Tracing the Evolution of Temperature in Near Fermi Energy Heavy Ion Collisions

0.24 MB·English

by  J. Wang

Tracing the Evolution of Temperature in Near Fermi Energy Heavy Ion Collisions
J. Wang,1,∗ R. Wada,1,2 T. Keutgen,1,† K. Hagel,1 Y. G. Ma,1,‡ M. Murray,1,§ L. Qin,1 A. Botvina,1 S.
Kowalski,1 T. Materna,1 J. B. Natowitz,1 R. Alfarro,3 J. Cibor,4 M. Cinausero,5 Y. El Masri,6 D.
Fabris,7 E. Fioretto,7 A. Keksis,1 M. Lunardon,7 A. Makeev,1 N. Marie,1,¶ E. Martin,1 Z. Majka,8 A.
Martinez-Davalos,3 A. Menchaca-Rocha,3 G. Nebbia,7 G. Prete,5 V. Rizzi,7 A. Ruangma,1 D. V. Shetty,1
G. Souliotis,1 P. Staszel,8 M. Veselsky,1 G. Viesti,7 E. M. Winchester,1 S. J. Yennello,1 and W. Zipper9
(The NIMROD collaboration)
A. Ono10
1Cyclotron Institute, Texas A&M University, College Station, Texas 77843∗∗
2Riken, Cyclotron Center, 2-1 Hirosawa, Wako, Saitama, Japan 351-0198††
3Instituto de Fisica, Universidad National Autonoma de Mexico,
5
Apactado Postal 20-364 01000, Mexico City, Mexico
0
0 4Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31-342 Krakow, Poland
2 5INFN, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy
6FNRS and IPN, Universit´e Catholique de Louvain, B-1348 Louvain-Neuve, Belgium
n 7INFN and Dipartimento di Fisica dell’ Universit´a di Padova, I-35131 Padova, Italy
a 8Jagellonian University, M Smoluchowski Institute of Physics, PL-30059, Krakow, Poland
J
9Institute of Physics, University of Silesia, PL-40007, Katowice, Poland
9 10 Department of Physics, Tohoku University, Sendai 980-8578, Japan
1
(Dated: February 8, 2008)

2 Thekineticenergyvariationofemittedlightclustershasbeenemployedasaclocktoexplorethe
v time evolution of the temperature for thermalizing composite systems produced in thereactions of
2 26A,35Aand47AMeV64Znwith58Ni,92Moand197Au. Foreachsysteminvestigated,thedouble
0 isotoperatiotemperaturecurveexhibitsahighmaximumapparenttemperature,intherangeof10-
0
25MeV,at highejectile velocity. Thesemaximumvaluesincrease withincreasing projectile energy
8
and decrease with increasing target mass. The time at which the maximum in the temperature
0
curveisreachedrangesfrom80to130fm/caftercontact. Foreachdifferenttarget,thesubsequent
4
cooling curvesfor all threeprojectile energies are quitesimilar. Temperatures comparable to those
0
of limiting temperature systematics are reached 30 to 40 fm/c after the times corresponding to
/
x the maxima, at a time when AMD-V transport model calculations predict entry into the final
e evaporativeor fragmentation stage of de-excitation of thehot composite systems. Evidencefor the
- establishment of thermal and chemical equilibrium is discussed.
l
c
u PACSnumbers: 25.70.Pq,24.60.Ky,05.70.Jk
n Keywords: Liquidgasphasetransition,criticalfluctuation, fragmenttopological structure
:
v
i
X INTRODUCTION Neutron Ball detection system. The data provide ex-
r perimental evidence for an initial rapid thermalization
a of the incident energy, into a participant matter subsys-
Thelightparticleemissionwhichoccursduringviolent
tem. The double isotope ratio temperature first rises to
collisionsoftwoheavynucleicarriesessentialinformation
a maximum, then decreases as further particle emission,
onthe earlydynamics andonthe degreeofequilibration
expansionand diffusion of the excitation energy into the
at each stage of the reaction. To obtain more specific
remainderofthecompositesystemoccurs. Aclosecorre-
information on the reaction dynamics and on the ther-
lationbetweenthe peak temperatures andspectralslope
mal evolution of multi-fragmenting systems produced in
temperaturesforearlyemitted particlesisalsoobserved,
near Fermi energy collisions [1, 2, 3], we have recently
suggesting local chemical and thermal equilibration for
focused on efforts to investigate the nucleon and light
thisearlyemittingsystem. Temperatureswhicharecom-
clusteremissionwhichoccurspriortodisassemblyasthe
parable to those of limiting temperature systematics [6]
system thermalizes and equilibrates. In some previous
are reached about 30 to 40 fm/c after the peak temper-
works, we have employed coalescence model analyses to
atures are observed.
probe the early dynamic evolution of the reacting sys-
tem [4, 5]. In this paper, we report on the use of similar
techniques to explore the temperature evolution of hot
nuclei produced in a series of reactions of 26A, 35A and
47A MeV 64Zn projectiles with 58Ni, 92Mo and 197Au
targetnucleiusing a combined 4π ChargedParticle– 4π
2
EXPERIMENTAL DETAILS hemispheresare150cmindiameterwithbeampipeholes
in the center and they are upstream and downstream of
the charged particle array. Thermalization and capture
The reactions of 26A, 35A and 47A MeV 64Zn projec-
ofemittedneutronsintheballleadstoscintillationwhich
tiles with 58Ni, 92Mo and 197Au target nuclei were stud-
isobservedwithphototubesprovidingeventbyeventde-
ied at the K-500 Super-Conducting Cyclotron at Texas
terminations of neutron multiplicity but little informa-
A&M University, using the 4π detector array NIMROD.
tion on neutron energies and angular distributions. Fur-
NIMROD consists of a 166 segment charged particle ar-
ther details on the detection system, energy calibrations
ray set inside a neutron ball. The chargedparticle array
andneutronballefficiencymaybefoundinreference[10].
is arrangedin 12 concentric rings around the beam axis.
