Relativistic medium effects for 208Pb(p,p′) at intermediate energies

Volume 205, number 4 PHYSICS LETTERS B 5 May 1988

RELATIVISTIC MEDIUM EFFECTS FOR 2°Spb (~,p') AT INTERMEDIATE ENERGIES

X.Y. CHEN, L.W. SWENSON, F. FARZANPAY Oregon State University, Corvallis, OR 97330, USA

D.K. McDANIELS, Z. TANG, Z. XU, D.M. DRAKE 1 University of Oregon, Eugene, OR 97403, USA

I. BERGQVIST, A. BROCKSTEDT Lund University, S-223 62 Lund, Sweden

F.E. BERTRAND, D.J. HOREN, J. LISANTTI Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

K. HICKS, M. VETTERLI and M.J. IQBAL TRIUMF, 4004 Westbrook Mall Vancouver, B.C., Canada V6T 2A3

Received 14 September 1987

Analyzing power and spectral data for the inclusive quasifree (~,p') reaction on 2°SPb at 290 MeV are presented. Cross sections were measured over an angular range of 4°-26 ° and for excitation energies up to 160 MeV. The free surface response model provides a good description of the shape of the continuum. At the quasifree peak the large angle Ay(0) data drop below the free nucleon values. This difference is a possible indication of relativistic medium effects.

Theoretical progress over the past few years has led to considerable improvement in the description of intermediate energy proton-nucleus scattering. One extremely important development has been the in- troduction of a relativistic treatment of proton -nucleus scattering starting from a Dirac phenomenological approach [ 1 ]. Impetus for this theoretical approach was provided by the successfully description [ 2 ] of the analyzing power, Ay, and the spin ro- tation function, Q, for the elastic scattering of 500 MeV protons by 4°Ca. This approach suggests that the proton-nucleus optical potentials involve large attractive Lorentz scalar and repulsive vector contri- butions. While both the non-relativistic and relativistic phenomenological treatments involve 12 free parameters which must be determined, the rela-

Los Alamos National Laboratory, University of California, Los Alamos, NNI 87545, USA.

tivistic treatment has spin treated implicity in the Dirac equation. Also, the change in the real part of the optical potential from attractive at lower incident proton energies to repulsive at higher energies comes about naturally in the Dirac approach.

The phenomenological approach was put on a firmer basis through the development of a relativistic impulse approximation [ 3 ] (RIA). In this case the optical potential in the Dirac equation was calculated from nucleon-nucleon (NN) scattering data and the nuclear density. The 4°Ca data at 500 MeV were bet- ter described by the Dirac impulse approximation [3,4] than by the traditional Schr6dinger impulse approximation [ 5 ].

It is important to extend these comparisons to inelastic scattering processes. So far no strong signal showing the existence of relativistic effects for inelastic scattering has been found. We believe that proton inelastic scattering to the continuum at intermediate

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energies, which is dominated by quasielastic scattering [ 6 ], provides a good way to look for such effects. This point has been emphasized by Horowitz and Iqbal [7 ] who calculated spin observables for quasielastic proton scattering in the RIA.

The RIA approach for quasielastic scattering is based on a covariant form of the amplitudes describing the NN interaction while the scattering is described through the use of the Dirac equation. In the nuclear medium the strong scalar and vector potentials enhance the lower two components of the four- component Dirac wave functions. In the treatment of Horowitz and Iqbal, this enhancement is parame- trized by an effective mass m* which can be calculated in an eikonal model. Quasielastic scattering to the continuum is an attractive problem to study because it minimizes the nuclear structure dependence of final states. By focusing on the spin observables at the quasielastic peak, multiple scattering and distor- tion effects are further minimized.

It is also useful to describe inelastic proton scattering in terms of the surface response [8,9 ] of a semi- infinite slab. This approach assumes that the reaction mechanism is dominated by quasifree proton scattering. Understanding the underlying continuum is an important topic for many aspects of nuclear physics. For example, the largest uncertainty in the determination of giant resonance strengths [10] arises because of a lack of knowledge of the shape and magnitude of the underlying continuum.

