Large angle elastic scattering of 200 MeV protons from 208Pb

Volume 169B, number 2,3

PHYSICS LETTERS

27 March 1986

LARGE ANGLE E L A S T I C S C A T T E R I N G OF 200 MeV P R O T O N S F R O M Z°spb C.A. M I L L E R , A. S C O T T t R. A B E G G , R. H E L M E R , K.P. J A C K S O N , M. W H I T E N 2, S. Y E N TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

L. LEE, T.E. D R A K E , D. F R E K E R S , S.S.M. W O N G , R.E. A Z U M A , L. B U C H M A N N , A. G A L I N D O - U R I B A R R I , J.D. K I N G , R. S C H U B A N K , R. D Y M A R Z 3 Department of Physies, University of Toronto, Toronto, Canada M5S 1A 7

H.V. V O N G E R A M B Theoretische Kernphysik, Universiti~t Hamburg, Luruper Chaussee 149, D-2000 Hamburg 50, Fed. Rep. Germarzy

and C.J. H O R O W I T Z Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technologp', Cambridge, MA 02139, USA

Received 3 January 1986

Differential cross sections and analyzing powers for elastic scattering of 200 MeV protons from 2o8pb are reported. The measurements range from 43° to 90° where differences between the microscopic relativistic impulse approximation (MRIA) and microscopic Schr6dinger calculations (MSC) for the analyzing power were predicted to be large. Results agree surprisingly well with the MSC and reveal, for the first time, a serious deficiency in the MRIA. This suggests that exchange and medium effects, both of which are included in the MSC, may be important at large angles. In fact. inclusion of these effects in a new relativistic calculation shows a much smaller difference between the Dirac and Schr6dinger approaches.

There is currently great interest in the microscopic approaches to nucleon-nucleus scattering because of their relative success in explaining experimental data at intermediate energies. Although phenomenological optical potentials' [1,2] can reproduce both cross section and analyzing power data very well, they are often o f limited significance because o f the number of parameters involved and the arbitrary choice of potential shape. Alternatively, the microscopic descriptions are attractive because they attempt to connect knowledge about the n u c l e o n - n u c l e o n interaction with manyb o d y theories [3]. 1 University of Georgia, Athens, GA 30602, USA. 2 Armstrong College, Savannah, GA 31419, USA. 3 University of Alberta, Edmonton, Alberta, Canada T6G 2El. 166

The success of the microscopic Schr6dinger calculation (MSC) in describing cross sections through many orders o f magnitude is remarkable [ 3 - 5 ] . Here, one makes use o f the idea of an "interaction zone" between the incident nucleon and the nucleus. This "interaction zone" is small when compared to nuclear dimensions, so, at any given point in the nucleus, that bit o f nuclear matter can be characterized b y a local density (or local Fermi momentum). One replaces the free n u c l e o n - n u c l e o n interaction with the local density approximation t-matrix, which includes medium effects. By folding in the single-particle density o f the target-nucleus ground state with this complex t-matrix and explicitly including exchange terms, the optical model potential is obtained. The results involve no ad0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Volume 169B, number 2,3

PHYSICS LETTERS

justable parameters, with the possible exception of the neutron density, and comparison with experimental data is quite good [ 3 - 5 ] . The success of the microscopic relativistic impulse approximation (MRIA) in predicting experimental data, particularly the spin observables, is also quite remarkable [6]. Here, the central theme is to use a Lorentz covariant form for the amplitudes describing the N - N interaction, and the Dirac equation to describe the scattering. The importance of relativity in nuclear physics had already been illustrated by Shakin et al. [7] who showed that a relativistic Br~ckner-HartreeFock approach was needed to describe the saturation property of the nuclear matter density. However, the more recent demonstration [2,6] that the 50 MeV deep effective optical model potential is really a remnant of a cancellation of much larger "covariant potential terms", which are on the order of the nucleon mass, suggests that a relativistic treatment of nucleonnucleus scattering is inescapable. Furthermore, the MRIA approach appears to have more success than the MSC approach in reproducing the spin observables, especially at higher energies, and particularly in predicting the spin rotation function Q [6,8]. On the other hand, the MSC approach reproduces, for example in 208pb(l~, p') elastic scattering, the variation in the experimental cross section da/d~2 as a function of energy at larger momentum transfers [9]. The MRIA gives almost no energy dependence. A further, more apparent, difference between these two approaches has been predicted in the analyzing power, Ay, for 200 MeV 208pb(I~, p') elastic scattering at large momentum transfer. Here, the MSC predicts a saturation to Ay ~ 1, while the MRIA predictions, which do not include exchange and medium effects, continue to oscillate [9] .1,2. We have, therefore, extended existing 200 MeV 208pb(-~, p') elastic scattering data to larger angles, with the hope of testing these competing models. The experiment was performed at TRIUMF in the 4B proton channel using the medium resolution spectrometer (MRS). A vertically dispersed beam of 200 MeV protons was delivered to a 101 mg/cm 2 isotopically enriched (99%) 208pb target. The scattered beam was then momentum analyzed in the MRS, which con,1 Calculations of yon Geramb [ 10]. ,2 Calculations based on work of ref. [ 11 ].

