Analyzing power in n+d elastic scattering at 67 MeV

Nuclear Physics North-Holland

A524 (1991) 377-390

ANALYZING

POWER

H. RfiHL,

Institut

IN ii +d ELASTIC

B. DECHANT, M. STEINKE,

AT 67 MeV

SCATTERING

J. KRUC, W. LUBCKE, G. SPANGARDT, M. STEPHAN’ and D. KAMKE

fGrE~per~rrtentalphysik I, Ruhr-Un~versit~t~ O-4630 Bochum, Germany

J. BALEWSKI, institute

K. BODEK,

L. JARCZYK

and

A. STRZALKOWSKI

ofPhysics, Jagellonian University, PL-30059 Krakdw, Poland

W. HAJDAS’, Institut fib Mitrelenergieph};sik,

St. KISTRYN’, Eidgeniissische

R. MiiLLER

Technische

and

Hochschule,

J. LANG CH-8093 Ziirich. Switzerland

R. HENNECK fnstitut fib Physik,

Universitiit

H. WITALA’, institut fiir Theoretische

Basel, CH-4056

Th. CORNELIUS

and

W. GLGCKLE

Physik I[, Ruhr-iJniversit&t, Received 28 June (Revised 3 October

Basel, Switzerland

O-4630 Bochum, Germany

1990 1990)

The analyzing power A, of ‘H(n, n)‘H elastic scattering at E, = 67 MeV has been measured in the angular range 30”~ f?, m < 165”. The data are in good agreement with the results of our rigorous three-nucleon calculations employing the PARIS and the BONN B potential.

Abstract:

E

NUCLEAR

REACTIONS

‘H(polarized calculations.

n, n), E =67 MeV; Scintillation target.

measured

A,(B).

Faddeev -1

1. Motivation

and aim

Very recently, the theoretical description of three-nucleon (3N, N = nucleon) systems on the basis of the Faddeev theory has reached an important new stage. Due to the increased computing power available and refined numerical techniques it is now possible to calculate the 3N observables rigorously employing virtually any 2N potential (without Coulomb interaction). The 3N system - as the simplest and best understood many-body system - is most appropriate for studying: (i) off-shell properties of the 2N force: for a given interaction, these are not independent of the on-shell behaviour of the force ‘); ’ Present address: KFA Jiilich, Germany. ’ Permanent address: Institute of Physics, 03759474/91/%03.50

@ 1991 - Elsevier

Jagellonian

Science

Publishers

University,

PL-30059

B.V. (North-Holland)

Krakow,

Poland.

378

H. Riihl et al. / Analyzing power

(ii) genuine 3N forces: 2N off-shell effects ‘). The degree dependent

these

upon the quality

This involved exhibit

to which

on a nucleonic

problem

different

basis these cannot

effects can be determined

of both the 2N on-shell

can only be solved by studying

degrees

of sensitivity

with respect

input

be distinguished

from

from

3N observables

is

and the 3N calculations.

various

3N observables

which

to the above effects.

Clearly, one should start with the “best” 2N potentials available, i.e. from realistic meson-theoretical potentials like the PARIS and the (new) BONN potential 3.4). Deviations between experiment as long as they can be removed input. Only if there remain effects like the 3N force.

and calculation may be attributed to the 2N force by proper tuning within the uncertainties of the 2N

