Measurements of analyzing powers Ay, Axx, Ayy and Axz in dp elastic scattering at Ed = 56 MeV

Nuclear Physics A426 (1984) 77-91 © North-Holland Publishing Company

M E A S U R E M E N T S O F A N A L Y Z I N G P O W E R S Ay, A,~, Ayy A N D Ax~ I N dp E L A S T I C S C A T T E R I N G AT Ed = 5 6 MeV K. HATANAKA*, N. MATSUOKA, H. SAKAI, T. SAITO, K. HOSONO, Y. KOIKE and M. KONDO

Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567, Japan K. IMAI, H. SHIMIZU**, T. ICHIHARA and K. NISIMURA***

Department of Physics, Kyoto University, Kyoto 606, Japan and A. OKIHANA

Department of Physics, Kyoto University of Education, Kyoto 612, Japan Received 2 March 1984 Abstract: The differential cross section and all components of the analyzing powers .4, A~, Ayy and Ax~ have been measured in dp elastic scattering at 56 MeV. This is the first measurement of A~z in the cyclotron energy region. Axz has been measured with the beam polarized in the horizontal plane using the polarization tagging method. Faddeev calculations have been performed for four cases of the NN interaction. The Coulomb correction gave smaller effects at the present energy than at lower energies. Three of them reproduce the experimental data well. The agreement between the calculations and data for Axz was better than that reported at lower energy. The deuteron asymptotic D- to S-state ratio has been obtained and is consistent within the limits of uncertainty with previously obtained values. NUCLEAR REACTIONS IH(polarized d, d), E = 56 MeV; measured ~(0), Ay(O), Axx(0), Ayy(0), Axz(O ). Faddeev calculations. Obtained asymptotic D- to S-state ratio.

1. Introduction I n recent years the n u c l e o n - d e u t e r o n scattering process has b e e n investigated extensively b o t h e x p e r i m e n t a l l y a n d theoretically. A theoretical m e t h o d to investigate details o f the n u c l e o n - n u c l e o n ( N N ) i n t e r a c t i o n s t h r o u g h n u c l e o n - - d e u t e r o n scattering has b e e n d e v e l o p e d u s i n g F a d d e e v t h e o r y 2). Sophisticated c a l c u l a t i o n s i n c l u d i n g h i g h e r - r a n k i n t e r a c t i o n s a n d P- a n d D-waves have b e e n made. There has also b e e n a r e n e w e d interest in d p elastic scattering for s t u d y i n g the a s y m p t o t i c D-state to S-state ratio o f the d e u t e r o n wave f u n c t i o n 3). * Present address: The Institute of Physical and Chemical Research, Wako, Saitama 351, Japan. ** Present address: High Energy Physics Division, Argonne National Laboratory, Argonne, USA. *** Present address: Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188, Japan. 77

78

K. Hatanaka et al. / tip elastic scattering

At energies lower than 22 MeV, all of the vector and tensor analyzing powers have been measured in dp elastic scattering [refs. ~,4-9), and references therein]. In a recent data analysis using Faddeev theory, the tensor analyzing power T21 was not well reproduced in comparison with other analyzing powers 9). At higher energies, T2~ has not been measured yet and measurements have been limited to other components of the analyzing powers 8,to), because it has been difficult to obtain a deuteron beam polarized in the horizontal plane by a cyclotron. It is of particular interest to measure all components of the analyzing powers including the T2~ (or Axz) in order to compare them with Faddeev calculations at higher energies. Here we report the results of measurements and Faddeev calculations, and comparisons made between them. The quantities tr(0), Ay(0), Axx(0), Ayy(O) and Axz(O) were measured in dp elastic scattering at 56 MeV. Ax, was measured with deuterons polarized in the horizontal plane employing the polarization tagging method which was recently developed ~). Faddeev calculations were performed with four different sets of N N interactions. The asymptotic D-state to S-state ratio of the deuteron wave function was obtained using the present data. The experimental procedure and results are given in sects. 2 and 3, respectively. Faddeev calculations are presented in sect. 4 and compared with the experimental data, The asymptotic D-state to S-state ratio is obtained in sect. 5. A summary is given in sect. 6.

