Elastic scattering of polarized deuterons from 4He Between 18 and 22 MeV

I

2.L

I I

Nuclear Physics A94 (1967) 663--672; (~) North-Holland Publishiny Co., Amsterdam N o t to be r e p r o d u c e d by photoprint or microfilm without written permission from the publisher

ELASTIC SCATTERING OF POLARIZED DEUTERONS

F R O M 4He BETWEEN 18 AND 22 MeV J. ARVIEUX, P. DARRIULAT, D. GARRETA, A. PAPINEAU, A. TARRATS and J. TESTONI t Centre d'Etudes Nucl~aires de Saclay, BoFte Postale no. 2-91, Gif/ Yvette, France Received 10 October 1966

Abstract: Angular distributions of polarized deuterons scattered from 4He are presented for 17.7, 19.7 and 21.4 MeV incident energy. Experimental problems linked to the use of deuterons polarized before acceleration are discussed in detail. Vector and tensor polarization parameters are small and do not show important energy dependence. measured polarization (0). Natural target.

1. Introduction Elastic scattering of deuterons from 4He in the vicinity of the 3 H e + 3H threshold has recently been the subject of several experimental investigations. This process appears to be a convenient tool to investigate the level scheme t, 2) o f 6Li and it has the further interest o f serving as a generator or analyser of polarized deuterons. Van Oers and B r o c k m a n 3) measured differential cross sections with a 24.85 MeV unpolarized incident deuteron beam and found a m a x i m u m in the angular distribution around 60 ° centre-of-mass angle, where a m i n i m u m occurs at lower energies. Broek and Y n t e m a ~) and Erramuspe and Slobodrian 5) measured differential cross sections between 21.0 and 27.3 MeV incident energy and deduced a smaller energy dependence than might be expected from the 24.85 MeV data. It appeared desirable to measure polarization parameters in this region in order to extract phase shifts f r o m the scattering data; at these energies, this is no longer possible with cross sections alone since the number of partial waves involved and the importance o f absorption give rise to large ambiguities. We report measurements of vector and tensor polarization parameters at 17.7, 19.7 and 21.4 MeV incident energy.

2. Experimental set-up and procedure The polarized deuteron beam of the Saclay fixed frequency cyclotron is scattered in a helium gas target before entering a carbon polarimeter. We discuss briefly those t I.A.E.A. Fellow on leave from CNEA, Laboratorio del Sincrociclotron, Buenos Aires, Argentina. 663

664

J. ARVIEUXet

al.

parts of the experimental set-up and procedure which are conventional and rather emphasize the description of their less usual aspects which are linked to the use of a deuteron beam polarized before acceleration. After extraction from the cyclotron, the beam passes two pairs of quadrupole magnets. In the centre of the gas target, the target spot (3 m m x 10 ram) may be oriented in the horizontal or vertical direction depending upon which scattering plane is investigated. The energy and width of the beam were measured by switching it to a calibrated analysing magnet and were found to be equal to 21.9 0.3 MeV and 400 keV, respectively. Two aluminium absorbers, 0.2 mm thick, are used to degrade the beam energy. They are placed either both upstream, or one upstream, one downstream, or both downstream the gas target, leaving the energy in the polarimeter constant. In the centre of the gas target, the incident energy is calculated to be 17.7, 19.7 or 21.4 MeV depending upon the location of the degraders. The beam intensity fluctuates around 2 • I08 deuterons per sec. The gas target (8 cm in diam, 8 pm Havar windows) is filled with helium, the pressure of which (2 atm) is kept constant by means of a mercury manostat. Two counter telescopes (2.2 ° angular resolution) can be rotated around the gas target on each side of the beam, either in a vertical or in a horizontal plane, depending upon which parameters are measured. Each counter is made of a pair of solid-state silicon detectors (one surface-barrier 0.18 cm thick, one lithium-drifted 1.5 mm thick) in order to discriminate between scattered deuterons and break-up protons and to detect the c~recoils at forward angles. For each counter, the pulses are preamplified, added and amplified through standard electronic circuitry 6) before entering a 4000-channel kicksorter where they are analysed. Routing signals are generated from the thincounter pulses after lower level discrimination. In a few instances, two additional counter telescopes are used with only one counter each; small background corrections have to be applied in this case, but the accompanying uncertainties are always negligible compared to statistical errors. The polarimeter is made of a 64 mg/cm 2 carbon target located 16 cm downstream the centre of the gas target; it is separated from the latter by a 5 mm diam collimator which avoids too important changes in polarimeter geometry, this collimator and an entrance collimator define the direction of the beam to within 0.8 ° but excludes the use of the polarimeter as a monitol to extract cross-section data. The proton group from the reaction 12C(d, p)l 3C is detected in two lithium-drifted silicon detectois at 50 ° lab angle, left and right. Aluminium absorbers are used in front of the counters to stop the deuterons, the proton pulses being fed in scalers after lower level discrimination. Cross sections are measured with an unpolarized incident beam; the polarimeter is removed and a Faraday cup used instead. The scattered deuterons are detected on the right, the left counter being set at 45 ° lab angle and serving as a monitor. Difficulties encountered in using the ion source for low-beam intensities cause high dead-time (10 ~ or more) in the analyser.

