targets

PHYSICAL REVIEW C VOLUME 36, NUMBER 1 JULY 1987

Probing the direct step of relativistic heavy ion fragmentation:('2C, "B+ p) at 2.1 GeV/nucleon with C and CH2 targets

M. L. WebbUniversity of California at Davis, Davis, California 95616

H. J. Crawford and J. EngelageUniversity of California Space Sciences Laboratory, Berkeley, California 94720

M. E. Baumgartner, ~ D. E. Greiner, P. J. Lindstrom, D. L. Olson, ~ and R. Wada~Lawrence Berkeley Laboratory, Berkeley, California 94720

(Received 18 December 1986)

We have measured the momentum distributions and the excitation energy of the p, "B pai. r in the(' C,"B + p) reaction at 2. 1 GeV/nucleon with C and CH2 targets. The cross section separates intothree regions: (1) nucleon-nucleon quasi-elastic scattering, (2) nucleon-nucleon inelastic scattering,and (3) a low excitation energy and momentum transfer peak. The cross sections, by region, are asfollows: (1) 8.8+2.5 mb, (2) 10.1+2.2 mb, and (3) 0.81+0.45 mb for H(' C, "B + p)X and (1)11.1+2.4 mb, (2) 24. 1+3.7 mb, and (3) 4.50+0.67 mb for C("C,"B + p)x. The shapes of the firsttwo regions can be fit with a nucleon-nucleon cascade model including m production. However, thecascade model prediction for the quasi-elastic component is too large by a factor of 3. The lowmomentum transfer peak is consistent with two mechanisms, (1) an excitation and decay via protonemission of the carbon projectile and (2) a projectile proton scattering diffractively off the C target.Finally, the Fermi momentum determined from the transverse momentum distribution is 160+11MeV/c compared to 190+11 MeV/c from the longitudinal momentum distribution.

I. INTRODUCTION

Most theoretical models of relativistic heavy ion col-lisions use some variation of the participant-spectatorprescription. When the colliding nuclei interpenetrate,some nucleons in the overlap region scatter directly; theseare the participants. The remaining nucleons comprisethe projectile and target spectators. The process injectsenergy into the spectators and they can then decay byparticle emission. Thus there are two types of sourceseach producing fragments by different mechanisms. Inperipheral collisions the momentum signatures of thesources overlap, and inclusive measurements cannotadequately distinguish between them, allowing markedlydifferent models to explain the sam. e results.

We will focus on the direct process in this paper. Asimple reaction for studying the direct component ofheavy ion fragmentation is ' C fragmenting into "B+p.There are two possibilities: (1) a participant nucleon isscattered directly with the "B remaining a spectator, or(2) the projectile is collectively excited and dissociates intoa "B,p pair. At this projectile energy, one would expectthe participant nucleon to be the result of nucleon-nucleon quasi-elastic scattering or nucleon-nucleon inelas-tic scattering with m production. The dissociation processhas been observed in (' C, 3a). The simplicity of the(' C, "B+p) reaction offers the hope of an unambiguouscomparison with the models, and must be understood be-fore more complicated reactions can be attempted withconfidence.

To study this reaction one needs a measurement ex-clusive in projectile fragments. Previous quasi-exclusivemeasurements of this type have been made with photo-graphic emulsions and streamer chambers. ' These ap-proaches suffer from poor statistics. They also lack com-plete particle identification and cannot unambiguouslyselect the reaction of interest.

The data presented here were measured at the HeavyIon Superconducting Spectrometer (HISS) facility" atLawrence Berkeley Laboratory. The aperture was largeenough so that we were able to determine simultaneouslythe vector momenta of all charged projectile fragmentsdown to zero momentum transfer over a region of phasespace containing all the "B fragments and 72+19% ofthe protons in the H(' C, "B+p)X reaction.

II. EXPERIMENTAL SETUP

The experimental setup (Fig. 1) included event triggerscintillators, a large volume magnetic dipole, 0.815 g/cmC and 1.03 g/cm CH2 targets, track defining driftchambers, and a scintillator wall for time of Aight andcharge determination. The trigger required a single ' C toenter the dipole and no charge-six particle in the beam en-velope after the dipole. The aperture (Fig. 2) was limitedby the second downstream drift chamber and the regionof phase space covered by the momentum reconstructioncode.

