Table Of ContentCompetition of coalescence and ”fireball” processes in nonequilibrium emission of
light charged particles from p+Au collisions
A.Budzanowski,1 M.Fidelus,2 D.Filges,3 F.Goldenbaum,3 H.Hodde,4 L.Jarczyk,2 B.Kamys,2,∗
M.Kistryn,1 St.Kistryn,2 St.Kliczewski,1 A.Kowalczyk,2 E.Kozik,1 P.Kulessa,1,3 H.Machner,3
A.Magiera,2 B.Piskor-Ignatowicz,2,3 K.Pysz,1,3 Z.Rudy,2 R.Siudak,1,3 and M.Wojciechowski2
(PISA - Proton Induced SpAllation collaboration)
1H. Niewodniczan´ski Institute of Nuclear Physics PAN, Radzikowskiego 152, 31342 Krako´w, Poland
2M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30059 Krak´ow, Poland
3Institut fu¨r Kernphysik, Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany
4Institut fu¨r Strahlen- und Kernphysik, Bonn University, D-53121 Bonn, Germany
(Dated: February 4, 2008)
Theenergyandangulardependenceofdoubledifferentialcrosssectionsd2σ/dΩdE wasmeasured
for p,d,t,3,4,6He, 6,7,8,9Li, 7,9,10Be, and 10,11,12B produced in collisions of 1.2 and 1.9 GeV protons
8
withAutarget. Thebeamenergydependenceofthesedatasupplementedbythecrosssectionsfrom
0
previousexperimentat2.5GeVisverysmooth. Theshapeofthespectraandangulardistributions
0
2 almost does not change in the beam energy range from 1.2 to 2.5 GeV, however, the absolute
value of the cross sections increases for all ejectiles. The phenomenological model of two emitting,
n
moving sources, with parameters smoothly varying with energy, reproduces very well spectra and
a
angulardistributionsofintermediatemassfragments. Thedoubledifferentialcrosssectionsforlight
J
charged particles were analyzed in the frame of the microscopic model of intranuclear cascade with
9 coalescenceofnucleonsandstatisticalmodelforevaporationofparticlesfromexcitedresidualnuclei.
2
However, energy and angular dependencies of data agree satisfactorily neither with predictions of
microscopicintranuclearcascadecalculationsforprotons,norwithcoalescencecalculationsforother
]
x lightchargedparticles. Phenomenologicalinclusionofanotherreactionmechanism-emissionoflight
e chargedparticlesfroma”fireball”,i.e.,fastandhotmovingsource-combinedwiththemicroscopic
- model calculations of intranuclear cascade, coalescence and evaporation of particles leads to very
l
c gooddescriptionofthedata. Itwasfoundthatthenonequilibriumprocessesareveryimportantfor
u productionoflightchargedparticles. Theyexhaust40-80%ofthetotalcrosssections-depending
n on the emitted particles. Coalescence and ”fireball” emission give comparable contributions to the
[ cross sections with exception of 3He data where coalescence clearly dominates. The ratio of sum of
allnonequilibriumprocessestothoseproceedingthroughstageofstatisticalequilibriumdoesalmost
1
not change in the beam energy range from 1.2 GeV to 2.5 GeV for all light charged particles.
v
2
PACSnumbers: 25.40.-h,25.40.Sc,25.40.Ve
1
Keywords: Protoninducedreactions,productionoflightchargedparticlesandintermediatemassfragments,
5
spallation,fragmentation,nonequilibriumprocesses,coalescence,fireballemission
4
.
1
0 I. INTRODUCTION most indistinguishable from the target residuum created
8 in microscopic models as result of the intranuclear cas-
0 cade, andthelighterprefragmenthastypicallyamassof
In the recent publication [1] we have shown that
v: the inclusive spectra of double differential cross sections about 20-30 nucleons. IMF’s, i.e., the particles heavier
Xi d2σ/dΩdE for light charged particles (LCP’s) and inter- than the α - particle but lighter than fission fragments,
cannot be emitted from the ”fireball” because it consists
mediatemassfragments(IMF’s)producedinproton-Au
r only several nucleons, however, contributions from both
a collisions at proton beam energy 2.5 GeV are compati-
heavierprefragmentshavebeenwellvisibleintheirspec-
ble with the mechanism similar to cold breakup model
tra [1].
proposed by Aichelin et al. [2]. According to this model
This simple picture of the reaction mechanism is very
the proton impinging on to the target drills a cylindri-
appealingbecauseitgivesapossibilitytounderstandthe
cal hole in the nucleus what results in presence of three
presence of large nonequilibrium contribution to cross
sources emitting LCP’s, namely a small, fast, and hot
sectionsobservedexperimentally, whichcannotbequan-
”fireball”consistedofseveralnucleons[3],andtwoheav-
titatively reproduced by any of the existing microscopic
ier,excitedprefragments. Theydiffersignificantlyinsize
modelsbasedontheassumptionoftwostagesofthereac-
because distribution of impact parameters favors non-
tion,i.e.,thefaststageconsistinginintranuclearcascade
central collisions which lead to asymmetric mass values
of nucleon-nucleon collisions - described by INC, BUU
oftheproducts. Therefore,theheavierprefragmentisal-
or QMD models, and the slow stage of reaction in which
heavytargetresiduumreachesstatisticalequilibriumand
evaporates particles - described by statistical models.
