Universality in fragment inclusive yields from Au Au collisions

Transcription

1 Universality in fragment inclusive yields from Au Au collisions A. Insolia, 1 C. Tuvè, 1 S. Albergo, 1 F. Bieser, 2 F. P. Brady, 5 Z. Caccia, 1 D. Cebra, 2,5 A. D. Chacon, 6 J. L. Chance, 5 Y. Choi, 4, * S. Costa, 1 J. B. Elliott, 4,2 M. Gilkes, 4 J. A. Hauger, 4 A. S. Hirsch, 4 E. L. Hjort, 4 M. Justice, 3, D. Keane, 3 J. Kintner, 5 M. Lisa, 2, H. S. Matis, 2 M. McMahan, 2 C. McParland, 2 D. L. Olson, 2 M. D. Partlan, 2,5 N. T. Porile, 4 R. Potenza, 1 G. Rai, 2 J. O. Rasmussen, 2 H. G. Ritter, 2 J. Romanski, 1 J. L. Romero, 5 G. V. Russo, 1 R. Scharenberg, 4 A. Scott, 3 Y. Shao, 3 B. K. Srivastava, 4 T. J. M. Symons, 2 M. L. Tincknell, 4, S. Wang, 3, P. G. Warren, 4 H. H. Wieman, 2 T. Wienold, 2, and K. L. Wolf 6, ** EOS Collaboration 1 Università di Catania and INFN, Catania, Italy 2 Nuclear Science Division, LBNL, Berkeley, California Kent State University, Kent, Ohio Purdue University, West Lafayette, Indiana University of California, Davis, California Texas A&M University, College Station, Texas Received 19 April 1999; published 10 March 2000 The inclusive light fragment (Z 7) yield data in Au Au reactions, measured by the EOS Collaboration at the LBNL Bevalac, are presented as a function of multiplicity. Moving from central to peripheral collisions the measured charge distributions develop progressively according to a power law which can be fitted, within errors, by a single exponent independently of the bombarding energy except for the data at 250A MeV. In addition, the location of the maximum in the individual yields of different charged fragments, for a given beam energy, shifts towards lower multiplicity as the fragment charge increases from Z 3 toz 7. This trend is common to all six measured beam energies. Moments of charge distribution are also reported. The universal features observed in the present Au Au data are consistent with previous experimental findings in the Au C multifragmentation reaction at 1A GeV. PACS number s : q PHYSICAL REVIEW C, VOLUME 61, I. INTRODUCTION Multifragmentation reactions between heavy ions are a subject of intense experimental and theoretical investigations both at low as well as intermediate energies. The mechanism of the multifragmentation reaction can be described in terms of a two-step process: the formation of the remnant occurs in the first step involving prompt particle emission while the breakup of the remnant involves a slower second step 1. The subject has triggered additional interest since a power law dependence 2 in the fragment yield measured in p Xe and p Kr reactions was reported by the Purdue group, and proposed this as a possible signature that, under proper conditions, nuclear matter could undergo a phase transition 2,3. Since then a lot of scientific effort has been devoted to the subject, which has led to the experimental discovery of *Present address: Department of Physics, Sungkyunkwan University, Suwon , Republic of Korea. Present address: Brookhaven National Laboratory, Upton, NY Present address: Ohio State University, Columbus, OH Present address: Lincoln Laboratory, S1-257, 244 Wood Street, Lexington, MA Present address: Harbin Institute of Technology, Harbin , People s Republic of China. Present address: University of Heidelberg, Heidelterg, Germany. **Deceased. universal features in nucleus-nucleus collisions in the energy range 100A 1000A MeV 4. In particular, the EOS Collaboration, in an event-by-event analysis of the Au C reaction at 1A GeV, has been able to characterize the experimental data in terms of critical exponents 5 7, thus bringing the first clear evidence for a continuous liquid-gas phase transition in multifragmentation reactions between heavy ions. The same type of experimental evidence has been found in other finite systems as well see, for instance, the recent study of hydrogen cluster fragmentation in collision H 25 C The EOS Collaboration has measured fragment production in Au Au collisions at the LBNL Bevalac. The effective Au beam energies in the midpoint of the target were 0.25A, 0.4A, 0.6A, 0.8A, 1.0A, and 1.15A GeV. The experiment has been conducted with the EOS Time Projection Chamber TPC 9,10 and a multiple sampling ionization chamber MUSIC 11 as well as a time-of-flight TOF wall and a neutron detector MUFFINS. Details about the MUFFINS spectrometer are to be found in Refs Only data from the TPC detector are used in the present analysis. The TPC 9,10 provides almost complete coverage in the forward hemisphere 1. Particle identification is achieved via specific energy loss along particle tracks. The EOS TPC resolution allows one to identify particles up to Z 7, measuring their momentum with virtually no p t cut. The purpose of the present analysis of Au Au collisions is to report new data concerning inclusive yields and moments of charge distributions in the projectile spectator frag /2000/61 4 / /$ The American Physical Society

