Intermediate-rapidity fragments with A=1-14 emitted from 42-137-MeV/nucleon Ar + Au have been measured. Evidence is presented that these fragments arise from a common moving source. Entropy values are extracted from the mass distributions by use of quantum statistical and Hauser-Feshbach theories. The extracted entropy values of S/A&#8776;2-2.4 are much smaller than the values expected from measured deuteron-to-proton ratios, but are still considerably higher than theoretically predicted values

Gelbke, Claus-Konrad

Harwood, L. H.

Jacak, Barbara V.

Lynch, W. G.

Scott, D. K.

Stöcker, Horst

Symons, T. J. M.

Tsang, M. B.

Westfall, Gary D.

English

Lynch, William G.

Symons, Timothy James MacNeil

Hochschulschriftenserver - Universität Frankfurt am Main

VOLLIME  51,  NUMBEI<  20  PI-IYSIICAL  REVIEW  LETTEKS  I4  N~\EMB~.K  1983 Measurement of  Complex Fragments and Clues to the Entropy Production from 42-137-MeV/nucleon  Ar  + Au B.  V.  Jacak, C.  D.  Westfall,  C.  K.  Gelbke,  L.  M,  Harwood, W. G.  Lynch, D.  K.  Scott, H.  StÖker,  and M.  B.  Tsang National Superconducting Cyclotron Laboraforq~,  Michigan Stute University, East Lansing, Michigan  48823 and T. J. M.  Symons Lazurence Berkeley Laboratory,  University of  California, Berkeley, Cal-ifornia  94720 (Keceived 22 August  1983) Intermediate-rapidity  fragments with A=  1-14  emitted from 42-137-MeP/nu- cleon Ar + Au  have been measured.  Evidence is presented that these fragments arise from a common moving source.  Entropy values are extracted from the mass distributions by use of  quantum statistical and Hauser-Feshbach  theories. The extracted entropy values of  S/A  F= 2-2.4  are much smaller than the values ex- pected from measured deuteron-to-proton  ratios, but are still considerably higher than theoretically predicted values. PACS numbers:  25.70.Np We report the first systematic measurements of  complex nuclear fragments emitted at inter- mediate rapidities from reactions of  Ar with Au at 42,  92, and 137 MeV/nucleon,  an eilergy re- gion where only sparse measurements exist.'- The observed fragments with A= 1-14  are  ex- plained by emission from a common thermal source and the mass distributions are analyzed by use of  quantum statistica14 and Hauser-Fesh- bach5 theories to deduce the entropy created in the collision.  Because it stays constant during the expansion, the extracted entropy may give information about the hot,  compressed stage of the ~ystem.~*~-~~  The entropy may provide in- formation on the nuclear equation of  state and phase transitions in nuclear matter.7v  ''-  l3  It has been proposed that the entropy can be deduced from the ratio of  deuterons to pr~tons,~  but more recent calculations indicate that heavier frag- ments must be included in the analy~is.~  Indeed our values are considerably Jolver than those deduced from a prescription based only on deu- terons and protons, but they differ from current theoretical expectati~ns,~ The measurements were carried out at the Lawrence Berkeley Laboratory Bevalac using 40Ar  beams of  42,  92, and 137 MeV/nucleon  with typical beam intensities of  1  X  107  particles/sec, and targets of  80 and 200 mg/cm2 Au.  Heavy fragments were measured with two stacks of silicon detectors (0.1,  0.3,  5.0  mrn  and 0.8,  0.8, 5.0,  5.0,  5.0 mm).  Light particles (P, d,  t,  'He, 4He, and 6He)  were measured simultaneously with a telescope consisting of  two silicon AE detectors (0.4 and 5 mm) and a 10-cm Na1 E  detectoa.,  All telescopes covered an angular range of  30" to 130" in 20" steps, with isotope resolution for hydrogen through carbon fragments.  The energy spectra of  the light particles were corrected for reaction losses in the Na1 detector, and the heavy-fragment spectra were corrected for en- ergy loss in the target.  The relative normaliza- tion between different angles is accurate to 5%, whereas the absolute normalization is known to 20%. Measured energy spectra of  ''Be  are shown in Fig. 1.  These spectra are typical of  fragments with A> 6; the complete results will be published elsewhere.  The error  bars reflect statistical errors  only.  