300 ~m thick CH2 film, used as a beam polarimeter, and
subsequently collected in a well-shielded Faraday cup. The beam intensity was
10-80 nA on the target . The beam charge was integrated using a standard current
integrator with an absolute accuracy of 0 .1 ~.
A schematic view of the experimental set-up is shown in fig. 1 . The gas target cell
was a cylindrical cell of 26 .6 cm outer diameter with 25 ~m Mylar windows positioned
on the central post of the scattering stand. This cell contained deuterium gas at a
pressure of about 1000 Torr. The pressure and temperature of the deuterium gas
were monitored continuously during the runs with a precision electric pressure gauge
and an electric thermometer, with accuracies of ±2 Ton and 0.2 °C, respectively .
For the extreme forward angles of 5.5°-18° lab, another gas cell, 32 cm in outer
diameter, was used. This cell is same one used in the previous 13- 4He scattering
experiment ' ).
Particles scattered from the target were detected with two pairs of detector systems.
The detector systems in each pair were placed at a 20° interval on one of the arms of
the scattering stand. Measurements were made with the scattering stand arms at
equal angles on opposite sides of the beam . Detectors for smaller angles were intrinsic Ge detectors and those for larger angles NaI(T1) scintillators. The collimatoon
system used with each of the counter assemblies consisted of front and rear collimators between which an evacuated tube was placed in order to reduce the ef%ct of
multiple scattering due to the air. The angular acceptance of the collimators was
± 1° at larger angles than 20° lab. For measurement in the small angular region, it
was limited to ±0.4°. The energy resolution of the intrinsic Ge detectors was about
0.3 ~ which was sufficient to discriminate contaminants . The scattering angles could
be read with an accuracy of ±0.05°. The angle scale was calibrated by cross-over
N. Shimizu e! al . l
Analyzing powers
a~
Y
C
O
m
4
C
C
E
â.
K
N
NO
N~
OU
O
+~ >
-_~ a~
Nv
~..
O
3
u
.'>
.U
W
.t!
Oq
LL,
H . Shimizu et
al. ~ Analyzing powers
245
angle measurements of p-p elastic scattering and p- 12C inelastic scattering with a
CH4 target. A NaI(Tl ) scintillation detector was used as a monitor at a fixed angle of
B = 30° in the vertical plane.
The beam energy was evaluated to be 64.8 MeV by passage through a momentum
analyzing magnet, the field of which was monitored with a NMR device . The beam
polarization was monitored continuously during the runs by the beam polarimeter,
in which a pair of NaI(Tl) scintillation detectors were placed at angles of 47.5°
symmetrically to the beam direction.
The data for larger angles than 20° lab were taken with the old spin handling
system in which the sign of the beam polarization was switched every few seconds by
reversing the magnetic field of the ionizer at a polarized ion source . The false asymmetry correlated with the reversal of the spin direction was checked by using a nearly
unpolarized proton beam which was produced by turning ofF the radiofrequency
oscillator power of the r.f. transition section of the ion source . The artificial asymmetry caused by possible displacements or angular shifts of the beam correlated with
the reversal of spin direction was negligibly small .
The measurements at forward angles between 5.5° and 18° were made after installation of the new spin handling system in which a sequence of weak-field and
Detector
(Left 2)
Detector
(Right 2)
Up Gate
Fan-out
Spin Fllp
Controller
Pol . Ion
Source
u
Down Gote
Fan-out
Fig . 2 . Block diagram of the electronics . SCA : single channel analyzer ; ADC : analog to digital converter.
H. Skimi~u et al. l Ana1yzing poK~ers
246
strong-field r.f. transitions was used in the polarized ion source and the change in
sign of the beam polarization was obtained by switching these two transitions
alternately . The possibility of displacements or angular shifts of the beam correlated
with the reversal of the polarization axis was removed completely in this system .
The switching frequency was 2 Hz.
The electronic instruments consisted of standard linear electronic modules and
multichannel pulse-height analyzers. A block diagram of the electronics is shown in
fig. 2. The dead-time corrections applied to the data by means of scalers never
exceeded 1 .5 ~.
