k+ elastic scattering from c and 6li at 715 mev/c

ELSEVIER

1 August 1996

Physics Letters B 382 (1996) 29-34

PHYSICS LETTERS B

K + elastic scattering from C and 6Li at 715 MeV/c R. M i c h a e l d, M.B . Ba raka t i, S. Bar t a, R.E. Chr ien a, B.C. Cla rk f, D.J. ErnstJ , S. H a m a c,

K .H. H i c k s d, W e n d y H i n t o n b, E.V. H u n g e r f o r d i, M . E J iangJ , T. K i s h i m o t o e

C .M. K o r m a n y o s h, L.J. Kur th f, L. Lee g, B. M a y e s i, R.J. Pe t e r son h, L. P i n s k y i,

R. S a w a f t a a, R. Sut ter a, L. Tang b, J.E. W i s e h a Brookhaven National Laboratory, Upton, NY 11973, USA

b Hampton University, Hampton, VA 23668, USA c Hiroshima University of Economics, Hiroshima 731-01, Japan

d Ohio University, Athens, OH 45701, USA e Osaka University, Toyanaka, Osaka, Japan 560

f The Ohio State University, Columbus, OH 43210, USA g TRIUMF, 4004 Wesbrook Mall, Vancouver B.C. V6T 2A3 Canada

h University of Colorado, Boulder, CO 80309-0446, USA i University of Houston, Houston, TX 77204, USA J Vanderbilt University, Nashville, TN 37235, USA

Received 12 March 1996; revised manuscript received 19 May 1996 Editor: J.P. Schiffer

Abstract

Elastic differential cross sections for K + mesons scattered from natc and 6Li targets have been measured at an incident momentum of 715 MeV/c and at angles of 7 ° to 42 ° in the laboratory frame. The experimental cross sections agree, within errors, with two different parameter-free impulse approximation calculations. To reduce the effects of the systematic errors, the ratio of the experimental cross sections for natc to 6Li is compared to the theoretical values, and these ratios do not agree with theory. This discrepancy suggests either a density-dependent alteration of K+-nucleon amplitudes or a failure of the optical potential calculations to describe these nuclides adequately.

PACS: 25.80.Nv; 12.40.Aa; 13.75.Jz

Conventional nuclear physics pictures the nucleus as a system of nucleons interacting by the exchange of mesons. The physical characteristics of the nucleons when they are in the nucleus are taken to be identical to that of the free nucleon. On the other hand, the un- derlying theory of the strong interaction is believed to be quantum chromodynamics (QCD) with the funda- mental degrees of freedom being quarks and gluons. Asymptotic freedom implies that at high momentum

transfer the QCD description is appropriate while the success of conventional nuclear physics implies that nucleons and mesons are the natural degrees of freedom at low momentum transfers. In both descriptions, it is possible that the basic properties of the nucleon could be modified when the nucleon is in the nuclear medium.

Lepton scattering has been a particularly useful probe of nuclear structure because the electromag-

0370-2693/96/$12.130 Copyright © 1996 Elsevier Science B.V. All rights reserved. Pll S0370- 2 6 9 3 ( 9 6 ) 0 0 6 6 4 - 8

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netic interaction is well understood. The long-range character of the interaction makes it less useful as a probe - unless one goes to the short-wavelength limit of deep inelastic scattering - for examining modifi- cation of nucleon properties in the nuclear medium. A particularly useful [ 1] probe is the K + meson at low energies; it is the most weakly interacting of the strong-interaction probes. This has two advantages. First, the K + can penetrate [2] into the center of a light nucleus such as 12C. Second, the theoretical uncertainties, always present when working with the strong interaction, are much smaller. It was thus a surprise to find that the K + elastic scattering [ 3 ] and total cross section [4] data from C were higher than theoretically predicted [5]. This was interpreted [6] as an indication that the nucleons within the nuclear medium do not behave as they do in free space.

It was shown in Ref. [6] that the elastic and total cross section data sets could be understood if the dominant Sll K+-nucleon phase shifts were increased by 20% or 10%, respectively. This could be indicative of an increase of the nucleon's radius, a "swelling" of the nucleon within the nuclear medium [7]. A some- what different approach to rescaling was presented in Refs. [ 8,9 ] where it was suggested that the vector meson masses within the nuclear medium decrease with increasing nuclear density. A combination of meson- exchange currents and correlations [ 10] has also been put forth as a possible explanation. Although similar to the description of a rescaled nucleon radius, any mechanism which invokes meson exchange currents would be expected to have a noticeable energy dependence [ 11 ] when the energy increases above the threshold for pion production. The discrepancy for the total cross sections [ 12], however, does not appear to have any noticeable energy dependence.