2. Experimental procedure 2.1. MEASUREMENTS OF tr, A~, Axx AND Ayy The present experiments were performed with 56 MeV polarized deuterons from the AVF cyclotron at Research Center for Nuclear Physics (RCNP), Osaka University. Polarized deuterons were produced by use of an atomic-beam-type polarized ion source ~2). Polarization states were selected by combinations of the r.f. transitions. They are summarized in table 1. The beam polarization was changed every second. The polarized deuteron beam from the cyclotron was momentum-analyzed and focused onto a target. After passing through the target, the beam was refocused onto the second terget of a 30-120 v~m thick CH2 film, used as a beam polarimeter, and subsequently collected in a Faraday cup. The differential cross section tr and the vector and tensor analyzing powers Ay, Axx and Ayy in dp elastic scattering were measured with a beam whose quantization axis was aligned vertically. The measurements were performed with three detectors placed at the same angle in the horizontal (left and right) and vertical (up) planes t3). The cross section measured by a detector in the horizontal plane is given by ~4) or(O) = cro(O)(1 + ~pzAy +½p~zAyy),

(1)

where tro is the cross section with an unpolarized beam and the plus and minus

tC Hatanaka et aL / dp elastic scattering

79

TABLE 1 Beam polarizations used in the present experiments

Ideal polarization

Actual polarization

Transitions (2-6) + (3-5) (1-4)

(2-6) (3-5)

P~

P=

Pz

Pzz

_2a

0

~(e2 + e3)

e2 - e3

0

--2E 1

2

±3 ½

1 -1

½e2 ~e3

0

e2 - e3

el, e2 and e3 are the elticiencies of the 1-4, 2-6 and 3-5 transitions, respectively.

signs c o r r e s p o n d to the left and right detectors, respectively. This m e t h o d provides a set o f eight countings at a given scattering angle 0. The set o f equations were solved for O-o, Ay a n d Ayy by taking suitable combinations o f the eight countings to minimize the systematic errors. The cross section by a detector in the vertical plane is written a s 14) or(O) = O'o(O)(1 +lp=A=).

(2)

The tensor analyzing p o w e r A,= was obtained from the f o u r countings o f the u p detector. The h y d r o g e n gas was used as a target and filled in a 38 cm diameter scattering c h a m b e r with 25 ~ m mylar windows. The entrance and exit o f the c h a m b e r were sealed with 10 i~m thick havar foils. The pressure and temperature o f the h y d r o g e n gas in the c h a m b e r were monitored continuously during the experiments with a precision electronic pressure gauge and a thermometer, respectively. The typical gas pressure was 820 Torr at 20 °C. A double-slit system was used to define the scattering angle. The laboratory angular resolution was 4-0.7 °. The b e a m polarizations were m o n i t o r e d continuously during the experiments by a ]2C polarimeter and were 7 0 - 8 0 % o f the ideal values in table 1. The b e a m intensity on the target was adjusted between 10 and 100 n A in order to keep the signal count rate in each detector a b o u t 1 kHz. The scattered deuterons were detected in the laboratory angular range between 10° and 18 ° in 1° steps and the recoil p r o t o n s between 10 ° and 60 ° in 2 ° steps. E a c h counter telescope consisted o f a 300 fxm thick transmission-type Si detector and a 25.4 m m thick NaI(T1) scintillation detector. Particle identification was m a d e with AE a n d E signals. The overall F W H M energy resolution was about 600 keV. At the b e a m polarization monitor, a pair o f 9 m m thick NaI(T1) scintillation detectors were placed at 47.5 ° to the b e a m direction in the horizontal plane.

