Elastic scattering of π+ and π− mesons from 3He and 4He at energies from 300 TO 475 MeV

Nuclear Physics A466 (1987) 458-472 North-Holland, Amsterdam

ELASTIC

SCATTERING

OF

n+

AT ENERGIES

AND

r-

FROM

MESONS

FROM ‘He

AND

4He

300 TO 475MeV

J. BOSWELL, G.S. DAS, P.C. GUGELOT, J. KALLNE’, J. MCCARTHY, L. ORPHANOS, R.C. MINEHART, R.R. WHITNEY* Institute for Nuclear & Particle Physics, University

of Virginia, Charlottesville,

VA 22901, USA

P.A.M. GRAM Los Alamos

National

Laboratory,

Received

Los Alamos,

3 June

N.M. 87545, USA

1986

Abstract. The cross section for elastic scattering of pions from 3He and 4He was measured for incident energies from 300 to 475 MeV. The pions were detected in a magnetic spectrometer at scattering angles from 30” to 130”. Results on angular distributions are presented. A particularly interesting feature is that a deep minimum at llO”, previously observed at 295 MeV, is found to persist up to 400 MeV. The minimum is fixed in angle and is therefore not a simple function of q*. NUCLEAR

REACTIONS

3He,

4He(rr+, n+), (?r-, ?r-), measured o( 0).

E = 300,

350,

375,

475 MeV;

1. Introduction

Elastic scattering of particles from nuclei has been used to study both the one-body structure of the nucleus and the nucleon-nucleon interaction in the nuclear medium. Elastic electron scattering has been used extensively to study the ground state charge and magnetic moment distributions. The application of electron scattering to the study of the matter distribution is more difficult. Hadronic particles, such as protons, neutrons, or pions offer the possibility of probing the matter distribution. Among the hadrons, pions are especially attractive because the elementary pion-nucleon interaction is simplified by the pion having zero spin, and is well-known over a large range of energies. At energies up to about 300 MeV the pion-nucleon cross section is large and dominated by excitation of the A (I = $, J = 1) resonance. Because of the strong elementary TN interaction, pions with these energies tend to interact primarily in the surface region of a complex nucleus. At higher energies, however, ’ Present ’ Present

address: address:

JET, Abingdon, OX14 3EA, England. CEBAF, 12070 Jefferson Ave., Newport

0375-9474/87/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

News, VA. 23606, USA.

.I. Boswell et al. / Elastic T* scattering

the pion-nucleon is more probable. advantage component

cross section

is much smaller,

The availability

of the different

of both

cross sections

459

so that penetration

rTT+and

Y

beams

for these two particles

into the nucleus allows

one to take

on the same isotopic

of the nucleon.

With incident

energies

appropriate

for excitation

of the A -resonance,

elastic pion

scattering from the helium isotopes has been studied by several groups lm4). The measured cross sections have a minimum for scattering angles in the neighborhood of 75”, which is thought to be a consequence of the minimum at 90”c.m. in the p-wave part of the elementary TN cross section. At energies above 200 MeV the cross sections measured by Binon et al. ‘> for rTT-elastic scattering from 4He have a second shallow minimum for angles from 110” to 135”, but the statistical errors are rather large. Celenza, Liu and Shakin ‘) used a covariant multiple scattering theory with complete integration over the motion of the target particles to obtain good agreement with the Binon data for energies from 100 to 260 MeV, even to the point of producing a second minimum in the large angle region. Landau “) was able to fit the data for 3He and 4He in this energy region using an optical model derived from the TN phase shifts with the inclusion of spin. He found that in the region of the p-wave minimum,