DEUTERON SCATTERING

665

Before describing the experimental procedure, we recall briefly the various steps of the polarization of the incident deuterons 7). An atomic beam produced by high-frequency dissociation of molecular deuterium is injected in a Stern-Gerlach, six-pole magnet. It can then undergo three successive radiofrequency transitions 1, 2 and 3, before entering the cyclotron where it is ionized and accelerated. At each point of a trajectory, we choose as axis of quantization the magnetic field at this point and denote (rnD, me) an atomic state where the deuteron and electron spins have projections m D and m r, respectively. During and after acceleration, the axis of quantization is therefore vertical, positive upward (fig. 1). The

LEFT

CYCLOTRON FIELD

T Y

~ Z ,

~

(4)

A

J

R

G

E

T

~,1 (2)

DEUTERONBEAM

~ RIGHT

'It

2 DOWN

(I)

/ Fig. 1. Frame of reference and sign conventions. (1) is used to project the incident density matrix and to define the Plj, (2) is used in ref. 10) to define the '. (3) is used in the present work to define the t~, (4) is used in ref. 11) to define the < Tu~.).

six-pole magnet causes the atoms with magnetic moment antiparallel to the field to diverge; it eliminates the (roD, --½) states. Transitions 1 and 3 interchange (I, ½) with ( - 1 , -½); (0, ½) with ( - 1 , ½) and (0, -½) with (1, -½); they are induced in low magnetic field by R.F. oils axed on the beam and coupled to 7.5 MHz oscillators. They are switched on and off every 0.2 sec. We label hereafter 13, 13, 13 and 13 the quantities associated to 1 on 3 on, 1 on 3 off, 1 off 3 on and 1 off 3 off, respectively. Transition 2 is never switched off in normal operation and interchanges (0, ½) with (1, -½). It is induced in a strong, slowly varying, magnetic field by a rectangular cavity excited by a 350 W carcinotron. Continuous measurement of the field intensity is provided by a N M R probe. The density matrices of the incident beam are easily

J. ARVIEUXet al.

666

calculated to be (writing lines and columns in order + 1, 0, - 1)

Pla----'}

2 0

,

Pl? = ½

0 0

,

Pia = ½

2 0

,

Pig = ½

0 0

,

O)

or defining irreducible tensor operators •T~a = x/3

~

(2)

( - 1 ) t -"'D(1 lrnD - m £ 1 a ~ ) l m . ) ( m £ l ,

roD, m ' D l

(3)

l

with 1

1

x/6

\/'6 1

~'~=~'=

1

\/2'

(4)

~'~= f i ~ - ~ 2

Depending upon which transition is on, the four sign combinations of vector and tensor polarization are obtained; the differential scattering cross section in direction (0, q~) reads s) (0 and q~ being centre-of-mass angles defined in fig. 1)

-dQ ij

\dQ. o l - c q J x / 2

,c°sg°-flii(-zt°+vzt2C°S

'

where (&r/dr2) o, t~fi, 1 • teo and t22 are quantities to be measured. Measurements are performed in horizontal (0 = 0, rr) and vertical (~o = _+ ~2-~r)planes. Switching on and off of oscillators 1 and 3 is timed by a clock used to generate routing signals to the kicksorter (four spectra being recorded for each counter) and gate signals to the polarimeter scalers (four scalers being used for each polarimeter counter). The regularity of the clock is checked by sending pulser pulses to the kicksorter; no asymmetries larger than 0.1 ~ are observed in the corresponding peaks. To make sure that the switching times are negligible, various commutation rythms are tried (betweeen 0.I and 10 sec). Defining I

