Charged-pion photoproduction from 3He with positron-annihilation quasi-monochromatic photons

Nuclear Physics A!554 ( 1993) 679-700 Non-HoUaad

NUCLEAR PMYSKS A

C~~~~d-pion photoproduction from 3He with

positron-annihilation quasi-monochromatic photons

N. d’Hose , G. Audit, A. Bloch , N. de Botton , L, Ghedira , L. Jammes , J.M. Laget ,

J. Martin, E. Mazzucatto , C. Schuhl , G. Tamas and E. Vincent

Service de Physique Nucleaire, DAPNIA, Centre d’Ettides Nucleaires de Saciay, 91iQJ Gif-sw- Yvette Cedex, France

M. Rodgers and P. Stoler

P. Argan , A. Braghieri and P. Pedroni

IFFY Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy

Received 10 February 1992

Abstrack Cross sections were determined in the d( 1232) excitation region for the reactions 3He(y, rr* )3H, 3He(y, rc+ )nd,nnp and 3He(y, rr- )ppp at several photon energies and pion emission angles. Inclusive charged-pion photoproduction spectra were measured with a magnetic spectrometer using quasi-monochromatic positron-annihilation photons. Quasi-free mechanisms have been clearly observed, but pion-nucleon and nucleon-nucleon rescattering and Pauli exclusion mechanisms must be considered to explain the trend of the data for the different channels.

NUCLEAR REACTIONS “He(y, x+ )3H, ‘He(y, z+ )mi,nnp, 3He(y, Z-)PP~ ; EY from

E 210 to 450MeV ; Ok from 20’ to 72” ; measured d*o/dQdP(E,, 0%) ; estimated

du/d~(E*) at 6a z 40.@ ; estimated da/d9 (0%) at ET = 300 MeV.

1. IutrlMluetiou

The measurement of photodisintegration and pion photoproduction on light nuclei has been part of a program at the Saclay Linear Accelerator which seeks to characterize the rn~h~~srns of photon-induced reactions in few-nucleon systems. Such systems ai- low us to study fund~ental processes in the nuclear en~ronment and to compare data with microscopic calculations which are performed using “exact” few-body nuclear wave functions derived from model nucleon-nucleon interactions. Previously reported experi- ments on three-body systems, e.g. 3He ( y, p )np [ref. ’ ) ] and 3He ( y ,pp) n f refs. 2*3 ) I, were

Correspondence to: Dr. F. Lepap, DAPNIA, Dot. Bat. 703, Centre d’Etudes Nucleaires de Saclay, 9 1 f 9 1 Gif-sur-Yvette Cedex, France.

0375-9474/93/%06.00 @ 1993-Elsevier Science Publishers B.V. All rights reserved

680 N. &Hose et al. / Charged-pion photoproduction

performed to emphasize and to study the two- and three-body photon-absorption mech-

anisms. However in the A-resonance region, inclusive pion photoproduction on 3He is

dominated by the quasi-free process on the individual nucleons, although medium correc-

tions are also expected to play important roles. Pion and nucleon final-state interactions

(FSI) from uncorrelated as well as correlated nucleons, meson-exchange currents (MEC)

and possibly off-shell operator effects have to be considered.

In a previous article 4), we described the results of a systematic study of the inclusive

reactions *H ( y, n+ )nn and *H ( y, n- )pp. Multiple-scattering calculations reproduced the

measured momentum spectra rather well, successfully accounting for the enhancement in

the cross section at pion momenta corresponding to the strong interaction ofthe two recoil

nucleons emerging in a relative s-state. However, the momentum-integrated theoretical

cross sections were generally somewhat higher than the experimental values, especially

at the forward pion angles where the discrepancies were about 10%.

In order to further test the multiple-scattering model, and our understanding of the

reaction mechanism in the context of a three-nucleon system, we have performed a similar

study of the inclusive reactions 3He(y,a+)nnp,nd and 3He(y,a-)ppp. We have also

measured the cross section of the exclusive reaction 3He ( y, 7c+ ) 3H, and of the elementary

reaction H(y, rr+ )n under the same kinematics.

This article reports angular distributions of pion spectra obtained at a series of photon

energies from 210 to 450 MeV, which spans the kinematic region from near threshold,

through and beyond the free A, which peaks at Ey N 320 MeV. The results for the

inclusive reactions are compared with a multiple-scattering calculation as described in

refs. 5,6), and for the exclusive reaction with recent DWIA calculations as in refs. 7*8).