where spin-flip

scattering

makes a significant

contribution,

the cross section for 3He depends strongly on the magnetic radius of the nucleus. He pointed out that above 300 MeV the minimum in the nuclear form factor ought to appear in the pion scattering cross section. Liu and Shakin ‘) also used their covariant model to obtain a good representation of measurements on 4He at pion energies of 960 MeV [ref. “)I and 1120 MeV [ref. ‘)I. At these higher energies the cross section has a diffractive minimum at a squared four-momentum transfer Q’ = 2.4 (GeV/ c)‘. Dozier and Chalmers lo) also obtained good agreement with the higher energy data with a model based on a single-scattering optical potential. Their model was sensitive to the choice of Z-N phase shifts, as well as to the behavior of the nuclear form factors at large Q2. In an earlier experiment4) at LAMPF the elastic scattering cross sections for pions on 3He and 4He were measured with the EPICS spectrometer using incident energies from 50 to 295 MeV. The r + 4He cross section was found to have a minimum at a constant center of mass scattering angle of 19,.,. = 110” for incident energies from about 200 MeV, the lowest energy for which the minimum was observed, to 295 MeV, where the minimum is very deep. The calculations of Celenza et al. ‘) do not produce a minimum at a fixed angle and provide a poor representation of the large angle data in general. An explanation of the observed structure is still lacking. The experiment described in this paper was designed to study pion scattering at energies from 300 to 500 MeV using the P3 beam at LAMPF. Measurements were made for 4He at 300 and 375 MeV, and for both 3He and 4He at 350, 400 and 475 MeV. The data show that the minimum at 110” remains a prominent feature of the 4He cross section up to 400 MeV. At 350 MeV, the minimum is also seen in the 3He cross section. At the higher energies the statistical accuracy is not sufficient to draw any conclusions about the existence of the structure.

J. Boswell et al. / Elastic T* scattering

460

2. Experimental A schematic line at LAMPF Acceptance

diagram

of the experiment

were focussed

spectrometer

is shown in fig. 1. Pions from the P3 beam

on a target

(LAS)

[ref. “)I.

12C, and 27A1. The CH2 and 12C targets

method

located

at the pivot point

The targets

of the Large

used were 3He, 4He, CH2,

were used to normalize

the observations

to

the 7rp elastic scattering cross section, while the 27A1 target was used to determine the background from the aluminum windows in the helium cryostat. The incident pion flux was measured by a pair of scintillation telescopes upstream from the target which were set to detect particles (mainly muons from pion decay in flight) emerging on either side of the beam at an angle of 5”. An ionization chamber was located in the beam 5 m downstream

from the target. liquid 3He and superfluid 4He The target system was ascryostat 12,13) containing in separate, identical cells. The target cells were mounted one above the other inside the cryostat and were of rectangular cross section, 15 cm wide by 10 cm high, with their thickness varying from 2.5 cm at the edges to 3.75 cm in the middle. The front and back windows were made of 0.094 cm-thick aluminum. The LAS spectrometer is a QQD (quadrupole-quadrupole-dipole) system equipped with a scintillation counter Sl at its entrance and two five-element scintillation counter hodoscopes, S2 and S3, at its focal plane. The spectrometer was

s3 s2

&

w7-8 \ W5-6 2

1 meter

/

I.C.

/

BEAM

Fig. 1. Schematic diagram of the experiment. The pion beam passes through the target, T, and the ionization chamber monitor, IC. It is also monitored by the pion decay telescopes, rwl and 7rp2. The scattered pions are detected in the LAS spectrometer by scintillators, Sl, S2 and S3, the latter of which are each 5 element hodoscopes. The trajectory is determined from the positions measured in the 8 wire chamber planes, Wl-W8.

J. Boswell et al. / Elastic T*

configured

for a central

the spectrometer input

bend angle of 30” in the dipole magnet.

were determined

bers, each consisting

with four sets of multi-wire

of an x- and a y-plane.

to the spectrometer

approximately

461

scattering

was limited

around

the central momentum. the momentum momentum, deviation).