In the projectile frame, the proton momenta were mea-sured to standard deviations of 10 MeV/c parallel to the

36 193 1987 The American Physical Society

194 M. L. WEBB et al. 36

TOF )

TOT) I -lY

DC+

Hl SSD I POLE

SLAT ¹55

WALLS

¹56

¹70

beam and 7.7 MeV/c transverse. The corresponding "Bstandard deviations were 105 MeV/c and 32 MeV/c. Thescintillator wall had a charge resolution of 0.1 chargeunits. Its time of Aight resolution was 250 ps for the pro-tons and 170 ps for the "B's over a 7.6 m Aight path.These gave mass resolutions of 87 MeV/c for protonsand 180 MeV/c for "B's. Requiring all proton tracks topoint back to the target eliminated target-out correctionsto the 0.4% level. The proton detection eKciency was80+5 % relative to that of the "B's. This was due mainlyto drift chamber inefTiciencies.

FIG. 1. Detector placement. Beam scintillators TOF1, TOT,HS, E, and DS defined the trigger with logic(TOF1 TOT E HS.DS). Drift chambers DC4 and DC3 deter-mined the incoming ' C trajectory, and drift chambers DC1 andDC2 determined the charged projectile fragments's trajectories.The time of flight (TOF) wall, an array of 10 cm wide scintilla-tors, determined the charge and time of flight for all projectilefragments.

III. RESULTS

A. Introduction

We have measured two processes, (' C, "B+x) and(' C, "B+p). Only the first was entirely within the ex-perimental aperture, so (' C, "B+-x) experimental crosssections were normalized to the "B inclusive measure-ments of 30.9+3.4 mb for the H target and 53.8+2.7 mb

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FIG. 2. Experimental aperture for protons shown as a func-tion of rapidity and perpendicular momentum (a) parallel and (b)perpendicular to the dipole field. Drift chamber DC2 and themomentum reconstruction code were the limits to the accep-tance. The crosses represent beam velocity protons. All "Bwere in the aperture.

EX CI TATI ON ENERGY (MeV)

FICx. 3. Excitation energy for the p, "Bpair from (a) a H tar-get and (b) a C target. Excitation energy is determined byfinding the invariant mass of the projectile fragments and sub-

tracting the ' C rest mass.

36 PROBINCx THE DIRECT STEP OF RELATIVISTIC HEAVY. . . 195

for the C target. This allowed us to extract cross sectionsfor the (' C, "B+p) process.

The projectile excitation energy spectra for(' C, "B+ p) in Fig. 3 show two components, a low exci-tation energy peak and a long tail. Experimental energyresolution for this reaction, 6 MeV, precludes theidentification of individual resonance peaks. Since we ex-pect nucleon-nucleon scattering to be a major componentof this cross section, we next examine the proton spectra.These (Fig. 4) display three features: (l) A ridge appearsin the data along the line of nucleon-nucleon quasi-elasticscattering. The width of the ridge is a measure of the ini-tial Fermi motion of the scattered nucleons. (2) There isalso a plateau at lower rapidity. The large rapidity lossindicates that these are inelastic events. (3) A sharp peakappears at 100 MeV/c transverse momentum and beamrapidity. This is due to a low energy and momentumtransfer process and is much stronger for the C target.

The "B spectra (Fig. 5) display only a single peak, sug-gesting that the "8 is indeed a minimally interacting par-

ticipant to the reaction. The presence or absence of asimultaneously detected proton made no difference to theshape of the "8 spectra; therefore we show only "8- in-clusive spectra.

It is useful to compare these proton and "8 cross sec-tions with free nucleon-nucleon scattering. For compar-ison to our data we used a Monte Carlo cascade modelwith m production mediated through the 6 resonance, thedominant inelastic mechanism. This model is a sum offree nucleon-nucleon processes and any differences be-tween it and the data can be attributed to collectiveeffects.

In what follows we will first discuss the cascade modeland the modifications made. We then will compare themodel and data for the "8 inclusive spectra. Next a com-parison for the proton exclusive spectra will be made. Fi-nally we will discuss that part of the exclusive spectrawhich cannot be fit by the cascade model.

600(a)

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FICx. 4. Rapidity versus transverse momentum for protonsfrom (a) a H target and (b) a C target. Contours units are 10mb rapidity ' (MeV/c ) '. The line shows the location ofnucleon-nucleon quasi-elastic scattering.

