Breakup temperatures in central collisions of 197Au + 197Au at bombarding
energies E/A = 50 to 200 MeV were determined with two methods. Isotope
temperatures, deduced from double ratios of hydrogen, helium, and lithium
isotopic yields, increase monotonically with bombarding energy from 5 MeV to 12
MeV, in qualitative agreement with a scenario of chemical freeze-out after
adiabatic expansion. Excited-state temperatures, derived from yield ratios of
states in 4He, 5Li, 6Li, and 8Be, are about 5 MeV, independent of the
projectile energy, and seem to reflect the internal temperature of fragments at
their final separation from the system.
  PACS numbers: 25.70.Mn, 25.70.Pq, 25.75.-qComment: 10 pages, RevTeX with 4 included figures; Also available from
  http://www-kp3.gsi.de/www/kp3/aladin_publications.htm

A. Moroni

A. Ohnishi

A. Ono

A. Saija

A. Schüttauf

A. Strachan

A. Trzcinski

A. Wörner

B. Ocker

B. Zwieglinski

C. Groß

C. Nociforo

C. O. Dorso

C. Schwarz

C. Sfienti

D. H. Boal

D. H. E. Gross

D. J. Morrissey

F. Gulminelli

F. P. Romano

F. Petruzzelli

G. Immé

G. J. Kunde

G. Raciti

G. Riccobene

G. Verde

H. Dabrowski

H. Feldmeier

H. J. Rabe

H. Stöcker

H. W. Barz

Hongfei Xi

I. Iori

J. A. Hauger

J. B. Natowitz

J. Knoll

J. Konopka

J. P. Bondorf

J. Pochodzalla

L. G. Moretto

M. Begemann-Blaich

M. J. Huang

M. Mahi

M. Schmidt

M. Schnittker

P. Danielewicz

P. J. Siemens

R. Bassini

R. Donangelo

R. K. Puri

S. Albergo

S. Fritz

S. J. Gaff

T. Alm

T. K. Nayak

T. Möhlenkamp

T. Odeh

U. Kleinevoß

U. Lynen

V. Maddalena

V. Serfling

W. D. Kunze

W. F. J. Müller

W. Reisdorf

W. Seidel

W. Trautmann

Y.-G. Ma

English

arXiv

Crossref

Temperatures of Exploding Nuclei

Breakup temperatures in central collisions of 197Au + 197Au at bombarding energies E/A = 50 to 200 MeV were determined with two methods. Isotope temperatures, deduced from double ratios of hydrogen, helium, and lithium isotopic yields, increase monotonically with bombarding energy from 5 MeV to 12 MeV, in qualitative agreement with a scenario of chemical freeze-out after adiabatic expansion. Excited-state temperatures, derived from yield ratios of states in 4He, 5Li, 6Li, and 8Be, are about 5 MeV, independent of the projectile energy, and seem to reflect the internal temperature of fragments at their final separation from the system. PACS numbers: 25.70.Mn, 25.70.Pq, 25.75.-