The recent total cross section data indicate that the phenomenon of an enhanced in-medium K+-nucleon cross section is not limited to 12C. These more recent experiments, as cited in Ref. [ 12], measured ratios of the nuclear total cross sections to that for the deuteron and thus greatly reduced the difficulties inherent in the systematic errors that occur in measuring kaon cross sections.

Quasi-free [13] data for K + scattering are also available, and they show that the positive kaon has the expected long mean free path in nuclear matter. How- ever, a consistent analysis of these and the total cross

R. Michael et al . / Physics Letters B 382 (1996) 29-34

Table 1 Differential cross sections for elastic K + scattered from natC and 6Li (all values in the center-of-mass frame). The angular bin size for all measurements was 2.0 ° , and the angles are quoted for the bin centers. Errors are statistical (fitting), followed by the total errors obtained by combining fitting errors and systematic errors in quadrature. The authors acknowledge the assistance of E. Friedman and A. Gal of Hebrew University in correcting an error in the draft version of this table.

0 do' /dfl Error(stat) Error(tot) (deg) (mb/sr) (mb/sr) (mb/sr)

natc 9.67 149.6 4-3.9 +22 14.99 57.8 +1.45 4-9. 18.19 30.8 +0.71 4-4.6 20.36 12.52 4-0.46 4-1.9 25.59 1.46 4-0.06 4-0.22 30.90 0.15 4-0.02 4-0.047 36.19 0. l 1 4-0.017 4-0.022 41.46 0.098 4-0.011 4-0.018 46.77 0.032 4-0.009 4-0.010

6 Li 10.33 28.1 4-0.73 4-4.2 12.62 21.2 +1.2 4-3.2 16.05 12.7 +0.46 4-1.9 21.76 3.9 -4-0.19 4-0.75 27.44 0.82 4-0.06 4-0.22

section data does not as yet exist. The measurement that stimulated the original inter-

est in K + nucleus reactions was elastic K + scattering [3] from carbon and calcium targets at an incident momentum of 800 MeV/c. These data are about 30- 50% higher than calculations [6,14,15] based on the impulse approximation. If one adopts the increase in the $11 phase shift or the exchange current calculations of Ref. [ 10], the effect seen in the elastic data is almost twice as big as the increase needed to fit the total cross section data. However, the elastic data of Ref. [ 3 ] have a normalization uncertainty of + 17%, which alone could account for much of the discrepancy.

The present experiment overcomes the effect of normalization uncertainty by comparing the scattering from natural carbon to the scattering from 6Li, as the data were taken with the same apparatus under similar running conditions.

The experiment resulted in differential cross sections for elastic scattering of K + mesons from natc and 6Li targets (98% enriched) at 715 MeV/c. A K + beam momentum of 715 MeV/c was chosen to be low enough so that the $11 phase shift was the dominant

R. Michael et a l . / Physics Letters B 382 (1996) 29-34 31

contribution to the K+-N interaction, yet high enough so that the beam flux was not unduly weakened by kaon decays along the beamline. These targets were chosen to compare two nuclides of different average nuclear densities. The average nuclear density of 6ti is about half that of 12 C or 4°Ca; the rms radius of 6Li ac- tually exceeds that of 12C [ 16]. The total cross section measurements already indicate [12] a much smaller cross section enhancement for 6Li than for 12C; hence they provided a strong motivation for choosing 6Li as a target in this experiment.

The experiment was carded out on the low-energy separated beamline (LESB-II) at the Alternating Gra- dient Synchrotron (AGS) of the Brookhaven National Laboratory. The "Moby-Dick" spectrometer was used to analyze the momentum of the scattered K + with a resolution of about 3.5 MeV (FWHM). The angular range covered was from 7 to 42 ° in the laboratory, in 5 ° steps. The incident kaon flux was varied from about 40,000 per one-second spill at forward angles to a maximum of 300,000 per spill at back angles. Kaons were identified by their time-of-flight (TOF) in both the beamline and spectrometer, with essentially com- plete separation from pions. For most of the measurements, the TOF root-mean-square resolution was 0.4 ns and the pion to kaon ratio was near 1:1. Attention was paid to the data normalization conditions. The TOF scintillators had rates of less than 2 MHz, so that random coincidences in the 2-ns TOF window were less than a few percent. Computer livetime was kept above 90% except at the most forward angle. Both a CH2 target and a CH1.1 scintillator target were used to compare with the known K+-proton cross sections near 700 MeV/c [ 18]. Thicknesses for all targets are known to within a 2% uncertainty. The spectrometer acceptance was modeled with Monte Carlo simulations and checked against H(p,p)H and H(K,K)H reactions [ 18]. The spectrometer solid angle near maximum momentum acceptance is believed known to 15%, based on the consistency between known cross sections and the Monte Carlo simulations. The beam was tracked using drift chambers so that the incident kaon flux could be corrected for the beam halo which missed the target. Drift chambers were arranged in a redundant geometry so that the overall efficiency ex- ceeded 95% in the spectrometer and multiple beam tracks ( ~ 5%) were eliminated from the data. A correction was made for kaon decays over the average