K. Hatanaka et al. / dp elastic scattering

80

2.2. MEASUREMENTS OF Axz

The tensor analyzing power Ax~ was measured with the beam polarized in the horizontal plane. The spin direction was rotated into the horizontal plane by a Wien filter installed just downstream the ion source. When the beam polarized in the horizontal plane is accelerated by the cyclotron, the spin precesses around the vertical magnetic field. Since the precession angle of the spin is related to the rotation angle of the ion, the distinction of the turn numbers of accelerated ions makes it possible to determine the spin precession angle. The beam from the ion source was pulsed and injected into the cyclotron in order to distinguish the turn numbers of the extracted beam by means of the time-of-flight method. The procedure (polarization tagging method) for determining the angle between the polarization axis and the beam direction is described in detail in ref. ~1). Axz was measured using the detectors placed at a symmetric angle to the beam direction in the horizontal plane. In this case the cross section is given by 14) tr(0) = tro(0)[1

:r½pzzAxzsin 2/3 +lpzz(Axx- A y y )

+¼pz~A~z(3 cos 2/3 - 1)],

sin 2/3 (3)

where /3 is the angle between the spin quantization axis and the incident beam direction, and the minus and plus signs correspond to the left and right detectors, respectively. Two polarization states (p~, p~) = (½, l) and (½, - 1 ) in table 1 were used. Axz was then determined by the equation

Ax~

1

rNL-N.~+.+N~-N~I

pz~ sin 2/3 L N [ + NL

N~ + N~J'

(4)

where the quantity N~, for example, denotes counting in the left detector with positive tensor polarization. The angle/3 was determined from the least-squares fit to the horizontal polarization using a sine function 11). The measurements were carried out using a beam which had the angle/3 of about 45 °. The beam-transport system and the detector system were same as those for measurements of other analyzing powers. A 120 I~m thick CH2 foil was used as a hydrogen target for the measurements of A~. A single slit was used in this case and the laboratory angular resolution was +0.5 °. The beam polarization was continuously monitored with the carbon polarimeter during the experiments and was 80-90% of the initial polarization at the ion source.

3. Experimental results The results of the present experiments are shown in fig. 1 and the numerical values are given in tables 2 and 3. The errors indicated are the statistical ones only. The effects of nuclear reactions in NaI(T1) detectors were corrected by using published results 16,~7).The uncertainty of the absolute normalization of the differen-

K. Hatanaka et aL / dp elastic scattering __-

I

I

I

I

[

I

l

81

I

d-p

Ed=56MeV "C" 102 111

-

-~.~.....

-

E 101

- - GRAZ Tr

I

10

d

I

Ay

r

I

--

I

1,

J

80 120 e C. rn.(deg.) (a)

40

0.5

l

\~.

I

1

I

160

I

/

~_p

--

Ed=56MeV

**

0.0

-0.5

_

--

4T4B

_

- -

GRAZ

l

I 40

I

]I

I

I

i

80 120 e c.m.(deg.)

f 160

0a) Fig. 1. The differential cross section and the vector and tensor analyzing powers for dp elastic scattering at 56 MeV. The solid and dashed curves show the results of Faddeev calculations with the NN interactions 4T4B and GRAZI1, respectively. The dotted curves show the results of calculations using GRAZII without the Coulomb correction. tial cross section was estimated to be 3%. T h e u n c e r t a i n t y was m a i n l y due to the b e a m integration. The v a l u e of the vector a n a l y z i n g p o w e r Ay used for the elastic scattering b y t2C was 0.433 +0.045 at 56 M e V a n d 47.5 ° [ref. ~s)]. The u n c e r t a i n t y in the n o r m a l i z a t i o n of the a n a l y z i n g p o w e r for the c a r b o n p o l a r i m e t e r caused a n o r m a l i z a t i o n error o f 10% in the a n a l y z i n g - p o w e r m e a s u r e m e n t s .