FIG. 5. Rapidity versus transverse momentum for "B in-

clusive from (a) a H target and (b) a C target. The beam rapiditywas 1.84. Contours units are 10 ' mb rapidity ' (MeV/c)


B. Monte Carlo cascade model

The model has been changed ' since its publisheddescription. The model has no binding energy, so the nu-clei expanded with time. Freezing the nuclear distribu-tion until an interaction occurs stops this. To betterreAect knowledge about 6 production gained fromproton-proton scattering, ' two changes were made. The5 was given an exponentia1 lifetime, and the functionalform of the 5 production cross section was changed. Ofthese changes only the latter significantly altered the mod-el results for our case.

Under the original assumption of isotropic 6 produc-tion, only 20% of the protons from the decay of 6's werewithin the detector aperture. Using a production crosssection of cr(t) ~ e ', where t is the Mandelstam t andb= 10.11 GeV, '

53%%uo of the protons from the decay of6's are within the aperture. If the isotropic productioncross section is used, the cascade model cannot be recon-ciled with the ratio of (' C, "B+ p) to (' C, "B+ x) mea-sured. Finally, to better fit our data we use Fermimomentum as an adjustable parameter.

The major problem in comparing these cascade modelresults with the data is that the cascade model does notexplicitly account for isospin. A significant fraction of the6 production channels involve charge exchange. If such areaction leaves a neutron in the projectile frame, it is in-distinguishable from a "B+ p event with the proton out-side our aperture. Thus, for a valid comparison, the mod-el predictions for the "B inclusive cross sections and the(' C, "B+p) cross sections in aperture must be consistentwith the data. Fortunately charge independence holdswell in this energy region' and this reaction channel isdominated by single nucleon-nucleon interactions, so it ispossible to separate the cascade model results into com-ponents which can be weighted by isospin branching ra-tios.

To derive cross sections from the cascade model resultswe found the fraction of the interactions that scatteredonly one projectile nucleon. Any number of target nu-cleons were allowed to scatter. We then multiplied thatfraction by the total fragmentation cross section to obtain

a single nucleon scattering cross section. Using the totalfragmentation cross section of 250+10 mb for a H tar-get, ' the cascade model predicts 100.4+4. 1 mb for singlenucleon scattering with a H target. What follows is ananalysis for a H target; the C target analysis is similar,and both results are shown in Table I. Assuming thescattered projectile nucleon is a proton 50% of the time,the cascade cross section for producing "B's is 50.2+2.0mb, significantly higher than the previously measuredvalue of 30.9+3.4 mb. We conclude that even at thisbasic level nucleus-nucleus collisions cannot be consideredas just a sum of free nucleon collisions.

This cross section can be further separated into: (1)quasi-elastic scattering, 25.6+1.1 mb; (2) b, production inthe projectile, 12.30+0.52 mb; and (3) b, production inthe target, 12.30+0.52 mb. From isospin considerations,

of the proton-proton collisions resulting in 6's in thetarget leave a proton in the projectile, while —,", of the pro-jectile 6's decay into a proton. The "B+x and "B+pcascade model cross sections for both targets are shown inTable I.

C. "Binclusive spectra

In the Monte Carlo cascade model the "Bhas a projec-tile frame momentum equal and opposite to the initialFermi momentum of the scattered proton, so its spectrum(Fig. 6) has the same shape for both targets. These spec-tra are inclusive, since what happens to the proton afterscattering is immaterial to the "B momentum distribu-tion. To obtain the best fit to the data we allowed boththe Fermi momentum and the cross section to vary in a

fit to the transverse momentum distribution.The integral cross sections obtained from the fit were

18.6+1.3 mb for the H target and 26.0+1.7 mb for the Ctarget. These are 60.2+2. 9%%uo and 48.3+1.9% of thedata, respectively. The difference is due to a tail at hightransverse momentum which we excluded from the fit.The tail is more pronounced in the C target data and isabsent from the model.