flight path through the spectrometer and for the dis- tance between the last beam TOF counter and the target.

Corrections were applied for beam absorption, target thickness, kaon decay, chamber efficiencies, computer dead time, and fraction of the beam missing the target. These are all at the level of 1-2%, except for the intercepted beam correction, which was 5%. The dominant systematic uncertainty, however, was the 15% error in the spectrometer acceptance and it is common to both C and 6Li targets.

Data for 715 MeV/c are shown in Fig. 1. The size of the scattering angle cut was limited to a 2 ° bin at the center of the acceptance to reduce acceptance shape corrections to 5% or less. The angle cut resulted in retaining only about 40% of the data, which was ade- quate for the forward angle scattering. Elastic scattering was separated from inelastic scattering by analyz- ing the spectrum with a standard least-squares fitting routine using the known energy levels of the targets. The uncorrelated statistical errors of the data of Fig. 1 are small compared to the overall 15% systematic error, except at the backward angles. No correction was applied for the acceptance variation across the 2 ° angle cut, as this was a small effect.

These data are compared with calculations from two recent models of K+-nucleus elastic scattering in the impulse approximation. The solid line is from a calculation by Jiang, Ernst, and Chen[ 14], which uses a momentum-space first-order optical potential in the Klein-Gordon equation. Although this is a sophisti- cated calculation that includes Fermi-averaging, a fi- nite range off-shell two-body model, covariant kine- matics, and covariant normalizations and phase-space factors, all such conventional first-order optical potential calculations [5,6,8] produce very similar results for both total cross sections and elastic differential cross sections. The dashed line is from a calculation by Kurth, Clark and Hama, which uses the relativistic Kemmer-Duffin-Petiau (KDP) equation [ 15]. The KDP-IA calculations are motivated by the success of the Dirac equation based analysis of proton-nucleus scattering. This equation resembles the Dirac equation in form, and one can construct the meson-nucleus optical potential in a manner similar to the relativistic impulse approximation (RIA) [ 19]. The meson-nucleus optical potential in the KDP approach consists of a cancellation between large scalar and vector (time-

32 R. Michael et a l . / Physics Letters B 382 (1996) 29-34

v

b

10 2

10 0

1 0 - 2

\ \ \ \

• aLl( K+

\ \

\

x

1 1 1 I" i i i i i i i i 1 l i i t t i i i \ i i i

0 I0 20 30 40 50

Oo.m. (deg)

Fig. 1. Calculated differential cross sections for the 12C(K+,K + ) 12C and 6Li(K+,K+)6Li reactions at 715 MeV/c . Cross sections are shown for the center-of-mass frame. The solid curve shows the results using the model of reference [ 14] ; the dashed curve shows the results using the model of reference [15] . Plotted experimental points are for natural carbon and for the enriched 6Li targets. The plotted error bars include both statistical and systematic errors.

' 1 . . . . I . . . . I . . . . I . . . . I . . . . i i i

5 -

4 - <~ --

0 3 -

2 --

1

0 5 ~0 ~ 2 0 2 5 30

8 (deg) Fig. 2. Ratios for the carbon and lithium cross sections of Fig. 1 are shown. The errors on the ratios are statistical only. Calculated ratios from both models are also plotted. The solid curve shows the results using the model of reference [ 14]; the dashed curve shows the results using the model of reference [15] .

R. Michael et a l . / Physics Letters B 382 (1996) 29-34 33

. . . . + 1 + . . . . t . . . . I . . . . , . . . . I . . . .

e 4 o

2 -

0 i I i i

0 5 10 15 2 0 2 5 30 0 c = (deg)

Fig. 3. Ratios for the 800 MeV/c clastic scattering of K + from C and Ca facets from Ref. [3] are shown. The errors on the ratios are statistical only. The solid curve shows the results using the model of Rcf. [ 14] ; the dashed curve shows the results using the model of

reference [ 15].

like) components. Both calculations use the same K +- nucleon amplitudes taken from Arndt [ 18], thus the calculated differential cross sections in both cases are subject to a common 15% uncertainty in the elemen- tary amplitudes. We wish to emphasize that, while the two calculations start with very different assumptions about the basic scattering equation, it is impressive that there is such good agreement between them.