Serfling, V

collaboration, ALADIN

UCL Discovery

VOLUME 80, NUMBER 18 P HY S I CA L REV I EW LE T T ER S 4 MAY 1998Temperatures of Exploding NucleiV. Serfling,1 C. Schwarz,1 R. Bassini,2 M. Begemann-Blaich,1 S. Fritz,1 S. J. Gaff,3 C. Groß,1 G. Immé,4 I. Iori,2U. Kleinevoß,1 G. J. Kunde,3,* W.D. Kunze,1 U. Lynen,1 V. Maddalena,4,† M. Mahi,1 T. Möhlenkamp,5,† A. Moroni,2W.F. J. Müller,1 C. Nociforo,4 B. Ocker,6 T. Odeh,1 F. Petruzzelli,2 J. Pochodzalla,7 G. Raciti,4 G. Riccobene,4F. P. Romano,4 A. Saija,4 M. Schnittker,1 A. Schüttauf,6 W. Seidel,5 C. Sfienti,4 W. Trautmann,1 A. Trzcinski,8G. Verde,4 A. Wörner,1 Hongfei Xi,1,† and B. Zwieglinski81Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany2Istituto di Scienze Fisiche, Università degli Studi di Milano and I.N.F.N., I-20133 Milano, Italy3Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University,East Lansing, Michigan 488244Dipartimento di Fisica dell’ Università and I.N.F.N., I-95129 Catania, Italy5Forschungszentrum Rossendorf, D-01314 Dresden, Germany6Institut für Kernphysik, Universität Frankfurt, D-60486 Frankfurt, Germany7Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany8Soltan Institute for Nuclear Studies, 00-681 Warsaw, Hoza 69, Poland(Received 17 December 1997)Breakup temperatures in central collisions of 197Au 1 197Au at bombarding energies EyA ­ 50 to200 MeV were determined with two methods. Isotope temperatures, deduced from double ratios ofhydrogen, helium, and lithium isotopic yields, increase monotonically with bombarding energy from 5to 12 MeV, in qualitative agreement with a scenario of chemical freeze-out after adiabatic expansion.Excited-state temperatures, derived from yield ratios of states in 4He, 5,6Li, and 8Be, are about 5 MeV,independent of the projectile energy, and seem to reflect the internal temperature of fragments at theirfinal separation from the system. [S0031-9007(98)05934-1]PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn, 25.75.LdRecently, a caloric curve of nuclei has been obtainedby correlating the values of temperature and excitationenergy measured for spectator fragmentation in reactionsof 197Au 1 197Au at 600 MeV per nucleon [1]. The tem-peratures were derived from double ratios of helium andlithium isotopic yields while the excitation energies wereobtained by adding up the kinetic energies of the productnuclei and the mass excess of the observed partition withrespect to the ground state of the reconstructed spectatornucleus. The double-bended shape of the caloric curveand its similarity to predictions of microscopic statisticalmodels [2–4], has stimulated considerable experimentaland theoretical activities. In particular, the second rise ofthe temperature to values exceeding 10 MeV at high ex-citation energies has initiated the discussion of whethernuclear temperatures of this magnitude can be measuredreliably (see Refs. [4–6], and references given in theserecent papers) and whether this observation may indeedbe linked to a transition towards the vapor phase [7,8].Obviously, a well-founded understanding of the signifi-cance of the employed temperature observables [9] isindispensable when searching for signals of the predictedliquid-gas phase transition in nuclear matter.Here, we present the results of temperature measure-ments for central collisions of 197Au 1 197Au at incidentenergies EyA ­ 50 to 200 MeV. These collisions arecharacterized by a collective radial flow of light parti-cles and fragments which, over the covered energy range,evolves as a dynamical phenomenon closely connected tothe initial stages of the reaction [10]. Global equilibrium3928 0031-9007y98y80(18)y3928(4)$15.00is clearly not achieved. If local equilibrium is reached, theassociated temperatures should reflect the adiabatic cool-ing of the rapidly expanding system.Two temperature observables were used simultane-ously. Isotope temperatures were deduced from doubleratios of isotopic yields [11] and excited-state tempera-tures were derived from the correlated yields of light-particle coincidences [9,12,13]. It will become evidentfrom the diverging results that this represents more thana methodical test and that the two types of thermometersare sensitive to different stages of the fragment formationand emission.Beams of 197Au with EyA ­ 50, 100, 150, and200 MeV, provided by the heavy-ion synchrotron SIS,were directed onto targets of 75 mgycm2 areal density.Two multidetector hodoscopes, consisting of 96 and of64 Si-CsI(Tl) telescopes in closely packed geometries,were placed on opposite sides with respect to the beamaxis. Four high-resolution telescopes [4] were