Q = R =

/2(!, 2

v2,2.o +4'9~,). ,'-~{!'2- "N'/3-t 2~ 2 2]'

%/ 2 ' 2 " 0

(6)

we find by direct inspection of eq. (5) and denoting N u the number of counts for in-

DEUTERONSCATTERING

667

.cident density matrix Pu, (7) in the horizontal plane, and do"

(s)

in the vertical plane. p

=

(N,a+N;3) -(N,3+NTg)

,

~p = O,

,

~=~,

Z Nij t,j P = (N13+N~a)-(Utg+U~3) ~.Nij t,J Q = (N'3+N~3)-(N~+N~g), Ni) i,j R

=

q~ = 0 or re,

(N'3+N~3)-(N'~+N]-~)

,

q~ =

+½re.

(9)

E Nij t,j Three further relations are obeyed by the N~ i

¢=0

Nx3+NI-3 = N ~ 3 + N ~ g , N13 --= N ] 3 ,

NI~ = N~g,

or ~,

q~ = +__½7z.

(10) (11)

Taking into account the efficiencies, we find for the vector and tensor components of the incident density matrices 0~13 •

%/1~[( l - - 2 ~ 1 ) ( 1 - - 2 ~ 3 ) - - g 2 1 ,

~ 3 = --~j16[1--Zea+~2],

ill3 -- -- X/~[( 1 --2e3)(1--ez)],

/~73 = --~/~[(1--2~3)( 1 --ez)-],

where the efficiency of transition i is written 1 - e~. Substituting these values in eq. (5), we see that relations ( l l ) must be fulfilled even when the transitions are not 100 ~o efficient. We check this by computing [(Nx 3 - N~3 )E/NI a + N;3 ] and ~ [(Nx~ - N ~ ) Z / N 1g + Ni~ ], the sums being extended over all ~p = ½~ data; the results are consistent with eq. (11) within statistical limits. Relation (10) is no longer valid when transition 3 is not 100 ~ efficient. It becomes in

668

J. ARVIEUX et al.

fact l--2g 3 -- Nla--N-13

(13)

.

N~x-NI~ The average (statistically weighted) value of this quantity over all q0 = 0 or 7r runs (including polarimeter) is c o m p u t e d and found equal to 1.022 +0.013, which is consistent with e 3 = 0. There is no such direct check o f efficiency for transition 1, but by switching off transition 2 we see that N~3 must equal N~2 if, and only if, both transitions 1 and 3 are 100 /o/o efficient. This was done in a few instances and found consistent with e I = e 3 -- 0. In any case, a lack o f efficiency o f oscillator 1 has no effect on Q and R and multiplies P by 1 - c ~ ; this factor, being the same for the polarimeter and the chamber counters, disappears after normalization. A lack o f efficiency of transition 2 causes a decrease in the tensor asymmetries (1 - ~ 2 ) Q and (1 - e 2 ) R being measured in place of Q and R, respectively. Nevertheless it cannot be detected by the polarimeter, its Q-value being too small ( - 2 O//o),. we must rely on other effects. Let PL and PR be the asymmetries o f eq. (9) measured in the left and right polarimeter counters, respectively, L and R the total n u m b e r of counts ( ~ i j N i j ) recorded in these counters. Denoting P the c o m m o n value o f P c and PR when e 2 = 0, we find, assuming e3 = 0 and el = 0 P

PC --

,

PR --

1 +~2 P

P

,

(14)

1--g2 P

R

o 1-e2P

where (L/R)o accounts for differences in solid angle between the left and right counters. A change in transition 2 efficiency should affect L / R and e z = ( I / P L ) - ( 1 / P R ) , but no correlation between these numbers can be found a m o n g the polarimeter data. F r o m this and from data collected with transition 2 switched off (e2 = 1 ), we deduce e2 < 26 %. We cannot give a better upper limit to e2 because high statistical uncertainties arise in the checks just described, but all data are perfectly consistent with ~2 ~- 0 .

F r o m eq. (14) we see that P is the h a r m o n i c mean of Pc and Pg 2

P

-

1

PL

+

l

--.

(16)

PR

To take advantage of this relation, we always set the two counter telescopes symmetric with respect to the beam; this cancels the effect on P o f a lack of efficiency in transition 2.