Duringtheexperiment,dataweretakenemployingtwo
Theeightforwardringshavethesamegeometricaldesign
different trigger modes. One was a minimum bias trig-
astheINDRA detector,buthavelessgranularity [7]. In
ger in which at least one of the CsI detectors detected a
thoserings,theindividualsegmentsarefrontedbyioniza-
particle. The other was a high multiplicity triggerwhich
tion chambers (IC) filled with 30 Torrof CF gas. Front
4
requireddetected particles in 3-5 CsI detectors (depend-
andbackwindowsweremadeof2.0µmaluminizedMylar
ing upon the reaction studied).
foil. In each of these forward rings, two of the segments
havetwoSidetectors(150and500µmthick)betweenthe
IC and CsI detectors (super telescopes) and three have
one Si detector(300 µm thick). Each super telescope is DATA ANALYSIS
further divided into two sections. The CsI detectors are
10 cm thick Tl doped crystals read by photomultiplier An inspection of the two dimensional arrays depict-
tubes. For these detectors, a pulse shape discrimination ing the detected correlation between charged particle
method is employed to identify light particles [8]. In all multiplicity and neutron multiplicity in NIMROD (not
telescopes particles are, identified in atomic number. In shown),revealsa distinctcorrelationin whichincreasing
the super telescopes, all isotopes with atomic number Z charged particle multiplicity is associated with increas-
10 are clearly identified. ing neutron multiplicity. Although there are significant
≤
The energy calibration of the Si detectors was carried fluctuations reflecting both the competition between dif-
outusing botha 228Th alphaparticle sourceandthe ob- ferentdecaymodesandtheneutrondetectionefficiencies,
servedpunchthroughenergiesofidentifiedreactionprod- thesecorrelationsprovideameansforselectingthe more
ucts. The punch through energies were calculated using violentcollisions. Fortheanalysisreportedinthispaper,
a range-energy table [9]. Since the energy losses of the we have selected events corresponding to the largest ob-
lighter particles, in particular the high energy Hydrogen served neutron and charged particle multiplicities. This
isotopes, are rather small in the Si detectors, evaluation selection corresponds to the 10% of the minimum bias
oftheenergydepositedintheCsIcrystalfromtheenergy triggereventswiththehighesttotalmultiplicityandem-
loss in the Si detectors requires special care for higher phasizes the lower impact parameter collisions. We refer
energy particles. Therefore, an additional energy cali- to these events as violent collisions. Many of the tech-
bration was performed to measure energy spectra from niques applied in this analysis have been discussed pre-
the reaction 64Zn + 92Mo at 47A MeV. In this run, Si viously in greater detail in references [4, 5, 11]. Only a
detectorsofthicknesses1mm,backedbyCsIdetectorsof brief summary of these is included in the present work.
three different lengths (1cm, 3cm and 5cm), were used
to measure the inclusive energy spectra of light charged
particles. The energy spectra were measured at all an- Moving source analysis
gles corresponding to those of the 12 rings of NIMROD.
ThecombinationofthickerSi∆Edetectorsandobserva-
A common technique to characterize light particle
tionofhighenergypunch-throughpointsfortheparticles
emissioninthisenergyrangeistofittheobservedspectra
whichtraversedthesethinnerCsIdetectorsallowedusto
assuming contributions from three sources; a projectile-
determine the energy spectra with a high degree of con-
like (PLF)source, an intermediate velocity (IV)source
fidence. We then used the 64Zn + 92Mo at 47A MeV as
andatarget-like(TLF)source. Forasymmetriccollisions,
a standardreactionto determine the CsI energy calibra-
suchfitstypicallyexhibitaPLFsourcedominancelocal-
tions for all other runs.
ized at high rapidity, an IV source dominance at mid-
Neutron multiplicity was measured with the 4π neu- rapidityandTLFsourceemissionlocalizedatlowrapid-
tron detector surrounding the charged particle array. ity [4, 5, 12, 13, 14]. In the present work, except for the
This detector, a neutroncalorimeter filled with Gadolin- most forward detector rings, the data are dominated by
ium doped pseudocumene, consists of two hemispherical particles associated with the IV and TLF sources and a
end caps and a cylindrical mid-section. The mid-section goodreproductionoftheobservedspectraisachieved. In
is divided into four separate 90 degree quadrants. The thisanalysis,thesourcevelocities,temperatures,particle
3
20 ZnNi26 ZnNi35 ZnNi47 theless, the information derived can be very instructive.
15 We have employed such analyses to estimate the mul-
10 tiplicities and energy removed at various stages of the
5 reaction. To follow the time evolution of the system in
moredetail, a more sophisticatedanalysisofthe particle
V)20 ZnMo26 ZnMo35 ZnMo47 emission is necessary. Both theoretical models [18, 19]
e15
M and experiments [20, 21] indicate that the early colli-
(pe10 sion dynamics leads to a correlation between emission
o
Tsl5 time and energy for the early emitted particles. This
correlationcan be exploited to follow the time evolution
20 ZnAu26 ZnAu35 ZnAu47
of the system. We have previously used this correlation
15
incoalescencemodelstudiesofseveralsystems[4,5,11].
10
Forthepresentsystems,extensivecalculationshavebeen
5
made employing the AMD-V model of Ono [19]. Many
0 p d t 3He a p d t 3He a p d t 3He a of the results of the AMD-V calculations for the present
LCP LCP LCP
systemsarecomparedtoexperimentalobservablesinref-
erence [10]. In the present work, we have employed the
FIG. 1: Slope temperatures from 3-source fits to the experimen-
tal spectra. Open circles represent apparent temperatures for the calculated correlation between particle energy and time
emissionfromtheIVsource. Filledcirclesrepresentapparenttem- predicted by those AMD-V calculations to calibrate the
peraturesfortheemissionfromtheTLFsource. emission time scales for these reaction systems.