The Fermi momenta obtained from the fit were 160+11MeV/c for the H target and 160+17 MeV/c for the C

TABLE I. Monte Carlo cascade model (Ref. 7) cross section predictions for "8+x and "B+ p production from H and C targets.From isospin considerations, for the H target, 4 of the proton-proton collisions resulting in 6's in the target also produce a proton inthe projectile while —'„' of the projectile 6's decay into a proton. For the C target —', of the proton-nucleon collisions resulting in a target6 leave a proton in the projectile while —,'4 of the projectile b's decay into a proton. Also quasi-elastic charge exchange is 2.86+0.65 %(Ref. 13) of quasi-elastic scattering from the C target. The cross sections have been normalized to total fragmentation cross sections of250+10 mb for a H target and 810+20 mb for a C target (Ref. 14).

Monte Carlo cascade model processcross sections "B~x

H target (mb)11B+ "B~x

' C target (mb)11B~p

Nucleon-nucleon elastic scattering6 production in the projectile6 production in the target

25.6+ 1.112.30+0.5212.30+0.52

25.6+ 1.111.28+0.483.08+0.13

33.99+0.9323 ~ 43+0.6723.43+0.67

33.02+0.9316.59+0.478.79+0.25

Model total 50.2+2.0 39.9+1.6 80.8+2.1 58.4+ 1.5

Measured total 30.9+3.4 53.8+2.7

36 PROBING THE DIRECT STEP OF RELATIVISTIC HEAVY. . . 197

600

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FIG. 6. Rapidity versus transverse momentum for "B in-clusive from the Monte Carlo cascade model for a H target. Thedata (Fig. 4) have a high transverse momentum tail this modellacks. Contours units are 10 'mb rapidity ' (MeV/c )

target. This differs from previous measurements of 22IMeV/c, derived from electron scattering, ' and 182+5MeV/c derived from fragment momentum distributions.The difference between the latter value and our measure™ments is surprising, since both use momentum distribu-tions to derive the Fermi momentum. However our mea-surement is derived from the transverse momentum distri-bution while the other is derived from the longitudinalmomentum distribution. Detector resolution made itmeaningless to use our "B longitudinal momentum forcomparison. However it is possible to extract the Fermimomentum from the proton longitudinal momentum (Sec.III D) and get a result that is consistent with the 182+5MeV/c measurement. This difference between the Fermimomenta determined from longitudinal and transversemomenta is inconsistent with the usual model of the nu-cleus as a free Fermi gas. It has been suggested' that thisdifference is due to the peripheral nature of the reaction,but no quantitative predictions have been made.

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FIG. 7. Rapidity versus transverse momentum for protons from the Monte Carlo cascade model for (a) quasi-elastic scattering and(b) inelastic scattering with m. production from the H target. Also shown are plots summing both processes from (c) H and (d) C tar-gets. These should be compared with the data (Fig. 4). Contours units are 10 mb rapidity ' (MeV/c)

198 M. L. WEBB et aI. 36

D. Proton exclusive spectra

The cascade model proton spectra (Fig. 7) display twoof the features that are in the proton data, the ridge andplateau. The ridge is due to nucleon-nucleon quasi-elasticscattering. The width of the ridge is dependent on the ini-tial Fermi momentum. This is a longitudinal momentummeasurement and should be equal to the previously mea-sured 182 MeV/c. The Fermi momenta fits were190+11 MeV/c for the H target and 190+25 MeV/c forthe C target. The low rapidity plateau is populated by in-elastic scattering associated with ~ production. The peaksat 100 MeV/c transverse momentum do not appear, andthe plateau shape is not duplicated well. These will bediscussed later (Sec. III E). These spectra have been fit tothe data, and we discuss the fit and its implications next.

Having corrected the cascade model for charge ex-change effects (Sec. III B), we can now compare the modelprediction for (' C, "B+p) in the detector aperture withthe exclusive data. As with the "B inclusive data, scalingwas required to get a good 7 fit. We found it necessaryto vary both the quasi-elastic and inelastic cross sectionsas well as the Fermi momentum in fitting the cascademodel proton spectra to the data. It was necessary tomultiply the quasi-elastic components by 0.34+0.10 forthe H target and by 0.34+0.07 for the C target. The in-elastic components were scaled by 0.70+0. 16 for the Htarget and by 0.95+0.15 for the C target. Thus thequasi-elastic component is smaller by a factor of 3 thanwhat would be expected from free nucleon-nucleonscattering, while the inelastic component is consistentwith the prediction. This suppression of the quasi-elasticcomponent shows clearly that the cascade model is not avalid microscopic description of the interaction process.