discrepancies

will one have to look for higher-order

This concept applies to the 3N bound state as well as to the continuum state observables. For the bound states, discrepancies have been found which appear to indicate a 3N force 5,6). There is good reason to expect that a study of the continuum states in elastic and break-up channels will yield still more and independent information. Actually, 3N continuum observables have been shown to be sensitive to the 2N interaction ‘). Specifically, measurements and predictions of the vector analyzing power A, in n + d elastic scattering at low energies (8-14 MeV) have revealed a distinct discrepancy between experiment and theory ‘-16). At these low energies the analyzing power sensitively depends on the ‘P-state contribution to the 2N forces ‘). The reason for the discrepancy could therefore be a lack of fine-tuning of the on-shell ‘P force properties, including their charge symmetry breaking I’). Indeed, a recent study of Witala and Glockle demonstrated that a possible modification of the 2N forces in the 3P states simultaneously reproduces the 2N data and the low-energy analyzing powers in N + d scattering. At energies between 16 and 50 MeV the agreement between experiment and theory proves to become increasingly better with increasing energy - although still not As shown being perfect ‘8-22). Above 50 MeV the P-forces are no longer dominant. in ref. ‘), the theoretical predictions without the elastic amplitude are already close to the A), in 2H(ii, n)‘H elastic scattering at E, = enough to be free from the correlation of the energy which exists at lower energies where hardly attainable 6,23,24).There are only very above.

the ‘P partial-wave contributions to full prediction. In this work, we study 67 MeV. This energy should be high 3N observables with the triton binding independent off-shell information is few 3N data at E, = 50-100 MeV and

2. Experiment The experiment was performed by using the polarized proton beam (E, = 72.2 MeV; P,, = 0.90; 1, = 0.7-1.0 kA; 17 MHz repetition rate) of the injector Philips cyclotron of the Paul Scherrer Institut (PSI) at Villigen, Switzerland. The polarized

H. Riihl et al. / Analyzing power

neutrons

were produced

the final-state

via the ‘H(p, ii)‘(p~)~~,

interaction

of the two outgoing

379

reaction

protons,

at 0” which, by virtue of

leads to a quasi-monoenergetic

neutron beam of energy E, = 67 MeV. Since the transverse polarization parameter K :I’is 0.407 *0.016 at E, = 72 MeV, the neutron polarization 0.37 5 0.015. The polarized

neutron

facility

has been described

transfer was P, =

in detail 2s). Here we

only outline the important parts of our set-up, cf. fig. 1. Polarized protons were focussed onto a 200 pg/cm’ thick carbon foil in a poiarimeter chamber where their polarization was continuously monitored by observing the left/right asymmetry of scattering at 44” (where A,, = 0.986, see ref. ‘“)) with a pair of scintillation detectors, NaI,,,. The sign of the beam polarization was reversed every 4 s at the polarized ion source. Simultaneously, the proton-beam pulse width, typically ~2.5 ns, was measured by an additional “timing” plastic scintillation detector (TM) at 30” “below the beam” (A, = 0, see ref. “)). Behind the polarimeter the beam was refocussed onto the neutron-production target (LD,, 1 cm thick), mounted in a chamber inside the shielding. A deflection magnet bent the protons into the Faraday cup (FC); their charge was used for normalization. The neutrons pass through an 1.5 m long collimator (A& = 0.07 msr, 3.5-5.0 x 10’ neutrons/s) and impinge on the actual deuterium target (TS) at a distance of 2.1 m from the collimator exit. The deuterated target (liquid scintillator NE 213d) was contained in a glass cylinder, 4.9 cm 0 x 6.0 cm, oriented vertically. It was coupled to a photomultiplier tube (Valvo XP 2020, selected for low dark current: <3 nA). Recoiling deuterons could be measured with an energy deposit down to Ed = 4 MeV. The scintillator NE213d was selected because of its excellent pulse shaping properties. Four pairs of NE213 detectors (D:‘) were placed symmetrically at angles &,,, = +20”, . . , *150” on both sides of the beam. Two different sizes of the scintillator

Fig. 1. Schematic

set-up

w

lead

m

steel

B

concrete

n

polyethylen

of the experiment.

