Non-equilibrium emission of complex fragments from p+Au collisions at 2.5 GeV proton beam energy
A.Budzanowski, D.Filges, F.Goldenbaum, A.Heczko, H.Hodde, L.Jarczyk, B.Kamys, M.Kistryn, St.Kistryn, St.Kliczewski, A.Kowalczyk, M. Smoluchowski, E.Kozik, P.Kulessa, H.Machner, A.Magiera, W.Migdal, N.Paul, B.Piskor-Ignatowicz, M.Puchala, K.Pysz, Z.Rudy, R.Siudak, M.Wojciechowski
aa r X i v : . [ nu c l - e x ] S e p Non-equilibrium emission of complex fragments from p+Au collisions at 2.5 GeVproton beam energy
A.Bubak,
1, 2
A.Budzanowski, D.Filges, F.Goldenbaum, A.Heczko, H.Hodde, L.Jarczyk, B.Kamys, ∗ M.Kistryn, St.Kistryn, St.Kliczewski, A.Kowalczyk, E.Kozik, P.Kulessa,
1, 3
H.Machner, A.Magiera, W.Migda l, N.Paul, B.Piskor-Ignatowicz,
M.Pucha la, K.Pysz,
1, 3
Z.Rudy, R.Siudak,
1, 3
M.Wojciechowski, and P. W¨ustner (PISA - P roton I nduced S p A llation collaboration) Institut f¨ur Kernphysik, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany Institute of Physics, Silesian University, Uniwersytecka 4, 40007 Katowice, Poland H. Niewodnicza´nski Institute of Nuclear Physics PAN, Radzikowskiego 152, 31342 Krak´ow, Poland M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30059 Krak´ow, Poland Institut f¨ur Strahlen- und Kernphysik, Bonn University, D-53121 Bonn, Germany M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30059 Krak´ow, Poland (Dated: November 20, 2018)Energy and angular dependence of double differential cross sections d σ /dΩdE was measured forreactions induced by 2.5 GeV protons on Au target with isotopic identification of light products (H,He, Li, Be, and B) and with elemental identification of heavier intermediate mass fragments (C, N,O, F, Ne, Na, Mg, and Al). It was found that two different reaction mechanisms give comparablecontributions to the cross sections. The intranuclear cascade of nucleon-nucleon collisions followedby evaporation from an equilibrated residuum describes low energy part of the energy distributionswhereas another reaction mechanism is responsible for high energy part of the spectra of compositeparticles. Phenomenological model description of the differential cross sections by isotropic emissionfrom two moving sources led to a very good description of all measured data. Values of the extractedparameters of the emitting sources are compatible with the hypothesis claiming that the high energyparticles emerge from pre-equilibrium processes consisting in a breakup of the target into threegroups of nucleons; small, fast and hot fireball of ∼ ∼
20 nucleons and moves with velocity larger than the CM velocity of the proton projectileand the target. The heavier prefragment behaves similarly as the heavy residuum of the intranuclearcascade of nucleon-nucleon collisions.
PACS numbers: 25.40-h,25.40.Sc,25.40.VeKeywords: Proton induced reactions, spallation, fragmentation
I. INTRODUCTION
The mechanism of proton - nucleus interactions at GeVenergies is still not well understood. Even the gold nu-cleus which is the most frequently studied target, at leastas concerns the measurements of total cross sections foremission of different products (cf. Refs.[1–9] and refer-ences herein), reveals unexpected phenomena when moreexclusive observables are investigated. Recently measure-ments of differential cross sections in 4 π geometry wereundertaken [10, 11] for light charged particles (LCP’s),i.e. H and He ions, as well as for intermediate massfragments (IMF’s) - Li and Be ions. The measurementswere done at 1.2 GeV proton energy for , , H, , , He, , , , Li and , , Be isotopes [10], and at 2.5 GeV for , , H, , He, and , Li isotopes [11].It was found that the shape of energy spectra of emit-ted composite particles as well as their angular depen-dence cannot be explained using the conventional picture ∗ Electronic address: [email protected] [corresponding author] of the intranuclear cascade of nucleon-nucleon collisionsfollowed by fragment evaporation from excited remnantnucleus in competition with fission process. Whereas thelow energy part of spectra - up to 60 - 80 MeV - seems tobe reasonably well described by this conventional mecha-nism, the high energy part of spectra is generally stronglyunderestimated by any of the existing models. It is moreflat than the low energy part of the spectrum and itsslope increases monotonically with the emission angle.This behavior indicates the necessity to include non-equilibrium processes in the description of the reactionmechanism. Authors of Refs. [10–12] propose the sur-face coalescence of emitted nucleons as process respon-sible for high energy part of the , H and He spectra.They claim, however, that such a mechanism is ruled outfor He and heavier ejectiles [10, 11].In the present study the task was undertaken to mea-sure double differential cross sections ( d σ/d Ω dE ) withisotopic identification of the light reaction products fromproton - gold collisions at proton beam energy of 2.5 GeV,extending the range of detected ejectiles to heavier thanthose from previous reported investigations [10, 11].It should be emphasized that for the gold target thedouble differential cross sections ( d σ/d Ω dE ) of interme-diate mass fragments, i.e. fragments with mass number A F >
4, were not measured up to now with isotopicidentification . The only available data are publishedby Letourneau et al. [11] for , Li. Low statistics ofisotopically identified data in publication of Herbach etal. [10] did not allow to analyze double differential crosssections ( d σ/d Ω dE ) for isotopes heavier than He. Forindividual isotopes only the analysis of angle integrated( dσ/dE ) spectra or energy integrated ( dσ/d
Ω) angulardistributions was possible.The goal of the present study was to gain new exper-imental information on the proton - gold interaction atproton energy of 2.5 GeV. Those new double differentialdata ( d σ/d Ω dE ) should allow to gain deeper insight inthe mechanism of non-equilibrium processes.Details of the experimental procedure are discussed inthe second section and the obtained data in the next,third section. The fourth section is devoted to modeldescription of the measured spectra. The interpreta-tion, summary and conclusions are presented in thelast section. Formulae applied in the phenomenologicalparametrization are collected in the appendix. II. EXPERIMENTAL PROCEDURE