K. Hatanaka et aL / dp elastic scattering

0.5 Axx

i

_

I

I

I

I

I

'4

d-p

~ d -= 5~6Me ' ~v E

0.0

-

~ 4 T 4 B

-

--

-

-

GRAZ

-0.5

-i

I

0

I

i

40

i

i

i

80 120 8 c.m.(deg.)

160

(c)

_1

Ayy

I

1

I

I

I

I~

I

q

~-p Ed=56MeV

0.5

-

/7

~/

-

0.C _

--

4T/-,B -

i o

40

GRAZ'IT

I

I

i

80 120 8 c.m.(deg.)

(d) Fig. 1. cont.

I

l 160

83

K. Hatanaka et aL / dp elastic scattering

I

I

I

I

I

I

I

I

i

_ p

05-

t

Axz _--

0.0 -.__<_=a~_~, • r

_

;

E d ~ !

-

i

r

]

/-,T 4 B

-

- - GRAZ"IT 0

1

/-.0

I

I

I

80 120 e c.m.(deg.)

I

160

(e) Fig. 1. cont.

The analyzing powers obtained in the present experiments have larger values than those at lower energies. The energy dependence of the analyzing powers was discussed by Sawada et al. for deuteron energies from 10 to 22 MeV [ref. 9)]. The present results and the values calculated by extrapolating their empirical formulae to the present energy'of 56 MeV are compared in table 4. It is rather surprising that the experimental values agree with the predictions fairly well, although the scattering angle corresponding to the maximum value of each analyzing power is slightly different from that at lower energies. 4. Faddeev calculations

Faddeev calculations were performed with four sets of N N interactions. We included the 1So, ~P~, 3Po,~,2, ID2 a n d 3D2,3 waves and the 351-3D I coupled wave. The same potentials were used for all the waves except for the 381-3D I coupled wave. In the 'So wave, a rank-2 separable potential G R A Z I I ,8) was introduced instead of a rank-1 Yamaguchi-type separable potential used in ref. 9). This force GRAZ II in the ~So wave reproduces well the recent phase shift in the ISo pn wave 18). Since the incident energy in the present experiment is considerably higher than in previous cases 1,9,19), it is necessary to include D-wave interactions. For the P- and D-waves, rank-1 separable potentials of ref. 20) were used. They reproduce the phase shifts of the P- and D-waves very well.

K. Hamnaka et al. / dp elastic scattering

84

TABLE 2 dp elastic scattering at 56 MeV 0. . . . (deg)

dtr/d/2 (mb/sr)

±A d~r/d/2 (mb/sr)

Ay

a:AAy

30.50 33.62 36.78 39.96 43.17 46.42 49.71 53.05 56.45 59.35 63.33 67.31 71.29 75.27 79.26 83.25 87.25 91.25 95.25 99.26 103.27 107.28 111.30 115.32 119.35 123.38 127.41 131.44 135.48 139.51 143.56 145.58 147.60 149.62 151.65 153.67 155.69 159.74

66.0 63.7 58.5 54.5 50.3 46.9 42.8 39.3 35.3 30.2 26.7 23.5 20.5 18.07 15.70 13.65 11.92 10.33 8.85 7.60 6.34 5.35 4.42 3.63 2.87 2.39 2.19 2.33 3.02 4.52 6.88 8.57 10.45 12.06 14.85 17.44 20.40 27.40

0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.04 0.04 0.04 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.05 0.10 0.07 0.13 0.10 0.19 0.12 0.27

0.043 0.041 0.038 0.039 0.039 0.028 0.037 0.024 0.016 0.009 -0.005 -0.027 -0.042 -0.057 -0.082 -0.110 -0.128 -0.154 -0.176 -0.196 -0.206 -0.232 -0.233 -0.187 -0.159 -0.061 0.096 0.224 0.290 0.310 0.239 0,219 0.198 0.185 0.146 0.117 0.101 0.060