acceptance

resulted

through

proportional

The range of scattering

to +4”, which

9 msr. The useful momentum

Trajectories

angles

chamat the

in a solid angle

of

ranged from - 10% to +20%

In a momentum range of *lo% resolution was approximately

around the central 1.2% (standard

3. Data reduction The details

of the analysis

paper on the inelastic

scattering

are for the most part the same as described measurements

r4) and will therefore

in our

be summarized

only briefly here. After placing acceptance limits on the wire chamber coordinates to define the edges, the measured x- and y-coordinates were fitted by x2 minimization to the initial momentum and position of the particle at the target. Approximately 10% of the events were discarded because they were fitted poorly by the assumption of a single smooth trajectory with constant momentum. It is thought the poor fits are due either to scattering from an aperture such as a magnet pole tip, or to pion decay. Protons in the spectrometer were eliminated by measuring the time-of-flight from scintillators Sl to S2 and S3. Background from the aluminum walls of the target was subtracted using spectra measured with the aluminum targets. Corrections were made for the wire chamber inefficiencies, which were measured continuously. A correction was also made for pion decay in the spectrometer. The two pion flux monitors generally agreed to within 5-7% for the positive beams and to about 2% for the negative beams. They were calibrated by scattering pions from the CH2 and the C targets, which gave data on rrp scattering. The phase shifts of the Karlsruhe 15) analysis of TN scattering data were used to obtain the reference cross section for 7rp scattering. By comparing measurements at several angles for the same incident beam, the uncertainty in the absolute values of the cross sections

is estimated

to be on the order of lo-15%,

except at 400 MeV where

it is on the order of 20%. The uncertainties, discussed in more detail in ref. r4), are due to statistics, monitor fluctuations, to systematic problems in extracting the GTP peak from the CH2 data and to corrections for the spectrometer acceptance, which varies significantly over the PP peak. The momentum resolution of the LAS spectrometer was adequate to resolve the elastic peak for 4He, as shown in fig. 2 where two examples of typical spectra are illustrated. The small tail from the inelastic scattering was fit to the calculated phase space for a three-body final state in a narrow momentum region (25 MeV/c) just below the Reak. This was then subtracted from the spectrum to leave the elastic peak, which was subsequently fit to a gaussian function plus a constant term, using

462

J. Bowel1 et al. / Elastic ST* scattering

n+ SCATTERING FROM 4He 350 MeV

1250

n

DO 300

MOMENTUM

325

350

375

400

425

450

OF SCATTERED PION (MeV/c)

Fig. 2. Momentum spectra of positive pions with 350 MeV incident energy scattered from 4He through angles of 30”, @a), and 120”, (2bf.

a chi-square minimization routine. The area of the gaussian function was corrected for the fact that a chi-square minimization of a distribution for which the errors are determined by Poisson statistics underestimates the area by an amount proportional to the minimum chi-square 16). The area of the gaussian function was compared to the direct sum of the data in the peak region to check for inconsistencies. Examples of the fitting process are illustrated in fig. 3. For 3He, the elastic scattering is less we&resolved from the inelastic scattering so that systematic errors in separating the two can be expected to be larger. For energies above 350 MeV the number of angles for which a cross section for elastic scattering can be extracted at all is rather limited.

4. Results The center of mass differential cross sections measured for both 7rTTt and GT-are given in table 1 and the n+ cross sections are plotted in figs. 4 and 5. The earlier measurements at 295 MeV are plotted with the present data at 300 MeV to show

J. Boswell et al. / Elastic d

scattering

463

TABLEA

Scattering cross sections for T+~H~ center of mass system T = 300 MeV e”

T=350 e”

dw.b/sr)

?r+

6380*260 2100+50

37*4 11*4 5*3 l.OztO.8 10*1

33.5 44.5 55.3 66.0 76.5 86.7 96.7 106.6 116.2 125.7 135.0

15400* 325 408OdC140 670* 22 131542 45*3 22*3 10* 1 2*1 2.3 * 0.8 6.4+ 1.0 15.1* 1.1

33.9 44.9 55.8 66.6 77.0 87.3 97.3 126.2

8200*200 1810*60 244*13 55*4 25*5 11*3 5*2 2.9* 1.7

dWsr) IT+

158*11

66.3 76.7 87.0 97.0 106.9 116.5 125.9

42*3 13*1

8*1

lP

hWsr) 7r+

iv

MeV

126*7 53*4 30*3 8*1 2.1 zko.4 2.OztO.4 5.7kO.6

T = 475 MeV

T = 400 MeV e”

t+

h.Wsr)

7r+

44.1 54.9 65.4 75.9 86.1 96.1 106.0 115.7 125.2

T=375

MeV

w-

59*4

d@Isr) ?r+

v-

34.4 45.6 56.6 67.4

3800* 500 530*60 63*17 23*6

21*4

88.2

9*4

7.3 * 0.7 5*1

that the two data sets are in reasonable

agreement.