The results pictured in Fig. 1, which span two orders of magnitude, show both the calculated differential cross sections and the the measured ones. The error bars for the data in this figure include the statistical error and a 15% systematic error. Given the size of the systematic error, the data are in agreement with either curve for both nuclides.

In Fig. 2 we present the ratios, natc to 6Li, for the elastic differential cross sections, and compare them to the model calculations. In this plot, only the statistical (uncorrelated) errors are used, which, as dis- cussed above, are appropriate for these ratios. There- fore the errors are much smaller, about 3-5%, compared to the cross section errors of Fig. 1. It should be noted that a small interpolation for the data points was required to produce the ratios for identical center

of mass angles. This was done for successive neigh- boring pairs of carbon and lithium points, and the interpolation used the shapes of the theoretical curves. The amount of interpolation was typically about one degree and produced consistent ratios, independent of the interpolation technique. These results are shown in Fig, 2. This figure shows a pronounced difference at small angles between the calculated ratios and the experimental values. The effect is outside the statistical error and in the forward direction is nearly a 50% effect. Similar comparisons to the non-relativistic impulse approximation code of Ref. [6] yield similar deviations.

Conclusions which might be drawn from the ap- parent failure of the models to describe the measured ratios should be considered in the light of the differ- ences in the structure of 6El and 12C. Although 6Li has a 1 + ground state, the present calculations assume a 0 + ground state. In addition, both 6Li and 12C are deformed, and for the former, the first excited 3 + state lies only 2.19 MeV above the ground state. One can ar- gue that its influence is small in forward scattering. In pion scattering, the excitation of the 3 + state at small angles is known to be negligibly small compared to

34 R. Michael et al . / Physics Letters B 382 (1996) 29-34

elastic scattering [ 17]. We have also applied the same ratio technique to the

earlier 800 M e V / c K+-nucleus data [3] , which orig- inally stimulated the suggestion of the medium modi- fication o f the kaon-nucleon amplitude. In this case a standard rational function interpolation is used to ob- tain the 12C data at the 4°Ca angles, but a cubic spline interpolation gives essentially the same results. The results are shown in Fig. 3; where only statistical errors are used in calculating the errors on the ratios. In this case the agreement between the experimental and theoretical ratios is quite good. However, one should note that the average nuclear densities of carbon and calcium are nearly the same, and that the nuclear shadowing is more important in calcium, simply because of its size. Thus any medium effects in the Ca to C ratio could be reduced by nuclear shadowing. This point was already emphasized in the total cross section work of Ref. [ 13 ].

In summary, the present results indicate the useful- ness o f considering ratios when comparing K + scattering theory to experiment, as this method, limited only by statistical uncertainties, is sensitive to subtle differ- ences in the nuclear densities. What is clear from this work is that there is a significant difference in agreement between theory and experiment for the ratios of natCa/natc as compared to natc/6Li. If we assume that

the calculations for 6Li are as reliable as those for 12C then one could speculate that the natc/6Li results indicate the presence of medium effects.

It is the nature of strong interaction physics that a convincing discovery often requires a systematic explanation of related but independent data. The total cross section data of Ref. [ 12], the quasi-elastic data of Ref. [ 13], and the differential cross section data and their ratio presented here present the challenge of producing a coherent and consistent explanation of all the observed phenomena, possibly including a significant density-dependence in the K+-nuclear scattering.

The research described here forms the substance of the doctoral dissertation of Rodney Michael of Ohio University. The Brookhaven Medium Energy Group would like to thank Carl Dover and Peter B. Siegel for useful discussions and criticism, and to thank Eli Piasetzky and Jonas Alster of Tel Aviv

University for their helpful suggestions. Research has been supported in part by the United States Depart- ment of Energy under contract DE-AC02-76CH00016 (BNL), DE-FG02-86ER40169 (Colorado), DE- FG03-94ER40836 (Houston) and by NSF Grants PHY-9112739 (Ohio) and PHY-9511923 (Ohio State). The support by the NSF and DOE are grate- fully acknowledged.

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k+ elastic scattering from c and 6li at 715 mev/c

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