The experiment has been performed using the internalbeam of the Cooler Synchrotron COSY in the ResearchCenter in J¨ulich. Due to multiple passing of the circulat-ing internal beam through the target it was possible toachieve as high luminosity as that which can be reachedonly with very intensive external beam of accelerators(with the particle current of order of mA). Circulationof the beam without its immediate absorption demandedusing of very thin, self supporting targets (of order of300 µ g/cm ) what in turn resulted in negligible distor-tion of the reaction product spectra by interaction of theemitted particles with the target. Furthermore, duringeach cycle of injection and acceleration, the protons werecirculating in the COSY ring slightly below the target,being slowly bumped onto the target until the beam wascompletely used up. Then a new cycle was started. Thespeed of the vertical shift of the proton beam was con-trolled by feedback of the observed reaction rate to avoidoverloading of the data acquisition system.The scattering chamber and the detecting system wasdescribed in detail in ref. [13]. There, however, the maininterest was focused only on performance of the griddedionization chambers which are used in the experiment forcharge identification as well as for energy measurementof the reaction products by means of the Bragg curvespectroscopy. For this reason, a description of the othercomponents of the detection system, relevant to the datadiscussed in the present paper, will be given here in amore detailed way.The PISA apparatus consists of nine independent de-tection arms comprising various kinds of detectors. Two of these arms (placed at 15 and 120 ◦ angles in respect tothe beam direction) are equipped with the Bragg curvedetectors (BCD), which permit the Z -identification ofthe reaction products and determination of their kineticenergies with low detection energy threshold (of about1 MeV/nucleon). The telescopes consisted of silicon de-tectors are installed at the detection angles of 35, 50, 80and 100 ◦ . The detectors operate in the ultra high vac-uum (UHV) of the COSY accelerator and are cooled to atemperature of -10 ◦ C. The cooling improves the energyresolution of the detectors, thus the isotopes of all ejec-tiles up to carbon can be identified. Due to geometricalconstraints the silicon telescope detectors placed in thevacuum at 35, 50, and 80 ◦ cannot be supplied with addi-tional detectors. Consequently light charged particles ofhigh energies, not being stopped in the silicon detectors,cannot be detected. The upper limit of energies of par-ticles stopped by these telescopes is about 30 - 40 MeVfor protons, deuterons and tritons but increases signif-icantly for heavier particles, e.g. for alpha particles itis around 120 MeV. Therefore these telescopes are suit-able to measure the low energy part of the spectra forhydrogen isotopes, a large range of energies for heliumisotopes and the full energy spectra of intermediate massfragments. The silicon detector telescope placed at 100 ◦ in the ultra high vacuum has another construction thanthe telescopes mentioned above, thus it was possible tosupplement it with a 7.5 cm thick CsI scintillator detec-tor standing behind it in the air (outside the chamber),separated by a steel window of 50 µ m thickness from theultra high vacuum of COSY. At three angles (15.6, 20,and 65 ◦ ), the telescopes built of silicon detectors with7.5 cm CsI scintillator detectors standing behind themare positioned outside the chamber. The destination ofthese telescopes as well as that at 100 ◦ is to significantlyincrease range of energies of detected light charged par-ticles and IMF’s.The particles observed at different angles in the presentexperiment and the energy ranges covered by the detect-ing system are listed in the Table I and in the Table II forisotopically identified and elementally identified ejectiles,respectively.The absolute normalization of the data was achievedby comparison of the total cross section for Be ejec-tiles extracted from angular and energy integration ofthe spectra measured in the present experiment with thecross section obtained from parametrization of experi-mental Be production cross sections in proton-nucleuscollisions, ref. [14]. Accuracy of the absolute normaliza-tion was estimated to be better than 10%.
III. EXPERIMENTAL RESULTS
In the present study the double differential spectra d σ/d Ω dE were determined for the first time for manyisotopically identified intermediate mass fragments emit-ted from proton - gold collisions at GeV energies. This TABLE I: Range of energies (in MeV) of isotopically identified reaction products detected at various scattering anglesAngle [degrees]Ejectile 15.6 20 35 50 65 80 100 p d t He 20.5 – 296.5 20.5 – 296.5 8.5 – 95.5 8.5 – 86.5 20.5 – 292.0 13.5 – 19.5 9.5 – 161.5 He 23.5 – 277.5 23.5 – 253.0 9.5 – 120.5 8.5 – 113.5 23.5 – 182.5 13.5 – 25.5 9.5 – 122.5 He 26.5 – 83.5 26.5 – 74.5 11.5 – 122.5 10.5 – 106.5 26.5 – 77.5 15.5 – 24.5 11.5 – 53.5 Li 43.5 – 145.5 42.5 – 147.5 17.5 – 178.0 14.5 – 178.0 41.5 – 143.5 18.5 – 48.5 18.5 – 105.5 Li 44.5 – 155.5 35.5 – 156.5 18.5 – 159.5 16.5 – 136.5 44.5 – 152.5 19.5 – 55.5 18.5 – 117.5 Li 47.5 – 113.5 47.5 – 110.5 19.5 – 115.5 17.5 – 98.5 46.5 – 112.5 21.5 – 51.5 19.5 – 85.5 Li 49.5 – 85.5 49.5 – 118.5 19.5 – 82.5 17.5 – 53.5 49.5 – 85.5 22.5 – 52.5 20.5 – 65.5 Be 61.5 – 136.5 62.5 – 146.5 24.5 – 123.5 24.5 – 138.5 61.5 – 136.5 27.5 – 69.5 27.5 – 90.5 Be 68.5 – 116.5 68.5 – 119.5 25.5 – 94.5 25.5 – 94.5 68.5 – 107.5 29.5 – 80.5 27.5 – 84.5 Be 71.5 – 116.5 71.5 – 128.5 26.5 – 101.5 23.5 – 98.5 71.5 – 122.5 30.5 – 87.5 29.5 – 80.5 B 90.5 – 123.5 92.5 – 122.5 35.5 – 92.5 30.5 – 99.5 90.5 – 111.5 38.5 – 86.5 36.5 – 90.5 B 94.5 – 136.5 94.5 – 130.5 35.5 – 116.5 31.5 – 100.5 96.5 – 114.5 39.5 – 105.5 37.5 – 91.5 B 36.5 – 96.5 35.5 –83.5 41.5 – 83.5 39.5 – 78.5TABLE II: Range of energies (in MeV) of elementally identified reaction products detected at various scattering anglesAngle [degrees]Ejectile 15 35 50 80 100 120C 11.5 – 136.5 46.5 – 118.5 40.5 – 118.5 50.5 – 116.5 48.5 – 102.5 12.5 – 57.5N 14.5 – 69.5 56.5 – 116.5 48.5 – 108.5 61.5 – 109.5 57.5 – 99.5 15.5 – 70.5O 15.5 – 80.5 67.5 – 103.5 58.5 – 103.5 74.5 – 119.5 69.5 – 99.5 18.5 – 68.5F 21.5 – 98.5 22.5 – 88.5Ne 25.5 – 109.5 23.5 – 100.5Na 29.5 – 127.5 26.5 – 117.5Mg 29.5 – 106.5 28.5 – 98.5Al 31.5 – 94.5 30.5 – 72.5 concerns He, , Li, , , Be, , , B spectra which werenot measured by Letourneau et al. at 2.5 GeV [11]whereas the experiment of Herbach et al. [10] at 1.2 GeVwhich detected IMF’s lighter than boron had statisticsallowing to extract only elemental spectra. Typical spec-tra for isotopically identified particles from the presentexperiment are shown in Fig. 1 together with data mea-sured by Letourneau et al. [11]. Excellent agreement ofthe present data with those published by Letourneau etal. was achieved for all products measured in both exper-iments, i.e. , , H, , He, and , Li. Note, that statisticalerrors, which are only shown for selected Li data of Ref.