At intermediate energies, the observed spectral slope
parametersderivedfromthe sourcefits arenotadequate
multiplicitiesandemissionbarriersforthethreedifferent
asmeasuresofthetemperatureevolution,astheobserved
sources were the parameters searched.
spectra are convolutions of the spectra at different emis-
InFigure1,theslopetemperatureparametersforemis-
sion times and excitation energies and include high en-
sion from the IV and TLF sources, derived from the
ergyparticleswhichareemittedpriortotheachievement
fits, are shown for the nine reactions studied. For both
of thermal equilibrium. For a system at chemical and
sources the measured spectra result from a summation
thermal equilibrium at a suitably low density, Albergo
of the spectra of particles emitted over a range of time. et al. [22] have shown that the temperature of the emit-
Thus the observed slope temperature values are affected
ting system canbe derived directly from the first chance
by the relative emission probabilities over that time pe-
emission
riod. The IV source slope temperatures for p, d, t, 3He
double isotope yield ratios of two adjacent isotopes of
and 4He range from T 7 to 17 MeV for the
∼ twodifferentelements. InamorerecentworkbyKolomi-
different systems studied. The temperatures from the ets et al. [23], essentiallythe sameresultis derivedwhen
particles with A 3 are quite similar. They follow the
≤ onlythermalequilibriumis initiallyassumed. Therefore,
trendsofearlierreportedvaluesforpre-equilibriumemis-
to characterize the temperature at a particular emission
sionatsuchprojectileenergies[12,13,15]. TheIVsource
time, we have employed double isotope yield ratio mea-
temperatures derived from the alpha spectra are typi-
surements. Inthecaseofstrongsystemevolution,double
cally lower than those measured for the other particles.
isotope yield ratio temperatures derived from integrated
These softer slopes for the alpha particles appear to re-
yields are certainly suspect if the isotopes being utilized
flect larger relative contribution of lower energy alphas
are in fact produced at very different times or by dif-
which are attributed to the IV source in the fitting pro-
ferent mechanisms. However, if chemical equilibrium is
cedure. The slope parameters for the TLF sources are
achieved and the particles corresponding to particular
much lower, in the range of T 2 6 MeV. For this
∼ − emissiontimes canbe selected,derivationsofdouble iso-
source,theapparenttemperaturesforalphaemissionare
tope yield ratio temperatures as a function of emission
thehighest. Suchaneffecthaspreviouslybeennotedand
time shouldallowus to followthe temperature evolution
attributed to the relatively higher emission probabilities
of the system.
for alpha particles in the early stage of the evaporation
Tofocusontheearlyevolutionofthe temperature,we
cascade [16, 17].
have first selected clusters observed at mid-rapidity, i.e.,
specificallythosedetectedatanglesbetween70o and80o
intheIVsourceframe. Inthisway,weattempttoisolate
Temperature Determinations the emission associated with the IV source which occurs
duringthe thermalizationstageofthe reaction[4, 5, 11].
Giventhecontinuousdynamicevolutionofthesystem, Wehavethenmadedoubleisotoperatiotemperaturede-
source fit parameters should be considered as providing terminations as a function of ejectile velocity in the IV
only a schematic picture of the emission process. Never- frame. The velocities used are the “surface velocities”
4
of the emitted particles. The surface velocity, V , is
surf 250
defined as the velocity of an emitted species at the nu- ZnNi26 ZnNi35 ZnNi47
200
clear surface, prior to acceleration in the Coulomb field
[5, 12]. V , is obtained in our analysis by subtraction 150
surf
of the Coulomb barrier energy derived from the source
100
fits. Since the early emitted light particle energies are
50
stronglycorrelatedwith emissiontimes, and evaporative
orsecondaryemissioncontributetothespectraprimarily 250
at the lower kinetic energies, the yields of higher energy ZnMo26 ZnMo35 ZnMo47
c)200
particles should be relatively uncontaminated by later m/
emission processes. This is an important advantage in (f150
e
such double isotope yield ratio determinations. At mid- av100
e
rapidity there is little contributionfromthe PLFsource. m
There is, however some observed contribution from the Ti 50
TLFsourceatlowvelocitiesintheIVsourceframe. Since 250
ZnAu26 ZnAu35 ZnAu47
thethreesourcefitsareonlyapproximationstotheemis-
200
sion from the continuously evolving system, particles in
150
this low velocity range may be viewed alternatively as
thelastparticlesemittedfromtheIVsourceorthe earli- 100
estfromthe TLFsource. Inthe followinganalysisyields
50
assigned to the TLF source have been subtracted from
0
the experimental yields.
0 3 6 9 12 3 6 9 12 3 6 9 12
The temperatures employed are THHe, derived from Vsurf (cm/ns) V (cm/ns)
the yields of d, t, 3He and 4He clusters. For particles surf
emittedfromasinglesourceoftemperature,T,andhav-
FIG.2: Correlationofaverageemissiontimewithsurfacevelocity
ingavolumeMaxwellianspectrum(√ǫexp ǫ/T),where forearlyemittednucleonsascalculatedbytheAMD-Vcode. Solid
−
ǫ is the particle energy, the HHe double isotope yield ra- symbolsdepicttheresultsfortheninedifferentreactionsaslabeled.
tioevaluatedforparticlesofequalV ,is 8 timesthe
surf q9
ratioderivedfromeitherthe integratedparticleyieldsor
the four systems studied, we have derived from AMD-
theyieldsatagivenenergyabovethe barrier [22]. Thus
Vcalculations,whichcoveredthe rangeoftime fromthe
timeofcontactuptoto300fm/c,thecorrelationbetween
14.3
T = (1) average emission times of emitted neutrons and protons
ln(cid:16)q98(cid:0)1.59Rvsurf(cid:1)(cid:17) and their energies. For each reaction the resultant time-
surface velocity relationship is represented in Figure 2.