3. Results
The numerical results of our experiment are presented in table l . The analyzing
power A(B) was given by
r-1
A(9) - t
r+ 1 '
PB
with a geometric mean ratio
r =
L?~Rl
JLl . Rj
TABLE 1
A(B) and dQ/did(B) in ßd elastic scattering at 64 .8 MeV
c . m . angle
B(deg)
Particle
detected
p or d
8 .37
9 .14
10.66
12.18
15 .21
18 .24
21 .27
23 .53
24 .28
26 .54
27 .29
30 .29
34 .02
37 .73
41 .43
45 .10
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
Analyzing power
A(B) fdA(B)
0 .1286
0 .1457
0 .1518
0 .1502
0 .1524
0 .1677
0 .1785
0 .1921
0 .1952
0 .2025
0 .1912
0 .2217
0 .2337
0 .2445
0.2472
0.2413
0 .0051
0 .0050
0 .0043
0 .0046
0 .0048
0 .004b
0 .0045
0 .0034
0 .0049
0.0038
0 .0058
0.0047
0.0038
0 .0043
0.0059
0.0056
Differential cross section
da /dl3(B)±ddaJdid(B)(mb/sr)
22 .09
21 .87
23 .89
26 .33
29 .02
29 .23
27.82
26 .33
25 .77
23 .98
23 .41
21 .17
18 .07
15 .26
12 .77
10 .68
0.40
0.31
0.27
0.29
0.33
0 .34
0 .33
0 .27
0 .30
0 .25
0 .29
0 .22
0 .19
O .16
0 .14
0 .12
H. Shimizu et al. / Analyzing gorets
247
TABLE 1 (continued)
A(0) and da /df2(0) in ßd elastic scattering at 64.8 MeV
c . m . angle
0(deg)
48 .02
52.36
53.08
55 .95
59.50
63 .02
66.51
69 .96
73 .36
76 .06
80 .05
83 .32
86 .54
90 .29
90 .44
92 .83
94 .56
95 .89
98 .90
99 .57
101 .26
104.58
109 .59
110 .33
115 .60
119 .62
120 .77
124 .64
129 .66
134 .69
139 .72
144.75
147 .76
148 .77
151 .80
155 .82
159 .85
163 .SR
165 .90
167 .91
168 .92
Particle
detected
p or d
p
p
p
p
p
p
p
p
p
p
p
p
p
p
d
p
d
p
p
d
p
d
d
p
d
d
p
d
d
d
d
d
d
d
d
d
d
d
d
d
d
Analyzing power
A(0) fdA([1)
0 .2404
0 .2265
0 .2189
0 .2035
0 .1664
0 .1381
0 .0815
-0 .0030
-0 .071
-0 .1118
- 0.194
-0 .270
-0 .323
-0.362
-0 .394
-0.471
-0.480
-0.496
-0.539
-0 .518
-0 .577
-0 .612
-0 .589
-0 .593
-0 .547
-0 .492
-0 .473
-0 .410
-0 .266
-0 .017
0 .133
0 .178
0 .178
0.226
0.270
0.183
0.154
0 .050
0.037
0 .082
0 .064
0.0067
0.0080
0 .0069
0.0059
0 .0073
0 .0063
0 .0068
0 .0084
0 .010
0 .0094
0 .014
0 .015
0 .013
0 .017
0 .014
0 .015
0.016
0 .017
0 .025
0 .017
0.018
O.OlS
0 .015
0.020
0 .015
0 .014
0 .025
O .Ol6
0 .013
0 .013
0 .015
0 .012
0 .032
0 .010
0 .027
0 .019
O .Ol7
O.OlS
O.Ol3
0.017
0.021
Differential cross section
da/df?(0)±dda/df2(0)(mb/sr)
9 .22
7 .330
7 .038
6 .086
5 .064
4 .247
3 .640
3 .127
2 .700
2 .433
2 .062
1 .928
1 .766
1 .596
1 .588
1 .494
1 .457
1 .355
1 .301
1 .357
1 .249
1 .205
1 .102
1 .098
1 .054
1 .021
0 .971
0 .932
0 .873
0 .898
1 .036
1 .271
1 .60
1 .690
2 :00
2 .78
3 .59
4.45
5 .00
5 .52
6.14
0 .10
0 .085
0 .075
0 .065
0.055
0 .045
0 .039
0.035
0 .031
0.028
0.026
0.024
0.022
0.022
0.083
0.020
0.077
0.018
0 .028
0 .072
0.018
0 .064
0 .058
0 .017
0 .055
0 .053
0 .017
0 .049
0 .045
0 .046
0 .054
0 .066
O .14
0 .086
0 .15
0 .14
0 .16
O.18
0 .17
0 .26
0.34
The quoted errors are relative only . Normalization uncertainties for the analyzing power and cross
section data are 1 .3 ~ and 1 .4 %, respectively.