27 March 1986

sists of one quadrupole and one dipole magnet, bending in the vertical plane. A six quadrupole "twister", located upstream of the target, was used to rotate the beam dispersion from the horizontal to vertical plane to match the MRS. Vertical drift chambers (VDC) located near the focal plane and a multiwire front-end chamber (FEC) located at the spectrometer entrance allowed event by event ray tracing through the MRS. A more detailed description of the facility is presented elsewhere [ 12]. The FEC, which has an angular acceptance of 3 °, was used to determine \ the scattering angles and the solid angle. Absolute scattering angles were estimated to be accurate to +0.1 °. Efficiencies for the FEC and VDC were determined via the redundancy in ray-tracing. An overall energy resolution of about 230 keV was more than sufficient to separate the elastic peak from the first inelastic (3-) peak. The deadtime of the system was monitored on-line and was typically around 10%. An in-beam polarimeter [13], located upstream of the target, was used to monitor both the beam polarization and intensity. Downstream of the target, a secondary emission monitor (SEM) also measured the beam intensity and provided a check against the polarimeter measurement. Further checks were made by periodically measuring proton-proton elastic scattering from a CH2 target. Typically, the beam polarization was 0.74 -+0.01. The beam current, limited either by the event rate in the FEC or the data acquisition system, ranged up to about 300 nA. This large current combined with the relatively thick high-Z target was possible only because the spectrometer drift chambers operate at low gas gains, tolerate high background fluxes and provide redundant ray-tracing for background rejection and because a quadrupole doublet, located downstream of the target, reduces beam spill when the MRS is at large angles. Cross section and analyzing power angular distributions for 208pb~, p') elastic scattering have been extended from 45 ° out to 90 ° (lab). Agreement with previous data [14] in the overlap region of 45 ° to 57 ° is good (see figs. 1 and 2). The differential cross section data is compared to the microscopic Schr6dinger calculation (MSC) in fig. 1. The theoretical calculation [10], which uses Ray densities [15] and a finite-range spin--orbit force, follows the data quite well although it becomes slightly out of phase with, and overesti167

Volume

169B, number

10 3

•

.

,

i

2,3

,

,

PHYSICS

,

i

.

,

,

i

,

,

,

i

,

,

,

10 5 10 4

,--g. o~ ,.Q

10 3 103

i0 l

LETTERS

27 March 1986

mates, the data at angles larger than 50 ° . Coupled channel effects to the 3- state are included in the calculation but produce only small differences in the cross section and analyzing power at large angles. In fact, these differences are not noticeable in the figures. It should be noted that the MRIA calculation gives similar results for the cross section. In fig. 2, the MSC calculation is compared with the analyzing power data. It is seen that saturates at values close to one for angles greater than 60 ° . This saturation, as well as the behaviour at smaller angles, is described surprisingly well by the MSC calculation. Using three-parameter gaussian densities (Gauss set III from ref. [3]), the MRIA calculation [11 ] (solid curve) is compared to the analyzing power data in fig. 3. For angles less than 45 °, agreement with the data is good. However, at larger scattering angles, the data saturates = 1 and reveals, for the first time, a serious deficiency in the MRIA calculation as it continues to oscillate. This deficiency may be due, partly, to the way the N - N amplitudes are parameterized. Here, exchange effects are neglected and simple Yukawa functions are used to reproduce the amplitudes. This approximation, however, is really only valid

Ay

10 3

"~-I0 -I

i0-~ 10 -3

i0-~ 10-3

stAy

10-°0

'

'

' 2J0 '

'

' 4'0 '

'

' 6~0 '

'

' 8'0 '

'

'100

0crn Fig. 1. Differential cross section data for 2°spb(~,p')

elastic

scattering at Tp = 200 MeV is compared to the MSC prediction (solid line). The small angle data is from Hutcheon et al. [141.

1.0

0.5

-0.5

-1.0

,

~

0

,

I

,

20

,

,

I

,

,

4.0

I

60

~

,

,

I

,

80

,

,

100

Ocm Fig. 2.