2. Description of the experiment

The experimental set-up was similar to that described in ref. 4), and is shown schemat-

ically in fig. 1.

Quasi-monochromatic photons were produced by the method of positron annihilation

in-flight. The annihilation photons were produced by passing a positron beam (typi-

cally 50nA average current at 1% duty factor) through a 8.9 cm thick liquid-hydrogen

conversion target with thin mylar windows (0.0 12 cm). In addition to monochromatic

annihilation photons, a continuous energy spectrum of bremsstrahlung photons was also

produced. In order to eliminate the pion spectra due to the bremsstrahlung contribu-

tion, a second pion yield was obtained at each kinematic setting using a copper radiator

of the same thickness in radiation lengths (0.015 cm) which produced a nearly pure

bremsstrahlung spectrum because of its high Z. After passing through the radiator the

positrons were swept by a magnet into a Faraday cup where their integrated charge was

measured. The photon beam was collimated to a 3 cm diameter cross section at the tar-

get position, and its flux was monitored downstream by a Wilson-type gas quantameter

whose calibration constant was determined with an accuracy better than 1%. Such a facil-

ity gives typically 5 x lo7 annihilation photons per second in the 150 to 550 MeV energy

N. d’Hose et al. / Charged-pion photoproduction 681

Fig. 1. The experimental set-up.

range with a few MeV resolution.

The cryogenic targets consisted of two identical stacked vertical cylinders, each having

a diameter of 7 cm, height 4.5 cm, and walls consisting of 0.005 cm thick stainless steel.

The two cells contained liquid 3He and hydrogen.

The pions were detected by two magnetic spectrometers with nominal maximum mo-

menta of 400 and 700 MeV/c. Solid angles for these spectrometers were respectively

3.34 and 2.24 msr, and momentum acceptance 9O/o and 12%. Each focal plane was instru-

mented with an array of plastic scintillator detectors, which were used for momentum

analysis (in 16 channels) and particle identification.

The experimental procedure consisted in the measurement of pion spectra for hydrogen

and copper radiators for the same quantameter integration. As previously indicated, the

subsequent subtraction of these spectra yields essentially the contribution of the annihila-

tion component of the hydrogen photon spectrum, since the bremsstrahlung component

is to first order well approximated by the copper photon spectrum. Figs. 2a, 2b and 2c

show measured pion spectra for the elementary reaction H (y, n+ )n, obtained (a) with a

hydrogen radiator, (b) with a copper radiator, (c) the result of subtracting (b) from (a),

and (d) the result of applying the correction to account for the negative tail in (c) The

spectrum shape was calculated by folding the photon spectrum with the response func-

tion of our experimental set-up. (The dashed line corresponds to the initial calculation

which was further corrected to fit on the best the bremsstrahlung spectrum on hydrogen

radiator). Since the subtraction corresponds to equal quantameter integrations on the

hydrogen and copper radiators, the resulting spectrum displays below the annihilation

peak a low-energy tail whose shape is due to a slight difference between the hydrogen

and copper bremsstrahlung spectra. A small correction has been made in order to elim-

H

(6 ,

x+)n

S

W L

e ra

diat

eur

H

Es

: 33

7.9

MeV

230

240

251)

26

6 2?

0 28

0 29

0 33

0 24

6 25

0 26

0 27

0 2a

o 29

0

230

240

250

260

270

280

290

Pn+f

W'/c

J

6.0

I ,

f ,

f ,

1 ,

-2.0

I

I ,I

, I

L 1,

1

)

230

240

250

260

270

280

290

PTtc

lM*V

/c

J

Fig.

2.

II+

phot

opro

duct

ion

spec

trum

on

hyd

roge

n at

E,

= 33

7.9

MeV

and

B,+

= 4

0.6”

.