wherethe constants14.3and1.59reflectbindingenergy, As is seen there, the calculations indicate a near linear
spin, masses and mass differences of the ejectiles. If Y decrease of Vsurf , from near projectile velocity into the
representsaclusteryield,R(Vsurf)=YdY4He/YtY3He for 3 to 3.5 cm/ns range as the average emission times in-
clusters with the same surface velocity. crease from 50 fm/c to 150 fm/c. In the following we
∼
have employed these correlations to determine the aver-
age emission times corresponding to particular observed
Calibration of Timescales values of Vsurf in the experiment. However,since below
3.5 cm/ns the experimental data contain large contribu-
tions from TLF evaporative emission, the sensitivity of
Tocalibratethetime-scaleassociatedwithourdata,we
the emission energy to time is significantly reduced, and
have employed results of the AMD-V calculations [10].
we do not attempt to assign emission times for particles
In the AMD-V calculations, the particle emission starts
with surface velocities below 3.5 cm/ns.
attimesnear50fm/c,andvariesdependingonprojectile
velocity and entrance channel masses. From that point,
the calculations predict an initial rapid decrease of the
average kinetic energies of the emitted particles with in- RESULTS AND DISCUSSION
creasing time of emission. This is followed by a much
slower rate of decrease at later times, 140 to 200 fm/c We present, in Figure 3, experimental results for the
for the systems studied. The time of the transition from double isotope ratio temperatures as a function of ve-
rapidtorelativelyslowkineticenergydependsonprojec- locity in the IV frame. For each system investigated,
tile velocity and entrance channel mass. Such trends are the double isotope ratio temperature determination ex-
typically observed in transport model calculations. For hibits a high maximum temperature in the range of 10-
5
27 MeV. These maximumtemperatures are muchhigher
25 ZnNi26
than the limiting temperatures determined from caloric
ZnNi35
curvemeasurementsinsimilarreactions[6]. Ineachcase, 20
ZnNi47
theapparenttemperaturedecreasesmonotonicallyonei- 15
ther side of this maximum. The AMD-V model calcula- 10
tions [10, 19] indicate a significant slowing in the rate of
5
kinetic energy change in the 3-3.5 cm/ns velocity range.
The shaded vertical bars in Figure 3 indicate that ve-
locity value. These points signal the end of the IV (or 25 ZnMo26
pre- equilibrium) emission stages. At lower velocities, V) 20 ZnMo35
e ZnMo47
the slower nuclear de-excitation modes evaporation, fis- M 15
sion and/or fragmentation determine the properties of (He10
the ejectile spectra. At these lower velocities, values of H
T
T are3to4MeV,similartothosespectralintegrated 5
HHe
values seen in other experiments [23, 24, 25, 26, 34].
ThesevaluesarealsoverysimilartoT temperatures
HHe 25 ZnAu26
calculated when the sequential evaporation code GEM-
20 ZnAu35
INI [27] is used to simulate the de-excitation of the TLF ZnAu47
source [16]. We take this as further evidence that the 15
spectra at these lower velocities still contain contribu- 10
tions from late stage evaporation. Temperatures derived 5
from the yield ratios in this velocity range require cor-
rections for secondary decay effects. 60 80 100 120 140 160 180
Time (fm/c)
Figure 4 presentsthe derivedT temperatures as a
HHe
function of time. While all nine reactions show a qual-
itatively similar evolution with time, we now see that, FIG. 4: THHe vs time. See text. Times terminate at points
for each energy, the time at which the maximum in the correspondingtosurfacevelocitiesof3-3.5cm/ns.
temperature curve is reached increases with increasing
target mass and decreases with increasing projectile en-
ergy. The former observation suggests a longer period emitted. Nonequilibriumeffects maybe mostevidentin
required for establishment of a thermal and/or chemi- theparticularlyhighapparentpeaktemperaturesforthe
cal equilibrium as the total system size increases while 35Aand47AMeV64Zn+58Nicase. TheAMD-Vcalcu-
the latter observation suggests a more rapid thermaliza- lations for the different systems predict a higher degree
tion of the initial projectile energy for the initially faster of transparency in those reactions[10].
projectiles. The dynamic transport calculations indicate Figure 4 also indicates that the time of entry into the
that the condition of thermal equilibrium of the whole evaporation or disassembly stage, taken to be the time
system is not yet established as the earliest ejectiles are correspondingtosurfacevelocitiesof3.5cm/ns,increases
with target mass, from 135 fm/c for the Ni target to
∼
165 fm/c for the Au target. We note that at such
∼
30 times the temperatures are very similar to the limiting
24
temperatures derived from a systematic investigation of
18 ZnNi26 ZnNi35 ZnNi47
12 caloric curve measurements [6]. Except for the 64Zn
6 + 58Ni reactions at 35A and 47A MeV, the time for the
V)2340 initialcoolingstage,i.e.,thetimedifferencebetweenthat
Me18 ZnMo26 ZnMo35 ZnMo47 corresponding to the maximum in the temperature and
(e12 that correspondingto the startof the evaporationstage,
H
H 6 is 30 to 40 fm/c.