∗Electronicaddress: [email protected] It should be pointed out, that phenomenological anal-
2
ysis published in our previous work is not able to unam-
biguouslydistinguishprocessesproceedingthroughphase
of statistical equilibrium of heavy target residuum from
4 7
reactions in which a nonequilibrium mechanism, i.e., the He Li
101 10-1
fast breakup of the target, produces heavy, excited pre-
fragment moving slowly and therefore being almost in-
distinguishable from the target residuum. 100 10-2
To get more insight into the reaction mechanism it r]
s
is necessary to investigate energy dependence of the re-
V
action processes as well as to study interaction of pro- e10-1 10-3
tons with various targets. A goal of the present work M
was to examine beam energy dependence of the emis- b/
sion of LCP’s and IMF’s from the collisions of protons m
withAutargetinabroadprotonenergyrange-from1.2 [
GeVto2.5GeV.Forthispurposenewexperimentaldata Ωd 9Be 11B
were measured and analyzed, confronted whenever pos- E10-1
sible with a microscopic description of the data instead d 10-2
/
σ
of pure phenomenological treatment as in Ref. [1].
d10-2
Experimental data are discussed in the next section,
the theoretical analysis is described in the third section, 10-3
discussion of obtained results is presented in the fourth 10-3
section, and summary of results is given in the last sec-
tion.
0 50 100 0 50 100 150
II. EXPERIMENTAL DATA E [MeV]
The experiment was performed with the selfsupport-
ing Au target of the thickness of about of 300 µg/cm2, FIG.1: (Coloronline)Typicalspectraof4He, 7Li, 9Be, and
irradiated by internal proton beam of COSY (COoler 11B ejectiles (upper left, upper right, lower left, and lower
SYnchrotron) of the Ju¨lich Research Center. The ex- right parts of the figure, respectively) measured at 35◦ for
perimental setup and procedure of data taking were in three energies of the proton beam; 1.2, 1.9, and 2.5 GeV,
details described in Refs. [1] and [4]. Thus, here we only impinging on to the Au target. Open circles represent the
lowestenergy,fullsquares-theintermediateenergy,whereas
point out that the operation of the beam was performed
open triangles show the data for the highest energy. The
in so called supercycle mode, i.e. alternating for each
crosssectionsat2.5GeVprotonbeamenergywerepublished
requested beam energy several cycles, consisting of pro-
in Ref. [1] and the data at 1.2 and 1.9 GeV were obtained in
tons injection to COSY ring, their acceleration with the
the present experiment.
beam circulating below the target, and irradiation of the
target. Due to this all experimental conditions; setup,
electronics, thetargetthicknessanditspositionwereex-
actly thesame for allthree studied protonenergies - 1.2, an equilibrated, excited nucleus, and high energy expo-
1.9 and 2.5 GeV. In this way the energy dependence was nentialcomponent-interpretedasnonequilibriummech-
not biased by systematic effects caused by possible mod- anism contribution. The data for LCP’s, represented in
ifications of the experimental conditions for experiments Fig. 1 by α-particles, have similar character and energy
with different beam energy. dependence as those for IMF’s, however, the nonequilib-
Doubledifferentialcrosssectionsd2σ/dΩdE weremea- rium component is more pronounced.
suredasafunctionofscatteringangleandenergyofejec-
tiles, which were mass and charge identified for isotopes
ofH,He, Li, Be, andB.Heavierejectilesi.e. C,N,O,F, III. THEORETICAL ANALYSIS
Ne, Na, Mg, and Al were only charge identified. Typical
spectra of isotopically identified ejectiles obtained in the The equilibrium emission of LCP’s and IMF’s may
present experiment are shown in Fig. 1. As can be seen be portrayed by statistical model of particle evapora-
in this figure the shape of spectra does not vary signifi- tion from excited heavy target residuum created in the
cantlywithbeamenergy. Themaineffect,presentforall fast stage of the reaction. This is, however, not the
products is monotonic increase of the absolute value of case for nonequilibrium emission of composite particles,
thecrosssectionswithbeamenergy. Furthermore,allthe which cannot be satisfactorily described by models used
spectra contain two components; low energy component for reproduction of the first stage of the reaction, i.e.,
of the Gaussian shape - attributed to evaporation from by intranuclear cascade, Boltzmann-Uehling-Uhlenbeck
3
orQuantumMolecularDynamicsmodels. Allmentioned
models of the reaction neglect to large extent possi- 1.5
ble multinucleon correlations, which can be crucial for
nonequilibrium processes. Whereas it is possible to take
effectively these correlations into account for LCP’s - by
introducing coalescence of emitted nucleons into clus- V) 1.0
ters - such a procedure is not sufficient for description e
G
of IMF’s nonequilibrium emission. From this reason dif- 5
ferent theoretical analysis has been performed for LCP’s 2.
and for IMF’s. σ(2 0.5 0.57
The IMF’s data have been analyzed in the frame of / 2
phenomenological model of two moving sources as it was σ
0.23
done for the data measured at 2.5 GeV beam energy in
the previous investigation of these reactions [1]. In this
0.0
waytheenergydependenceofIMF’sproductioncouldbe
studied in a consistent way. This analysis is described in
subsection IIIA.
)
TheLCP’snonequilibriumemissioncanbe,onthecon- V
1.0
e
trary, analyzed in the frame of the microscopic model, G
which assumes that the mechanism of nonequilibrium 5
reactions consists in intranuclear cascade of nucleon- (2. 0.75
1
nucleon collisions [5] accompanied by coalescence of the σ
nucleons escaping from the nucleus as it was done in / 1 0.5 0.39
σ
Refs. [6],[7]. The authors of these papers claimed that
themainpropertiesofnonequilibriumemissionofLCP’s
are well reproduced by the proposed microscopic model.
0.0
Thus, in the present study the INCL4.3 computer pro-
6 8 10 12
gram [7] has been used for description of the intranu-
A
clear cascade of nucleon-nucleon collisions with inclusion
of coalescence of nucleons, whereas the GEM2 computer
program [9],[10] served for evaluation of evaporation of
FIG.2: (Coloronline)Symbolsσ andσ correspondtoslow
1 2
particlesfromheavytargetresiduumremainingafterthe and fast emitting source, respectively. Full dots represent
intranuclear cascade. It was also investigated whether ratioofproductioncrosssectionsatbeamenergy1.9GeVto
eventual disagreement of the microscopic model calcu- thosefoundat2.5GeVasafunctionofmassofemittedIMF’s.
lations with experimental results leaves still a room for Opencirclesdepictsucharatioforcrosssectionsmeasuredat
contribution from another mechanism, namely the ”fire- 1.2 GeV to those determined at 2.5 GeV. The lines, present
ball”emissionpostulatedinourpreviouspaper[1]. This inthefigureshowaveragevaluesoftheratios: 0.23,and0.57
for the fast source at 1.2 GeV, and 1.9 GeV, respectively, as
analysis is described in subsection IIIB.
well as 0.39, and 0.75 for the slow source at these energies.