0.006 0.007 0.007 0.005 0.004 0.006 0.006 0.005 0.005 0.004 0.004 0.008 0.008 0.009 0.009 0.009 0.010 0.009 0.010 0.010 0.009 0.010 0.010 0.009 0.009 0.009 0.009 0.010 0.011 0.014 0.012 0.021 0.012 0.021 0.011 0.019 0.013 0.019

A~x

-0.045 -0.052 -0.062 -0.064 -0.081 -0.086 -0.101 -0.123 -0.127 -0.152 -0.155 -0.169 -0.134 -0.120 -0.098 -0.059 0.013 0.058 0.137 0.206 0.313 0.389 0.375 0.298 0.006 -0.312 -0.550 -0.641 -0.583 -0.515 -0.497 -0.475 -0.399 -0.342 -0.279

±AA~

0.003 0.005 0.003 0.006 0.004 0.006 0.004 0.006 0.006 0.012 0.013 0.014 0.013 0.012 0.013 0.012 0.012 0.013 0.013 0.014 0.014 0.016 0.014 0.014 0.012 0.015 0.023 0.018 0.016 0.025 0.017 0.027 0.015 0.021 0.016

Ayy

-t-AAyy

0.037 0.039 0.033 0.018 0.045 0.050 0.042 0.059 0.070 0.076 0.082 0.094 0.123, 0.145 0.151 0.148 0.179 0.195 0,206 0.247 0.277 0,308 0.387 0.448 0.499 0.546 0.587 0.536 0.392 0.229 0.162 0.138 0.099 0.051 0.076 0.036 0.034 0.008

0.006 0.006 0.006 0.004 0.004 0.005 0.005 0.004 0.005 0.004 0.004 0.008 0.009 0.010 0.010 0.009 0.011 0.010 0.011 0.012 0.011 0.012 0.013 0.015 0.013 0.015 0.016 0.016 0.016 0.011 0.009 0.017 0.009 0.017 0.009 0.015 0.010 0.014

The errors quoted are relative only. Normalization uncertainties for the cross section and analyzing powers are 3% and 10%, respectively.

85

K. Hatanaka et al. / @ elastic scattering TABLE 3 Tensor analyzing power Axz in dp elastic scattering at 56 MeV Oc'm" (deg)

A~

±~A~z

30.50 38.36 46.42 54.75 63.46 64.32 69.30 74.28 79.26 84.25 89.25 94.25 99,26 104.27 109.29 114.32 119.35 124.38 129.42 134.47 139.51 144.57 149.62 154.68 159.74

0.002 -0,005 0.016 0.049 0.093 0.088 0.128 0.180 0.270 0.298 0.358 0.381 0.447 0.486 0.529 0.401 0.273 -0.060 -0.306 -0,333 -0.108 -0,030 0.107 0.095 0A31

0.00~ 0.008 0.008 0.005 0.006 0.007 0.007 0.012 0.008 0.011 0.013 0.022 0.014 0.013 0.019 0.015 0.017 0.033 0.018 0.016 0.022 0.017 0.025 0.021 0.021

The errors quoted are relative only. Normalization uncertainty is 10%.

TABLE 4 Maximum absolute values of the analyzing powers Prediction at 56 MeV Analyzing power

iTlt T2o T22 T2z

c.m.

Present result 0¢.m.

(deg)

value ~)

(deg)

value

130 115 130 90

0.2684 -0.626 -0.3096 -0.2589

139.51 119.35 135.48 109.29

0.268 ± 0.012 -0.618± 0,014 b -0.272 ± 0.008 b -0.305 ± 0.011

~) Calculated using the empirical formula in ref. 9). b) Calculated using the experimental values of A~x and A,.,.