The continuum predictions of the surface response model have recently [ 11 ] been compared to intermediate energy (p ,p ' ) spectra. The main features of the data appear to be reasonably well described by the surface response model. For a given excitation energy and momentum transfer, the agreement im- proved with increasing beam energy. More detailed comparisons between data and model predictions are needed in order to evaluate the usefulness and extent of validity of this approach. We are particularly inter- ested in determining the utility of the free surface response approximation [9] in which no residual interactions are incorporated.

In this note we present new differential cross section and analyzing power data for the inelastic scattering of 290 MeV protons by a 2°Spb target. The new analyzing power data for the quasifree peak at 290 MeV provide evidence for the expected relativistic

medium effect. These data, when combined with our earlier cross section measurements [ 12,13 ] at 200 and 400 MeV, were also utilized to study the validity of the surface response model. Our spectral data support the free surface response approach, at least for incident proton energies of 290 MeV and above.

Measurements for 2°SPb were made using a 290 MeV polarized proton beam and the MRS facility at TRIUMF. A broad range of excitation energy (0-160 MeV) has been studied over the 4°-26 ° angular range. At the largest angles up to three different mag- netic field settings for the MRS were needed to cover an excitation energy range which included the quasielastic peak. The incident protons were scattered from a 51 mg/cm 22°Spb target. Beam intensity ( 1-5 nA) was measured with a Faraday cup. The beam polari- zation was monitored by a polarimeter in the beam line.

The double differential cross section for inelastic proton-nucleus scattering in the surface response model [8,9] can be written as

d2o - =Nerr~ | ~ 1 Sr, s(q, to). ( l )

dO dto T.S-- \ u~'~ / r.s

A detailed explanation of the three factors contained in the above expression is given elsewhere [ 11 ]. Briefly Neff is the effective number of target nucleons and is determined by Glauber theory for single scattering including Pauli blocking effects. For each spin-isospin channel (da/d~2)r,s represents the differential nucleon-nucleon (NN) cross section, and ST, s(q, E ) is the surface response function for semi- infinite nuclear matter. The spin, isospin and multi- polarity strength distributions in the continuum are interesting and important and have been the subject of recent investigations [ 14,15 ]. We have utilized the above relation with the free response (no residual interactions) S(q, to) calculated in a slab geometry [ 8 ]. The NN differential cross section is the total elastic scattering value.

In fig. 1 we show representative spectra measured at 0L=6 °, 10 ° and 14 ° in the present experiment at 290 MeV along with those measured with 400 MeV protons [No Ay(0) data were measured at 400 MeV. ] It is seen that the spectra at both energies are repro- duced reasonably well by the surface response model calculations. The description of the continuum at 290

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30

20

E

c,d

O0 10

20 r >

i

GO

I0

i 0 10

10 . . . .

2O

i

I 2O

i

30 40 50 60 ,9

i i i

~L = 10 °

i i • • i i _ . ~

30 40 50 60 o 10 20 30

0 L 15 -

k,,,,~.. I0

~L= 14°

40

0 ¢ 0 ~,, I I o lo zo 30 40 50 oo o lO zo 30 40

E x ( M e V ) E x ( M e V )

Fig. 1. Spectra of 290 and 400 MeV protons scattered from 2°Spb at laboratory angles of 6 °, 10 °, and 14 °. The solid curve corresponds to the semi-infinite slab model and the solid square points are the relativistic predictions based on the Dirac equation. See text for details about the absolute normalization.

MeV is almost as good as that obtained at 400 MeV. This is in sharp contrast to the situation [ 13 ] at 200 MeV where the free surface response predictions do not describe the continuum very well, at least for low momentum transfers. The free response predictions, shown by the solid lines in fig. 1, appear to reproduce the overall shape of the spectra sufficiently well to justify the use of this approach in describing the continuum in the giant resonance region. In the prediction of the free response for both 290 MeV and 400 MeV, an overall renormalization upwards of the calculation of about 20% was needed to match the continuum at higher excitation energies. Extraction of

giant resonance cross sections using the free response prediction for the continuum gives the same strengths [ 13 ] as are obtained by our more conventional phenomenological approach [ 12 ].