used tomeasure the isotopically resolved yields of light chargedparticles and fragments. The choice of angles, betweenulab ­ 24– and 58– for the hodoscopes and ulab ø 40–for the telescopes, was motivated by the aim of a goodcoverage at midrapidity.Additional detectors were employed in order to probethe charged-particle multiplicity for impact parameterselection. The angular range of ulab ­ 6– to 20– wascovered by an azimuthally symmetric array of 36 CaF2-plastic phoswich detectors [14]. Within the angular range30– to 55–, a solid angle of 0.7 sr was covered by an array© 1998 The American Physical SocietyVOLUME 80, NUMBER 18 P HY S I CA L REV I EW LE T T ER S 4 MAY 1998of 48 elements of Si-strip detectors. The results presentedin the following were obtained after selecting an eventclass of highest associated multiplicity, corresponding toabout 10% of the total reaction cross section.The populations of particle-unstable resonances werederived from two-particle-coincidence yields measuredwith the Si-CsI hodoscopes. The peak structures wereidentified by using the technique of correlation functions,and background corrections were based on results ob-tained for resonance-free pairs of fragments with Z # 3,such as p-d, d-d, up to 3He-7Li. Examples of correla-tion functions constructed for p-4He and d-3He coinci-dences are shown in Fig. 1. They are dominated by theresonances corresponding to the ground state (g.s.) and16.66 MeV excited state of 5Li. This pair of states rep-resents a widely used thermometer for nuclear reactions[12,13,15]. The observed weak peak intensities are ex-pected for large source sizes and may indicate breakupdensities considerably below normal nuclear density [16].Correlated yields of p-t, d-4He, 4He-4He, and p-7Li co-incidences and 4He singles yields were also measuredand used to deduce temperatures from the populations ofstates in 4He (g.s.; group of three states at 20.21 MeV andhigher), 6Li (2.19 MeV; group of two states at 4.31 and5.65 MeV), and 8Be (g.s.; 3.04 MeV; group of five statesat 17.64 MeV and higher). The probabilities for the coin-cident detection of the decay products of these resonanceswere calculated with a Monte Carlo model [13,17]. Theuncertainty of the background subtraction is the main con-tribution to the errors of the deduced temperatures.FIG. 1. Correlation functions constructed for d-3He (top) andp-4He (bottom) coincidences as a function of the relativemomentum q of the two particles for central collisions atEyA ­ 150 MeV. The observed states in 5Li are indicated.The lines represent the adopted upper and lower bounds of thenonresonant background (see text).The obtained values for two isotope and three excited-state temperatures are given in Fig. 2. The isotopetemperatures THeLi and THedt were derived as describedin [4], and correction factors of 1.2 have been applied inorder to account for the effects of sequential feeding. Thethree excited-state temperatures are characterized by largeenergy differences of the considered states (for TBe8 the18 MeVy3.04 MeV result is shown), and no correctionsfor sequential feeding were applied (fully justified onlyfor 5Li; see below and [12,15]). At EyA ­ 50 MeV, alltemperature values coincide within the interval T ­ 4 to6 MeV, an observation made also at EyA ­ 35 MeV byHuang et al. [18]. With increasing bombarding energy,however, the isotope temperatures rise approximatelylinearly up to THeLi ø 12 MeV and THedt ø 9 MeV atEyA ­ 200 MeV. The excited-state temperatures, on theother hand, mutually consistent with each other, appearto be virtually independent of the bombarding energy.Their mean values, over the covered range of bombardingenergies, are 4.6 6 0.6 MeV, 5.1 6 0.3 MeV, and 6.1 60.7 MeV for TLi5, THe4, and TBe8, respectively. Thesedifferences may be significant but seem marginal incomparison to the apparent qualitative difference betweenthe isotope and excited-state temperatures [19].The momentum-space acceptance of the detectors, keptat fixed positions in the laboratory, changes with bom-barding energy in the center-of-mass frame. For the caseof EyA ­ 150 MeV, the acceptance of the 96-elementhodoscope for p-a coincidences in the momentum inter-val corresponding to the 5Li-g.s. resonance is shown inFig. 