T
30
24
18 ZnAu26 ZnAu35 ZnAu47
12 Interpretation of Temperature Evolution Curves
6
0
0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 The experimental temperature curves show an initial
Vsurf (cm/ns)
risetoamaximumandasubsequentdecline. Itistempt-
ingtointerpretthe initialriseasreflectingthe earlyrate
FIG. 3: THHe vs surface velocity. See text. Horizontal bars are
at 3-3.5 cm/ns, taken to be limitfor time derivations. Solid lines ofconversionofprojectilekineticenergyintothermalen-
indicatefitstodata. ergy of the composite system. However, it appears more
6
likely that the double isotope temperature is not accu- 30
rately reflecting the temperature of the emitting system
atearliertimes. Thetime requiredforthe establishment
of chemical equilibrium is presumably longer than that 25
required for thermalization. We are not able to separate
these with the present data. Rather, in this section we )
V
20
address the interpretation of the temperatures and the e
M
degree to which they can be taken as reflecting thermal
(

andchemicalequilibration,atleastlocallyifnotglobally. e
p
o15
sl
T
Comparison of T with T from source fits
HHe slope
10
If both thermalandchemicalequilibriumare achieved
and the density is not too high [35], an agreement be-
5
tween the thermal temperature and the double isotope 5 10 15 20 25 30
ratio temperature THHe can be expected. T (MeV)
HHe
FortheTLFsourcethefitslopeparameters,T pre-
slope
sentedinFigure1arenormallylowerthanthelatesttime
T temperaturesseeninFigure4. Thisisnotsurpris- FIG. 5: Relationship between THHe peak values and Tslope of
HHe the IV source. Dotted line represents locus of equality of the two
ingsincethesourcefitcanbeexpectedtoreturnonlyan temperatures. Open symbols show results for the reactions with
apparent temperature reflecting the entire cooling stage Moand Autargets. Solidsymbols show resultsforreactions with
of the TLF source. In our previous work [13, 16, 17], Nitragets
we have found that the slope parameters for the alpha
particle emission from the TLF source most closely ap-
perature parameter of the fit, this result is understand-
proximatestheintialthermaltemperatureofthissource,
able. In such a case, the agreement seen between this
reflectingthehigherfractionofthealphaemissioninthe
thermal slope parameter and the chemical temperature
earlier part of the de-excitation cascade. The alpha par-
determinedfromtheisotopeyieldratiosforthelowesten-
ticleslopeparametersarepresentedincolumn5ofTable
ergy 26A MeV 64Zn + 58Ni reaction and for the 64Zn +
I. The relationship between these thermal fit apparent
92Mo and 64Zn + 197Au reactions at all three projectile
temperatures and the late time chemical temperatures
energies provides a strong indication that a simultane-
obtained from the TLF isotope ratio temperatures, as
ous thermal and chemical equilibrium is achieved in the
presented in column 6, is quite reasonable, given the as-
emitting system, at least locally, at times corresponding
sociated uncertainties.
to those of the peak temperatures.
The observed time evolution of T also prompts
HHe
us to inquire about the relationship between the maxi-
mum temperatures and the slope temperature parame-
ters which characterize the ejectile kinetic energy spec- Model estimates of peak temperature and source
tra of the IV sources. These latter are also determined sizes
from the three source fits to the experimental spectra.
As is seen in Table I and Figure 5, there is actually a We have attempted to make a first order estimate of
close agreement between these two values for all but the the maximum temperature to be expected. In the AMD
35 and 47A MeV 64Zn + 58Ni reactions. The appar- calculations for our systems, only a small fraction of the
ently high values of the peak temperatures for these last available mass and excitation energy has been removed
two reactions were already seen above. As noted there, fromthesystembypre-equilibriumemissionatthetimes
thismayreflectnon-equilibriumeffectsresultingfromthe which we associate with the observedmaximumtemper-
veryhighdegreeoftransparencyforthose tworeactions. atures [10]. For the reaction being considered, we then
Atfirstglance,thegoodagreementseenforthe restof ignorethe massloss andestimate the maximum thermal
the reactions still seems surprising because the IV spec- excitation energy to be E∗ = E + Q, where E is
CM CM
trumisknowntoresultfromaconvolutionoftheejectile the available Center of Mass energy and Q, the fusion
emission from the evolving system. Thus, it depends on reaction Q value. Excitation energies per nucleon of 5.9
the time-dependent rates of both the ejectile emission to 11.2 MeV/u are obtained in this way. The results of
and the temperature evolution of the system. However, thesecalculationsarepresentedincolumn7ofTableI.At
if the requirement that the global fit to the IV source the times corresponding to the maximum observed tem-
reproduce the high energy tail of the IV spectrum plays perature, the AMD-V calculations show the composite
a dominant role in determining the overall slope tem- systemstohavereboundedfromaninitialsmallcompres-
7
TABLE I: Temperatures and Excitation Energies
Target Projectile Tslope(Avg) Max THHe Tslope(TLF) THHe(TLF) E∗max Tmax
Energy IV alpha (vsurf =3.5cm/ns) Apart=Atot
ρ=ρ0
(MeV/u) (MeV) (MeV) (MeV) (MeV) (MeV/u) (MeV)
58Ni 26.0 9.68±0.68 9.74±0.25 5.66±0.30 4.34±0.40 5.92 9.49
35.0 11.4±1.05 16.6±0.99 5.91±1.43 5.06±0.45 8.17 11.1
47.0 13.7±1.28 24.8±2.57 6.12±0.80 5.34±0.46 11.2 13.0
92Mo 26.0 9.60±0.97 10.0±0.42 4.18±0.50 4.50±0.40 5.55 9.19
35.0 11.9±1.44 13.3±0.99 5.50±0.50 5.74±0.54 7.73 10.8
47.0 15.1±1.73 17.6±1.13 5.41±0.30 5.71±0.53 10.6 12.7
197Au 26.0 9.95±0.69 9.02±0.18 5.13±0.13 4.92±0.45 3.96 7.76
35.0 11.8±0.81 11.9±0.31 5.22±0.35 5.81±0.54 5.62 9.25
47.0 14.1±0.78 15.7±0.54 6.54±0.32 6.53±0.60 7.84 10.9
sionandthe systemdensity,ρ,tobe atorbelownormal. roundedbycolderspectatormatterandthederivedtem-
If ρ/ρ = 1, we can estimate the maximum temperature peratures are interpreted as representing a local thermal
0
which we might expect. Here we assume a uniform nor- equilibrium. AsimilarpictureisobtainedintheAMD-V
mal density Fermi gas [29] with a Fermi Energy which calculations of reference [10]. Further, such a result is
we take from the interpolation or extrapolation of the consistent with results of earlier experimental studies of
values reported in reference [30]. Since the system is pre-equilibriumemissionwhichfoundthattheIVspectra
quiteexcited,wefurtherassumeanucleoneffectivemass could be equally well modeled either within the frame-
of 1 [31]. Ignoring the small mass loss expected, we cal- workofnucleon-nucleoncollisiondynamicsorasemission
culate the temperature, T, from E∗ =aT2, where a, the from a hot thermalized participant zone [12, 15].