Because the rTT-beam at LAMPF

is much less intense than the rTT+beam, measurements of Y scattering were more limited than for 7r+. Generally for 4He the rTT+and Y cross sections agree within statistical and normalization uncertainties. The cross sections for scattering from 3He and 4He are similar at all the energies measured in this work. The distinctive minimum at 110” is observed with 4He at 300,350,375 and 400 MeV, and shows no change over this energy range within the experimental accuracy. The position of the minimum exhibits no significant dependence on the incident energy. For rTT+ + 3He at 350 MeV incident energy the scattering

J. Boswell et al. / Elastic

464

n+ 350

60 ~ f

+ -

40

350

**

b

2

+*+

3He

l:~

MeV, 50”

++* *+

scattering

4He

100 80

6

li -

MeV, 90* -d d

20 0 300 325 350 375 400 425 450

0.4

r

P,=397.0

-

m = 5.8

0 -25 350 375 400 425 450 475 500 P,t (MeV/c) Fig. 3. Momentum spectra for scattering of 350 MeV positive pions from %Ie at So”, and from 3He at 90”. In the upper plot, the solid line shows the three-body phase space that is subtracted. In the lower plot, the remaining elastic peak is fitted to a gaussian.

TABLE 2 Scattering cross sections for x + 3He center of mass system T = 350 MeV 80

34.6 45.0 56.9 67.8 78.3 88.6 98.7 108.4 118.0 127.3 136.4

T = 400 MeV

e”

o(!.Wsr)

7r+

m-

10450*250 2470+ 130 540*22 92*9 25*12 19*3 ?.7* 1.6 6*3 1*1 3.8kO.6 3.9* 1.3

6190*420 1630*97 324+22 19* 10

4.9* 1.6

4.1 f 1.3

4&W

w+ 35.0 46.4 57.6 68.5 79.1 89.4 99.4

T = 475 MeV

4970* 120 980*50 222* 15 50*5 27*18 9*4 7*2

80

?r+

6

7*5

2.7 * 1.0

4.&W

35.7 47.2 58.5 69.5

2000 f 260 347*38 43+8 13*6

J. Boswell et al. / Elastic

6

465

scattering

cross section also has a minimum at 1 lo”, but it is less pronounced than that observed from 4He, just as was observed in ref. “) for 295 MeV pions. It seems likely that this less pronounced scattering,

minimum

which cannot

for 3He is related

to that exhibited

by 4He. Spin-flip

occur in 4He, but which can occur on the unpaired

in 3He, may tend to fill in the minimum is larger than the rr+n cross section

for GT++~H~. Since the r-n

at 295 MeV, this effect should

neutron

cross section

be even stronger

for Y+3He, and, indeed, the previous measurements at 295 MeV showed no minimum at all for this case “). In fig. 6 the data are plotted as a function of the four-momentum transfer, Q = 2p sin $3, where p is the incident pion momentum and 0 is the scattering angle in the center of mass of the T + He system. The Q-dependence of the form factor for 4He obtained from electron scattering 13*17)is also shown. At forward angles, with Q < 600 MeV/c, the pion scattering appears to depend strongly on the nuclear form factor:Although the observed minimum is not at a fixed Q, there is an indication from the existing data that it is most prominent at 300 MeV where its position is almost

coincident

to confirm

with the form factor minimum.

However,

better data are needed

this hypothesis.

-rr’(*He,

0

50

*He)n’

100 O,,

150

(degrees)

Fig. 4. (a) Elastic scattering cross section for positive pions on 4He at 300 MeV. (b) 350 MeV, (c) 375 MeV, (d) 400 MeV, (e) 475 MeV. The horizontal error bars represent the angular range included in each point, not an experimental error in measurement of angle.

466

J. Boswell et al. / Eiustic7~* scatteriflg

TT+(~II~,

0

50

4He)ni

100

O,,

150

(degrees)

Fig. 4. (b) Elastic scattering cross section for positive pions on 4He at 350 MeV.