A. Intermediate mass fragments
rier. In our recent paper [1] we used another method,
Themainassumptionsofthephenomenologicalmodel namelywemultipliedtheMaxwellianenergydistribution
of two moving sources have been formulated in the pa- by smooth function corresponding to transmission prob-
per of Westfall et al. [8]. They consist in description of ability through the barrier. Presence of Coulomb bar-
double differential cross sections d2σ/dΩdE as incoher- rier introduces two parameters which influence mainly
ent sum of contributions originating from isotropic emis- low energy part of the spectra: k-parameter, i.e., height
sion of particles from two sources moving in direction of the Coulomb barrier in units of the height of barrier
parallel to the beam direction. Each of the sources has B of two charged, touching spheres of radius 1.44 A1/3;
Maxwellian distribution of the energy available for the B = Z Z e2/1.44 (A1/3 + A1/3), and ratio B/d , where
1 2 1 2
twobodydecayresultinginemissionofthedetectedpar- d is a diffuseness of the transmission function through
ticles. Velocityofthesource-β,itstemperature-T,and the barrier: P(E) = (1+exp((E−kB)/d)))−1. Details
contribution to the total production cross section - σ are of this procedure, as well as interpretation of parameters
treatedasfreeparameters. ThepresenceoftheCoulomb of the model can be found in Appendix of Ref. [1].
barrierwhichhindersemissionoflowenergyparticleswas The parameters of two moving sources were fitted to
originally taken into account by energy sharp cut off, experimental data consisted of energy spectra measured
smoothed in turn by weighting with uniform or Gaus- at seven angles: 16◦, 20◦, 35◦, 50◦, 65◦, 80◦, and 100◦.
sian probability distribution of the height of the bar- To decrease the number of parameters it was assumed
4
TABLE I: Parameters of two moving sources for isotopically identified IMF’s: k, β, T, and σ correspond to reduced height
of the Coulomb barrier for emission of fragments (see the text for the explanation), source velocity, its apparent temperature,
and total (integrated over angle and energy of detected particles) production cross section, respectively. The left part of the
Table(parameterswithindices”1”)correspondstotheslowmovingsource,andtherightpartoftheTableIcontainsvaluesof
parametersforthefastmovingsource. Theupperrowforeachejectilecorrespondstobeamenergy1.2GeV,theintermediate
row to 1.9 GeV, and the lowest one to the energy 2.5 GeV. Velocities for slow sources are fixed at value 0.003c estimated as
velocities of heavy target residua from intranuclear cascade calculations.
Slow source Fast source
Ejectile k T /MeV σ /mb k β T /MeV σ /mb χ2
1 1 1 2 2 2 2
6He 0.97 ± 0.09 9.3 ± 1.1 8.1 ± 1.1 0.47 ± 0.05 0.034 ± 0.007 13.6 ± 1.2 3.9 ± 1.0 2.7
0.95 ± 0.04 9.1 ± 0.6 18.5 ± 1.2 0.36 ± 0.05 0.040 ± 0.007 19.1 ± 1.3 4.9 ± 1.1 2.6
0.97 ± 0.04 9.0 ± 0.6 24.8 ± 1.4 0.35 ± 0.05 0.040 ± 0.007 21.6 ± 1.4 7.5 ± 1.4 2.1
6Li 0.89 ± 0.05 12.4 ± 0.9 10.5 ± 0.8 0.43 ± 0.08 0.047 ± 0.008 22.2 ± 1.3 2.85 ± 1.3 2.4
0.85 ± 0.04 12.1 ± 0.7 19.5 ± 1.2 0.43 ± 0.05 0.040 ± 0.004 23.6 ± 0.7 7.7 ± 1.1 2.4
0.86 ± 0.04 11.1 ± 0.8 25.3 ± 1.7 0.44 ± 0.04 0.034 ± 0.003 23.7 ± 0.6 14.5 ± 1.7 2.0
7Li 0.89 12.3 18.0 0.47 0.039 16.4 4.8 4.7
0.88 ± 0.03 11.7 ± 0.5 38.1 ± 1.8 0.37 ± 0.04 0.040 ± 0.005 20.3 ± 0.7 10.3 ± 1.7 4.2
0.88 ± 0.03 11.6 ± 0.6 50.8 ± 2.6 0.36 ± 0.03 0.035 ± 0.003 20.9 ± 0.5 20.3 ± 2.6 3.1
8Li 0.94 ± 0.11 11.1 ± 1.6 3.51 ± 0.45 0.48 ± 0.08 0.040 ± 0.008 14.4 ± 2.0 1.15 ± 0.45 1.8
0.90 ± 0.08 11.8 ± 1.3 6.65 ± 0.90 0.43 ± 0.05 0.032 ± 0.006 17.2 ± 1.1 3.65 ± 0.93 2.5
0.90 ± 0.09 11.9 ± 1.5 9.1 ± 1.4 0.45 ± 0.05 0.029 ± 0.005 18.0 ± 1.0 6.4 ± 1.5 2.1
9Li 1.01 ± 0.19 11.9 ± 2.9 0.92 ± 0.09 0.58 ± 0.33 0.044 ± 0.008 4.1 ± 1.8 0.25 ± 0.12 1.1
0.84 ± 0.09 10.4 ± 3.0 1.92 ± 0.37 0.51 ± 0.08 0.034 ± 0.008 11.9 ± 2.5 0.77 ± 0.33 1.5
1.00 ± 0.22 10.4 ± 3.0 2.1 ± 0.5 0.39 ± 0.07 0.025 ± 0.003 18.2 ± 1.6 2.1 ± 0.6 1.2
7Be 0.89 13.3 1.22 0.52 0.036 25.3 0.88 1.1