The solid lines are  fits to the spec- tra assuming particle emission from a single moving source.I4  The source temperature and velocity and the fragment Cross section are ob- tained by fitting the double differential spectra with a relativistic Boltzmann distribution in the rest frame of  the source, with use of  a least- Squares method.14  This parametrization is used to isolate the component of  inclusive spectra arising from an intermediate velocity source. Fragments with As  4 observed at angles s 30" include substantial contributions from the pro- jectile remnant, and are not included in the fits. Low-energy particles which may be evaporated from the target are also excluded.  All of  the measured data for fragments with A  > 4 are  fit- ted because the thickness of  the first heavy-ion detectors was chosen to exclude evaporation products,  and measurements at angles 3  30" eliininate the heavy projectile fragments.  The resubtiilg temperatiire for each fragment is shown VOLLTME  51,  NL  MU~R  20  PHYSICAL  REVIEW  LETTERS  14 NOV~MUER  1983 FIG. 1.  Energy spectra for   OB^  from Ar + Au at (a) 137,  (b) 92,  and  (C)  42 MeV/nucleon.  The solid lines correspond to fits with a single moving source. in Fig. 2 as  a function of  the fragment mass. The similarity of  the temperatures over the measured range of  fragment masses suggests that the fragments originate from a thermal source and that the Same type of  source gives rise to the heavy and the light fragments.  The source temperature increases with bombarding energy:  T(ave)=18,25,35  MeV atElab=42,92, 137 Me~/nucleon,  respectively.  The fluctuations FIG. 2.  Temperatures obtained from moving-source fits to the fragment energy spectra, as a function of the fragment mass.  Two points for a single mass are shown where two fragments of  that mass were observed. in the temperature extracted from the 137-MeV/ nucleon data may be due to the fact that the heavy- ion telescopes onl y measured particles to  80 Me~/nucleon,  thus sampling only a portion of  the intermediate-rapidity data.  It would be difficult to account for the production of  A=  14  fragments at intermediate rapidity with models based on. few nucleon-nucleon  scatterings; therefore we believe that our results convey evidence for thermalization of  the emitting system. Figure 3(a) shows the relative mass yields as a function of  mass.  The Cross sections are ob- tained by integrating the moving-source fits in order to focus on the intermediate-rapidity source and exclude particles originating from the projectile and target.  The error  bars in Fig. 3(a) reflect the error introduced by extra- polation to the unmeasured angles and energies. The solid histograms show the results of  a quantum statistical calculation4 of  the mass yield. This calculation assumes statistical equilibrium among all accessible quantum states in the late Stage of  the reaction.  The thermodynamic equi- librium state is then fixed by  the total isospin, energy, and volume of  the system.  Ground and excited states with identified spin for nuclei with As 20 are included in the calculation,  as well as  known particle-unstable states with AG  10. Pions and delta resonances are  also included. In-medium interactioiis are incorporated via excluded-volume effects.  The shape of  the cal- VOLL~IE  51,  NLIMBER  20  PHYSICAL  REVIEW  LbTTERS  14 NC)LEMBEK  1983 61-L_ 1'0  I2  3 4 5  6  7  8  9  101 12  13  14 FRAGMENT  MASS FIG. 3.  (a) Production cross sections of  fragments with A= 1-14.  The solid and dashed histograms are results of  quantum statistical and Hauser-Feshbach calculations,  respectively.  (b) Entropy extracted from the model fits to the fragment distributions,  as a function of  bomharding energy.  The solid line is the entropy expected froin a hydrodynamic calculation, and the dashed line for a viscous fluid  (Ref. 8). culated mass yield is well determined by the total entropy in the system for densities of  (0.3- 0.7)~~  where p,  = 0.15  fm-  3.  This allows ex- traction of  the entropy from the experimentally determined mass yield through a least-squares fit of  the calculated yields.  The histograms are results for p = 0.5~~. Figure 3(b) shows the entropy values obtained: S/A=2.Oi  0.2,  2.21  0.2,  and 2.351 0.2  for EI„ = 42,  92,  and 142 MeV/nucleon,  respectively. The solid line shows the average entropy per nucleon expected for participants with use of  a conventional hydrodynamic calculation, and the dashed line the result for a viscous fluid.8  En- tropie~  in the range of  4-6  were previously ex- tracted from the observed deuteron-to-proton ratios based on the formulaS/A= 3.945 - whicli is applicable for high entropy values only. It has been shown4 that R„  rises to a maximum for medium entropies and drops to small values at low entropies as  a result of  the formation of heavier clusters.  