2 A. INSOLIA et al. PHYSICAL REVIEW C FIG. 1. Fragment rapidity distributions vs normalized rapidity y y/y beam, with multiplicity cut M bin 3,4,5,6, at E lab 1000A MeV. mentation. We will show that the inclusive yields, in spite of the unavoidable smearing produced by averaging the yields over many events within multiplicity bins, exhibit typical features that on the one hand were already observed in multifragmentation reactions and that, on the other hand, can be still traced back on a qualitative level to the universal features proposed earlier as signatures for the critical behavior of nuclear matter 4,16,17. The fingerprints of a continuous liquid-gas phase transition will reveal themselves as coarse signatures in the power law trend observed in the inclusive yields for peripheral collisions as well as in the moments of charge distributions. These coarse signatures yield necessary but not sufficient signals that the system undergoes a continuous phase transition, as shown in 7, where both coarse and fine signatures are widely discussed in the case of the Au C reaction. II. EXPERIMENTAL RESULTS According to the Plastic Ball analysis prescription 18, in order to define the centrality of the collision, the multiplicity spectrum is divided in eight bins from 0 to the maximum multiplicity. The latter is defined as the multiplicity value, near the end of the multiplicity distribution, where the distribution falls down to 1/2 of its plateau value. Multiplicities greater than the so-defined M max contribute to a ninth bin. This multiplicity scale is therefore a sort of scale on excitation energy even if we cannot define an exact correspondence between multiplicity bin and excitation energy. The measured inclusive rapidity distributions allow one to define proper cuts to select the fragmentation of the projectile spectators. Typical rapidity distributions versus normalized rapidity y y/y beam are shown in Fig. 1 for E beam 1A GeV and multiplicity bins M bin 3,4,5,6. Similar distributions are found at the remaining beam energies. The strong suppression of targetlike fragments is due to the cut in the TPC acceptance for the backward hemisphere 1. We can see that rapidity spectra for Z 1,2 exhibit a large prompt component at low rapidity. Fragments with larger Z values are produced with rapidities close to the beam rapidity with an almost symmetric distribution. In the present analysis we use to select projectile spectator fragmentation a sharp cut close to beam rapidity, y In this way the prompt component is strongly suppressed. The problem posed by the presence of prompt particles has been discussed widely in the literature 1, In addition, one should recall the result of Ref. 1, where it has been shown, for the Au C reaction at 1A GeV, that the total multiplicity is proportional to the second stage multiplicity. This fact makes less crucial the

3 UNIVERSALITY IN FRAGMENT INCLUSIVE YIELDS... PHYSICAL REVIEW C FIG. 2. Yields as function of the fragment charge Z for different multiplicity bins at E lab 1150A MeV. problem of a complete suppression of the prompt component. TABLE I. Fragment yields counts/event at E beam 1150A MeV for given multiplicity bins. The statistical errors are also reported. Z M bin 3 M bin 4 M bin 5 M bin FIG. 3. Yields as a function of the fragment charge Z for different multiplicity bins at all six beam energies. Data points for M bin 3,4,5,6, corresponding to peripheral collisions, are represented by different symbols almost overlapping each other. Two multiplicity bins corresponding to more central collisions, denoted by rhombohedrons (M bin 9) and circles (M bin 8), are shown in all panels. At all beam energies the solid lines correspond to a fit with a power law Y q 0 Z and a fit with an exponential Y Y 0 e cz, for the peripheral and central collisions, respectively, except for the data at 250A MeV see text. A. Yields versus fragment charge The measured inclusive yields for all multiplicity bins except M bin 1) and E beam 1150A MeV are reported in Fig. 2 versus the fragment charge Z. There is insufficient statistics in M bin 1 to build a yield. Data points are represented by different symbols for different multiplicity bins and, for multiplicity bins 3, 4, 5, and 6 corresponding to peripheral collisions and intermediate mass fragments IMFs with Z 3, are almost undistinguishable for they fall one on top of the other. For a better comparison, the yields of Fig. 2 are reported in Table I for peripheral collisions and all Z values. The inclusive yields of Fig. 2 have large error bars for high multiplicity bins. Even so, for IMFs with Z 3, we can still recognize that for central collisions, M bin 7 and higher, an almost linear dependence in semilogarithmic scale is observed. Approaching the semiperipheral domain a power law begins to develop (M bin 6). The power law dependence is then fully developed for the multiplicity bins M bins 3, 4, and 5. In Fig. 3 the measured inclusive yields for the six beam energies are reported versus the fragment charge Z for selected multiplicity bins: M bin 3,4,5,6 for peripheral collisions and two multiplicity bins corresponding to more central collisions (M bin 8,9). An energy by an energy fitting procedure has been applied to the IMF yields in Fig. 3. The results of the fit are reported as solid lines in the figure starting from Z 1 to give a better feeling of different trends. We do not report any fit for the data at E 250A MeV because the separation among the multiplicity bins is not so clear as it is at the higher energies. We have found that the IMF yields for central collisions can be fitted, within errors, at all beam energies by an exponential Y Y 0 e c * Z. The two-parameter fit produces c values which show only a slight fluctuation with energy. Those values look consistent within the error bars, with weighted average c Data points for M bin 3,4,5,6 are still represented by the same symbols as in Fig. 2. Again, IMF data corresponding to peripheral collisions are almost undistinguishable for they fall on top of each other at all six beam energies. For these bins, the experimental dependence on Z can be fitted, again within errors, by a power law Y q 0 Z. The weighted average of over all beam energies except 250A MeV is At 250A MeV an exponent lower than 2 was obtained. The numerical values of the q 0 parameter have been fixed by normalizing to the yields. Thus, the observed power law is independent of the beam energy in the range ( )A MeV. This indicates that the main mechanism for fragment production from the projectile remnant might very much be the same in this energy range. This power-law-like distribution has already been reported for Au Au reactions by the ALADIN Collaboration 22. Indeed, they found that the fragment yields at