TABLE 1

--1.5

--1.4

--2.2 --4.8 --3.1 1.3 5.0 7.9 7.0 7.9

9.7

12.4

0.4

0.5

0.9 1.3 1.8 1.5 1.7 1.5 1.3 1.3

2.0

1.1

0.0

1.0

4.5 7.7 12.8 9.3 2.4 0.5 --2.4 --0.7

4.3

9.3

23.5 26.5 29.5 33.2 36.9 37.6 44.2 51.3 58.5 65.5 72.3 78.9 85.5 91.7 97.8 98.1 98.4 103.7 109.4 114.8 120.0 142.4 144.1 147.7 150.5 153.5 154.4 156.5

Q

de

P

000rn

1.1

1.3

0.9 1.4 1.8 1.5 1.7 1.5 1.3 1.3

0.4

0.4

dQ

1 7 . 7 i 0 . 3 MeV

2.1

1.4 1.2 2.0

--6.5

--5.2 --5.0 --4.0

1.1 1.4 1.3 1.2 1.1 1.1 1.0

0.9

3.0 0.8 --2.7 --2.1 1.9 --2.1 --3.5 --4.9

0.4

0.4

dR

1.2

1.5

R

--18.1 --22.8

0.2 6.2 7.7

3.5 7.8 15.6 9.1 2.3 0.0 --4.2 --2.4

1.0 1.6 2.1 2.1

P

1.1 1.6

1.3 1.9 1.3

0.7 1.0 1.4 1.1 1.0 0.8 1.2 1.8

0.4 0.3 0.4 0.5

de

--7.6 --8.5

13.1 9.7 12.4

--3.1 --3.5 --2.4 1.2 5.0 2.8 7.6 9.8

--1.6 --1.3 --1.9 --2.0

Q

1.1 1.6

1.3 1.9 1.3

0.7 1.0 1.4 1.1 1.1 0.8 1.2 1.8

0.4 0.3 0.4 0.5

dQ

19.7±0.3 MeV

8.8

--7.0 --5.6 --7.0 --2.7

--7.0

2.0 --1.9 --2.7 --2.8 --0.8 --3.5 --7.6

2.7

1.5

1.0

R

1.2

1.4 1.1 2.4 1.8

1.3

1.2 1.0 1.3 1.0 1.1 1.2 0.8

0.7

0.5

0.4

dR

1.3

1.6 1.5 1.2

--4.8 --13.6 --17.7 --24.8

1.3

1.1 1.6 1.9

2.0

0.3 0.4 0.5 0.5 0.6 0.9 0.9 0.8 1.8 2.0 2.0 1.0 1.5 1.0

dP

9.9

3.8 6.6 10.7

2.4

0.6 1.6 2.2 2.6 3.8 4.5 7.1 12.4 6.3 5.8 --0.9 --1.2 --6.4 --3.3

P

--9.3

--0.5 --7.7 --10.4

8.1

7.9 9.7 10.2

10.9

--0.3 --2.2 --1.2 --1.5 --1.2 --3.4 --1.3 2.2 2.8 0.7 0.9 4.9 9.8 7.0

Q

1.3

1.6 1.5 1.2

1.3

1.1 1.6 1.9

1.4

0.3 0.4 0.5 0.5 0.6 0.9 1.0 1.1 1.0 1.0 2.0 1.1 1.7 1.4

dQ

21.4:L0.3 MeV

Asymmetry parameters P, Q and R are tabulated versus centre-of-mass angle for 17.7, 19.7 and 21.4 MeV incident deuterons

9.1

5.1

2.8

--7.0 --8.5 --8.1

--9.7

--1.2 --2.0 0.0 --0.6 -3.1 --6.9 --5.8

4.8

1.6

1.9

R

1.3

1.3

1.7

1.7 2.4 2.1

1.4

1.4 1.4 1.6 1.4 1.9 1.4 1.5

0.8

0.4

0.3

dR

~D

©

670

J. ARVIEUXet al.

The following effects may cause the measured asymmetries to be smaller than the actual ones: incomplete separation in the Stern-Gerlach six-pole magnet, depolarization in the ion source or elsewhere or presence of an unpolarized deuteron background in the cyclotron. Normalization of the data is achieved by measuring in the same run P(45 ° lab angle, 22 MeV, a2C(d, p)l 3C) ) known from Beurtey v) and P in 30

60

90

120

30

60

90

120

150 30

60

90

120

150

r

s

I

20%

-10 -20

R

-20

-

I

17.7 MeV

r _

l

I

-~

~

19.7 MeV

I

I

1

l

21.4 MeV

Fig. 2. Asymmetry parameters P, Q and R are plotted versus centre o f mass angle for 17.7, ] 9.7 and 21.4 MeV incident energy. The curves are phase shifts fits to the data 13).

the polarimeter (14.6 0.7 %); this is done by using a carbon foil in place of the gas target. The normalization factor measured in this way (1.16+0.06) is applied to all the data.