N. d’Htxe et al. I ~ha~g~d-~io~ ~hato~rod~tion 683

inate the negative part of the spectrum and to keep only the annihilation contribution. The photon spectrum was calculated using annihilation and bremsstrahlung differential cross sections due to Tsai 9, together with an analytical treatment of positron multiple- scattering, collision and radiation losses inside the radiator. The positron-beam emittance and momentum dispersion as defined by the analyzing slits in the beam transport system were also folded into the calculation. We have also taken into account the kinematic variation of the momenta of pions entering the spectrometers at different angles and the variation of the cross section with the photon energy. The results shown in figs. 2a, 2b, 2c agree very well with the data except for a small discrepancy in the low-energy range of the spectrum which can be accounted for by a loo/b empirical correction applied to the calculated hydrogen bremsstrahlung distribution. This does not affect at all the dominant annihilation contribution. The data thus corrected (fig. 2d) yields a final spectrum due to the positron-annihilation photons only. Uncertainties in the positron-beam divergence at the radiator (typically 3 x 10m3 rad as measured using wire chambers profile moni- tors) and in the radiator thicknesses gives an error in the absolute number of photons estimated at i4%.

The measured pion spectra were corrected for the following effects: (a) The relative efftciency of the momentum channels in the spectrometer ladder coun-

ters was checked by changing the magnetic field in small steps in order to allow the overlap of the different channels.

(b) The in-flight pion decay between target and detectors, and contamination by muons were calculated using a Monte Carlo simulation which includes the exact geometry, the field map of the spectrometers, and utilizes the theoretical pion-photoproduction differential cross section. Muon contamination ranged from S”k to 15% depending on the kinematical conditions.

(c f The nuclear abso~tion in the target and the detectors was calculated using experimental pion cross sections for H [refs. l”,li ) 1, ‘He and 4He [ refs. 12*13 I] and predictions from Landau for 3He [ref. I4 ) 1. The correction ranged from 4% to TONI depending on the pion momentum and the target nucleus.

(d) The contamination due to electrons and target walls were found to be about 0.6% and 2% respectively of the contribution of 3He target for both the “400 MeV/c” and the “700 MeV/c” magnetic spectrometer. This was observed by setting the spectrometer magnetic fields for negatively charged particles and looking for events originating in the hydrogen target. Fu~he~ore we did not see any counts above the pion maximum momentum allowed by kinematics.

As a verification of the overall system normalization, the differential cross section for H ( y, II+ )n extracted from our experimental procedure was compared to previous mea- surements and theoretical cross sections calculated using the Blomqvist-Laget model 5 ). An angular distribution obtained for 300 MeV photon incident energy and an excitation curve obtained for 8,+ = 40.6” are shown in fig. 3. Statistical errors are better than 5%, and systematic errors (which are not taken into account on the figure) are estimated to be about 6% ; the overall agreement is satisfactory within the quoted errors.

684 N. d’Hose et al. / Charged-pion photoproduction

I I I I I I

H (E.n+)n

$ 20 - t3s+,ab = 40.6’ 9

,?_?---i-+-.,,,+

+ ‘\ ‘\ -

=L 4 ‘\

&y/’

,,/f ” ‘.

0 cr

d .$ ,. __+&Le*-q- 0 LEBEDEV 68

- 0 BONN 70

V ORSAV 67

. SACLAY a)

0 I I I I I

200 250 300 350 400

Eli ( MeV 1

I III ( 1111 1 III

H (x,n+)n

- Ea = 300.0 MeV

A STANFORD 58

n STANFORD 66

V ORSAY 67

0 BONN 70

l SACLAY

b) - 0 I I , , I I I I I I III

0 50 100

efl+cnl 1 deg.1

Fig. 3. (a) The differential n+ photoproduction cross section in the laboratory as a function of the photon energy for 0,+ = 40.6”. The dashed curve is a fit on the experimental data. (b) The c.m. differential II+ photoproduction cross section on hydrogen as a function of the c.m. angle for

Ey = 300 MeV. The curve is the Blomqvist-Laget calculation.

3. Results

Fig. 4 shows the IC+ momentum spectrum for photoproduction on 3He at EY =

337.9 MeV and 9,+ = 40.6”. Two features are apparent. The narrow peak at the high-

momentum limit corresponds to the exclusive channel 3He(y, a+ )3H. The large broad

peak with a maximum near P,+ = 274 MeV/c is the contribution corresponding to the

inclusive channels 3He(y, a+ )nd and 3He( y, 7c+ )nnp. The latter is a clear signature of the

absorption of the interacting photon by a quasi-free proton in the nucleus. Its maximum

occurs at the momentum of a rr+ emitted at the same angle as in the reaction H(y, n+ )n


t 3He (y,n+l

220 240 260 260

P,,+ (MeV/c)

300 320

Fig. 4. Typical II+ photoproduction spectrum on 3He measured at photon energy Ey = 337.9 MeV and pion emission angle 13 = 40.6O. The solid curve gives the theoretical predictions without normalization. The dotted curve presents a quasi-free calculation. The shape is given by the nucleon momentum distribution in 3He, and the amplitude is adjusted to the data. All the calculations are

folded with the experimental response.

if we take into account the binding energy. The broadening is due to the Fermi motion

of the active nucleon in 3He.