0.86 ± 0.21 14.1 ± 5.3 1.7 ± 1.0 0.61 ± 0.06 0.025 ± 0.007 22.8 ± 1.2 2.9 ± 1.0 1.2
0.92 ± 0.27 11.2 ± 4.3 2.6 ± 0.8 0.48 ± 0.05 0.038 ± 0.005 24.0 ± 1.2 4.6 ± 0.9 1.4
9Be 0.86 9.7 5.2 0.50 0.030 15.2 1.24 1.7
0.88 9.8 9.5 0.59 0.022 15.0 4.41 1.4
0.86 ± 0.12 9.6 ± 1.7 12.5 ± 1.9 0.53 ± 0.06 0.020 ± 0.005 16.6 ± 0.8 8.1 ± 2.3 1.4
10Be 0.86 ± 0.16 12.4 ± 2.1 3.5 ± 1.3 0.62 ± 0.14 0.024 ± 0.011 9.0 ± 3.7 1.9 ± 1.3 1.8
0.86 12.0 7.34 0.47 0.027 13.3 13.3 1.8
0.90 ± 0.08 11.8 ± 1.2 10.0 ± 1.4 0.44 ± 0.04 0.026 ± 0.004 14.5 ± 0.9 6.8 ± 1.5 1.3
10B 0.83 11.7 1.61 0.78 0.017 15.9 0.83 2.8
0.87 10.2 4.93 0.70 0.021 17.7 1.64 1.5
0.85 ± 0.20 10.5 ± 3.4 6.6 ± 1.3 0.73 ± 0.14 0.020 ± 0.010 18.2 ± 2.7 2.7 ± 1.7 1.8
11B 0.84 ± 0.11 10.6 ± 1.4 5.9 ± 0.7 0.53 ± 0.08 0.032 ± 0.008 10.6 ± 2.2 1.9 ± 0.6 0.94
0.90 10.2 8.2 0.57 0.019 13.9 8.7 1.6
0.93 ± 0.18 10.5 ± 2.1 12.8 ± 2.5 0.50 ± 0.05 0.022 ± 0.004 14.5 ± 0.7 12.8 ± 2.8 1.7
12B 0.83 11.9 1.39 0.54 [0.032] 12.5 0.46 1.3
0.88 7.8 2.12 0.71 0.017 13.5 2.57 1.2
0.87 8.8 1.6 0.73 0.012 13.2 5.1 1.0
that velocity of the slow source emitting IMF’s is equal of parameters were present. Therefore, some values of
to velocity of the heavy residuum from intranuclear cas- the parameters are quoted without estimation of errors.
cade, i.e., β =0.003. Variation of this velocity influences In this case it may happen that the accuracy of deter-
1
very slightly values of other parameters, e.g., its modifi- mination of this parameters is poorer then that for the
cationby30%causeschangesofotherparameterssmaller parameters accompanied by estimates of errors.
thantheirerrorsestimatedbyfittingcomputerprogram. Very good description of the spectra of all IMF’s has
Furthermore, the B/d ratio was arbitrarily assumed to beenobtainedascanbejudgedfromχ2 valuesquotedin
be equal to 5.5. In evaluation of k-parameter it was as- the Table I, which vary usually between 1 and 2.
sumed that B is defined as the Coulomb barrier between
AscanbeseenfromtheTableI,valuesoftheparame-
the emitted particles and the target nucleus. This as-
tersfoundfromthefittothedataobtainedat1.2andat
sumption allows for easy comparison of k-parameter val-
1.9GeVareveryclosetothosewhichweredeterminedin
ues for different ejectiles and emitting sources.
the analysis of the data at 2.5 GeV beam energy. This is
Thecomputerprogramsearchingforthebestfitvalues nottrueforthetotalcrosssectionswhichincreasemono-
of the parameters was able in most cases to provide esti- tonically with energy for both emitting sources. This
mation of errors of the parameters. However, sometimes increase is illustrated by Fig. 2 where ratios of the total
thiswasnotpossible, especiallywhenstrongambiguities crosssectionsfoundfordataat1.2GeV,andat1.9GeV
5
to cross sections found for data at 2.5 GeV are shown
as open circles and full dots respectively. The ratios of 1.2
total cross sections for the fast source are shown in the 1.0 6Li 7Li 8Li
upperpartofthefigureandthosefortheslowsourceare
depicted in the lower part of the figure. The following σ)2 0.8 9Be 10Be 11B
+
conclusions can be derived from inspection of Fig. 2 : 1 0.6
σ
(
(i) The ratios of the cross sections for σ/2 0.4
both sources σ1(E,A)/σ1(2.5GeV,A) and 0.2
σ (E,A)/σ (2.5GeV,A) are independent of
2 2
0.0
the mass A of ejectiles (with exception of the
12B cross sections, which are, however, not well
10
determined because of poor statistics of the data).
]
b
m
(ii) Crosssectionsforbothsourcesarealwayslargerfor
[
E=1.9GeVthancrosssectionsforE=1.2GeV(full 2
σ
dots are above open circles) and cross sections for 1
E=2.5 GeV are the largest (the ratios are always
smaller than unity). 100
(iii) The averaged over mass of ejectiles ratios of
the cross sections for the slow source, i.e.
]
b
< σ1(1.2 GeV) / σ1(2.5 GeV) >= 0.39, and m 10
< σ1(1.9 GeV) / σ1(2.5 GeV) >=0.75, are larger [
than the corresponding ratios for the fast source, σ1
i.e. < σ (1.2 GeV) / σ (2.5 GeV) >= 0.23,
2 2
and < σ (1.9 GeV) / σ (2.5 GeV) >= 0.57.