[11], present indeed typical errors for all Li data fromthat paper.The energy distributions of emitted ejectiles haveshapes resembling Maxwellian evaporation spectra, butbecause of an instrumental low-energy cutoff it was notpossible to observe the maxima of these distributions forfragments heavier than boron. Although for heavier frag-ments the Coulomb barrier moves the position of maxi-mum of the yield towards higher values, the large energyloss in first silicon detector of telescope prevent us fromdetecting heavy ejectiles at energies close to the maxi-mum of the energy distributions. To avoid this problem, i.e. to measure low energy part of the spectra, two Braggcurve ionization chambers (BCD) were applied. Theywere placed at 15 and 120 scattering angles. SinceBCD’s allow for the identification of the charge of ejec-tiles only, the spectra of heavy products, i.e. C, O, N,F, Ne, Na, Mg and Al were obtained only with elementalidentification. As far as we know, similar spectra were upto now investigated for the gold target only in the exper-iment performed at 1.0 GeV by Kotov et al. [17], wheredouble differential cross sections were measured withoutisotopic identification.Typical properties of the spectra, characteristic forall ejectiles, are depicted in Fig. 1. At low energy theangle independent - Maxwellian like - contribution iswell visible. This isotropic energy distribution may bereproduced by the two stage model discussed below. Thedashed line shown in the figure, represents predictionsof this model. Another contribution, i.e. an exponentialdistribution, strongly varying with angle is present athigher energy in all experimental spectra. The slope ofthis anisotropic energy contribution increases with theangle, what may be interpreted as effect of fast motionof an emitting source in the forward direction. E / MeV Au(p, Li) d σ / d Ω d E [ m b / s r M e V ] E / MeV Au(p, He) FIG. 1: Typical energy spectra of He (left column) and Liparticles (right column) measured in the present experiment(open circles) and published in Ref. [11] (full dots) for corre-sponding emission angles. The lines show prediction of evap-oration of He and Li evaluated by means of GEM programof S. Furihata [15, 16] from excited residual nuclei of the firststage of the reaction with properties extracted from BUU cal-culations.
IV. THEORETICAL ANALYSIS
In the most frequently considered scenario of theproton-nucleus collision at GeV proton energies it is as-sumed that reaction proceeds via two stages.In the first stage of the reaction the proton impingingon to the target nucleus initiates a cascade of nucleon-nucleon collisions which leads to emission of several fastnucleons and pions, and to excitation of the nucleus.This fast stage of reaction is described by intranuclearcascade (INC) model, e.g. [18, 19], Boltzmann-Uehling-Uhlenbeck (BUU) model, e.g. [20] or by quantum molec-ular dynamics (QMD) model, e.g. [21]. The first ofthe mentioned models gives an account of the nucleon-nucleus interaction by static (time-independent) meanfield, the BUU allows for dynamic evolution of the meanfield as caused by time dependence of an average nucleondensity, and the QMD treats the nucleon-nucleus interac-tion as a time dependent sum of elementary two-nucleonand three-nucleon interactions of all nucleons. The QMD Li slow source fast source sum d σ / d Ω d E [ m b / s r M e V ] E / MeV
FIG. 2: Open circles represent experimental energy spectrumof Li particles measured at 35 in the current experiment.The lines present result of phenomenological model describedbelow; the short-dashed line shows contribution of the slowemitting source, the long-dashed line depicts contribution ofthe fast source, whereas the solid line presents sum of bothcontributions. Please note, that the shape of this experimen-tal energy distribution as compared with spectra shown inright part of Fig. 1 also confirms the monotonic change ofthe exponential slope with the scattering angle. introduces the largest fluctuations of the density distri-bution of nucleons and, therefore, allows for emission ofclusters of nucleons from the first stage of the reaction.The static mean field description used by INC model au-tomatically precludes possibility of nucleon distributionfluctuations. The BUU model takes into consideration atime dependent modification of the nucleon density dis-tribution, however, the averaging over many test parti-cles, present inherently in BUU, prohibits appearing offluctuations large enough for nucleon clusters emission.The emission of fast nucleons (in the case of INC andBUU) or fast nucleons and light clusters (in the case ofQMD) terminates after a short time, leaving the residualexcited nucleus in a status close to the thermodynamicequilibrium.The second stage of reaction consists in the evapo-ration of nucleons and clusters from this equilibratedsystem, which can also undergo fission with emissionof two heavy fragments. Thus, in the two-step modelof reaction mechanism, the non equilibrium emission ofnucleons and clusters can appear only in the first stageof the reaction. It is believed that statistical model codeslike, e.g. GEM [15, 16] or GEMINI [22] are capable towell reproduce emission of nucleons and fragments fromequilibrated, excited nucleus. Therefore, observation ofany disagreement of the data with predictions of thetwo-step model would suggest that (i) the model isnot adequate to the real situation (e.g. an additional, E [ MeV ] d σ / d Ω d E [ m b / s r* M e V ] H H FIG. 3: Open circles represent typical spectra of protons,deuterons and tritons measured in the present experimentby telescope consisted of silicon semiconductor detectors and7.5 cm thick scintillating detector CsI placed at scatteringangle of 65 degree in respect to the proton beam. The dashedlines show evaporation contribution evaluated by means ofthe BUU and Generalized Evaporation Model whereas the fulllines correspond to phenomenological model of two emittingsources described below. Note change of the scale for thetriton spectrum. intermediate stage of the process is necessary beforeachieving thermodynamic equilibrium), or (ii) descrip-tion of the emission of particles from the first stage ofthe reaction (nucleons or clusters) is not properly takeninto consideration.