86

K. Hatanaka et aL / dp elastic scattering

Four different potentials were employed for the 3Sr3O I coupled wave: 4T4B, G R A Z I I , 2T4 and 2T7. The rank-4 separable potential 4T4B of ref. 20) reproduces the phase shift in this state including the mixing parameter. The rank-3 potential G R A Z I I 18) reproduces 3S1 and 3DI phase shifts very well but fails to reproduce the mixing parameter. On the other hand, G R A Z I I seems to have a more reasonable off-shell behaviour than 4T4B since half-off-shell functions at several energies are similar to those of the Paris potential. 4T4B and GRAZ II give a deuteron D-state probability of 4% and 5%, respectively. While the two potentials 2T4 and 2T7 reproduce the phase shift except for the mixing parameter, they have different off-shell behaviour, and especially different deuteron D-state probabilities of 4% (2T4) and 7% (2T7). Svenne et al. 21) calculated tensor analyzing powers in the pd breakup reaction at Ed = 51.4 MeV and obtained large differences between analyzing powers calculated with the 2T4 and 2T7 potentials. They attributed this difference to that of the deuteron D-state probability. Since the energy in the present experiment is close to that in ref. 21), it is interesting to use both potentials in our calculation. Hereafter, sets of interactions are distinguished by the potentials used in the 3S1-3D I w a v e . The first-order approximation to the Coulomb effect 1,19) was introduced into the calculated neutron-deuteron amplitude. The results of the Faddeev calculations are shown in figs. 1 and 2 and compared with the experimental data. In fig. 1, calculated values without the Coulomb modification are also shown. The interaction used is GRAZII. It can be seen that the Coulomb correction by this approximation gives smaller effects at the present energy of 56 MeV than at 20 MeV [refs. x,,9)].

d-p

Ed=56MeV "C" 102 v

E X~o. \xaQ

"0 ~" 101 --

10o 0

I

I 40

2T7

I

~ " ~

I I I I 80 120 0 c.m.(deg.) (a)

I 160

Fig. 2. The differentialcross section and the vector and tensor analyzingpowers for dp elastic scattering at 56 MeV. The solid and dashed curves are results of Faddeev calculations with the NN interactions 2T4 and 2T7, respectively.

87

K. Hatanaka et aL / dp elastic scattering

0.5 Ay

I

r I ~_p

_

0.0

Axx

-

_

_ --

I

40

I

I

I

I

I

I

I

I. I I

120 ® c.m.(deg.) (b)

I

160

80

I

I

I

I

I -Y-m

'~_p

÷h~,

+,~

Ed=56MeV ~ j

,'Yl

- - 2T4 -- 2T7

I

0

I

2T7

t,

0.0

-0.5

I

I --

I

\~\\\

I

--

0.5

I

Ed=56MeV ~ ~

I

-0.E 0

I

40

I

I

I

80 120 (~ c.m.(deg.) (c)

i

f160

Fig. 2. cont.

Faddeev calculations using the N N interactions 4T4B, G R A Z II and 2T4 reproduce the experimental data well including Ax, as shown in figs. 1 and 2. The agreement between the calculations and data for Ax~ is better than that reported at 22 MeV [ref. 9)]. As far as the first-order polarization observables are concerned, it

K. Hatanaka et al. / dp elastic scattering

_1

Ayy

I

I

I

I

~-p

--

_

0.5

I

Ed=56MeV

1

I |

/~/~

--

/L~

_

0.0 " _

--

2T4

- -

2 T 7

I

I

I

- =..=

I

40

[

I

I

80 120 O c.m.(deg.)

I 160

(d)

--F--i-0.5 - -

] ,I, Ed=56MeV / '

Axz --

I l/ ii ///

--

i/

O

• *

0.0

--

--

2T4

--

- -

2T7 ~j

- 0 . 5

0

40

80 120 e c.m.(deg.) (e)

Fig. 2. cont.

160

K. Hatanaka et aL / dp elastic scattering

89

is difficult to strictly distinguish between these three sets of NN interactions 22.23). On the other hand, Faddeev calculations with the interaction 2T7 give poorer fits to the data than those with other interactions. The difference between the calculations with the interaction 2T7 and the data is most remarkable for Axz as shown in fig. 2. At angles smaller than 120°, the calculated Axz is larger than the experimental one and the calculation overpredicts the maximum value of Axz by a factor of about 1.2. Recently, it has been pointed out that one can distinguish the NN interaction 2T7 from 2T4 by measuring the tensor analyzing powers Ax~ a n d / o r Ayy for the breakup reaction IH(d, 2p)n [ref. 21)]. From the present analysis of Axz for elastic scattering at 56 MeV, the interaction 2T4 is favoured.