3 (top). It covers the region around ucm ­ 90– and,FIG. 2. Measured isotope temperatures (full symbols) andexcited-state temperatures (open symbols) as a function of theincident energy per nucleon. The indicated uncertainties aremainly of systematic origin. The meaning of the lines isexplained in the text.3929VOLUME 80, NUMBER 18 P HY S I CA L REV I EW LE T T ER S 4 MAY 1998FIG. 3. Top: Acceptance of the 96-element ho-doscope for p-4He coincidences with relative momenta25 # q # 75 MeVyc in the plane subtended by relative trans-verse momentum and normalized rapidity of the corresponding5Li fragment for EyA ­ 150 MeV. The loci of Qcm ­ 30–,45–, 90–, 135–, and 150– (thick lines) and of 5Li energiesElabyA ­ 30, 50, and 70 MeV (thin lines) are indicated.Bottom: Temperatures derived from the yields of 5Li groundand excited states for the four intervals of the 5Li laboratoryenergy. Note that the errors are mainly of systematic origin.in addition, extends to forward and backward angles witha varying transverse-momentum acceptance. The wideacceptance and its shift with bombarding energy shouldnot be crucial, however, because no significant variationof TLi5 within the covered momentum space was found(Fig. 3, bottom).It is not immediately obvious that the divergence of theisotope and excited-state temperatures, growing dramati-cally with bombarding energy, contradicts the concept ofa common fragment freeze-out at a single temperature.Xi et al. report that their recent statistical calculations in-dicate a strongly reduced sensitivity of the helium-lithiumthermometer at high temperature, such that it may pre-vent reliable temperature measurements at T . 7 MeV[5]. Accordingly, a consistent common temperature, if ex-isting, should be low. The excluded-volume effect, as in-corporated in the quantum-statistical model by Gulminelliand Durand [6], causes a suppression of particle-unstableresonances decaying into loosely bound products, such asthe 16.66-MeV excited state of 5Li. It will have the effectthat the apparent TLi5 is low while a common emissiontemperature may be high. These calculations demonstratethat large effects can be caused by sequential decay andby structural differences of the nuclear states employed inthe temperature measurements, even though they may notsuffice to give a consistent explanation of all the presentobservations.3930The dynamical evolution of the fragment formationhas very recently been investigated with transport models[20], including nuclear molecular-dynamics [21,22] andquantum molecular-dynamics [23,24] models, applied tothe present and similar reactions. These studies suggestthat the asymptotic fragments can be identified at anearly stage of the reaction, typically at ø40 fmyc. Thesetimes coincide with the development of the collectiveflow component of the fragment motion [20–22]. Iflocal chemical equilibrium has been reached the isotopiccomposition should reflect the temperature of the systemat that particular time.According to various flow analyses, between 40% and60% of the collision energy is converted into collectiveflow energy [10]. In the simplest approximation, thebreakup temperature is then estimated as T ­ sEyAdy12.This assumes complete stopping of the incident nuclei anda classical gas with 3 3 2A degrees of freedom carrying athermal energy component of 50% of the collision energy.This relation (dashed line in Fig. 2) does not describe thedata very well, but it illustrates the expected linear riseand shows that the measured isotope temperatures haveabout the right order of magnitude. Better agreementwith the data at the lower energies is obtained if, forthe same thermal energies, the experimental temperaturevs energy relation of Ref. [1] is used (Fig. 2, full line).Even though it remains to be understood why THedt isconsiderably lower in the present case (cf. [4,25–27]),the comparison suggests that the isotope thermometers aresensitive to the local temperature at freeze-out in a blastscenario [28–30].The excited states used for the temperature evalua-tion are very specific quantum states with widths of1 MeV or less. They are unlikely to exist in the nu-clear medium in identical forms [20,31,32]. The ob-served asymptotic states can develop or survive onlyat very low densities that may not be reached beforethe cluster is emitted into vacuum. Accordingly, theexcited-state populations should reflect the temperatureand its fluctuations at this final stage of fragment emis-sion. The molecular dynamics calculations show that acluster continues to interact with the surrounding cool-ing and expanding matter for a considerable time after ithas been formed [21]. This will lower its internal excita-tion but, apparently, does not change as much the isotopiccomposition.Excited state populations have thermal characteristics[33] and have been shown to correspond to expectedtemperatures in compound reactions [15,34]. In thepresent case, the observed internal fragment excitations,associated with the