E [ MeV ] He d σ / d Ω d E [ m b / s r* M e V ] He FIG. 4: Typical energy spectra of helium ions , , He mea-sured in the present experiment by telescope consisted of sil-icon semiconductor detectors placed at scattering angle of 35degree in respect to the proton beam - open circles. Notedifferent vertical scales for each spectrum. The lines have thesame meaning as in Fig. 3
A. Boltzmann-Uehling-Uhlenbeck model andevaporation model
The present data were compared with results of a twostage model in which the Boltzmann-Uehling-Uhlenbecktransport equation [20] has been applied for the descrip-tion of the first step of the proton - nucleus collisionleading to emission of fast nucleons leaving the heavyexcited remnant in a state close to equilibrium. MonteCarlo computer program developed at Giessen Univer-sity [23] was utilized to simulate this first stage of thereaction and to find properties of excited residual nuclei.Deexcitation of these nuclei, which proceeds by emissionof nucleons and complex fragments, was calculated inthe frame of statistical model using the GEM (General-ized Evaporation Model) computer program of Furihata[15, 16]. Theoretical energy spectra of various ejectilesfound from this two stage model are shown in Figs. 1 - 8as dashed lines. It can be concluded from examination ofthese figures that the model predictions describe well lowenergy part of spectra for hydrogen, helium and lithiumisotopes. For heavier ejectiles the theoretical cross sec-tions underestimate the experimental data. Moreover, itcan be observed that the high energy part of the spectrais clearly not reproduced by the two stage model, whichpredicts much steeper slope of the spectra than is ob-served experimentally. Thus, another mechanism seemsto give a significant contribution to the proton - nucleusreactions. As concerns hydrogen and helium production,the authors of [10], [11], and [12] papers propose the co-alescence of nucleons as the mechanism responsible forthis effect, however, no microscopic model is able to re-produce observed effects for heavier composite ejectiles.An extensive comparison of predictions resulting fromthe models mentioned above with our experimental datapresented here will be subject of a forthcoming paper. Werestrict ourselves here on conclusions we can draw fromthe application of a phenomenological model describedin the next section.Following properties of the spectra should be takeninto consideration when looking for an appropriate phe-nomenological model: (i)
The position of the peak present at low energies inthe experimental spectra of all observed particles(and its height for light ejectiles) is quite well re-produced by the two stage model discussed above.This means that the mechanism described by thismodel gives a large contribution to the reaction andtherefore it must be taken into account in the frameof any phenomenological model. (ii)
The slope of the exponential, high energy tail of theexperimental spectra for all ejectiles varies mono-tonically, increasing strongly with the scatteringangle as can be seen from Fig. 1. Such a behav-ior is in contradistinction to properties of the spec-tra evaluated in the frame of the two stage model,which are almost independent of angle. This in-dicates that high energy particles are not emittedfrom heavy residuum of the intranuclear cascadebut from another source which moves much fasterthan the residuum.These arguments call for using of a phenomenologicalmodel of two emitting sources; one source moving slowlywould imitate emission from heavy residuum of the in-tranuclear cascade whereas the second source should sim-ulate emission from faster (and thus probably lighter)nuclear system. Of course, one could imagine that morethan two sources of emitted particles are necessary forreasonable description of the data. The applied model oftwo moving sources corresponds to minimal number of
E [ MeV ] Li d σ / d Ω d E [ m b / s r* M e V ] FIG. 5: Typical spectra of lithium ions , , , Li measured inthe present experiment by telescope consisted of silicon semi-conductor detectors placed at scattering angle of 35 degreein respect to the proton beam - open circles. Note differentvertical scales for , Li and , Li. The lines have the samemeaning as in Fig. 3 parameters necessary to fulfill qualitative demands puton the model by the experimental data.