TT+(~H~, 4He)n+ 104

103

102

101

100

10-l

10-z O,,

(degrees)

Fig. 4. (c) Elastic scattering cross section for positive pions on 4He at 375 MeV.

J. Boswell et al. / Elastic T* scattering

nf( III,

4He,

467

4He)7-r+

II/,/,,,,

,I

I

104 w

2

MeV

400

t103

i

101

100

0

50

100 O,,

Fig. 4. (d) Elastic

scattering

cross section

150

(degrees) for positive

pions on 4He at 400 MeV.

nCc4He, 4He)nt I,,,

,,I,

m

475

w

0

50

scattering

I/

3

MeV

i

F

O,, Fig. 4. (e) Elastic

,,/,

cross section

100

150

(degrees) for positive

pions on 4He at 475 MeV.

J. Boswell et al. / Elastic CT* scattering

3He, 3He)7-r+

x’(

MeV

350

k,

1

I

I1

0

I

50

I

I

I,

/,I

100

O,,

I

I 150

I

I

I,

(degrees)

Fig. 5. (a) Elastic scattering cross section for positive p*ions from 3He at 350 MeV. (b) 400 MeV, (c) 475 MeV. The horizontal error bars represent the angular range included in each point, not an experimental error in measurement of angle.

The possible explanations for the constant angle of the minimum were discussed in ref. “1. A minimum fixed in Q at the location of the diffractive minimum in the form factor could be interpreted in terms of the nuclear structure and would imply the predominance of single TN scattering. The constancy in angle, however, argues against

this interpretation.

One possibility

is that second

order effects involving

two

nucleons, such as multiple scattering or the excitation of a two nucleon resonance, such as a dibaryon, might produce an interference minimum. The ratios of the r+ scattering on 3He to that on 4He are fairly constant at forward angles, where the measurements are most precise and are close to i at each of the energies, 350, 400 and 475 MeV. Finally, it should be mentioned that at 400 MeV no evidence for an elastic peak in T-+~H~ scattering was observed at 60” in the laboratory system, whereas one for r+ scattering was clearly evident. The two spectra are shown in fig. 7. This suggests that it is important to measure T +3He scattering at energies well above the resonance to confirm the large difference in the r+ and -r- elastic cross sections indicated here, and to investigate a possible minimum in the K+ ‘He cross section at f3rab= 60” and T, = 400 MeV.

J. Boswell et al. / Elastic 6

0

50 O,,

469

scattering

100

150

(degrees)

Fig. 5. (b) Elastic scattering cross section for positive pions from 3He at 400 MeV.

nf(3He,

“He)x+

Fig. 5. (c) Elastic scattering cross section for positive pions from 3He at 475 MeV.

470

J. Boswell et al. / Elastic d

\r

4He Elastic

n+-

104

scattering

Scattering +295

(Ref

4)

+300 x350 0375 El400

103

x475

10-l

20:

300

400

500

600

700

800

.Q=2 p sm(@/2) Fig. 6. Elastic scattering cross section of 4He as a function of momentum transfer. The data from ref. 4, for 295 MeV positive pions are included. The solid line is a plot of the squared form factor for electron scattering from 4He, as taken from refs. 13,17).

20

,

‘1,

/

I

I

I

I

I

T,

15 -

,

=

,

I

I

I

400

I

I I I t

MeV

0 = 60’

b

400

420

440

460

480

MOMENTUM

400

500 OF SCATTERED

Fig. 7. Momenta spectra for (a) positive and (b) negative energy of 400 MeV. In each figure the expected position

PIONS

420

440

460

400

500

(MeV/c)

pions scattered from ‘He at 60” for an incident for the elastic peak is marked with an arrow.

J. Boswell et al. / Elastic T* scattering

471

5. Conclusions We have reported cross section

the measurement

of angular

from 3He and 4He at energies

for pion

scattering

from 300 to 475 MeV. The cross sections

for the two nuclei

have similar

angular

sections

proportional

to the nuclear

are nearly

distributions

dependence.