H . Shimi~u et al. / Analy~=inp poss~ers
248
by which instrumental asymmetries were eliminated . Here L and R denote the number
of counts for proton scattering to the left and right, respectively, and the arrows
indicate the spin direction . The beam polarization Pe was determined from the data
taken simultaneously with the beam polarimeter . Differential cross sections were
evaluated by averaging over the numbers of Lj, Ll, RT and RJ, . The data were
corrected for the effects ofnuclear reactions in the intrinsic Ge and NaI(T1) detéctors
using various published results i . 3) .
The relative uncertainties in A(B) in the table include the errors due to the counting
statistics of elastically scattered protons or of recoil deuterons with uncertainties in
the background and inelastic subtractions and the statistical errors for polarimeter
yields . The uncertainty in the analyzing power of polarimeter 4), which was estimated
to be ±0.013, is not included in the errors in the table.
p-d
dp/ds2 (mb/sr)
64 .8 MeV
100
10
0
20
40
60
80
100
120
140
160
180
ec .m .
Fig. 3 . The differential cross section da/dL1(B) in p~ elastic scattering at 64 .8 MeV. The curves are
calculated results with three different potential sets . Thedashed curve represents the three-body calculation
result for the potential set YY7-P . The dotted curve corresponds to the result for the set YY7-P-D' . The
solid curve is for the set YYO-P-D .
249
H. Shimizu et al. / Analyzing powers
p-d
0
20
40
60
80
100
64 .8 MeV
120
140
160
180
ec,m
Fig. 4. The analyzing power A(B) in p-d elastic scattering at 64 .8 MeV. The curves are three-body calculation results, as described in the caption of Pig. 3.
The angular distributions of the differential cross section Q(B) and the analyzing
power A(6) at 65 MeV are shown in figs . 3 and 4. The figures also show the results of
three-bony calculations which will be described in detail in the following section .
250
H . Shimizu et al. / Analyzing powers
4. Calculation
In momentum space, the Yamaguchi-type separable potential can be written as
v~(P, P) _ %~~9~(P~~(P),
where the two-body channel c can be characterized by the usual spectroscopic
notation such as 1 So, 3 P1 . The form factor in eq. (3) is
where l is the orbital angular momentum of the interacting pair . The two states 3 S 1
and 3 D 1 couple with each other by the tensor force. According to Yamaguchi S), the
form factor ofa rank-1 separable potential for the coupled state is given by a sum of
the 3 S1 and 3 D1 states,
with
P +ßo
(P +ßz)
s(P) _ (3~Pz)(Qa .p)(Q°'P)-(an .Q~) .
(()
We use a rank-1 potential YY7 obtained by Phillips e) in the coupled state. As is
well known, this potential predicts a Hulthén-type deuteron wave function with 7
D-state probability.
In this paper we use three potential sets with separable potential discussed above.
The simplest potential set YY7-P contains separable potentials in'S °, 3S,-3 D1 , and
all P-waves of the NN interaction. This potential set was used in the first work of
Doleschall'), and was also used in the breakup calculation by Bruinsma 8). Recently
it was shown that the low energy data of ~-d elasticscattering offered from Tsukuba
could be reproduced fairly well by this simple potential set 9). This set does not
contain any D-wave interaction except for the 3 D, wave. And the 3 D1 wave phase
shift is not reproduced at all by this set. At the present energy, however, it is expected
that the D-wave interaction would play an important role .