B. Phenomenological model of two moving sources
In the frame of the phenomenological model of twomoving sources the angular and energy dependence of thedouble differential cross sections d σ/d Ω dE is describedby analytical formulae. The details of the model andinterpretation of its parameters are presented in the Ap-pendix. An example of the description of the experimen-tal energy spectrum by the two source model is shownin Fig. 2. The symbols depict the data from present ex- E [ MeV ] 7Be d σ / d Ω d E [ m b / s r* M e V ] Be FIG. 6: Typical spectra of beryllium ions , , Be measured inthe present experiment by telescope consisted of silicon semi-conductor detectors placed at scattering angle of 35 degree inrespect to the proton beam - open circles. The lines have thesame meaning as in Fig. 3 periment obtained for Li ejectiles detected at scatteringangle 35 whereas the lines show result of the fit of thephenomenological model. The short-dashed line presentscontribution from the slowly moving source, the long-dashed line shows contribution from the fast source andthe solid line corresponds to sum of both contributions.As can be seen, very good description of full energy spec-trum could be achieved.The parameters of the theoretical formula of the twomoving sources model have been searched for by fittingsimultaneously experimental spectra at several scatteringangles for each ejectile. Exceptions from this rule werethe spectra of ejectiles heavier than oxygen (F, Ne, Na,Mg, and Al), which were measured only at these two an-gles at which Bragg curve ionization chambers have been d σ / d Ω d E [ m b / s r* M e V ] B B E [ MeV ] 10 B FIG. 7: Typical spectra of boron ions , , B measured inthe present experiment by telescope consisted of silicon semi-conductor detectors placed at scattering angle of 35 degree inrespect to the proton beam - open circles. The lines have thesame meaning as in Fig. 3 positioned, i.e . at 15 and 120 . Such spectra were fittedassuming that only one moving source gives contributionto the reaction. Furthermore, the spectra of C, N, andO which were measured both, by silicon detectors at 35 ,50 , 80 , and 100 as well as by Bragg curve ionizationchambers at 15 and 120 degree were fitted using oneemitting source and two emitting sources. The parame-ters of sources for light charged particles and isotopicallyidentified IMF’s are listed in Table III whereas those forheavier IMF’s, which were only elementally identified, arecollected in Table IV.The first source should simulate evaporation of par-ticles from heavy remnant of the first stage of the re-action, i.e. intranuclear cascade of nucleon-nucleon col-lisions. Thus, its velocity was fixed at value β =0.002 E [ MeV ] C d σ / d Ω d E [ m b / s r* M e V ] N O FIG. 8: Typical spectra of carbon, nitrogen and oxygen ionsmeasured in the present experiment without isotopic separa-tion by telescope consisted of silicon semiconductor detectorsplaced at scattering angle of 35 degree in respect to the pro-ton beam - open circles. The lines have the same meaning asin Fig. 3 (in units of velocity of light) as it was extracted fromBUU calculations. This value was constant for all cal-culations. Other parameters characterizing the source, i.e. k -parameter (ratio of the actual height of Coulombbarrier to its value found from simple estimation for twotouching, charged spheres), T -parameter (apparent tem-perature), and σ (energy and angle integrated cross sec-tion for production of given ejectile) were free parametersof the fit.All parameters of the second source were freely mod-ified in fits since no hypothesis concerning origin of thissource was made before the analysis. Usually the pro-gram was able to find unambiguously the best parame-ters, corresponding to the minimum value of chi-square.In such a situation the routine provides estimation of er- Al 15 Al 120 d σ / d Ω d E [ m b / s r M e V ] Ne 15 Ne 120 E [MeV] O 15 E [MeV]O 120 FIG. 9: Examples of energy spectra for heavier, elementallyidentified IMF’s obtained in the current experiment by meansof Bragg curve ionization chambers. The open circles repre-sent experimental data and the solid lines show results ofphenomenological model analysis obtained with assumptionof only one moving source, discussed in the next section ofthe paper. rors. In some cases, however, the valley of chi-squarevalues was so complicated that the program was not ableto produce reasonable estimation of errors. The ambigu-ity of parameters lead sometimes the searching procedureto nonphysical values of the parameters, as e.g. negativeheight of the Coulomb barrier. Then it was necessary tofix these parameters at values, which still have physicalmeaning. Such values of parameters are quoted in thetables as closed in square parentheses.Thorough inspection of the parameter dependenceleads to the following conclusions:1.
The contribution σ of the first (slow) emit-ting source is comparable to contribution σ of the second source. It is illustrated by Fig. 10 in which ratio of thetotal cross section for emission of ejectiles from thefirst source to the sum of the total cross sections foremission from both sources is shown as function ofmass number of the ejectiles. The average value of
TABLE III: Parameters of two moving sources for isotopically identified productsSlow source Fast sourceEjectile k T /MeV σ /mb k β T /MeV σ /mb χ p ± ± ±
46 [0.05] 0.147 ± ± ±
86 22.6 d ± ± ±
29 0.07 ± ± ± ±
24 13.2 t ± ± ±
17 [0.05] 0.072 ± ± ±
13 6.1 He 0.75 ± ± ± ± ± ± He 0.82 ± ± ±
43 0.30 ± ± ± ±
30 59 He 0.97 ± ± ± ± ± ± ± Li 0.86 ± ± ± ± ± ± ± Li 0.88 ± ± ± ± ± ± ± Li 0.90 ± ± ± ± ± ± ± Li 1.00 ± ± ± ± ± ± ± Be 0.92 ± ± ± ± ± ± ± Be 0.86 ± ± ± ± ± ± ± Be 0.90 ± ± ± ± ± ± ± B 0.85 ± ± ± ± ± ± ± B 0.93 ± ± ± ± ± ± ± B 0.87 8.8 1.6 0.73 0.012 13.2 5.1 1.0TABLE IV: Parameters of one or two moving sources for elementally identified productsSlow source Fast sourceEjectile k T /MeV σ /mb k β T /MeV σ /mb χ C 0.879 12.3 28.4 0.150 0.0367 15.8 11.8 3.340.759 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± the ratio σ / ( σ + σ ) is equal to 0.560 ± ∼
25 % of protons.2.
The parameters of the slow source havevalues which agree with the assumptionthat this source simulates evaporation froma heavy nucleus corresponding, e.g. to theresiduum of the target after the intranuclear cas-cade of nucleon-nucleon collisions, namely: • The apparent temperature of the slow sourceis independent of the mass of emitted inter-mediate mass fragments, what can be seen inFig. 11 where the slope parameter of the solidline is equal to zero within the limits of er-rors : - 0.15 ± T = 11.9 ± • The k parameter, which determines the heightof the effective Coulomb barrier between theemitted fragment and the rest of the emittingsource (cf. Appendix) is very close to unity,what means that the charge of the source doesnot differ significantly from the charge of thetarget. It is illustrated by Fig. 12 where k parameters for both sources are shown for in-dividual ejectiles. The full squares representthe slow source and open squares correspondto the second, fast source. The dashed line k = 1 is shown in the figure to facilitate judg-0 σ / ( σ + σ ) A F FIG. 10: Ratio of total production cross section correspondingto emission from the slow source to sum of the total crosssections representing emission from both sources versus massnumber of the detected reaction product. The parameters σ and σ were taken as total cross sections because theycorrespond to angle and energy integrated double differentialcross sections d σ/d Ω dE . The solid line shows average valueof the ratio (0.560 ± ment on the magnitude of the k – parameter.3. The second (fast) source is much lighterthan the residual nucleus of the intranuclearcascade because: • Its velocity is always larger than limiting ve-locity of the proton-target center of masswhich would be obtained only when totalbeam momentum is transferred to the target( β ≈ . β values for individual ejectiles as well asthe horizontal line β = 0 . • The Coulomb barrier between the source andthe ejectile is several times smaller than theCoulomb barrier of two touching chargedspheres representing the target nucleus andthe ejectile. This is well illustrated by opensquares in Fig. 12. • The recoil effect (cf. Appendix) is clearly visi-ble in the dependence of the apparent temper-ature of the source on the mass of the ejectileas it is shown in Fig. 11 - open squares.4.