3.1. THE 3He(y,lr+)3H CHANNEL

Table 1 gives the differential cross sections obtained at the various kinematics studied

in the present experiment. The variation of the cross section as a function of photon energy

for fixed values of momentum transfer to the nucleus (Q* = 0.48, 1 .OO, 2.20,3.10 and 3.9

fm-* ) are shown in fig. 5. For the three largest momentum transfers, our results (filled

circles) are compared to earlier data from Illinois (open circles) [ref. “) ] and Orsay

(triangles) [ref. I6 ) ] which are in good agreement, and recent data from Bonn (squares)

[ref. I’) ] which exhibit a large variation in cross section as a function of photon energy

which is not in accord with other data. The new and specific feature of our experiment

is the use of monochromatic photons.

This reaction was first studied theoretically in the framework of the plane-wave impulse

approximation (PWIA) (short-dashed) [ refs. “,19) 1. The corresponding results overesti-

mated the experimental data. Two recent calculations 7S8 ) have been performed within the

framework of the distorted-wave impulse approximation (DWIA) and have attempted to

deal with pion rescattering mechanisms. Realistic correlated three-body wave functions

obtained from Faddeev calculations were used. The elementary pion-photoproduction

amplitude is the most recent unitary version of the Blomqvist-Laget amplitude 20) which

describes the real and imaginary parts not only for the resonance magnetic M: multipole

but also for the resonance electric ET multipole. The pion-nucleus final-state interaction

was described in terms of an optical potential including the spin and isospin dependence


12.50

2.50

0.00

7.50

5.00

s 2.50

2 0.00 c: 5 4.00

-Cl 3.00

2.00

1.00

0.00

2.00

1.50

1 .oo

0.50

0.00

1 .oo

0.75

0.50

0.25

0.00

I I I

!.2 fm.2 5 Q2 5 2.4 frn4

200 300

E, WeV)

400

Fig. 5. Energy dependence of the differential cross section for the channel 3He(y, 7c+ )3H at fixed values of momentum transfer Q2 to the nucleus.


TABLE 1

3He(y,n+)3H

EY

(MeV)

e Q2 da/d9

(de;; (fme2) W/sr)

5.68f0.97 208.2 28.0

40.6

114.0

0.28

0.48

2.20

6.52zt0.39

1.16zt0.49

248.1 33.2 0.48 5.83f0.88

40.6 0.68 6.00f0.49

50.7 1.00 6.08f0.88

82.7 2.20 2.40f0.52

106.9 3.10 1.74kO.30

133.0 3.90 1.02f0.15

218.0 40.6 0.87 6.08f0.43

297.7 20.0 0.28 5.70zko.47

27.1 0.48 7.13zk0.83

40.6 1 .oo 5.78f0.33

63.9 2.20 4.20f0.7 1

72.0 2.68 2.52f0.42

79.4 3.10 1.57f0.33

93.2 3.90 0.58&O. 11

EY 4+ (MeV) (deg. 1

308.0 40.6

Q2 (fme2)

1.07

da/dG’

W/w)

7.15ztO.38

61.1 2.20

63.3 2.33

68.4 2.65

337.9 40.6 1.30

54.4 2.20

56.3 2.33

60.7 2.65

347.6 23.0 0.48

34.0 1 .oo

40.6 1.38

52.7 2.20

397.5 20.0 0.48

29.4 1 .oo

40.6 1.82

45.1 2.20

447.3 40.6 2.32

2.81f0.18

3.38f0.34

2.23f0.26

5.26f0.37

2.66f0.30

2.1160.22

1.25f0.15

8.60h0.53

5.02f0.50

3.99f0.31

1.47f0.25

9.64zt1.52

5.16f0.93

2.52f0.24

1.13f0.24

1.35f0.17

which turns out to be very important for a nucleus like ‘He. Furthermore in one of the

calculations ’ ) the two-step charge-exchange 3He( y, rr”) 3He (no, n+ ) ‘H has also been in-

troduced. These complete calculations give better agreement with the experimental data,

except for the smallest Q2.