DEUTERON

671

SCATTERING

3. Results

The normalized values of P, Q and R in percent versus centre-of-mass scattering angle 0 are tabulated and plotted in table 1 and fig. 2, respectively. The quoted uncertainties include statistical and systematic errors and are given in percent. The t, appearing in relation (6) have a simple physical meaning 8); they are the irreducible components of the density matrix which would describe the scattered particles if the incident beam were unpolarized. These components are expressed in the helicity formalism 9). When rotated to the incident beam as axis of quantization, they become Senhouse's 1°) ( T ,~) .' When rotated to the lab scattering direction, they I

I

lo

20

I ~o

I0

4

1 so

I 60

p 2 ( d O. ~ - dLO- Lab

I 70

I 80

OLab

(d)

[ 90

20

--10

l

--5

m 2

35 I

30 I

25 I

20 I

15 I

10 I

ELob( d ) 5 I

0 1

Fig. 3. Figure of merit P~(da/d~2)lab for generation of polarized deuterons through ZH(c~,d)4He with 40 MeV incident e-particles. become Seiler's 11) (T~). The relations between these quantities are easily expressed with the rotation matrices = =

E /z ~ , , Z p ~,,

~,t.u, 0, ,,~u, O - Olab "

,0)4,

where 0j.b denotes the lab scattering angle corresponding to 0. The asymmetries measured in the present experiment are smaller than the ones observed at lower energies; they never exceed 20 ~o whereas 30 ~o asymmetries are reported 11, 1z) around 8 M eV incident energy, where the D 1 and D z waves are largely splitted. No important energy dependence is found, as could be expected 3), neither in asymmetry nor in cross section. The solid curves in fig. 2 are phase-shift fits to the data 13).

672

J. ARVIEUXet al.

As a n analyser of polarized deuterons in the 20 MeV region, 4He does not appear to be very efficient, the m a x i m a o f P being weak a n d occurring at angles where the differential cross section is small. F o r reasonable polarimeter geometry the figure of merit P2(da/dg2)lab is a b o u t equal to the ~2C(d, p)13C value, but c a r b o n is a more convenient target t h a n helium. More interesting is the use of the inverse reaction to generate polarized deuterons where advantage is taken of the centre-of mass to lab t r a n s f o r m a t i o n . Fig. 3 shows the figure of merit P Z ( d o / d f 2 ) ~ a b for 40 MeV incident alpha particles versus the angle a n d energy of the recoil deuterons in the lab system. The P-values are o b t a i n e d by averaging the present data (17.7, 19.7 a n d 21.4 MeV). We are indebted to Mrs. A. G a r i n , M m . R. Maillard and R. Cafiot for technical assistance.

References 1) D. R. lnglis, Phys. Rev. 87 (1952) 915 2) J. L. Gammel, B. J. Hill and R. M. Thaler, Helv. Phys. Acta Supp. 6 (1961) 409; G. C. Phillips and T. A. Tombrello, Nuclear Physics 19 (1960) 555 3) W. T. H. Van Oers and K. W. Brockman, Jr., Nuclear Physics 44 (1963) 546 4) H. W. Broek and J. L. Yntema, Phys. Rev. 135 (1964) B678 5) H. J. Erramuspe and R. J. Slobodrian, Nuclear Physics 49 (1963) 65 6) R. Chaminade, A. Falcoz, M, Lechaczynski and J. Pain, I.E.E.E. Trans. Nucl. Sci. (June 1964) 7) R. Beurtey, Rapport CEA-R.2366; R. Beurty et al., J. Phys. Rad. 24 (1963) 1038 8) J. Raynal, Rapport CEA-R.2511 9) M. Jacob and G. C. Wick, Ann. of Phys. 7 (1959) 404 10) L. S. Senhouse and T. A. Tombrello, Nuclear Physics 57 (1964) 624 11 ) F. Seiler, S. E. Darden, L. C. Mclntyre and W. G. Weitkamp, Nuclear Physics 53 (1964) 65 12) A. Trier, P. Extermann and L. Veeser, preprint 13) P. Darriulat, D. Garreta, A. Tarrats and J. Arvieux, Nuclear Physics A94 (1967) 653