The fast source describing LCP’s emission(hydrogen and helium ions up to He) ismuch lighter than the fast source responsi-ble for emission of intermediate mass frag-ments. T [ M e V ] A F FIG. 11: Apparent temperature of the slow source (fullsquares and solid lines) and that of the fast source (opensquares and dashed lines) versus mass number of the ejectiles.The lines were fitted separately for light charged particles ( H- He) and intermediate mass fragments (A F ≥ This may be inferred from different recoil effectsvisible as different slopes of two lines which de-scribe the dependence of the apparent temperatureon the mass of ejectiles (cf. Fig. 11). The line cor-responding to LCP’s is more steep, giving the massof the source equal to A S =(8 ±
2) nucleons, andvery high temperature of the source τ =(62 ± τ ). Velocity ofthis light source is very high; β = 0 . − . fireball created by the proton impinging on to thetarget together with nucleons present on its straightline way through the target nucleus [24],The line describing temperature of IMF’s corre-sponds to mass of the source A S =(20 ±
3) nucleonsand its temperature τ = (33 ±
2) MeV. Velocity ofthis source is much smaller ( β = 0 . − .
04) thanvelocity of source emitting LCP’s.Very different properties of the fast source emittinglight charged particles (LCP’s) and the fast source emit-ting intermediate mass fragments (IMF’s) leads to con-clusion that the picture of two sources is oversimplified.The presence of a fireball, which can give contributionto emission of LCP’s only and occurrence of the light( A S ≈ k A F FIG. 12: The ejectile mass number dependence of the factorscaling the Coulomb barrier of two touching spheres to theactual height – necessary for good description of the data.Full squares represent the slow source and open squares showresults for the fast source. The line k =1 is also depicted tofacilitate interpretation of the figure. V. SUMMARY AND CONCLUSIONS
The double differential cross sections ( d σ/d Ω dE )were for the first time measured with good statisticsfor isotopically identified intermediate mass fragmentsproduced by interaction of 2.5-GeV protons with thegold target. The following individual isotopes of theelements from hydrogen to boron were resolved: , , H, , , He, , , , Li, , , Be, , , B, whereas for heavierejectiles (from carbon to aluminium) only elementalidentification was done. The energy spectra for allnuclear fragments, determined at several scatteringangles, appear to be of the Maxwellian shape withexponential, high energy tail. The low energy part ofthe distribution is almost independent of angle, butthe slope of high energy tail of the spectrum increasesmonotonically with the angle. The shape of the angleindependent part of spectra can be reproduced by thetwo-stage model of the reaction, i.e. intranuclear cascadeof the nucleon-nucleon and meson-nucleon collisionsfollowed by statistical emission from an equilibratedresidual nucleus. However, the absolute magnitudeof the spectra predicted by two-stage model, usingBoltzmann-Uehling-Uhlenbeck program [23] for the in-tranuclear cascade and Generalized-Evaporation-Model(GEM) [15, 16] for statistical emission of fragments, isin agreement with the experimental data only for thelight charged particles (H and He ions). Furthermore,the theoretical cross sections underestimate significantlythe yield of heavier fragments at high kinetic energiesfor all ejectiles. This indicates that another mechanism β A F FIG. 13: Velocity of the second (fast) source as a functionof emitted fragment mass number - open squares. Thin solidline β =0.018 represents velocity of the common center ofmass of the proton projectile and the target and thick solidline β =0.002 shows velocity of the first (slow) source fixedat velocity of heavy residuum of intranuclear cascade. plays an important role besides the standard two-stagemechanism.To get information on possible origin of this additionalmechanism a phenomenological analysis was performedassuming that the ejectiles originate from two movingsources. The slow moving source was identified withthe heavy remnant nucleus of the first stage of thetwo-step process mentioned above while no assumptionshave been made as concerns the second emitting source.The properties of both sources were treated as freeparameters with exception of the velocity of the slowsource which was taken to be equal to the velocity of theheavy residual nucleus from the intranuclear cascade,namely β =0.002.Excellent agreement of the phenomenologicalparametrization with experimental data was achievedwith values of the parameters varying smoothly fromejectile to ejectile. Their behavior indicates that theparameters of the slow source are compatible withthe assumption that it is a heavy nucleus which maybe described as equilibrated system of ∼
12 MeVapparent temperature, whereas the second source hascompletely different properties. It corresponds eitherto very small ( A S ∼ τ ∼