5. Asymptotic D-state to S-state ratio

Recently, much attention has been paid to the asymptotic D-state to S-state ratio PD [refs. 24-30) and references therein]. The ratio PD was obtained using the present data. The ratio PD can be obtained from the tensor analyzing powers T2~ in dp elastic scattering at the neutron-exchange pole [refs. 1o,31-33), and references therein]. The neutron exchange pole zp in the unphysical plane is given by 34) 5 +9 B~

(5)

where B is the deuteron binding energy and E is the deuteron laboratory kinetic energy. A suitable quantity for extrapolation to the pole was proposed by Amado et al., and is given by 31)

f(z)= k 2 [ ~ ]

T22(z)(;-_z:)2 ,

(6)

where do-/dO is the unpolarized differential cross section, k is the c.m. wave number introduced to make f dimensionless and z = cos 0. The PD is determined from the equation 32) Po = -v/3(8x/~) -1( 1 - RK)f(Zp) = --0.0542

f(zp),

(7)

where R = 1.75 fm is the np triplet effective range and K = 47.5 MeV/c the deuteron wave number. The value f(zp) is obtained by fitting the function f(z) with a polynomial expansion in z, and by extrapolating this function to the pole zp. At the present incident energy of 56 MeV, the value of zp is -1.339. The leastsquares fitting of the function f(z) was carried out with the Legendre polynomials up to 1 = 4. The results is shown in fig. 3. From the present analysis, the pD was determined to be 0.030±0.004, which is consistent with the values obtained from

90

K. Hatanaka et al. / dp elastic scattering 1.5

I

I

I

I

dp e l a s t i c s c a t t e r i n g 1.0 _ ~ .

Ed = 56 M e V

_

I

0.5

0.0 1.0

i

0.5

O~ -0.5 Z=COSO

-1.0

? Zp

Fig. 3. The dimensionless quantity - f ( z ) [from eq. (6)] plotted versus z = cos 0 at Ed = 56 MeV. The curve is a Legendre-polynomial-seriesfit to the data with LmaX= 4. The position of the neutron-exchange pole Zp= -1.339 is also indicated.

the previous analyses of the data at lower energies 33). The error indicated is that due to uncertainties in the absolute normalization of the differential cross section (3%) and the analyzing powers (10%) only. The large error in pD is caused by the normalization error of the analyzing power in the carbon polarimeter.

6. Summary The differential cross section o" and the vector and tensor analyzing powers Ay, Axx, Ayy and Axz have been measured in dp elastic scattering at 56 MeV. The tensor analyzing power Ax~ has been measured with the b e a m polarized in the horizontal plane using the polarization tagging method. The m a x i m u m values of the analyzing powers agreed with those calculated by extrapolating the empirical formulae obtained from the analysis of data at 10-22 MeV. Faddeev calculations were performed with the four sets of N N interactions. The Coulomb correction gave smaller effects at the present energy of 56 MeV than at 20 MeV. Calculations with three of them, 4T4B, G R A Z I I and 2T4, reproduced the experimental data well. The agreement between the calculations and the experimental data for Axz was better than that reported at lower energy. On the other hand, calculations with the interaction 2T7 gave poor fits to the experimental data, especially for Axe. The asymptotic D-state to S-state ratio was obtained using the present data as PD = 0.030 + 0.004 and is consistent with values derived at lower energies, in spite of the relatively large error of the present value. The authors wish to thank the staff members of R C N P for their generous support during the experiments. The experiments were performed at R C N P under Program Numbers 14A-5 and 15C-7. The calculations were performed at the R C N P computer center.

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