168

" power data for Analyzing

2O8

-+ p ' ) elastic scattering at Tp = 200 MeV is compared again to the MSC prediction. Pb(p,

Volume 169B, number 2,3

PHYSICS LETTERS

27 March 1986

°I/

!

0.5

-0.5

--1.0

I

0

20

,'

L

,

I

! ,

, 1

~

40

I!

,

60

,

,

I

80

,

100

Ocrn Fig. 3. The MRIA predictions (solid line) for the analyzing power is compared to the same data set as in fig. 2. The dashed line is a new relativistic calculation by Horowitz which explicitly includes exchange and medium effects.

for small m o m e n t u m transfer, q, and leaves the MRIA rather ill-defined at larger q. The dashed line in fig. 3 is a new calculation b y Horowitz and Murdock based on a relativistic L o v e - F r a n e y model [16]. The calculation, which uses Gauss III densities for the vector densities and a model to determine the scalar densities, explicitly includes exchange and medium effects. Results for the cross sections are similar to those from the MSC and MRIA calculations. Note, however, that the saturation at Ay --~ 1 is qualitatively reproduced although the depth o f the minima, which are sensitive to the densities, are somewhat underestimated at smaller angles. Nevertheless, these results seem to indicate that exchange and medium effects are very important at these large angles. A more stringent test o f the various exchange- and medium-corrected models, relativistic and nonrelativistic, might be provided b y inelastic proton scattering, since the resulting analyzing powers are known to be sensitive to medium effects [ 17 ]. Accordingly, we have made measurements are TRIUMF o f inelastic ~ , p') scattering from 208pb. When our theoretical calculations are completed, a comparison with this

inelastic data [18] will hopefully provide further insight into the role o f "relativity" in nuclear physics. This work was supported in part b y the Natural Sciences and Engineering Research Council o f Canada.

References [ 1] P. Schwandt et aL, Phys. Rev. C26 (1982) 55; P. Schwandt, in: The interaction between medium energy nucleons in nuclei, AIP Conf. Prec. No~ 97, ed. H.O. Meyer, (AIP, New York, 1983) p. 89. [2] B. Clark, in: The interaction between medium energy nucleons in nuclei, AIPConf. Prec. No. 97, ed. H.O. Meyer (AIP, New York, 1983) p. 260. [3] L. Rikus and HN. yon Geramb, Nucl. Phys. A426 (1984) 496. [4] HN. yon Geramb, in: Studying nuclei with medium energy protons, University of Alberta/Triumf Workshop, ed. J.M. Greben, TRI-83-3 (1983) p. 1. [5] F~A.Brieva and J.R. Rook, NucL Phys. A291 (1977) 299,317; 297 (1978) 206. [6] J.A. McNeil, in: Studying nuclei with medium energy protons, University of Alberta/Triumf Workshop, ed. J.M. Greben, TRI-83-3 (1983) p. 133;

169

Volume 169B, number 2,3

PHYSICS LETTERS

J.R. Sheppard, Jdk. McNeil and S.J. Wallace, Phys. Rev. Lett. 50 (1983) 1443. [ 7 ] M. Anastasio et al., Phys. Rep. 100 (1983) 327 ; M. Anastasio, L. Celenza and C. Shakin, Phys. Rev. Lett. 45 (1980) 2096. [8] L.Ray, in: Studying nuclei with medium energy protons, University of Alberta/Triumf Workshop, ed. J.M. Greben, TRI-83-3 (1983) p. 101 ; L. Ray and G.W. Hoffmann, Phys. Rev. C31 (1985) 538. [9] R. Dymarz, Phys. Lett. 152B (1985) 319. [ 10 ] H N. yon Geramb, communication (November 1985). [11] E. Rost, "DROP" Dirac code. [ 12 ] C.A. Miller, in: Studying nuclei with medium energy protons, University of Alberta/Triumf Workshop, ed. J.M. Greben, TRI-83-3 (1983) p. 339; C.A. Miller et al., TRIUMF preprint, in preparation.

170

27 March 1986

[13] R. Abegg et al., TRIUMF internal report. [14] ~D. Hutcheon et al., private communication. [ 15 ] L. Ray, private communication. [16] C.I. Horowitz, Phys. Rev. C31 (1985) 1340; C.J. Horowitz and D. Murdock, Bad Honnef Conf. preprint (1985); Phys. Lett. 168B (1986) 31. [17] J. Kelly et al., Phys. Rev. Lett. 45 (1980) 2012; W.G. Love, in: Studying nuclei with medium energy protons, University of Alberta/Triumf Workshop, ed. J.M. Greben, TRI-83-3 (1983) p. 29. [18] L. Lee et al., University of Toronto internal report.