62 MeV) andfast ( β = 0 . − .
15) fireball or to heavier ( A S ∼ τ ∼
33 MeV), and slower ( β = 0 . − .
04) cluster.The described above properties of two emittingsources observed in the interaction of 2.5 GeV protons2with the gold target lead to a conclusion that twodifferent mechanisms are observed giving almost thesame contribution to the cross sections. First of them iscompatible with the standard, two-stage model whereasanother one seems to be similar to the picture of coldbreak-up proposed by J. Aichelin, J.H¨ufner and R.Ibarra [25].In the model of cold break-up the energetic protonbombarding the target drills a cylindrical hole throughthe nucleus causing that the deformed remnant of thecollision breaks up into two pieces. Thus, three corre-lated groups of nucleons appear after first, short stageof the reaction : (i) the fast, small cluster consisted ofthe nucleons which were placed within the cylinder withthe axis along to the projectile path,(ii) two clusters- products of the break up. All three clusters act assources emitting light charged particles, whereas twoheavier clusters are also responsible for emission ofintermediate mass fragments. The two latter clustersare produced in result of a dynamical process in whichthe ”wounded” nucleus cannot come to its ground stateby emission of nucleons or small clusters, however, thecorrelation of the fast group of nucleons knocked out bythe projectile is of another, kinematic origin. The highenergy proton impinging on to the nucleus sees it - due toLorentz contraction - as a narrow disc. Therefore all thenucleons which lie on the path of the projectile interactsimultaneously, as one entity, with the projectile. It wasshown that this collectivity affects the multi particleproduction in proton-nucleus collisions [26] as well asmanifests itself in enhanced dependence of momentumtransfer on projectile energy in deep-spallation reactions[27]. Thus, it is not surprising that such correlated groupof nucleons can appear as a hot, fast moving sourceemitting light charged particles observed in the presentexperiment. Of course, it cannot give contribution toemission of intermediate mass fragments because thesource is consisted of a few nucleons only.It might be something confusing why in the presentparametrization only two sources were necessary forgood description of the data if the postulated coldbreak-up mechanism of the reaction calls for presence ofthree sources. This apparent inconsistency is easy to beremoved: The slow, heavy source represents the heavyresidual nucleus produced by the standard two-stepmodel of the reaction and/or the heavy fragment fromthe break up . The light, fast source is responsiblefor simulation of the hot fireball (for light chargedparticles) or the lighter fragment from the break up (forintermediate mass fragments).Consistency of the present phenomenological descrip-tion with the cold break up picture of the reaction cannotbe assumed as a proof of the underlying reaction mecha-nism. Additional experimental facts should be searchedfor establishing the confidence in such an interpretation. For example, it can be expected that similar phenomenahave to appear for other heavy target nuclei if they areobserved for the gold target. On the contrary, it is notobvious whether proton induced reactions on light tar-gets or at significantly different proton energies shouldshow similar behavior.
APPENDIX: PHENOMENOLOGICALPARAMETRIZATION
In this Appendix assumptions and details of theformulation of two moving source model are discussed.The content of the appendix is very close to informationcontained in the original paper of Westfall et al. [28],however, the additional modification and propertiesintroduced in the model need to be discussed for properunderstanding of the performed analysis.The model assumes that the nucleons and compositeparticles are emitted from two moving sources with thefollowing properties: (i)
Each source moves along the proton beam direction, (ii)
Angular distribution of emitted particles is isotropicin the source rest frame, (iii)
Distribution of the kinetic energy E ∗ available in thetwo-body break up of the source has a Maxwellianshape characterized by the temperature parameter τ : d σdE ∗ d Ω ∗ = σ πτ ) / √ E ∗ exp (cid:20) − E ∗ τ (cid:21) . The distribution is normalized in such a way thatintegration over angles and energies gives the total crosssection equal to the parameter σ .Since the mass of the source A S is finite, the energyand momentum conservation laws cause that the energy E ′ of the observed particle of mass A F differs from thefull kinetic energy E ∗ available in the source frame: E ∗ = νE ′ where ν ≡ A S A S − A F , thus the energy distribution of the emitted fragment inthe rest frame of the source is given by: d σdE ′ d Ω ′ = νσ πτ ) / √ νE ′ exp " − νE ′ τ . This formula is usually applied without explicit writingthe recoil correction, i.e. by introducing so called appar-ent temperature T ≡ τ /ν : d σdE ′ d Ω ′ = σ πT ) / √ E ′ exp " − E ′ T . τ as well as on the mass of the source A S from linear dependence of the apparent temperature T on the fragment mass A F : T ≡ τν = τ − (cid:18) τA S (cid:19) · A F . The charged particles emitted from the sourcemust overcome the Coulomb barrier, what significantlychanges the shape of the low energy part of their spec-trum. The presence of the barrier may be taken into ac-count by shifting the argument in the Maxwell formulaby the height of the barrier, as it was originally proposedin Ref. [28] or by multiplying the Maxwell distributionby the transmission factor. The first method is equiva-lent to the application of a sharp cut-off what is a toocrude approximation, thus the result must be averagedover some distribution of heights of the barriers [28]. Thesecond method explicitly introduces a smooth variationof the transition probability with energy, however, thismethod also must introduce some assumptions concern-ing height and curvature of the barrier. In the presentwork, the probability P to overcome the Coulomb barrierwas parameterized in the following form: P = 11 + exp (cid:2) − (cid:0) E − k · Bd (cid:1)(cid:3) , where B is the Coulomb barrier of two touching