level density parameter, is determined from the Fermi If, in fact, the early system consists of both partici-
energy. Here a = A/15.2 MeV−1 is used [30]. The tem- pant (nascent fireball [32]) and spectator matter then,
peratures thus derived are presented in Table I, column initially, the available energy may be distributed only
8. Whilethecalculatedtemperaturesreportedincolumn over a subset of the nucleons. Further, the density for
8 are indeed significantly higher than limiting termpera- this subsystem need not be ρ . Assuming still that such
0
turesofcaloriccurvemeasurements,theyarenotashigh ahotparticipantzonemaybemodeledasauniformden-
as the observed maximum temperatures in column 4. sityFermigasallowsustowritethemoregeneralexpres-
sion [33, 34]
The calculated values in column 8 follow from an as-
sumed thermalization of the entire system. In a re- 2
T =q(K0(ρ/ρ0)3(Ex/Apart),
centinvestigation,SoodandPurihaveemployedaQMD
transport model to calculate the maximum and aver- whereK istheinverseleveldensityparameteratnor-
0
age temperatures and densities achieved in symmetric maldensity(inanexcitednucleus)andA isthemass
part
or near symmetric heavy ion collisions at E , the bal- number of the participant zone. Taking K to be 15.2
bal 0
ance energy corresponding to the transition from posi- MeV and the observed peak temperatures from column
tive to negative flow [28]. Their calculation of the max- 4 of table I allows us to calculate A as a function
part
imum temperature, based upon a local density approx- of ρ/ρ for each system studied at each projectile en-
0
imation for the matter contained in a sphere of 2 fm ergy. TheresultsarepresentedinFigure6(a)-(c),where
radius around the center of mass of the system, clearly the calculated A , normalized to the projectile mass,
part
indicates that the entire system is not equilibrated at is plotted against ρ/ρ . Some initial compression and
0
the early times. In general, the available center of mass subsequent expansion is predicted by the AMD-V cal-
energies in the calculations of reference [28] are some- culation. The density at the time of the experimental
what higher than those of our reactions with 47A MeV peaking of the temperature is expected to be less than
64Zn and the calculations are made for varying impact normal density. The results of this calculation indicate
parameters. Nevertheless, the maximum double isotope that the number of participant nucleons at the time of
ratio temperatures derived in the present experimental the peaking of the temperature decreases with increas-
studyarequitecomparabletothosereportedinreference ingprojectileenergyandincreaseswithincreasingtarget
28. This is particularly noteworthy because the calcula- mass. The values of the ratios which would result from
tions by Sood and Puri strongly suggest the presence of participationofthetotalentrancechannelmassesarein-
an initial hot, locally equilibrated, participant zone sur- dicatedbythehorizontallinesinthefigure. Mostexperi-
8
curveexhibitsahighmaximumapparenttemperature,in
5 Zn + Ni 26 MeV/u (a) the range of 10-25 MeV. The maximum values increase
4 35 MeV/u with increasing projectile energy and decrease with in-
47 MeV/u creasingtargetmass. Thesemaximaoccurattimesfrom
3
80 to 130 fm/c after the nuclei contact. They are much
2
higher than the limiting temperatures determined from
1 caloric curve measurements in similar reactions [6]. For
most of the reactions studied, a close correlation is ob-
0
5 served between the peak temperatures for early emit-
Zn + Mo (b) ted particles, obtained from double isotope ratios, and
4
oj the spectral slope temperatures for the pre-equilibrium
Apr 3 (IV) source. The data indicate that atleasta localther-
/part 2 malandchemicalequilibrium is establishedduring these
A
times. After peaking, the temperatures decreaserapidly,
1
apparently reflecting particle emission, diffusion of the
0 excitation energy into the remaining system and expan-
5
Zn + Au sion. For each individual target nucleus, the later por-
(c)
4 tionsofthecoolingcurvesforallthreeprojectileenergies
3 are very similar, indicating that hot nuclei with similar
properties are produced. Temperatures comparable to
2
those derived from limiting temperature systematics are
1 reached 30 to 40 fm/c after the times corresponding to
0 themaxima,atthetimeswhenAMD-Vtransportmodel
0 0.5 1 r /r 0 1.5 2 2.5 calculations predict entry into the final evaporative or
fragmentation decay of the hot composite system.