At forward

angles

form factor, but deviate

the cross

significantly

from it at larger angles. The minimum previously observed at 110” for energies above 200 MeV is found to persist at this angle for energies up to 400 MeV. Since the minimum is fixed in angle it is therefore difficult to relate it to the shape of the nucleus.

We have

suggested

that

it may be associated

with interference

effects

dependent on the elementary VN interaction. It would be very desirable to repeat the measurement with better statistics, with more precise normalization and with better angle resolution. Continuation of the measurements into the unexplored energy region from 500 to 1100 MeV would help to determine the relationship of the apparently non-diffractive minimum observed in the 300 MeV region to the minimum observed at 1120 MeV.

We would like to thank the LAMPF staff for their assistance in mounting and operating the LAS spectrometer and the helium cryostat. This work was supported in part by the U.S. Dept. of Energy.

References 1) F. Binon, P. Duteil, M. Gouanere, L. Hugon, J. Jansen, J.-P. Lagnaux, H. Palevsky, J.-P. Peigneux, M. Spighel and J.-P. Stroot, Nucl. Phys. A298 (1978) 499 2) Yu.A. Shcherbakov, T. Angelescu, I.V. Falomkin, M.M. Kulyukin, V.I. Lyashenko, R. Mach, A. Mihul, N.M. Kao, F. Nichitiu, G.B. Pontecorvo, V.K. Sarychieva, M.G. Sapozhnikov, M. Semerdjieva, T.M. Troshev, N.I. Trosheva, F. Balestra, L. Busso, R. Garfagnini and G. Piragino, Nuovo Cim. 31 (1976) 249 3) Yu.A. Shcherbakov, T. Angelescu, I.V. Falomkin, M.M. Kulyukin, V.I. Lyashenko, R. Mach, A. Mihul, N.M. Kao, F. Nichitiu, G.B. Pontecorvo, V.K. Sarychieva, M.G. Sapozhnikov, M. Semerdjieva, T.M. Troshev, N.I. Trosheva, F. Balestra, L. Busso, R. Garfagnini and G. Piragino, Nuovo Cim. 31 (1976) 262 4) J. Kallne, J.F. Davis, J.S. McCarthy, R.C. Minehart, R.R. Whitney, R.L. Boudrie, J. McClelland and A. Stetz, Phys. Rev. Lett. 45 (1980) 517 5) L.S. Celenza, L.C. Liu and C.M. Shakin, Phys. Rev. Cl3 (1976) 2451 6) R.H. Landau, Ann. of Phys. 92 (1975) 205 7) L.C. Liu and C.M. Shakin, Phys. Rev. Cl4 (1976) 1885 8) J. Combe, J. Gardes and M. Wuerrou, Nuovo Cim. 3A (1971) 663 9) G. Brautti et al., Nuovo Cim. 19 (1961) 1270 10) A.K. Dozier and J.S. Chalmers, Phys. Rev. C23 (1981) 399 11) E. Colton, Nucl. Instr. Meth. 134 (1976) 243 12) L. Orphanos, J. McCarthy, R.C. Minehart, P.A.M. Gram, B. Hoistad, C.F. Perdrisat and J. Kallne, Phys. Rev. C26 (1982) 2111 13) J.S. McCarthy, I. Sick and R.R. Whitney, Phys. Rev. Cl5 (1977) 1396

472

.I. Bowel1

et al. / Elastic d

scattering

14) J. Boswell, G.S. Das, P.C. Gugelot, J. Kallne, J. McCarthy, L. Orphanos, R.C. Minehart, C. Smith, R.R. Whitney and P.A.M. Gram, Phys. Rev. C32 (1985) 1289 15) G. Hohler, F. Kaiser, R. Koch and E. Pietarinen, Handbook of pion-nucleon scattering, No. 12-1 (1979), Fachinformationszentrum, Karlsruhe. 16) Philip R. Bevington, Data reduction and error analysis for the physical sciences, pp. 248-250 (McGraw-Hill, 1969) 17) R. Frosch, J.S. McCarthy, R.E. Rand and M.R. Yearian, Phys. Rev. 160 (1967) 874