The different calculations are also presented in fig. 5. Those of ref. ’ ) : in the frame-

work of pion plane-wave (short-dashed), of distorted-wave (long-dashed) and with the

addition of the charge-exchange contributions (solid curves). The calculations of ref. 8,

made in distorted-wave are also indicated (dot-dashed curve) (the double-dot-dashed

curve does not include the ET multipole contribution).

3.2. THE ‘He(y, II+ )nd,nnp AND 3He(y, 1~~ )ppp CHANNELS

Figs. 6-10 present all the measured spectra with their statistical errors. In the momen-

tum region covered by the experiment the shape is well reproduced by a simple model

based on a quasi-free production on nucleons in 3He. The nucleon momentum distribu-

tion is empirically taken to be a sum of gaussians which reproduce the observed momen-

tum distributions obtained in the reactions ‘He (e,e’p)d and 3He (e,e’p)n [ref. ” ) 1.

2.0 I ’ 1 s I ’ I a I ’ , ’ 9 ’

1.5 - “y;y$y 71;+ _. I$,= 248.lMeV

, I 7c

+.

7l - 8, = 40.6O

1.0 L

.f

:ii ft i : 0.5 - *,0 - .A; (‘;

T - -0.5 I . t c I . I L L . I . I .

80 100 120 140 160 140 160 180 200 220

-0.25 * ’ * ’ . ’ ’ ’ ’ * ’ ’ I . ’ ’ ’ . ’ 160 180 200 220 240 200 220 240 260 280

PTL WV/c)

Fig. 6. x photoproduction on 3He at 40.6’ for E, = 208.2, 248.1, 278.0 MeV. The solid curve presents the theoretical predictions. The dotted curve indicates a quasi-free calculation. The shape is given by the nucleon momentum distribution in 3He, and the amplitude is

adjusted to the data. Ali the calculations are foided with the experimental response.

N. dWose et al. / Cogged-pio~ phot~pr~ucti~~ 689

2”. . . . . . . * . . . . . . . ,ffi I ,

- 0.5

, . I .

s * t I . -025 200 220 240 260 280 220 240 260 280 300

3 -0.5 I . * . t . f , . t . I .

220 240 260 280 300 300 320 340 360 380

%

-0.251 . ’ ’ . ’ ’ ’ . ’ . ’ . ’ . ’ * ’ 240 260 280 300 320 340 360 380 400 420

Px WWc)

Fig. 7. A photoproduction on 3He at 40.6O for E y = 308.0, 337.9, 347.6, 397.5, 447.3MeV. (See also the caption of fig. 6.)


v! 9 L? 9 t-i 4 0 0

2

‘9 I , I , I , I

+

I2

-

4

N. d’Hose et al. / Charged-pion photoproduction

I 1 I u I ’

+ I=!

I I I I I I I

-

+

- - :

I ’ I ’ I r

‘#

. . 1+1.-’

.:’

<

. . .

h I I I I I I -

692 N. &Hose et al. / Charged-pion photoproduction

-0.5 I .I. I .I . I. I .I.,. 180 200 220 240 260 220 240 260 280 300

P,(MWc)

Fig. 10. II photoproduction on 3He at backward angles 63.3” and 68.4” at E, = 308.0 MeV, and 54.S’, 56.3” and 60.7O at Ey = 337.9 MeV. (See also the caption of fig. 6.)

The effects of FSI on the high-momentum part of the pion spectrum, due to the strong

interaction of the nucleons emerging in a relative s-state was accounted for by an em-

pirical correction based upon the Watson formula 23). This simple model, folded with

the experimental response has an amplitude adjusted to the data (dotted curves). It is

used as an aid in eliminating the effects of the bremsstrahlung tail which was discussed

in sect. 2.

The solid curves are theoretical results without any renormalization. They were ob-

tained by means of a multiple-scattering calculation which was carried out within a la-

grangian framework utilizing the complete Blomqvist-Laget elementary operator 536P20).