final breakup of the system, are foundto be consistent with a thermal population at T ­ 5 to6 MeV (Fig. 4). The apparent temperatures LLi6 andTBe821 s3.04 MeVyg.s.d, derived from states not widelyseparated in energy, are lower but in accordance with theside-feeding effects predicted by the quantum-statisticalmodel [35].VOLUME 80, NUMBER 18 P HY S I CA L REV I EW LE T T ER S 4 MAY 1998FIG. 4. Six values of apparent excited-state temperaturesdeduced from states in 4He, 5Li, 6Li, and 8Be (open circles)in comparison to predictions of the quantum-statistical model(bars) for EyA ­ 100 MeV (top) and 200 MeV (bottom). Thecalculations were performed with T ­ 5 MeV (dashed lines)and ryr0 ­ 0.1. The notation for TBe8 is (1) 3.04 MeVyg.s.;(2) 18 MeVyg.s.; and (3) 18 MeVy3.04 MeV.The presented interpretation of the observed quali-tative difference between the isotope and excited-statetemperatures seems rather attractive. It implies thatisotope yields may be used to probe the early stages ofthe fragment formation process, and it may explain thesaturation of the excited-state temperatures that character-izes a wide variety of measurements at intermediate andrelatiistic energies [13,15]. This interpretation, therefore,should be confirmed by further work which may aimat a quantitative interpretation of the internal fragmentexcitation but also address current open questions suchas the role of initial correlations (see, e.g., [21,24,36,37])and of quantum effects in the fragment formationprocess [38–41]).Extensive discussions with J. Aichelin, H.W. Barz,F. Gulminelli, G. Röpke, and M. B. Tsang are gratefullyacknowledged. J. P. and M.B. acknowledge the financialsupport of the Deutsche Forschungsgemeinschaft underContracts No. Po 256/2-1 and No. Be1634/1-1, respec-tively. This work was supported by the European Com-munity under Contract No. ERBFMGECT950083.*Present address: Department of Physics, Yale University,New Haven, CT 06512.†Present address: National Superconducting CyclotronLaboratory, Michigan State University, East Lansing, MI48824.[1] J. Pochodzalla et al., Phys. Rev. Lett. 75, 1040 (1995).[2] D. H. E. Gross, Rep. Prog. Phys. 53, 605 (1990).[3] J. P. Bondorf et al., Phys. Rep. 257, 133 (1995).[4] Hongfei Xi et al., Z. Phys. A 359, 397 (1997).[5] Hongfei Xi et al., Phys. Rev. C 54, R2163 (1996).[6] F. Gulminelli and D. Durand, Nucl. Phys. A615, 117(1997).[7] J. B. Natowitz et al., Phys. Rev. C 52, R2322 (1995).[8] L. G. Moretto et al., Phys. Rep. 287, 249 (1997).[9] D. J. Morrissey et al., Annu. Rev. Nucl. Part. Sci. 44, 65(1994).[10] W. Reisdorf et al., Nucl. Phys. A612, 493 (1997), andreferences therein.[11] S. Albergo et al., Nuovo Cimento Soc. Ital. Fis. 89A, 1(1985).[12] J. Pochodzalla et al., Phys. Rev. C 35, 1695 (1987).[13] G. J. Kunde et al., Phys. Lett. B 272, 202 (1991).[14] H. J. Rabe et al., Phys. Lett. B 196, 439 (1987).[15] C. Schwarz et al., Phys. Rev. C 48, 676 (1993).[16] D. H. Boal and J. C. Shillcock, Phys. Rev. C 33, 549(1986).[17] V. Serfling, Ph.D. thesis, Universität Frankfurt, 1997(unpublished).[18] M. J. Huang et al., Phys. Rev. Lett. 78, 1648 (1997).[19] The same observation has recently been made for86Kr 1 93Nb central collisions. Hongfei Xi et al. (privatecommunication).[20] P. Danielewicz and Q. Pan, Phys. Rev. C 46, 2002 (1992).[21] H.W. Barz et al., Phys. Lett. B 382, 343 (1996).[22] A. Strachan and C.O. Dorso, Phys. Rev. C 55, 775(1997).[23] C. O. Dorso and J. Aichelin, Phys. Lett. B 345, 197(1995).[24] R. K. Puri et al., Phys. Rev. C 54, R28 (1996).[25] J. A. Hauger et al., Phys. Rev. Lett. 77, 235 (1996).[26] Y.-G. Ma et al., Phys. Lett. B 390, 41 (1997).[27] H. Xi et al., Report No. MSUCL-1055 (1997).[28] J. P. Bondorf et al., Nucl. Phys. A296, 320 (1978).[29] P. J. Siemens and J. O. Rasmussen, Phys. Rev. Lett. 42,880 (1979).[30] H. Stöcker et al., Z. Phys. A 303, 259 (1981).[31] M. Schmidt et al., Ann. Phys. (N.Y.) 202, 57 (1990).[32] T. Alm et al., Phys. Lett. B 346, 233 (1995).[33] T. K. Nayak et al., Phys. Rev. Lett. 62, 1021 (1989).[34] H. Dabrowski et al., Phys. Lett. B 247, 223 (1990).[35] J. Konopka et al., Phys. Rev. C 50, 2085 (1994).[36] J. Knoll and J. Wu, Nucl. Phys. A481, 173 (1988).[37] G. J. Kunde et al., Phys. Rev. Lett. 70, 2545 (1993).[38] R. Donangelo et al., Phys. Rev. C 50, R563(1994).[39] A. Ono and H. Horiuchi, Phys. Rev. C 53, 2958(1996).[40] A. Ohnishi and J. Randrup, Phys. Lett. B 394, 260(1997).[41] H. Feldmeier and J. Schnack, Prog. Part. Nucl. Phys. 39,393 (1997).3931

Temperatures of Exploding Nuclei

Abstract

Similar works

Full text

Available Versions

Crossref

UCL Discovery

GSI Repository