FIG. 6: Calculated values forthecorrelationof Apart/Aproj and As a final comment, we note that the present data
ρ/ρ0 consistentwithmeasuredpeaktemperatures.
suggest that if the Z=1 and Z=2 ejected light particles
are taken to represent the gaseous phase, as is usually
mentalvaluesarewellbelowthose. Theseresultssuggest assumed,the reactiondynamics ofcentralcollisionsmay
the existence of a hot zone at early times. For the case itself lead to a natural situation in which the gas is not
of47A64Zn+ 197Au, results ofthe AMD-V calculations outsidethe liquidmatterbutinitiallyconfinedinsidethe
reported in reference[10] indicate the existence of such a liquid matter, perhaps facilitating the establishment of
zoneatearlytime, withamassnumberabouttwicethat a liquid-gas equilibrium. This could somewhat mitigate
of the projectile. As seen in Figure 6, the Fermi gas es- arguments that the concept of establishment of a liquid
timate for this system at below normaldensities is quite gas equilibrium is not tenable in a nuclear collision as
close to that. there is no container to constrain the gas. Of course,
While the possibility of emission from a thermalized more recently it has also been argued, on the basis of
hot zone is one of the possible interpretations which detailed balance, that the actual physical equilibrium is
has previously been suggested in earlier comparisons of not necessary [36].
dynamic and thermal pictures of pre-equilibrium emis-
sion in similar collisions [12, 15], in the present study
it is inferred not from the slope parameters of the pre-
ACKNOWLEDGEMENTS
equilibrium sourcebut rather fromthe peak value of the
temperature, T . The double isotope ratio temper-
HHe
ThisworkwassupportedbytheUnitedStatesDepart-
ature measurements assume chemical equilibrium. We
ment of Energy under Grant # DE-FG03- 93ER40773
return to this point in the following section.
andbyTheRobertA.WelchFoundationunderGrant#
A330. The work of JSW is also partially supported by
SUMMARY AND CONCLUSIONS the NSFC under Grant # 10105011.
The kinetic energy variation of emitted light clusters
has been employed as a clock to explore the time depen-
dence of the temperature evolutionof thermalizing com-
∗ On leave from the Institue of Modern Physics, Chinese
positesystemsproducedinthereactionsof26A,35Aand
Academy of Science, Lanzhou 73, China.
47AMeV64Znwith58Ni,92Moand197Au. Foreachsys- † Now at FNRS and IPN, Universit´e Catholique de Lou-
tem investigated, the double isotope ratio temperature vain, B-1348 Louvain-Neuve,Belgium
9
‡ on leave from Shanghai Institute of Nuclear Research, sunomiya,R.Wada,G.Nardelli,G.Nebbia,G.Viesti,R.
Chinese Academy of Sciences, Shanghai 201800, China Zanon, B. Fornal, G. Prete, K. Niita, S. Hannuschke, P.
§ Now at University of Kansas, Lawrence, Kansas 66045- Gonthier,andB.Wilkins,Phys.Rev.C42,2125(1990).
7582 [18] J. Lukasik and Z. Majka, Acta. Phys. Pol. 24B, 1959
¶ Now at LCP Caen, ISMRA, IN2P3-CNRS, F-14050 (1993).
Caen, France [19] A.OnoandH.Horiuchi,Phys.Rev.C53,2958 (1996) .
∗∗ E-mail at:[email protected] [20] Z.Y. He , G.M. Jin, Z.Y. Li, L. M. Duan, G. X. Dai, B.
†† Riken Collaborative Scientist, Beam Technology Divi- G.Zhang,H.Y.Wu,W.X.Wen,Y.J.QiandQ.Z.Luo,
sion, Cyclotron Center Phys. Rev.C 57, 1824 (1998)
[1] E. Suraud, C. Gregoire and B. Tamain, Prog. Part. and [21] C. J. Gelderlos,R. Sun,N. N. Ajitanand, J. M. Alexan-
Nucl.Phys. 23 357 (1989). der, E. Bauge, A. Elmaani, T. Ethvignot, R. Lacey, M.
[2] B. Tamain and D. Durand University of Caen Report E. Brandan, A. Giorni, D. Heuer, S. Kox, A. Lleres, A.
LPCC 96-16 (1996) and references therein. Menchaca-Rocha,F.Merchez,D.Rebreyand,J.B.Viano,
[3] P. Chomaz, Proceedings of the INPC 2001 Conference, B.Chambon,B.Cheynis,D.DrainandC.Pastor,Phys.
Berkeley,Ca., July 2001 Rev. C 52, R2834 (1995).
[4] J.Cibor,R.Wada,K.Hagel,M.Lunardon,N.Marie,R. [22] S. Albergo, S. Costa, E. Costanzo, and A. Rubbino,
Alfaro,W.Q.Shen,B.Xiao,Y.Zhao,J.Li,B.A.Li,M. NuovoCimento A 89, 1 (1985) .
Murray, J. B. Natowitz, Z. Majka and P. Staszel, Phys. [23] A. Kolomiets, V. M. Kolomietz, and S. Shlomo, Phys.
Lett.B473, 29 (2000). Rev. C 55, 1376 (1997).
[5] K.Hagel,R.Wada,J.Cibor,M.Lunardon,N.Marie,R. [24] H. Xi, M. J. Huang, W. G. Lynch, S. J. Gaff, C. K.
Alfaro, W. Shen, B. Xiao, Y. Zhao, Z. Majka, J. Li, P. Gelbke, T. Glasmacher, G. J. Kunde, L. Martin, C. P.
Staszel, B.-A. Li, M. Murray, T. Keutgen, A. Bonasera, Montoya, S. Pratt, M. B. Tsang , W. A. Friedman ,
and J. B. Natowitz, Phys.Rev.C 62, 034607 (2000). P. M. Milazzo, M. Azzano, G. V. Margagliotti, R. Rui,
[6] J.B. Natowitz, R.Wada,K. Hagel, T Keutgen,M. Mur- G. Vannini, N. Colonna, L. Celano, G. Tagliente , M.
ray,Y. G. Ma , A. Makeev, L. Qin , P. Smith and D’Agostino, M.Bruno,M. L.Fiandri, F.Gramegna ,A.
C.Hamilton, Phys.Rev. C 65, 034618 (2002). Ferrero, I. Iori, A. Moroni, and F. Petruzzelli and P. F.
[7] J.Pouthasetal.,Nucl.Instr.&Meth.A357,418(1995). Mastinu, Phys.Rev. C 57, R462 (1998).