2 2 1
This means that the cross sections of the slow
1 2 3
source increase relatively slower in the beam en-
E [GeV]
ergy range from 1.2 GeV to 2.5 GeV than the
cross sections attributed to the fast source, thus
thecontributionfromthefastsourcebecomesmore
FIG.3: (Coloronline)Energydependenceofthecrosssection
important for higher beam energy. This is con-
σ , corresponding to emission from the slow source, is shown
1
firmed by the fact, that the relative contribution
inthelowerpartofthefigure,energydependenceofthecross
σ2(E,A)/(σ1(E,A)+σ2(E,A)) of the fast source sectionσ2,relatedtoemissionfromthefastsource,isdepicted
tothetotalproductioncrosssectionofIMF’s,eval- in the middle part of the figure, whereas energy dependence
uatedusingthenumbersfromtheTableI,increases of the relative contribution of the fast source is presented in
with energy in almost the same way for all IMF’s. the upper part of the figure.
Inaverage,thiscontributionisequalto0.27±0.03,
0.33±0.05,and0.44±0.05forbeamenergyequal
to 1.2, 1.9, and 2.5 GeV, respectively.
B. Light charged particles
The above findings are also illustrated by Fig. 3 in
which energy dependence of cross sections σ and
1
σ is shown for emission from the slow source and It is well known that the cross sections for production
2
fast source, respectively, as well as energy depen- ofLCP’sareatleastorderofmagnitudelargerthancross
denceoftherelativecontributionofthefastsource sections for emission of IMF’s. Therefore, knowledge of
σ to the total cross section σ +σ . Note using the mechanism of LCP’s production is crucial for under-
2 1 2
of different scales; linear for the upper part of the standing of the full interaction process. The coalescence
figure, and logarithmic for the middle and lower mechanismseemstobeverypromisingforexplanationof
parts of the figure. It may be observed, that σ nonequilibrium production of LCP’s [6],[7]. However, it
1
and σ , vary rather fast with energy; σ increases isobvious,thatsuchahypothesisreliesontheproperre-
2 1
∼2-3timesinthestudiedenergyrangewhereasσ productionofthenucleonspectrabyintranuclearcascade
2
increasesevenmore,i.e.,∼3-5times. Howeverthe mechanism. Inthecaseoflackofgooddescriptionofthe
relativecontributionofnonequilibriummechanism, proton spectra, the coalescence mechanism cannot alone
i.e., σ /(σ +σ ) increases much slower, as it was be responsible for the observed nonequilibrium emission
2 1 2
mentionedabove,becauseofthesameenergytrend of LCP’s. To study importance of the coalescence in the
for both cross sections σ and σ . productionofLCP’s,theexperimentalprotonspectrafor
1 2
threestudiedenergieswerecomparedwithpredictionsof
6
but underestimate big part of the spectra at beam en-
Au(p,p X)
ergy of 2.5 GeV in particular for most forward angles.
Tp=2.5 GeV It seems, that the theoretical proton spectra evaluated
o o o without coalescence have different beam energy depen-
101 16 65 100
dence then the experimental data. Inclusion of coales-
cencesignificantlydecreasesthetheoreticalcrosssections
100 for protons, what causes that theoretical spectra are be-
low the experimental data for all beam energies and for
allscatteringangles. Theheightoftheevaporationpeak
r] isslightlyoverestimatedinbothtypesofthecalculations.
s T =1.9 GeV
V p Further inspection of Fig. 4 leads to the conclusion
Me101 16o 65o 100o that there are two obvious trends in the difference of the
mb/ theoreticalspectraevaluatedwiththecoalescencemecha-
Ω [100 nismandtheexperimentaldata: (i)Thehigherthebeam
d energy,thelargertheunderestimationofthehighenergy
E
d part of the data by theory, and (ii) the smaller the scat-
σ/ tering angle in respect to the proton beam direction, the
d
Tp=1.2 GeV largerunderestimationofthedata. Thiseffectsmightbe
101 16o 65o 100o explained by the assumption, that an additional process
exists, which manifests itself mainly at small scattering
angles and gives increasing contribution to the emission
100 of protons for larger beam energies. Such a contribution
can correspond to the presence of the ”fireball” emis-
sion,whichduetofastmotioninforwarddirectionshould
modifythecrosssectionsmainlyatforwardscatteringan-
0 50 100 0 50 100 0 50 100 150
gles. However,inthemicroscopiccalculationsperformed
E [MeV]
according to intranuclear cascade model there is no ex-
plicit room for such a process. Therefore, inclusion of
FIG. 4: (Color online) Open circles represent experimental ”fireball”emissionshouldbeautomaticallyaccompanied
energy spectra of protons measured at selected angles: 16◦, bydecreasingthecontributionfromdirectprocessessim-
65◦, and 100◦ (left, central, and right column of the figure, ulated by intranuclear cascade and coalescence of escap-
respectively) for three proton beam energies: 1.2, 1.9 GeV ingnucleons. Accordingtothereasoninggiventoabove,
– present experiment , and 2.5 GeV – Ref. [1] (lower, cen- the spectra of protons evaluated from intranuclear cas-
tral,andupperrowofthefigure,respectively). Thesolidlines
cade with inclusion of coalescence and with contribution
showresultsofcalculationsperformedintheframeofintranu-
of evaporation of particles were multiplied by a factor,
clear cascade formalism by means of INCL4.3 program [7]
common for all scattering angles, treated as a free pa-
combinedwiththeevaporationofprotonsfromexcitedresid-
rameter of the fit and then added to the contribution
ual nuclei after fast stage of the reaction evaluated by means
from the ”fireball” emission calculated according to the
oftheGEM2programofS.Furihata[9],[10]. Thedashedlines
presentcalculationsmadealsowithINCL4.3plusGEM2pro- formulaofsinglemovingsourceemittingisotropicallythe
grams, however, the coalescence of nucleons into light com- LCP’s [8]. The parameters of the single moving source
plex particles is taken into account according to prescription - the ”fireball”, i.e. its temperature parameter - T, ve-
proposed in Ref. [7]. locity of the source - β, total production cross section
associated with this mechanism - σ was treated also as
free parameters. Height of the Coulomb barrier between
the”fireball”andemittedejectilewasarbitrarilyfixedat
theintranuclearcascademodelcoupledwithevaporation 2 % of the estimated Coulomb barrier for emission from
of nucleons. The calculations have been performed by thetargetnucleus. Valuesoftheparametersof”fireball”
meansofINCL4.3computerprogram[7]inwhichcoales- are given in the Table II.