The 3He wave function is the solution to Faddeev equations using a Reid nucleon-nucleon

interaction. The continuum wave function is taken as the sum of a plane wave and half-

N. #Hose et al. / Charged-pion photoproduction 693

-. x+nd quasi-libre

;; I.0

5 - n+nd + K+ nnp

E

$

.z

%

2 0.5

B

200 250 300

P,+ (MeV/c)

Fig. 11. The different contributions for the theoretical model.

b’

Fig. 12. The different multiple-scattering processes which are considered in the theoretical model.

off-shell nucleon-nucleon scattering amplitude for the same potential. Fig. 1 I presents the contributions of the different multiple-scattering processes which were included in

the calculation.

694 N. d*Hose et al. / Charged-pion photoproduction

o-- 200 300 400 500

ET (MeV)

Fig. 13. Energy dependence for the z+ and n- extrapolation value according to the theoretical model.

l 3Hely,n+)nd or nnp

0 50 3He( r,n-)ppp - Bn

= 40.6’

01 1 1 I

200 300 400 500 E, (MeV1

Fig. 14. Estimated cross section in the total momentum range as a function of Ey at Bn = 40.6”. As it is mentioned in the text the comparison between experiment and theory is independent of

the extrapolation.

(a) The dotted line is the quasi-free pion-photoprodu~tion mechanism for the case

‘He(y, n+)nd (diagram 12a).

(b) The short-dashed line takes into account also the nucleon and pion rescattering

N. d’ifose et al. / charged-pion photoprod~tion 695

I ET = 300MeV

-s 50 - l 3He (l,n+hd or nnp

> 40- ,I

$j 30- \ 8, 20-

IO -

0 , , , ,

0 IO 20 30 40 50 60 70 80

8, fdegl

Fig. 15. Estimated cross section in the total momentum range as a function of & at Ey = 300 MeV. As it is mentioned in the text the comparison between experiment and theory is independent of

the extrapolation.

@II = 40.6”

0- 300 400

Er (M&l

Fig. 16. Ratio between the cross section for rt+ and II- detected at & = 40.6O as a function of E,. We consider in the lower part only the differential cross sections integrated on the investigated momentum region, and in the upper part the differential cross sections estimated on the total

momentum range.

696 N. &Hose et al. I Charged-pion ~hotoprodu~t~on

TABLE 2

3He(y, 7c+ )nd,nnp

EY

integrated spectrum cross section

B A+ exp./theor. exp. theor. extrapol. exp. theor.

208.2

248.1

278.0

297.7

308.0

337.9

347.6

397.5

447.3

40.6

40.6

40.6

20.0

40.6

72.0

40.6

61.1

63.3

68.4

40.6

54.5

56.3

60.7

23.0

34.0

40.6

40.6

40.6

0.95f0.25

0.83&O. 11

0.74f0.08

0.64&O. 14

0.66f0.09

0.88iO.08

0.79f0.06

0.85f0.06

1.18f0.11

0.93zko.05

0.76ztO.06

0.68320.06

0.85zkO.06

0.78zkO.04

0.65ztO.06

0.72rtO.28

0.79rto.07

7.97f2.19

10.7911.46

13.57fl.35

5.52f 1.22

15.50*2.00

30.56f2.94

19.8611.51

30.88zt 1.96

42.891k4.05

33.18fl.69

22.9011.72

23.81f2.24

29.5812.17

26.94zk 1 SO

12.39hl.31

19.64f2.24

19.78Ikl.74

18.2417.03

16.36il.47

8.48 1.25

13.02 1.28

18.46 1.33

8.66 1.60

23.40 1.37

34.86 1.28

25.90 1.39

36.20 1.32

36.49 1.31

35.54 1.29

30.26 1.50

34.96 I .40

35.00 1.40

34.71 1.38

1.80

1.56

30.39 1.54

25.27 1.82

20.71 2.15

10.51

16.67

24.55

13.86

31.96

44.62

36.00

47.79

47.80

45.85

45.24

48.94

49.00

47.90

46.80

45.99

44.52

9.9612.72

13.81&1.87

18.05ztl.80

8.83A 1.95

21.16zt2.84

39.12f3.76

27.6lzk2.10

40.761t2.59

56.19f5.31

42.8Ok2.18

34.2412.57

33.3313.14

41.4If3.04

37.1812.07

22.30zt2.36

30.64f3.49

30.46f2.68

33.20f12.79

35.1713.16

for 3He(y, a+ )nd (diagram 12b). The antisymmetry of the final-state nucleons is also

treated. Note the deviations to the first curve: a significant quenching of the cross section

in the quasi-free region, an enhancement in the high-momentum region due to neutron-

deuteron s-wave scattering, and an impo~ant tail in the low-momentum region due to

both neutron-deuteron and pion-deuteron rescattering.