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FIG. 8. Monte Carlo cascade model normalized to the dataas a function of —t for (a) H and (b) C targets. Here t is amodified Mandelstam t =(p& —p3), where pl ——pb„ /12 beforethe reaction and p3 ——p~„, „after the reaction. The reduced massof a nucleon within a ' C nucleus is accounted for by using

/12. All p are four-vectors. The lines are natural splinefits to the normalized Monte Carlo cascade model.

FIG. 9. Rapidity versus transverse momentum for protonsfrom the data with the Monte Carlo cascade model subtractedfor (a) H and (b) C targets. The main features are residual in-elastic cross section in the low rapidity region and the lowmomentum transfer peaks. Contours units are 10mb rapidity ' (MeV/c )

PROBING THE DIRECT STEP OF RELATIVISTIC HEAVY. . .

TABLE II. Monte Carlo cascade model (Ref. 7) cross section predictions for "B+ p production in the proton aperture from H andC targets. These are compared to the data with the low momentum and energy transfer peak removed.

Monte Carlo cascade model processcross sections in aperture

H target {mb)Unscaled Scaled

' C target (mb)Unscaled Scaled


21.16+0.888.98+0.392.53+0.11

7.3+2.1

6.3+1.41.77+0.40

26.02+0.757.76+0.254.70+0.15

8.7+1.97.3+1.4

4.45+0.84

Model total 32.7+ 1.3 15.3+2.7 38.5+1.0 20.5+2.9

Measured total —peak 15~ 8+3.4 21.4+2.0

The fits were to the —t distribution excluding the lowmomentum transfer peak (Fig. 8). Here t is a modifiedMandelstam t =(p& —p3), where p&

——pb„ /12 before thereaction and p3

——pp„„„after the reaction. The reducedmass of a nucleon within a ' C nucleus is accounted forby using pb„ /12. All p are four-vectors. The modifiedMandelstam t allows comparison to (p, p) scattering data.A general check of the fit can be made by comparing thecascade model cross sections for (' C, "B+ p) in the aper-ture with the measured total cross section excluding thecross section in the peak (Sec. III E). This is done inTable II.

Having fit the (' C, "B+p) spectra in the aperture, wecan estimate the aperture corrected (' C, "B+p) crosssections by using the scaled cascade model values and themeasured peak cross section. We can also determine thecascade model (' C, "B+x) cross section. This lattercross section must be consistent with the "B inclusivedata which were not used in the fit. The scaled cascademodel plus peak underpredicts by 14+18 % for the H tar-get and overpredicts by 12+15 % for the C target. Theseresults are summarized in Table III.

E. Residual peak and inelastic cross section

Having normalized the cascade model, we now focuson the unexplained regions of the data by subtracting thecascade model. The subtracted spectra (Fig. 9) show twofeatures: resi.dual inelastic cross section in the low rapidi-

ty region and the low momentum transfer peaks. Thelarge rapidity loss of the residual inelastic cross section in-dicates that the other more highly inelastic processes mustcontribute to the inelastic region, such as pp~ppm+mThis is 6% of the free proton-proton total cross section. '

The low momentum transfer peaks that remain are0.81+0.45 mb for the H target and 4.50+0.67 mb for theC target. These cross sections were determined by sub-tracting the normalized cascade model t spectra from thedata t spectra (Fig. 8). Here t is the previously definedmodified Mandelstam r (Sec. III D).

Such peaks do appear in p-nucleus scattering. TheC(p, p)X cross section (Fig. 10) (Ref. 17) is shown as afunction of the Mandelstam t. This plot can be fit by thesum of two exponentials, es ' and e '. These can be in-terpreted as diffraction' from objects of radii 3.66 fm and0.90 fm, respectively; i.e., the C target nucleus and a tar-get nucleon. Alternatively, in the Glauber model' thelow t peak is explained as the proton diffracting elasticallyoff the target, while the rest of the cross section is due toexcitations of the target. To allow such a process to occurin our case we follow the argument of Good and Walk-er. Since the time of the interaction is short, the ' Cground state and the low excitation energy "B+ p statesare essentially degenerate in energy. Thus it is possiblefor the proton to diffract elastically off the target while the"B is not affected. The cross section for this diffractiveprocess has been calculated to be 10% (Ref. 21) of the' C(' 0, ' 0+ x)X reaction at 2 CJeV/nucleon.