cence of nucleons can be taken optionally into account, Thefitwasperformedfor7scatteringangles(16◦,20◦,
whereas evaporation of protons as well as complex parti- 35◦, 50◦, 65◦, 80◦, and 100◦). Results of the fit are pre-
cles was described by GEM2 computer program [9],[10].
sentedinFig. 5for3angles, thesmallest, theintermedi-
Such calculations, done with inclusion of coalescence ate and the largest, where the dashed lines show contri-
and without this mechanism, are presented in Fig. 4 as bution of intranuclear cascade with surface coalescence
dashed and solid lines, respectively, together with exper- and evaporation, the dash-dotted lines present contribu-
imental proton spectra - circles. tion from ”fireball” emission, and the solid line depicts
As can be seen, the theoretical spectra obtained from sum of both contributions. As can be seen the excellent
calculations neglecting the coalescence overestimate the agreementcouldbeobtainedforallscatteringanglesand
experimental spectra at proton beam energy of 1.2 GeV, beam energies. It is worth to emphasize, that the ”fire-
7
TABLE II: Parameters of the ”fireball”: β, T, and σ cor- Au(p,p X)
respond to ”fireball” velocity, its apparent temperature, and
T =2.5 GeV
total (integrated over angle and energy of detected particles) p
productioncrosssection,respectively,B/ddeterminesthera- 101 16o 65o 100o
tioofthethresholdenergyforemissionoftheparticles(height
of the Coulomb barrier) to diffuseness of the transmission
functionthroughthebarrier. ParameterFisthescalingfactor 100
ofcoalescenceandevaporationcontributionextractedfromfit
totheprotonspectra. Thenumbersinparenthesesshowfixed
valuesoftheparameters. Note,thatforαparticlesadditional ]
r
moving sourceshould beadded withparameters given in the s T =1.9 GeV
V p
Table III Me101 16o 65o 100o
E Ejectile β T σ B/d F χ2 b/
p m
GeV MeV mb [
1.2 p 0.136 36.7 1400 11.4 0.63 27.2 Ωd 100
d 0.160 39.1 190 12.1 [0.63] 9.5 E
d
t 0.073 21.5 87 4.5 [0.63] 2.9 σ/
3He [0.073] [21.5] 0.44 18 [0.63] 4.5 d T =1.2 GeV
p
4He 0.070 19.0 49 6.2 [0.63] 13.5
1.9 p 0.160 40.7 1950 11.9 0.69 46.5 101 16o 65o 100o
d 0.155 41.1 330 19.0 [0.69] 15.3
t 0.066 23.8 170 3.1 [0.69] 4.4
3He 0.045 15.0 15.6 5.2 [0.69] 3.3 100
4He 0.061 20.9 110 4.7 [0.69] 15.1
2.5 p 0.156 41.7 2720 12.0 0.73 39.0
d 0.130 42.3 530 8.6 [0.73] 10.5
0 50 100 0 50 100 0 50 100 150
t 0.050 23.3 300 5.7 [0.73] 3.2
3He 0.037 20.5 54 5.8 [0.73] 2.7 E [M eV]
4He 0.051 20.7 210 3.7 [0.73] 11.5
FIG. 5: (Color online) Open circles represent experimen-
tal energy spectra of protons measured at selected angles:
16◦, 65◦, and 100◦ (left, central, and right column of the fig-
ball” contribution to the spectra increases significantly
ure, respectively) for three proton beam energies: 1.2, 1.9
both, with the decrease of the scattering angle and with
GeV – present experiment , and 2.5 GeV – Ref. [1] (lower,
the increasing of the beam energy. central, and upper row of the figure, respectively). The
Successofdescriptionofprotonspectrabymicroscopic dot-dashed lines present the contribution of proton emission
model of intranuclear cascade with coalescence of nucle- fromthe”fireball”whereasthedashedlinesshowcalculations
ons and evaporation of protons from equilibrated target madewithINCL4.3plusGEM2programs. TheINCL4.3plus
residuum combined with phenomenological contribution GEM2contributionsarescaledbythefactors0.63,0.69,and
fromthe”fireball”emissionshowsthatthesamemethod 0.73 for beam energies 1.2, 1.9, and 2.5 GeV, respectively.
The solid lines show sum of all these contributions.
of data description might be applicable for other LCP’s.
It is natural to scale the model coalescence contribu-
tiontospectraofcomplexLCP’sbythesamefactor”F”
whichwasusedfortheprotonspectrabecausethecoales- illustrated by Figs. 6, 7, 8, and 9 for deuterons, tritons,
cence emission of complex particles is determined by the 3He, and 4He, respectively. The parameters of the ”fire-
yield of nucleons leaving the nucleus after intranuclear ball” source are listed in the Table II and parameters of
cascade of collisions. additional source used for α-particles are depicted in the
The fits of parameters characterizing the ”fireball” to Table III.
the experimental spectra of deuterons, tritons, 3He, and As can be seen from the figures, the spectra of
4He were therefore performed with the same scaling fac- deuterons and tritons could not be described, even qual-
tors of coalescence and evaporation emission as those for itatively, by coalescence and evaporation of particles
the proton spectra: 0.63, 0.69, and 0.73 for beam energy alone. The reason of this fact is difference between an-
1.2,1.9,and2.5GeV,respectively. Verygooddescription gular variation of the experimental spectra and those
of the experimental data was achieved for all particles evaluated from the microscopic model. For example,
with exception of α-particles for which it was necessary multiplication of coalescence spectra by factor which al-
to add a contribution of another moving source - with lows to well reproduce spectrum at 100◦ still leads to
parameters very close to those used for IMF’s. This ad- underestimation of the cross sections at smaller angles.