(c) The long-dashed line takes into account all the processes for 3He(y, X+ )nnp (dia-

gram 12~).

(d) Finally the solid curve is the sum of the two contributions 3He(y, rr+ )nd and

3He(y, ~+)nnp.

This theoretical model yields rather good agreement with the data except for n+ at

forward angles, where it overestimates the data by about 20% (see figs. 6-10, 14, 15).

This trend seems to increase with the photon energy. Two explanations could be given.


TABLE 3

3He(y, n-JPPP

integrated spectrum cross section

%- exp./theor. exp. theor. extrapol. exp. theor.

40.6 1.01*0.12 5.66YtO.66 5.60 1.18 6.59 6.68f0.78

20.0 1.29Lko.37 2.90f0.83 2.24 1.41 3.16 4.09f1.17

40.6 1.15ztO.08 8.69f0.62 7.56 1.19 9.00 10.34f0.74

72.0 l.Olf0.09 13.3641.18 13.24 1.13 14.96 15.10f1.33

40.6 1.07f0.07 9.12*0.58 8.51 1.19 10.16 10.89kO.69

61.1 0.98f0.05 14.39hO.77 14.74 1.14 16.80 16.40f0.88

40.6 0.711kO.06 8.6210.75 12.14 1.22 14.00 10.52f0.92

40.6 0.85f0.11 8.08f 1.07 9.51 1.27 12.11 10.25-fl.36

EY

278.0

291.1

308.0

347.6

447.3

3He/,

206 300 400

Ey(Mev)

Fig. 17. Ratio between the cross section for K + photoproduction on 3He and * H as a function of E, for a pion emission angle of 40.6O. We consider in the lower part only the differential cross section on 3He integrated on the investigated momentum region, and in the upper part the differential

cross section estimated on the total momentum range.


First the photoproduction on a nucleon bound in the final deuteron (diagram 12b’) has

not been taken into account. Second the wave function for the final states is not the general

solution of the Faddeev equations for a three-nucleon scattering state, but a truncated

multiple-scattering series: the initial and the final state are not strictly orthogonal.

Another theoretical [ref. 22) ] for n- photoproduction is also presented at E, = 297.7

MeV and 8, = 40.6” on fig. 6. This calculation uses a hyperspherical function where

the initial and final states are described using the same NN potential. No significative

difference with the previous model is observed except for the low-momentum region.

The measured pion spectrum covers on average only 80% of the quasi-free peak (de-

lined on the process ‘He( y, n+ )nd which is represented by the dotted curve in fig. 11).

So it seems important to present the experimental spectra integrated over the measured

pion momentum and to attempt to give an extrapolation. In order to do so, it is im-

possible to rely on the quasi-free model. In fact in the kinematical region of this pion-

photoproduction experiment, the pion-nucleon invariant mass is near that of the mass

of the S such that the pion-nucleon rescattering is at a maximum. This effect quenches

the quasi-free peak and enhances the cross section in the low-momentum part of the pion

spectrum.

The theoretical model takes into account the rescattering effects. Thus, we have ex-

trapolated from the data a tail with the shape of the theoretical spectrum from figs. 6-10,

which is renormalized such that, in the region of their overlap the area under the theoret-

ical curve equals that of the experimental data. Fig. 13 indicates the relative importance

of the extrapolation as a function of the photon energy for rr+ and 7c- at en = 40.6”. It

increases quite significantly for X+ above 300 MeV.

Tables 2 and 3 give the results for n+ and Z- of the integral of the experimental

(column 4) and theoretical (column 5 ) spectra over the pion momentum region covered

by the experiment at each angle (column 2) and energy (column 1). The ratio between

the experimental and theoretical values given for the investigated momentum region is

presented in column 3. The results for the estimated X+ and n- cross sections are given

in column 8, and compared to the theoretical values (column 7). Column 6 shows the

extrapolation.

Figs. 14 and 15 present the estimated momentum-integrated cross section as a func-

tion of Ey at 8, = 40.6” and as a function of 13~ at E, = 300 MeV, respectively. The

comparison between experiment and theory is obviously independent of the extrapola-

tion. Whereas for n-, experiment and theory agree rather well, for n+ the theory appears

to overestimate experiment, especially when the photon energy increases as it has been

mentioned previously. In fig. 15 we can note the decrease of the cross section at forward

angles due to phase-space reduction and the Pauli antisymmetrization.