TABLE III. Aperture corrected cross section for "B+x and "B+ p production from H and C targets. The peak cross section ismeasured. The quasi-elastic and inelastic cross sections are cascade model values scaled to fit the data inside the proton aperture.

Aperture corrected processcross sections

Low momentum transfer peak

"8+x

0.81+0.45

H target (rnb)11B+p

0.81+0.45

"8+x4.50+0.67

11B+p

4.50+0.67

' C target (mb)


8.8+2.58.6+1.98.6+1.9

8.8+2.57.9+1.8

2. 16+0.48

11.4+2.522.2+3.422.2+3.4

11.1+2.415.7+2.48.3+ 1.3

Aperture corrected total

Measured total

26.7+4.6

30.9+3.4

19.7+3.4 60.3+7.3

53.8+2.7

39.7%4.5

M. L. WEBB et al. 36

IO

O. I 0 O. I 0.2

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0.3

FIG. 10. C(p, p)X cross section versus Mandelstam —t (Ref.17). The line, o(t)=17.22e '+0.44e ', is a fit to the datapoints.

The momentum transferred to the projectile has to besmall compared with the separation momenta of the decayfragments, or the anticorrelation is not observable. In thenuclear Weiszacker-Williams model, energy transfer un-der 20 MeV would show no anticorrelation in our experi-ment. Perhaps the "8 cannot survive intact at these ener-

gy transfers, making the model inapplicable here. Howev-er the anticorrelation should be visible in the(' C,p + p + ' Be) reaction, and it is not seen.

It should be noted that other forms of excitation anddecay have not been ruled out, if they are associated withmomentum transfers larger than that of the nuclearWeiszacker-Williams model. Presumably, the 0.81+0.45mb peak in the H target data is due to such an excitationand decay. If this scales as the sum of the radii, then the4.50+0.67 mb peak in the C target is 27+16 % excitationand decay and 73+ 16 % diffractive scattering. Thiswould make the Pauli blocking kinetic energy 14.4 MeV,considerably closer to the 15.96 MeV Q value it is expect-ed to equal.

To compare the p-nucleus data to our data, we showthe proton cross section from the C target [Fig. 11(a)] as afunction of the previously defined modified Mandelstam t.Both diffractive peaks can be fit by e '. However ourpeak is 29%, or 4.50+0.67 mb, of the 15.6+2. 5 mb crosssection excluding particle production, whereas the p-nucleus peak is 70%, or 200 mb, of the 285 mb cross sec-tion. This comparison ignores the Pauli blocking of lowmomentum transfers to ' C projectile nucleons. We mustremove the same low momentum transfers from the (p, p)cross section for a valid comparison. To achieve the same29% ratio as the (' C, "B+p) cross section we use onlythe (p,p) cross section with

~

t~

& 0.022 GeV . Thisreduces the (p,p) peak to 30.6 mb of the remaining 106mb cross section, and is equivalent to requiring that thescattered proton have a kinetic energy of at least 11.6MeV in the projectile frame. This value was expected toequal 15.96 MeV, the Q value of the (' C, "B+p) reac-tion.

Finally we show the proton cross section for a H target[Fig. 11(b)]. Here, if the proton were independent, wewould expect to see only an e ' component. Insteadthere is an additional small peak which cannot be fit bye '. So, while diffractive scattering can explain the C tar-get low momentum transfer peak, another mechanism isneeded for the H target.

Such a mechanism could be excitation and decay viaproton emission of the ' C projectile, as in the nuclearWeiszacker-Williams model of Feshbach and Zabek. Inthis model the strong force "fringing field" of the targetgenerates a "phonon" that is absorbed by the projectilewhich subsequently decays by emitting a nucleon pair topreserve momentum and energy balance. In our case the' C projectile decays into a proton and a "B. In thisprescription the momenta of the proton and the "B areexpected to be anticorrelated in the projectile rest frame[Fig. 12(a)]. The data [Fig. 12(b)] show no obvious trend.The largest energy y known to be emitted from an excited"B is 26.5 MeV (Ref. 22) and would not materially aff'ect

the anticorrelation.