Predictions of the RIA model (using a Fermi gas approximation for the response function) for the spectra are shown in fig. 1 by the solid points. Good agreement with the continuum is obtained only at the larger angles due to the Fermi gas approximation [ 8 ]. Clearly, an RPA calculation, or a nuclear response calculation which explicitly takes the nuclear surface into account must be included in the RIA approach to obtain a useful description of the continuum

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The RIA treatment is expected to do a good job of describing various spin measurements at the quasielastic peak since the reaction mechanism will be a single-step process. Analyzing powers measured in the present experiment are shown in fig. 2. The Ay(O) value at each angle was obtained by averaging the spectrum over a 5 MeV interval of excitation energy centered at the location of the quasifree peak. The location of the quasifree peak was calculated using eq. (2) of ref. [6] with an energy shift B of 9 MeV (i.e., relativistic kinematics plus an energy shift ). The RIA predictions for m*= m (m = nucleon mass), and 0.83m are shown on the figure. The authors [7] of the RIA treatment obtained a value of m*=0 .83m on theoretical grounds. In the RIA model the effective mass m* is proportional to the average scalar field strength S, via m * = m + S. These data support an effective mass of m * = 0.77m if the trend of the calculation continues. The data in fig. 2 indicate a definite sensitivity of Ay (0) to m*, particularly at large angles.

The data shown in fig. 2 are an indication of relativistic medium effects. However, there are some al- ternative explanations which must be considered. For example the data could be wrong due to some un- known experimental defects. Another possibility which could lead to values of A~,(0) below the free NN values is multiple scattering. Finally, one might ask about the effects of Fermi motion of the struck nucleon.

We strongly believe that our Ay (0) data are correct

.6

.5

.4

v .3

.2

i i i

Ep -- 290 M e V

208pb (~" p')2OSpb ¢ . . : - - \

~ - ~ .

O0 10 20 0 40

0 L (deg)

Fig. 2. Analyzing powers for the quasifree peak obtained with 290 MeV protons scattered from 2°Spb. The two dashed curves correspond to relativistic impulse approximation predictions for effective mass values of m* = m and m* = 0.83m. The solid squares show the free surface response predictions.

within the uncertainties displayed in fig. 2. Our elastic scattering data at 290 MeV, measured along with the Ay(O) data are in agreement within a few percent with the precise elastic scattering data at Hutcheon et al. [ 16 ]. Also deformation lengths extracted for the low-lying states of 2°8pb are in excellent agreement with our earlier measurements [ 17 ]. The original RIA calculations [7 ] for quasielastic scattering did not take Fermi motion of the struck nucleon into account. However, correction [ 18 ] for Fermi motion was incorporated into the program used to calculate the theoretical Ay (0) values shown in fig. 2.

Multiple scattering effects [ 19,20 ] were not taken into account in the theoretical calculations. They are expected [ 11 ] to be small, at least forAy(0) near the quasielastic peak [ 6 ]. We have run a similar experiment at 500 MeV where multiple scattering effects should be considerably reduced. Our Ay (0) results at 500 MeV show the same good agreement with theory that is found in fig. 2.

In summary, inclusive (p ,p ' ) cross section and Ay(O) measurements at 290 MeV indicate that the continuum is dominated by quasielastic scattering. At small angles the Ay(O) data, the RIA predictions and the free NN values (the curve with m * = m ) are essentially identical. The larger angle data are crucial as the measured Ar(O ) values fall appreciably below the free NN values. The free response model calculations [8 ] (solid squares) yields essentially the free NN values. The fact that the measured Ay(O) data are in good agreement with the RIA prediction using m* = 0.83m is an indication of a genuine relativistic medium effect.

The authors gratefully acknowledge the assistance they have received from the TRIUMF staff. Dr. H. Esbensen not only provided the surface response model program, but also generously provided much useful advice. The ORNL collaborators were supported by Martin Marietta Energy Systems, Inc. un- der contract DE-AC05-840R21400 with the US Department of Energy. The University of Oregon and Oregon State University participants were supported in part by grants from the National Science Founda- tion. I. Bergqvist passed away in May 1987. His pen- etrating physical insight will be greatly missed by all of us.

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Relativistic medium effects for 208Pb(p,p′) at intermediate energies