H. Riihl et al. / Analyzing power

380

were used, 14 cm 0 x 6 cm (six detectors) and detectors). Photomultipliers Valvo XP 2040/2041 The energies

of the neutrons

from 3.05 m at forward detector

(NE213,

angles

were measured

10 cm 0 x7.5 cm (two backward and EMI 9823 kB were employed.

by their t.o.f.; the flight paths varied

to 1.10 m at backward

5.1 cm 0 x 2.5 cm) placed

angles.

in the neutron

An additional beam

5 m behind

t.o.f. the

target scintillator served as a monitor (M) for the incident neutron flux. All detectors were stabilized against gain shifts by using stabilized LEDs “)_ These LEDs were also used to apply “dead-time pulses” to the photocathodes of the neutron detectors and of the target detector. One minus the ratio of the number of pulses received by the data acquisition (see below) and the number of pulses applied gives the relative overall system dead-time. Pulse-shape circuitry *‘) was applied to the eight neutron detectors and to the target scintillator. The “pulse-shape signals” associated to the detectors have an amplitude which measures the decay time of the photomultiplier dynode pulses. A block diagram of the electronic circuitry depicting mainly its logic function is given in fig. 2. For good long term stability, the cyclotron timing signal (cycl. RF) was stabilized with respect to the timing scintillator signal 25). The common time reference signal for the neutron t.o.f. circuits is derived from the target scatterer (TS, coin. # 1): therefore, the time structure and width of the primary proton beam do not enter. We applied routing techniques as far as possible, but always in such a way that the analog and digital signals of any pair of detectors left/right at the same angle were fed through the same electronic paths in order to minimize instrumental asymmetry. There are two main branches for measuring t.o.f., pulse-shape (PS), and photomultiplier dynode output (pulse height), each one combining four detectors (two pairs), N4, respectively, NS, . _ . , N8. As a representative of the eight neutron Nl,..., detectors, Nl, the first detector of branch one, and the target scatterer are shown in the diagram along with their main circuitry. The routing was accomplished by successive gates which reduced the counting rates step by step. The first hardware condition {coin. # 1) required that a target scintillator signal occurred within a 20 ns wide window around the centre of the main primary neutron t.o.f. peak. For any neutron detector, the t.o.f. and pulse-shape PS were only accepted within 100 ns after the target scintillator signal (coin. #2), and in this case a linear gate in the corresponding linear dynode branch before analog routing (ROU) was opened. NO multiplexing was applied to the target scatterer. For any “true” event, valid t.o.f. and pulse-shape signals were required from the target scintillator as well as from (at least) one of the neutron detectors (coin. #3). Six spectra [“C(p, p)“C left/right for monitoring the p-beam polarization and the timing spectrum, for either spin direction] were accumulated in separate MCA regions and periodically (each 2h) read by the central data acquisition computer (PDP-11/60). The data were processed for on-line visual control and written onto tape in event mode for subsequent off-line analysis. Seven parameters per event were written onto tape: the six analog signals (cf. fig. 2) and a tagword (via IR)

H. Riihl et al. / Analyzing power

381 CAMAC

Fig. 2. Greatly

simplified

coding the occurrence detector identification

block diagram of the electronics (Nl: neutron detector linear gate; IR: input register; OR: output register).

#I (out of eight);

LG:

of an LED signal (DT) for monitoring dead-time losses, the (l-S), and the spin state of the primary proton beam (POL).

A critical problem was the radiation background in the experimental area. Due to neutrons which penetrate the collimator shielding in the epithermal energy region, 2.2 MeV capture y-radiation in the detectors was produced via ‘H(n, y)*H. The rates given below were obtained after adding additional layers of 50 cm of concrete and/or 10 cm of borated polyethylene to the original 60 cm Fe and/or 50 cm concrete of the shielding. The rate of events in the neutron detectors was then of the order of 104s-‘, and in the target scintillator it was 25 x 10’ SC’. Between any two runs (~10 h) the pulse height (light output) of both the neutron detectors and the target scintillator were calibrated by means of y-sources (22Na and **Y). The total time of data accumulation was eight days in two different beam times. 3. Data evaluation The following steps were performed in the off-line In step 1 the final r/n pulse-shape discrimination detectors. In fig. 3 a typical result is given.

analysis: was applied

to the neutron

H. Riihi et al. / Analyzing

382

power

<=

f

714

<

. <=

1071

<

0

<=

1428

1428

<

0

<=

1785

1785

<

= <=

2142

2142

<

m

Maximum

5

15

10

Fig. 3. Typical

20 25 Pulseform

30

35

pulse-shape

spectrum

714

357

:

1071

32930

40

of a neutron

detector.