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FICx. 11. Data cross section versus modified —t for (a) C and(b) H targets. The solid lines are natural spline fits to the nor-malized Monte Carlo cascade model. The dashed line shows theeffect of adding an e' ' component to the Monte Carlo cascademodel results.

36 PROBING THE DIRECT STEP OF RELATIVISTIC HEAVY. . . 201

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IV. CONCLUSION

We find that the direct step of a peripheral relativisticheavy ion collision involves at least four mechanisms: (1)quasi-elastic nucleon-nucleon scattering, (2) inelasticnucleon-nucleon scattering with vr production, (3)diffractive scattering, and (4) excitation and decay. Thecross sections for the (' C, "B+p) reaction are 19.7+3.4mb for the H target and 39.7+4.5 mb for the C target.

The free nucleon-nucleon prediction of the cascademodel for quasi-elastic scattering between projectile andtarget nucleons is significantly different from the data.Although the model reproduces the shape of the data

FICx. 12. Perpendicular momenta, "B vs proton, parallel tothe dipole field to maximize resolution. (a) Nuclear Weiszacker-Williams model. (b) Carbon target. Contours units are 10mb (MeV/c )

spectra, we must multiply its cross section by 0.34 to ob-tain agreement. This suppression of the quasi-elastic com-ponent shows clearly that the cascade model is not a validmicroscopic description of the interaction process. Also, aFermi momentum of 190 MeV is needed. This repro-duces the longitudinal momentum distribution of the pro-ton spectra. However the transverse momentum distribu-tion of the "B implies a Fermi momentum of 160 MeV.This discrepancy indicates that the usual assumption ofthe nucleus being a free Fermi gas of nucleons is inap-propriate in this reaction. It has been suggested' thatthis discrepancy is due to the peripheral nature of the re-action, but no quantitative predictions have been made.The cross sections for the quasi-elastic component are8.8+2.5 mb for the H(' C, "B+ p)X reaction and11.1+2.4 mb for the C(' C, "B+ p)X reaction.

The free nucleon-nucleon prediction of the cascademodel for the m production process does not reproducethe shape of spectra. However the cross section predictedfor this inelastic process is much closer than the factor of3 in the quasi-elastic fit. This inelastic component of thecascade model had to be multiplied by 0.70 for the H tar-get data and by 0.95 for the C target data. The differencein shape between model and data results in residual datacross section at high rapidity loss, indicating that othermore highly inelastic processes must contribute to the in-elastic region. The cross sections for this inelastic com-ponent are 10.1+2.2 mb for the H(' C, "B+p)X reac-tion, and 24. 1+3.7 mb for the C(' C, "B+ p)X reaction.

Diffractive scattering, and excitation and decay are notindependently resolvable for the C target since both pro-duce a peak at low momentum and energy transfer. Exci-tation and decay is 0.81+0.45 mb of 19.7+3.4 mb in theH(' C, "B+p)X reaction. Assuming the process scalesas the sum of the projectile and target radii, it is1.21+0.68 mb of the C(' C, "B+ p)X reaction. Thisleaves 3.29+0.96 mb of the reaction due to a proton inthe ' C projectile scattering diffractively from the C tar-get.

ACKNO%'LEDGMKNTS

We thank J. F. Gunion for his insight on diffractivescattering, and T. F. Hoang for many useful discussionsabout diffractive scattering. We also thank J. Alonso andthe Bevatron Operations staff for the beam and supportservices, F. Bieser and I. Flores for the design and fabri-cation of the detector electronics, and E. Beleal, M. Bron-son, and C. McParland for the data handling software.Finally, one of us (M.W. ) thanks F. P. Brady and J. L.Romero for many useful discussions. This work was sup-ported in part by the Division of Nuclear Physics of theOfhce of High Energy and Nuclear Physics of U.S.Department of Energy under Contracts DE-AC03-76SF00098 and DE-AS05-76ER04699, in part by Nation-al Science Foundation Grant PHY81-21003, and in partby National Aeronautics and Space Administration GrantNGR-05-003-513.


'Present address: Lawrence Livermore National Laboratory,Livermore, CA 94550.

Present address: Housman-LaRoche, CH-4002 Basel, Switzer-land.

~Present address: University of California at Riverside, River-side, CA 92521.

&Present address: Texas ASM University, College Station, TX77843.

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