[8] F. Bernachi et al., Nucl. Instr. & Method A 281, 137 [25] H.F. Xi, G.J. Kunde, O. Bjarki, C.K. Gelbke , R.C.
(1989). Lemmon, W. G. Lynch, D. Magestro, R. Popescu,R.
[9] F. Hubert, A.Fleury, R. Bimbot and D. Gardes Annales Shomin,M.B.Tsang,A.M.Vandermolen,G.D.Westfall,
dePhysiqueSupplementV5 (1980). G. Imme,V.Maddalena, C. Nociforo, G.Raciti,G. Ric-
[10] R. Wada, T. Keutgen, K. Hagel, Y. G. Ma, J. Wang, cobene, F. P. Romano, A. Saija, C. Sfienti, S. Fritz, C.
M. Murray, L. Qin, P. Smith, J. B. Natowitz, R. Al- Gro(, T. Odeh, C. Schwarz, A. Nadasen, D. Sisan, and
farro, J.Cibor, M.Cinausero, Y.ElMasri, D.Fabris, E. K.A.G. Rao, Phys.Rev. C 58, R2636 (1998).
Fioretto,A.Keksis,M.Lunardon,A.Makeev,N.Marie, [26] R.Wada,R.Tezkratt,K.Hagel, F.Haddad,A.Kolomi-
E.Martin,A.Martinez-Davalos,A.Menchaca-Rocha,G. ets, Y.Lou,J.Li,M.Shimooka,S.Shlomo,D.Utley,B.
Nebbia, G. Prete, V. Rizzi, A. Ruangma, D. V. Shetty, Xiao,N.Mdeiwayeh,J.B.Natowitz,Z.Majka,J.Cibor,
G. Souliotis, P. Staszel, M. Veselsky, G. Viesti, E. M. T. Kozik, and Z. Sosin, Phys. Rev.C 55, 227 (1997).
Winchester, S.J. Yennello, Z. Majka and A. Ono,Phys. [27] R. J. Charity, et al. Nucl. Phys.A483, 371 (1988).
Rev.C 69 044610 (2004). [28] A. D. Sood and R. K. Puri, ArXiv Preprint
[11] J.Ciboretal.,in”IsospinPhysicsinHeavy-IonCollisions nucl-th/0311013, Submitted to Phys.Rev.C (2003).
at Intermediate Energies”, Eds.Bao-An Li and W. Udo [29] M. A.Preston, Physicsof theNucleus,Addison- Wesley
Schroeder, NOVA Science Publishers, Inc. (New York), Publishing Company,Reading, Mass. (1962)
(2001) [30] EJ Moniz, I Sick, R.R. Whitney, J. R. Ficenec, R.P.
[12] T.C. Awes, G. Poggi, C.K. Gelbke, B.B. Back, B.G. Kephart, W. Trower, Phys.Rev.Lett. 26, 445 (1971)
Glagola, H. Breuer and V.E. Viola, Jr., Phys. Rev. C [31] S. Shlomo and J. B. Natowitz Phys. Rev. C 44, 2878
24, 89 (1981). (1991)
[13] R.Wada,D.Fabris,K.Hagel,G.Nebbia,Y.Lou,M.Go- [32] A.Z.Mekjian, Phys.Rev.C 17,1051 (1978); Phys.Rev.
nin,J.B.Natowitz, R.Billerey,B.Cheynis,A.Demeyer, Lett. 38, 640 (1977); Phys.Lett B89, 177 (1980)
D.Drain, D. Guinet, C. Pastor, L. Vagneron,K. Zaid, J. [33] J. B. Natowitz, K. Hagel, Y. Ma, M. Murray, L. Qin, S.
Alarja, A. Giorni, D. Heuer, C. Morand, B. Viano, C. Shlomo,R.Wada,andJ.Wang,Phys.Rev.C66,031601
Mazur, C. Ngo, S. Leray, R. Lucas, M. Ribrag and E. (2002).
Tomasi, Phys. Rev.C 39, 497 (1989) [34] V. Viola, submitted to PhysRev.Lett. (2004).
[14] V.E.Viola,K.KwiatkowskiandW.A.Friedman,Phys. [35] Z.Majka, P.Staszel,J. Cibor, J.B.Natowitz, K.Hagel,
Rev.C 59, 2260 (1999). J. Li,N.Mdeiwayeh, R.Wada,andY.Zhao,Phys.Rev.
[15] D. Fox, D.A. Cebra, J. Karn, C. Parks, A. Pradhan, A. C 55, 2991 (1997); M. Gonin, L. Cooke, K. Hagel, Y.
Vander Molen, J. van der Plicht, G.D. Westfall, W.K. Lou, J. B. Natowitz, R. P.Schmitt, B. Srivastava, W.
Wilson and R.S.Tickle, Phys.Rev.C 38, 146 (1988). Turmel, H. Utsunomiya, R. Wada,G. Nardelli, G. Neb-
[16] K. Hagel, D. Fabris, P. Gonthier, H. Ho, Y. Lou, Z. bia, G. Viesti, R. Zanon, G. Prete, P.Gonthier and B.
Majka, G. Mouchaty, M.N. Namboodiri, J.B. Natowitz, Wilkins, Phys.Lett. B 217, 406 (1989).
G. Nebbia, R. P. Schmitt, G. Viesti, R. Wada and B. [36] L.G. Moretto, J.B. Elliott, L. Phair and G. J. Wozniak,
Wilkins, Nucl. Phys. A486, 429 (1988). LBNL-51306, arXiv:nucl-ex/0209009 v1(2002).
[17] M.Gonin,L.Cooke,K.Hagel,Y.Lou,J.B.Natowitz,R.
P.Schmitt,S.Shlomo,B.Srivastava,W.Turmel,H.Ut-