The present entropy values are still considerably higher than expected from hydrodynamical calc~lations.~  The theoretical results correspond to an upper limit for the en- tropy produced because in the calculation the incident matter stops, while at low  energies there may be transparency and, hence,  no en- tropy production. To determine the extent to which the extracted entropy depends on the assumed breakup mecha- nism, we have performed a calculation based on the Hauser-Feshbach f~rmalism.~  These results are shown in Fig. 3(a) as  the dashed histograms. In this approach, particles are statistically emitted from an excited nucleus at constant density,  and the temperature,  charge,  and mass evolution of  the system are  followed.  Emission of  nuclei in ground and particle-stable excited states as  well as  unstable states with lifetimes long compared to  emission time is included.  A spherical initial system with Z=  34 and A=  82 is assumed, ~or~esponding  to a fireball formed at the most probable impact parameter.  The entropy extracted is  for the initial system with a level density corresponding to an ideal Fermi gas. Entropies determined by fitting the measured mass yields with respect to T at fixed Gf were found to be rather independent of  in the range of  24 s 8, s 60 MeV.  The histograms represent calculations for Ef = 38 MeV,  corresponding to an ideal Fermi gas at normal nuclear matter density. The entropy values deduced from the two very VOLUME  51,  NUNDER  20  PHYSICAL  REVIEW  LETTEKS  14  NOVEMBER  1983 different approaches, the Hauser- Feshbach and the quantum statistical models, are consistent to within S/A  of  0.2.  This agreement conf irms the independence of  the entropy determination from assumptions about the breakup dynamics. In Summary, we have measured isotopically separated f ragments f rom Ar on Au  at 42,  92, and 137 MeV/nucleon.  The double-differential Cross sections indicate that these fragments originate from a single intermediate-rapidity source.  The observed mass yields are fitted with two very different models of  fragment pro- duction which yield consistent values of  entropy. These entropies are lower than those based on deuteron-to-proton  ratios, but are still consid- erably larger than theoretical values.  This dis- crepancy may be due to several effects.  The detection of  a heavy fragment at intermediate rapidity correlates with a high multiplicity,  so that the measured fragments arise from central collisions, but some averaging over impact pa- rameter remains.  This averaging has been shown to alter the extracted entropy.15  Another possible factor would be a liquid-vapor phase transition, which would  cause the expansion to be no  longer isentropic and cause additional en- tropy to be pr~duced.~? We wish to thank the Bevalac operations staff for their cooperation, and to acknowledge the assistance of  Anne Werthmann in the data analy- sis.  This niaterial is  based upon work supported by  the National Science Foundation through Grant NO. PHY 80-17605-01. 'K.  A.  Franke1 and J. D.  Stevenson, Phys. Rev. C 3, 1511 (1981). 'B.  Jakobsson etal.,  Z. Phys. A 307,  293 (1982). 3~.  Gosset etal., Phys. Rev. C i.6,  629 (1977). *H. Stöcker et  al.,  Nucl.  Phgs. M,  63c  (1983). 5~.  A. Friedman and W.  G.  Lynch, Phys. Rev. C 28, 16 (1983). 6~.  Siemens and J. Kapusta,  Phys. Rev. Lett. 43, 1486 (1979). Stöcker, J, A. Maruhn,  and W.  Greiner, Phys. Lett. E,  303 (1979). *H. Stöcker,  Lawrence Berkeley Laboratory Report No.  12302 (unpublished). 'G.  Bertsch and J. Cugnon,  Phys. Rev. C 24, 2514 (1981). "G. Bertsch and P. J. Siemens,  Phys. Lett. -, 9 (1983). "P.  Danielewicz, Nucl. Phys. M,  465 (1979). "H.  Schulz et  al.,  Phys. Lett. E,  12 (1982). I3M. W.  Curtin,  H. Toki, and D.  K. Scott,  Phys. Lett. 123B,  289 (1983). 1"G.  D. Westfall et  nl.,  Phys. Lett. z,  118 (1982). I5H. H.  Gutbrod et  nl., Phps. Lett. X,  317 (1983). 

Measurement of complex fragments and clues to the entropy production from 42-137-MeV/nucleon Ar + Au

Measurement of complex fragments and clues to the entropy production from 42-137-MeV/nucleon Ar + Au

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