ditional contribution led to perfect description of the α On the contrary, adding the contribution of emission of
- particle spectra. Quality of the data reproduction is deuterons and tritons from the ”fireball” improves the
8
Au(p,d X) Au(p,t X)
Tp=2.5 GeV Tp=2.5 GeV
100 16o 65o 100o 100 16o 65o 100o
10-1 10-1
V sr] o Tp=1.9 GeV V sr] Tp=1.9 GeV
Me100 16 65o 100o Me100 16o 65o 100o
b/ b/
m m
Ω [10-1 Ω [10-1
d d
E E
d d
σ/ σ/
d Tp=1.2 GeV d Tp=1.2 GeV
100 16o 65o 100o 100 16o 65o 100o
10-1 10-1
0 50 100 0 50 100 0 50 100 150 0 50 100 0 50 100 0 50 100 150
E [MeV]
E [MeV]
FIG. 6: (Color online) Same as Fig. 5, but for deuterons. FIG. 7: (Color online) Same as Fig. 5, but for tritons.
description significantly because this contribution has much broader than that predicted by evaporation from
exactly such an angular and energy dependence which heavy target residuum. Since neither coalescence mech-
addedtomicroscopicmodelspectraassuresreproduction anism nor ”fireball” emission can produce such a peak
of the experimental data. in the spectrum, thus, another contribution is necessary
A different situation is present for 3He channel, where to reproduce the shape of the peak in the experimental
spectra. The naturally appearing solution is to take into
the ”fireball” contribution seems to be almost negligible,
considerationthecontributionfromthemovingsourceof
especially at lower beam energies. It means, that the co-
themasslargerthanthe”fireball”butsmallerthanheavy
alescence together with small evaporation contribution
target residuum. Such a source, moving faster than tar-
exhaust almost fully the experimental yield of particles
getresiduumbutslowerthanthe”fireball”,wasobserved
leaving no room for the ”fireball” emission. It should
in the analysis of spectra for all IMF’s, thus it is not as-
be, however, emphasized that this very good data repro-
tonishing that also α-particle spectra are modified by its
duction by the coalescence and evaporation mechanisms
contribution.
was obtained after scaling of the theoretical cross sec-
tionsfromINCL4.3+GEM2bythesamefactorsasthose
used for the theoretical cross sections for proton emis-
sion, thus the presence of ”fireball” emission influences IV. DISCUSSION
also indirectly the description of 3He emission.
Still another reaction mechanism seems to be respon- The temperature of the ”fireball” fitted to describe
sible for the α-particle production. The shape as well as LCP’s data varies only slightly with the beam energy.
magnitude of the experimental spectra for 3He and 4He Its values listed in the Table II do not change more than
isquitedifferent,showingthatevaporationofα-particles ∼ 10% for each ejectile in the beam energy range from
from excited target residuum after intranuclear cascade 1.2 to 2.5 GeV. This is also true for the temperature of
ofnucleon-nucleoncollisionsismuchmoreabundantthan the additional source necessary to be included for good
corresponding evaporation of 3He particles. However, description of α-particle data and for temperatures of
the peak present in the experimental spectra of 4He is both phenomenological sources applied for parametriza-
9
3 4
Au(p, He X) Au(p, He X)
T =2.5 GeV
p T =2.5 GeV
p
10-1 16o 65o 100o 101 16o 65o 100o
100
10-2 10-1
10-2
b/MeV sr]10-1 1 6o T p = 16 .59o GeV 1 00o b/MeV sr]110001 1 6o T p = 61 5.9o G eV 10 0o
m m
Ω [10-2 Ω [10-1
Ed Ed10-2
d d
σ/ σ/
d d
Tp=1.2 GeV 101 Tp=1.2 GeV
10-1 16o 65o 100o 100 16o 65o 100o
10-2 10-1
10-2
0 100 0 100 0 100 200 0 50 100 0 50 100 0 50 100 150
E [MeV] E [MeV]
FIG. 8: (Color online) Same as Fig. 5, but for 3He. FIG. 9: (Color online) Same as Fig. 5, but for α-particles.
The thin dotted line depicts contribution from fast moving
source of the mass intermediate between the ”fireball” and
the heavy target residuum.
tionofIMF’sdata. Thisfactallowstostudydependence
of the beam energy averaged temperature on the ejec-
tile mass instead temperature dependencies for individ-
ual beam energies. Beam energy averaged temperatures ature found in the fit (τ=11.1 MeV). The temperature
of all moving sources are depicted in the lower part of of ”fireball” extracted from the parameters of the fitted
Fig. 10 as function of the ejectile mass A. It is seen that straightlineisequaltoτ=49.9MeVandthe”fireball”is
temperatures of two sources emitting IMF’s are grouped built of AS=49.9/8.24 ≡ 6 nucleons.
into two sets: the full dots - representing slow sources These conclusions seem to be compatible with results
- lie along solid horizontal line T = 11.1 MeV whereas ofpurephenomenologicalanalysisoftwomovingsources
the open circles - representing fast sources - are spread performed in our previous investigation of LCP’s and
aroundthedashedlineT =30.6−1.61AMeV.Thesame IMF’s for Au+p collisions at proton beam energy 2.5
procedure applied to apparent temperatures of the ”fire- GeV[1]. Inthisstudythetemperatureoftheslowsource
ball” emitting LCP’s shows that the mass dependence for IMF’s was ∼ 12 MeV, the temperature of the fast
of this temperature may be described by linear function: source for IMF’s was ∼ 33 MeV, and the temperature of
T =49.9−8.24A MeV (dash dotted line in Fig. 10). ”fireball” was estimated to be ∼ 62 MeV. Mass of the
IftheejectilemassAdependenceoftheapparenttem- slow source must be very large - close to the mass of the
perature T of the source is caused only by recoil of the target - because apparent temperature of this source did
source during emission of registered ejectiles then it is not vary significantly with the product mass, i.e. recoil
possible to estimate mass of the source A and its true couldbeneglected. Themassofthefastsourcewasequal
S
temperature τ from parameters of the linear dependence to mass of ∼ 20 nucleons and mass of the ”fireball” was
T(A).ForthefastsourceemittingIMF’sthesourcetem- close to the mass of ∼ 8 nucleons.