In step 2 conditions were applied to the target scintillator signals. They were required to occur within a well-defined time window, 4 ns wide, set on the incident neutron t.o.f. peak, and final pulse-shape discrimination was performed. Fig. 4 shows

20 Fig. 4. Pulse-shape

30 40 Pulseform spectrum

50

of the target

285 <

<=

571

571 <

* <=

857

057 <

= <=

1142

1142 <

0 <=

1428

1428 <

l

<=

1714

1714 <

.

Maximum

:

60

scintiilator

(6, =40”).

1422

383

H. Riihl et al. / Analyzing power

a spectrum

at era,, =40” with four distinctly

separated

(ii) protons

from break-up

from ‘H(n, n)np and 12C(n, np)“B,

(iii) deuterons

y-events

(region

(I)),

regions:

processes

(i) electrons

(region

(II)),

from mainly

from ‘H(n, n)*H elastic scattering

(region (III)) and (iv) Lu-particles from various inelastic processes, among them 12C(n, cu)‘Be and “C(n, ncu)(‘Be) (region (IV)). To start with, the events from regions (II) and (III)

(p, d) were retained.

The resulting neutron t.o.f. spectrum in fig. 5a shows that further background reduction is necessary. In step 3 a window in the target pulse height, cf. fig. 6, is introduced which selects the region around the prominent nd elastic line; the result is given in fig. 5b. If finally in step 4 only deuterons are admitted in fig. 4. i.e. if only region (III) is selected, a further considerable background reduction is observed (fig. 5~). It is important to note that the results of steps 3 and 4 differ from the preceding ones in that also a certain fraction of true events is rejected. These losses do not influence the value of A,, as long as exactly the same fraction is rejected for the left/right detectors at the same angle or for both spin directions, since the corresponding factors cancel in the “superratio”, cf. eq. (1) below. Both conditions are met in the present experiment to a high degree, since the cuts 3 and 4 were placed on the common target detector signals and the neutron detectors were of identical construction operated under identical conditions. The intensity and the polarization of the primary proton beam did not significantly depend on the spin orientation. The analyzing power A?. was determined via the “superratio” r. Given the normalized integral number N,,, of elastic counts, corrected for deadtime, of the left/right detectors for the two spin orientations + / -, AJ is given by

/&r-l

P,r+l’

where

r=

J

N:N, ~ N;N+,’

(1))

and P, is the polarization of the incident neutrons. When eq. (1) is used to determine A,., effects of asymmetries due to different solid angles, different efficiencies or different dead times of the left/right neutron detectors cancel to first order. The results were corrected for finite-geometry effects on the basis of our theoretical predictions for A,.. For the uncertainties of the final results, the statistical uncertainties are dominant (AA = 0.015-0.096). Several systematic uncertainties were considered: - Background subtraction introduces uncertainties of AA = 0.010-0.020. The background results from multiple scattering of neutrons from n+d breakup and n+ “C reactions (its exact shape is not significant), - Finite-geometry effects (beam divergence, finite solid angles of the neutrons) lead to AA = 0.001-0.007, - Multiple scattering. A certain fraction of elastic events is removed from the elastic line (fig. SC), but if this fraction does not depend on the spin orientation its effect cancels in eq. (1). Evidence for spin independence can be derived from the background under the elastic lines (being always identical for analog left/right

H. Riihl et al. / Analyzing power

384

500

400 n/l z L 300 6 u 200

100

0 80

40

60

20

c

20

0

TOF Ins

500

400 VI z -E QI

300

3 200

100

0 80

40

60

TOF 600

I

,

I

I

,

,

r

/ ns ,

r

,

r

,

,

(c) 500

400 w z i?!