In order to discuss the role of the D waves, we introduce two more sets. We add
Yamaguchi-type separable potentials obtained by the Graz group 1°) for 1 Dz, 3 Dz,
3D3 waves to the potential set YY-P. This potential set is referred to as YY7-P-D',
which reproduces phase shifts in all of the S-, P-, and D-waves fairly well except for
the 3 D1 wave and the mixing parameter. The set YY7-P-D' fails to reproduce the 3D1
wave phase shift because a rank-1 separable potential is used for a complicated
3S,-3 D1 coupling state. One might overcome this difficulty by introducing higher
rank separable potentials. However it is very difficult to reproduce the 3 S1, 3 D1
phase shifts and the mixing parameter at the same time even if a higher rank separable
potential is used .
potential
P-waves,
5and
choice
potential
one
Same
we
of
This
a3Dt
3S,
introduce
standard
(mb/sr)
of
variable
asofthe
we
procedure
set
itfig
waves
introducing
while
and
Numerical
20
issolved
in
YYO-P-D
3,well
potential
the
3Dt
but
partial-wave
the
are
aKeeping
3Dt
the
known
rank-1
it
separately
corresponds
40
tensor
the
by
accuracy
solid
astate
the
higher
In
same
using
curve
that
Yamaguchi-type
all
this
Shimizu
force
deuteron
60with
decomposition,
Coulomb
aspartial
inrepresents
rank
was
athe
set,
to
those
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mainly
Padé
etform
achecked
proton
80
potentials
al
separable
cut-ofI'
is
efFect
/waves
in
completely
to
approximant
Analyzing
factor
the
YY7-P-D'
determines
reproduce
analyzing
results
100
by
separable
of
we
discussed
(4)
potential
in
comparing
the
64
powers
obtain
for
all
in
tensor
120
the
MeV
the
We
both
tensor
partial
power
and
potential
potential
coupled
into
above
3St
parametrized
force
the
phase
140
analyzing
isstate
waves
the
reported
method
mainly
set
in
integral
In
coupled
into
shifts
YYO-P-D
Thus
the
the
except
160
each
determined
low~nergy
amplitudes
powers
to
three-body
of
simultanewe
equations
3St-3D,
obtain
contour
including
for
partial
obtain
180 the
Ina
H.
Instead
state,
wave
ously .
experiment,
by
this
a
3St
.
25 1
.
.
.
new
After
with
equations,
deformation .
.
~-d
dCVd52
100
10
0
Fig. .
.
.
.
ec .m.
the
.
.8
.
252
H. Shimizu et al. / Analyzing powers
U
20
40
60
80
p-d
64,8 MeV
100
120
140
160
180
ec .m .
Fig. 6. Same as fig . 4, but the solid curve is the result for the set YYO-P-D including the Coulomb etFect.
H. Shimizu et al.
/ Analyzing
po~rers
25 3
in the low-energy region 9). Three-body partial waves up to J = 'z' are added to
construct the full scattering amplitude.
5. Discussion
The experimental data are compared in figs . 3 and 4 with three-body calculations
based on the Faddeev theory . The curves show differential cross sections and analyzing powers of 1~-d elastic scattering at 65 MeV calculated with three different sets of
potentials . The dashed curves are results for the potential set YY7-P and the dotted
curves are those for the set YY7-P-D . The solid curves are calculations with the set
YYO-P-D. The analyzing powers calculated with the three potential sets are significantly different. The figures indicate that calculations with the potential set YYOP-D are close to the experimental data. The potential YY7-P fails to reproduce the
analyzing power data. Thus, in order to reproduce the analyzing powers, it is necessary to use the potentials which can reproduce the NN D-wave phase shifts well.
Though the prediction of the differential cross section is not so sensitive as in the case
of the analyzing power, the set YYO-P-D reproduce the cross-section angular
distribution better than the others, especially in the region between 50° and 120°.
These mean that the D-wave part of the NN interaction plays an important role in
the p-d system at 65 MeV.
Recently Doleschall introduces the Coulomb effect in the amplitude of p-d elastic
scattering
~L~Tr d~Li = < L~ ndlGié(aL+a,, .~+~LITCaaI~L~ .
We estimated the Coulomb effect by this method in the amplitude of YYO-P-D.
Figs . 5 and 6 show the results. A remarkable improvement was obtained by including the Coulomb effect in the forward angular region . On the contrary, there is
no visible effect of Coulomb interaction in the backward region . More advanced
calculation is now in progress.
The authors wish to express their thanks to the cyclotron crew at Research Center
for Nuclear Physics for their efficient operation of the accelerator. They are grateful
to Drs. Y. Wakuta, H. Hasuyama and H. Sato for their ~rticipation in the early
stages of this work.
The computer calculation for this work was financially supported by Research
Center for Nuclear Physics, Osaka University.
254
H. Shimizu et al. / Analyziny powers
References
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