perature is equal to τ=30.6 MeV and mass of it is equal The largest deviation between previous results and
toA =30.6/1.61≡19nucleons. Thetemperatureofthe those found in the present work concern properties of
S
slowsourceisindependentoftheIMF’smasswhatmeans the ”fireball”. This is not surprising because the ”fire-
that the recoil effect is negligible, i.e. the source is very ball” of the present work is responsible only for a part
heavy and its temperature is equal to apparent temper- of the effect which was attributed to the ”fireball” in the
10
TABLE III: Parameters of the intermediate mass source
0.20
neededtodescribewelltheα-particlespectrabycombination
fireball
of microscopic model coalescence and evaporation contribu-
tions, the ”fireball” and intermediate mass source contribu- 0.16 second source for 4He
tions. Parametersβ,T,andσhavethesamemeaningasthat fast source for IMF
given in Table II for the ”fireball”. The k parameter is the 0.12 fixed for slow source
heightoftheCoulombbarrierinunitsofsimplebarrierheight trend for fast source
estimation by Coulomb potential of two uniformly touching β 0.08
spheres with the charge of the target nucleus and the charge
of the emitted particle with radii parameterized as R=1.44
0.04
A1/3.
0.00
Ep k β T σ
GeV MeV mb 50
1.2 [0.8] 0.0094 10.6 385
slow source
1.9 0.83±0.03 0.0062±0.0010 10.2±0.3 577±23
2.5 0.80±0.04 0.0047±0.0011 10.2±0.4 764±38 40 trend for slow source
trend for fireball
]
V 30
e
M
[ 20
previousstudy. However,inspectionofFig. 10showsalso T
another effect: The straight dashed line representing ap-
10
parent temperature of the fast source with the mass of
about 19 nucleons - found from analysis of IMF’s data -
0
crosses the dash dotted line representing apparent tem-
0 2 4 6 8 10 12 14
perature of the ”fireball” at mass of ejectile A ∼ 3. It
means that the temperature parameter of the ”fireball” A
and that of the intermediate mass source are the same
for tritons, 3He, and 4He. Moreover, the velocity of the
”fireball” emitting tritons, 3He, and 4He is very close to FIG. 10: (Color online) In the lower part of the figure the
velocity of the fast source emitting IMF’s as it is shown apparent temperature of the moving sources, averaged over
in the upper part of Fig. 10 where the beam energy av- beam energies is drawn as a function of the ejectile mass.
Open circles and full dots represent values of parameters ob-
eraged values of the velocity parameter are collected for
tained from analysis of IMF’s data for fast and slow source,
IMF’s(opencirclesforthefastsourceandsolid,horizon-
respectively. Full squares depict temperature of the ”fire-
talline-fixedatvelocityofheavyresiduumfromintranu-
ball” fitted to spectra of LCP’s together with the contribu-
clear cascade - for the slow source) and for LCP’s (full
tionofmicroscopicmodelofintranuclearcascade,coalescence
squares for the ”fireball” and the full triangle for addi- of nucleons and statistical evaporation. Full triangle shows
tionalsourcenecessaryfordescriptionoftheα-particles). the temperature of the second source fitted to spectra of α-
Thus,itisnotclearwhetheritisallowedtoextractmass particles. Thesolidanddashedlineswerefittedtothepoints
of the ”fireball” from mass dependence of the apparent representingIMF’sandextrapolatedtosmallermasses. Dash
temperatureofthesourcefittedtoproton, deuteron, tri- dottedlinewasfittedtoLCP’stemperaturesofthe”fireball”.
ton, and 3,4He data or it is necessary to assume that the Intheupperpart ofthefigurethedependenceofthebeamen-
ergy averaged velocity of the sources is drawn versus mass of
sourceforparticleswithmass3and4isidenticalwiththe
ejectiles. Thesymbolshavethesamemeaningasforthelower
intermediated mass source (A ∼ 19) found for IMF’s.
S part of the figure with one exception: The full dots are not
Ifthisisthecase,thenthegenuine ”fireball”contributes
shown because the velocity of slower source was fixed during
mainly to emission of protons and deuterons, thus it is
analysis(atvelocityofheavyresiduumoftargetnucleusafter
reasonable to conjecture that the mass of the ”fireball”
intranuclearcascade)anditisrepresentedbysolidlineinthe
should be very light (3-4 nucleons). figure. Thedashedlinewasfittedtoopencirclesrepresenting
Itisworthtopointoutthatvaluesoftemperatureand velocitiesof fastsourceforIMF’s. The linewas extrapolated
velocity of the additional source introduced to describe to lower mass region.
the α-particle emission (triangles in Fig. 10) are very
similar to values characterizing the slow, heavy source
emitting the IMF’s (solid line in Fig. 10.
All these findings agree well with conclusions derived in which three moving sources of ejectiles are created.
from pure phenomenological analysis of the p+Au data Thenewresultofthepresentworkisanobservationthat
measuredat2.5GeVprotonbeamenergy[1],whichcon- thenonequilibriumemissionofLCP’sismediatedbytwo
sistinthestatement,thatnonequilibriumcontributionto competing mechanisms: surface coalescence of outgoing
production of LCP’s and IMF’s indicates presence of the nucleonsandthecontributionfromthreemovingsources
mechanism similar to fast break up of the target nucleus appearing as result of the break up.