spherescorresponding to the emitted fragment of mass number A F and charge number Z F and to the remaining partof the source with the mass number of ( A S − A F ) andcharge number ( Z S − Z F ): B = Z F ( Z S − Z F ) e . (cid:16) A F / + ( A S − A F ) / (cid:17) . The quantities k and d are the parameters. The firstparameter ( k ) gives magnitude of the Coulomb barrierin units of B . To avoid ambiguity of B determinationarising from the fact that at least two different sourcesare present in the current analysis, we evaluated B valueassuming that Z S = 79 and A S = 197, i.e. there areatomic and mass numbers of the target. Such value of B is a good approximation of the Coulomb barrier for heavyresidua of the intranuclear cascade, thus one should ex-pect that then the k parameter is close to unity. How-ever, with such definition of B , the k parameter shouldbe significantly smaller than unity for light sources. Theparameter k was searched by looking for the best fit ofmodel spectra to the experimental data. The second pa-rameter ( d ) was arbitrarily fixed in the present analysis by keeping constant the ratio of the height of the barrier kB to its diffuseness parameter d : kB/d = 5 . P gives finally the following formula for the doubledifferential cross section d σ/dE ′ d Ω ′ : d σdE ′ d Ω ′ = σ πT / I ( kB, d, T ) · √ E ′ exp (cid:16) − E ′ T (cid:17) (cid:16) kB − E ′ d (cid:17) I ( B, d, T ) = ∞ Z dx · √ x · exp ( − x )1 + exp (cid:0) kB − T · xd (cid:1) The integral I ( B, d, T ) used for normalization of the dis-tribution (preserving previous interpretation of σ pa-rameter) has been evaluated numerically by the Gauss-Laguerre method.It is necessary to transform the model double differ-ential cross sections calculated in the rest frame of theemitting source to the laboratory system when compar-ing the model predictions to experimental data. It canbe shown that the transformation may be performed byfollowing formula: d σdEd Ω = pp ′ · d σdE ′ d Ω ′ ≈ r EE ′ · d σdE ′ d Ω ′ , where the first equality is exact and the second is validin nonrelativistic limit, normally realized in the motionof observed ejectiles. The nonrelativistic relationship be-tween kinetic energy E of the particle emitted at theangle θ LAB in the laboratory system and the energy E ′ of emitted particle in the rest frame of the source is asfollows: E ′ = E + mβ − √ mE · β · cos θ LAB , where m ( ≡ A F ) is the mass of the emitted particle and β - the velocity of the source in the laboratory system. ACKNOWLEDGMENTS
The quality of the beam necessary for the success ofthis work is due mainly to the efforts of the COSY op-erator crew. The authors acknowledge gratefully thesupport of the European Community-Research Infras-tructure Activity under FP6 ”Structuring the Euro-pean Research Area” programme (CARE-BENE, con-tract number RII3-CT-2003-506395 and HadronPhysics,contract number RII3-CT-2004-506078). The authorsappreciate the financial support of the European Com-mission through the FP6 IP-EUROTRANS FI6W-CT-2004-516520.4 [1] S. Kaufman and E. Steinberg, Phys. Rev. C , 167(1980).[2] Y. Asano, H. Kariya, S. Mori, M. Okano, and M.Sakano,J. Phys. Soc. Japan , 2995 (1988).[3] M. Cherry, A. D¸abrowska, P. Deines-Jones, R. Ho ly´nski,W. Jones, E. Kolganova, A. Olszewski, K. Sengupta,T. Skorodko, M. Szarska, et al., Phys. Rev. C , 2652(1995).[4] C. J. Waddington, J. R. Cummings, B. S. Nilsen, andT. L. Garrard, Phys. Rev. C , 024910 (2000).[5] F. Rejmund, B. Mustapha, P. Armbruster, J. Benlliure,M. Bernas, A. Boudard, J. Dufour, T. Enqvist, R. L. S.Leray, K.-H. Schmidt, et al., Nucl. Phys. A , 540(2001).[6] J. Benlliure, P. Armbruster, M. Bernas, A. Boudard,T. Enqvist, R. Legrain, S. Leray, F. Rejmund, K.-H.Schmidt, C. St´ephan, et al., Nucl. Phys. A , 469(2002).[7] M. K. Berkenbusch, W. Bauer, K. Dillman, S. Pratt,L. Beaulieu, K. Kwiatkowski, T. Lefort, W. c. Hsi, V. E.Viola, S. J. Yennello, et al., Phys. Rev. Lett. , 022701(2002).[8] V. Rodionov, S. Avdeyev, V. Karnaukhov, L. Petrova,V. Kirakosyan, P. Rukoyatkina, H. Oeschler,A. Budzanowski, W. Karcz, M. Janicki, et al., Nucl.Phys. A , 457 (2002).[9] V. Karnaukhov, H. Oeschler, S. Avdeyev, E. Duginova,V. Rodionov, A. Budzanowski, W. Karcz, O. Bochkarev,E. Kuzmin, L. Chulkov, et al., Phys. Rev. C ,011601(R) (2003).[10] C. M. Herbach, D. Hilscher, U. Jahnke, V. G.Tishchenko, J. Galin, A. Letourneau, A. P´eghaire,D. Filges, F. Goldenbaum, L. Pie´nkowski, et al., Nucl.Phys. A , 426 (2006).[11] A. Letourneau, A. B¨ohm, J. Galin, B. Lott, A. P´eghaire,M. Enke, C.-M. Herbach, D. Hilscher, U. Jahnke,V. Tishchenko, et al., Nucl. Phys. A , 133 (2002).[12] A. Boudard, J. Cugnon, S. Leray, and C. Volant, Nucl.Phys. A , 195 (2004). [13] R. Barna, V. Bollini, A. Bubak, A. Budzanowski, D. D.Pasquale, D. Filges, S. V. F¨ortsch, F. Goldenbaum,A. Heczko, H. Hodde, et al., Nucl. Instr. Meth. in Phys.Research A , 610 (2004).[14] A. Bubak, B. Kamys, M. Kistryn, and B. Piskor-Ignatowicz, Nucl. Instr. and Meth. in Phys. Research B , 507 (2004).[15] S. Furihata, Nucl. Instr. and Meth. in Phys. Research B , 251 (2000).[16] S. Furihata and T. Nakamura, Journal of Nuclear Scienceand Technology Supplement 2 , 758 (2002).[17] A. Kotov, L. Andronenko, M. Andronenko, Y. Gusev,K. Lukashin, W. Neubert, D. Seliverstov, I. Strakovsky,and L. Vaishnene, Nucl. Phys. A , 575 (1995).[18] S. V. J. Cugnon, C. Volant, Nucl. Phys. A , 475(1997).[19] A. Boudard, J. Cugnon, S. Leray, and C. Volant, Phys.Rev. C , 044615 (2002).[20] G. Bertsch and S. D. Gupta, Phys. Reports , 189(1988).[21] J. Aichelin, Phys. Reports , 233 (1991).[22] R. Charity, M. A. McMahan, G. J. Wozniak, R. J. Mc-Donald, L. G. Moretto, D. G. Sarantites, L. G. Sobotka,G. Guarino, A. Pantaleo, L. Fiore, et al., Nucl. Phys. A , 371 (1988).[23] W.Cassing, private information.[24] G. Westfall, J. Gosset, P. Johansen, A. Poskanzer,W. Meyer, H. Gutbrot, A. Sandoval, and R.Stock, Phys.Rev. Lett. , 202 (1976).[25] J. Aichelin, J. H¨ufner, and R. Ibarra, Phys. Rev. C ,107 (1984).[26] G. Berlad, A. Dar, and G. Eilam, Phys. Rev. D , 161(1979).[27] J. B. Cumming, Phys. Rev. Lett. , 17 (1980).[28] G. D. Westfall, R. G. Sextro, A. M. Poskanzer, A. M.Zebelman, G. W. Butler, and E. K. Hyde, Phys. Rev. C17