300

E u 200

100

0

‘I’/‘,,‘, 60

60

40

20

L

TOF I ns Fig. 5. Neutron t.o.f. spectrum (0,=40”) (a) selecting regions (II), (III) in fig. 4 (b) same as (a) with the window indicated in fig. 6, (c) same as (b) with only region (111) (deuterons) selected in fig. 4.

H. Riihl et al. / Analyzing

0

200

400

385

power

600

800

iooc

Pulsehelght Fig. 6. Pulse-height

spectrum

target

scatterer

(0, = 40”)

angles, in accordance with earlier results ‘43’8)) and also from refs. 28323).The assumption of spin independence is also supported by Monte Carlo simulations of our own. The corresponding uncertainty is small (~0.005), - Nonlinear effects like pile-up and dead-time losses do not necessarily cancel in the “superratio” r. Pile-up was negligibly small in the spectra ofthe neutron detectors. The deadtime for the whole system (17-19%) was caused predominantly by the target scintillator; this constant dead time, however, cancels in r. TABLE 1 Experimental

-%,,(deg) 20.0 30.0 35.0 40.0 51.5 60.0 70.0 75.0 80.0 88.5 100.0 105.0

results

(not including a normalization to P,=o.37*0.015)

L

(ded

uncertainty

A,

AA,

30.3

0.221

0.018

45.1

0.234

0.015

52.4

0.234

0.030

59.6

0.169

0.015 0.027

75.5

-0.068

86.6

-0.319

0.023

99.0

-0.564

0.070

104.8

-0.587

0.037

110.4

-0.671

0.063

119.3

-0.455

0.050

130.3

-0.131

0.068

134.6

-0.087

0.096

115.0

142.6

0.154

0.064

125.0

149.7

0.171

0.052

135.0

156.1

0.175

0.059

150.0

164.7

0.106

0.049

due

H. Riihl

386

et al. / Analyzing

power

0.6

o.at, 0

Fig. 7. Experimental

results

, , 30

,

, , /

60

90

, , , / 120

(our n+d data at 67 MeV), and theoretical PARIS; dashed line: BONN B potential).

150

results

,I 180

at 68 MeV (solid line:

We studied the effects of (slight) mechanical misadjustments of the target scintillator or the neutron detectors. Using the superratio method misadjustments of the order of 1 cm have no significant effect on A,,. It is very important to apply a well-defined window (At = 4 ns in our case) to the target scintillator neutron t.o.f. spectrum since the transverse spin transfer coefficient K :I’ for the neutron production reaction ‘H($, ii)’ depends on the neutron energy E, [ref. ‘“)I. We have performed Monte Carlo simulations which account for this energy dependence as well as for the time resolution of the target scintillator and for the primary proton beam pulse width. The measured t.o.f. spectrum of the neutrons in the target scintillator was well reproduced. With our time window we obtained K::‘=0.407,E=0.37*1% (P,,=O.90), and E=66.6MeV (En= 56-70 MeV, AE, = 2.6 MeV (FWHM)). The mean value of E, results from several facts: 1.1 MeV energy loss of the incident protons in the Havar foils and the LD2 target liquid, the Q-value for ‘H(p, n)‘(pp),s, (-2.2 MeV), ing to pp-FSI with an intrinsic width of -1.3 MeV unsymmetric with an extended low-energy tail. Our final results, with their total uncertainties, are fig. 7. A normalization uncertainty of 0.016 for K_;:’and, not included.

and the peak correspond(FWHM) [ref. “)I being given in table 1 and in hence, of 0.015 for P, is

4. Calculations We performed 3N-continuum calculations by summing up the multiple-scattering series for the n+d break-up process to infinite order. This is equivalent to solving

387

H. Riihl et al. / Anal_yzing power

the integral

equation T = tP+

tPG,,T,

where t is the two-body off-shell transition operator, and P the sum of two operators of cyclic permutation, The operator

for elastic

scattering

(2)

Go the free 3N propagator P = P,, P23+ P,3 P13.

is given by

U = PC,

+ PT.