The ratio between the cross section for rr+ and 7c- detected at the same angle is pre-

sented in fig. 16. This depends on the extrapolation and is the reason why the two cases

integrated on the investigated momentum region, and estimated on the total momentum

range are separated. The extrapolation is important for x+, as Ey becomes larger than 300

MeV: this trend is clearly apparent in this figure. If we consider only quasi-free processes


and assume equal cross sections for the neutron and proton, we would expect a ratio of

around Z/N or 2. The main deviation to this simple hypothesis stems from the effects

of rescattering and the Pauli exclusion principle which reduce the phase space more for

the final a-ppp state than for IZ+.

Fig. 17 gives the ratio of the cross sections for n+ photoproduction on ‘He and ‘H,

as a function of Ey at 8, = 40.6” in the two cases defined previously. This ratio is

nearly constant with energy when the cross section is integrated only over the pion-

momentum region covered by the experiment, while it steadily increases when the total

estimated cross section is used. This trend is more important above 300 MeV where the

pion rescattering is dominant.

4. Conclusion

The quasi-free mechanisms have been clearly observed in this experiment in the high-

momentum region, which has also been observed with pionic probes 24). However, multi-

nucleon processes (pion or nucleon rescattering and the Pauli exclusion mechanism) must

be considered to explain the global trends of the data, both in the 3He (y, rr+ )3H and

‘He(y, X*)X channels. They quench the quasi-free peak and shift the strength towards

the low-momentum part of the pion spectrum. Unfortunately, the positron-annihilation

method, as applied in this experiment, prevents the study of the low-momentum tail. This

is due to the large statistical errors at low pion momenta introduced with the subtraction

of a large bremsstrahlung component. The use of tagged photons with the new genera-

tions of high-duty-factor accelerators and large-acceptance detectors would be particularly

welcome to better identify all these different mechanisms.

References

1) N. d’Hose et al., Phys. Rev. Lett 63 (1989) 856 2) G. Audit et al., Phys. Lett. B227 (1989) 331 3) G. Audit et ab, Phys. Rev. C44 (1991) R575 4) J.L. Fame et al., Nucl. Phys. A424 (1984) 383 5) J.M. Laget, Phys. Report 69 (1981) 1 6) J.M. Laget, New vistas in electro-nuclear physics, ed. E.L. Tomusiak et al. (Plenum Press,

New York, 1986) p.361 7) S.S. Kamalov, L. Tiator and C. Bennhold, Few-Body Systems 10 (1991) 143 8) M.K. Cheoun, S. Ishikawa and T. Sasakawa, submitted to Nucl. Phys. 9) Y.S. Tsai, Rev. Mod. Phys. 46 (1974) 815

10) E. Pedroni et al., Nucl. Phys. A300 (1978) 321 11) P.M. Ogden et al., Phys. Rev. 137 (1965) 1115 12) F. Binon et al., Nucl. Phys. A298 (1978) 499 13) Y.A. Shcherbakov et al., Nuovo Cim. 31A (1976) 249, 263 14) R.H. Landau, Phys. Rev. Cl5 (1977) 2127 15) J.R. O’Fallon et al., Phys. Rev. 141 (1966) 889 16) D. Bachelier et al., Nucl. Phys. A251 (1975) 433 17) B. Bellinghaussen et al., Nucl. Phys. A470 (1987) 429 18) L. Tiator, A.K. Rej and D. Drechsel, Nucl. Phys. A333 ( 1980) 343

700 N. d%lose et ai. I Charged-pion photo~~~u&tiu~

19) J.L. Ballot, C. Lazard and Z. Marie, Nucl.Phys. A395 (1983) 471 20) J.M. Laget, Nucl. Phys. A481 (1988) 765 21) E. Jans et a/., Nucl. Phys. A475 (1987) 687 22) R.X. Dzhibuti and R.Y. Kezerashvili, Sov. J. Nucl. Phys. 40 (1984) 443 23) M.L. Goldberger and K.M. Watson, Collision theory (Wiley, New York, 1964) 24) A. Klein et al., Phys. Lett. B187 (1987) 253

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Charged-pion photoproduction from 3He with positron-annihilation quasi-monochromatic photons