(3)

The formalism and the technique for numerically solving these equations have been discussed in ref. “). We used two meson-theoretical 2N potentials, the PARIS potential ‘) and an OBE potential, the BONN B potential “). In the ‘S,, state we included the wellestablished charge-independence breaking of the 2N forces (the np forces are slightly stronger than the nn/pp forces). This effect can be described either by taking the neutron and the proton to be different particles or, as done in the present work, by using the generalized Pauli principle in the framework of isospin formalism. Then charge independence breaking in IS,, is equivalent to isospin breaking in that state causing transitions from the initial state of total isospin T = 4 to a mixture of T = 4 and T = 9 states. The small admixture of T = $ would vanish if the nn and np forces in ‘So were identical (as they are, apart from ‘P states and according to our present knowledge, in the higher angular momentum states). Technically the charge independence breaking is accounted for by the prescription of choosing {t:,z’+it:,n’ and $tl,’ +itf,F’ as the effective two-nucleon t-operators in the state ‘S,, with T = i and $, respectively, and f&( tl,’ - t:,,') as the effective t-matrix for the transitions between T = $ and $ states ‘I). The t-matrix t np was taken from the BONN B potential and the t-matrix t,, from the PARIS potential. Hence the same linear combinations of the t’s in ‘S, underly our calculations which, for the higher partial waves, were performed

with the PARIS

and the BONN

potential,

respectively.

The potentials were truncated to act only in 2N states of total angular momentum j c 3. Inclusion of j = 4 or higher is presently beyond the capacity of the computer resources, yet it is unlikely that their inclusion would change the results noticeably, as can be inferred from fig. 8. That figure shows A,. for n + d elastic scattering with the PARIS potential truncated to j s 1 with the exception of keeping the potential in the state 3P2-3F1, and to j s 2 and j s 3, respectively. While the additional j = 2 force components (ID, and ‘DJ still have an appreciable effect, the remaining j = 3 force components hardly contribute any more to A,.. The BONN B potential was found to give almost identical results. Together with the experimental data, fig. 7 shows our theoretical j s 3 predictions for the PARIS and BONN B potential. The two theoretical curves are very close to each other and both agree very well with our n + d data. In addition, it is important to note that the corresponding experimental

H. Riihl

388

AY

er al. / Analyzing

power

-0.2

-0.6

0

30

90

60

120

150

180

d/deg Fig. 8. Convergence

of the theoretical

result for js

1,2,3,

(PARIS

potential).

p+d data 33) (at 65 MeV, having smaller experimental unce~ainti~s) theory perfectly well except at the most forward angles.

agree with the

5. Summary and Conclusion We have measured the neutron analyzing power A,, of ii+d elastic scattering at E, = 67 MeV in the angular range @,.,. = 30”- 165” (@rat,= 20”- 1SO”). The experimental data agree well with the results of our rigorous 3N calculations, in which both the PARIS and the BONN potential have been employed; the difference between the results is negligible. Two-nucleon partial waves up to j =3 have been included, which appears to be sufficient. Our data agree also with the most recent results of another group 34). The tendency for better agreement between experimental data and theory at higher energies, which was indicated in the introduction, is confirmed. In the past, many efforts have been made to compare experimental n-t-d elastic A clear trend of increasing results with the corresponding p+d data ‘“~‘4~‘8~35-4’). agreement towards higher energies was found which, in view of our results, appears to be confirmed.

We gratefully appreciated the continuous The numerical calculations were performed of the KFA Jiilich, Germany. The work

support by the PSI technical services. at the H~chstleistungsrechenzent~m has been partially supported by the

H. Riihl et al. / Analyzing

Schweizerische Nationalfonds (contract CPBP 01.09>,

and by the Polish

power

Ministry

389

of National

Education

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