4 A. INSOLIA et al. PHYSICAL REVIEW C FIG. 4. Energy dependence of the IMF production (Z 3). The peripheral integrated yields are averaged over the multiplicity bins 3, 4, 5, and 6. For more central collisions a mean between bins 8 and 9 is reported. 1000A MeV gated with a constraint on large impact parameter peripheral collisions show a power law dependence on the fragment charge. This is at variance with the trend observed at 100A MeV in which, selecting central collisions, an exponential behavior was observed 22. This feature of the multifragmentation phenomenon has been, on the other hand, interpreted as a possible signature for a continuous liquid-gas phase transition 2,4. Other experimental data as well refer to the same type of power law behavior in the Z distribution of fragments emitted by the projectilelike system 23. Actually, if a liquid-gas phase transition takes place for a given value of excitation energy transferred to the system, one has to expect a typical power law dependence of the relevant physical quantity which, in our case, is just the fragment distribution 3,24. Different model calculations have reported very clearly this behavior. Baldo et al. 25 find that deterministic chaos inside the spinodal zone is associated with multifragmentation and the predicted fragment distribution shows a power law trend with an exponent very close to what was previously reported by the analysis of Au C EOS data at 1.0A GeV 4,5. Furthermore, in Refs. 26,27, in the frame of a simple purely classical molecular dynamic model, it is shown that the dynamical evolution of a system of 100 particles, excited to a temperature T giving a Maxwellian velocity distribution to its constituents, creates, under proper initial conditions for the excitation energy, a power law mass distribution of fragments with This value is close to the one predicted by the Fisher droplet model 24,28 and, again, it is very close to the critical exponents reported by the EOS Collaboration in the Au C reaction 7. In spite of some criticism raised on this point 29, we think that the observation of a power law for semiperipheral collisions in Au Au at all six beam energies is consistent with previous experimental findings in multifragmentation reactions. FIG. 5. Individual yields ln(n Z ) versus multiplicity bin for all fragment charges (Z 3) at E lab 1150A MeV. The number of fragments of each species has been divided by Z 79 the nuclear charge of gold. Error bars are omitted for clarity. The integrated intermediate mass (Z 3 7) fragment yield, N IMF, is shown in Fig. 4 as a function of the beam energy. We see that N IMF is strongly suppressed as the beam energy increases for central collisions multiplicity bins 8 and 9 while it is almost energy independent for more peripheral collisions multiplicity bins 3, 4, 5, and 6. B. Individual fragment yields It is interesting to examine the individual fragment yields versus multiplicity. The data at E beam 1150A MeV are reported in Fig. 5, for Z 3 7. The individual yields are divided by the charge of gold. Individual yields for all six beam energies are then reported in Fig. 6, where, for the sake of simplicity, only two typical fragment charge values (Z 3 and Z 6) are consid- FIG. 6. Individual yields ln(n Z ) versus multiplicity bins for Z 3 circles and Z 6 crosses. As in Fig. 5, individual yields are divided by the charge of gold, Z 79. Error bars are reported only when larger than the size of the symbols

5 UNIVERSALITY IN FRAGMENT INCLUSIVE YIELDS... PHYSICAL REVIEW C FIG. 7. a, b, c, d Second moment of the charge distribution for the indicated beam energies. The maximum is observed at M bin 3. e Correlation between the third and second moments for all six energies. Different symbols for the six different energies almost overlap each other. f Correlation between the fifth and second moments. Again, different symbols for the six different energies are used. They almost overlap each other. ered. The same type of comments applies to Figs. 5 and 6. Similar features are observed at all six energies. One can notice that increasing multiplicity corresponds to events with greater excitation energy of the projectile remnant. This produces a rise of the number of each species of IMFs as the multiplicity increases from the lowest M bin values. We do observe a strict ordering: the lighter species is always more abundant than the heavier. All IMF yields decrease at the highest multiplicity. For those M bin values, the excitation energy is so large that only the lightest fragments can survive. In addition, for a given Z value, the peak of ln(n Z )vs M bin is at a higher value of multiplicity at low bombarding energy than at high bombarding energy. Finally we observe that, in spite of the unavoidable smearing produced by averaging the individual yields over many events within the multiplicity bins, the location of the maximum, for a given beam energy, shifts towards lower multiplicity for the larger Z values. This is a very important feature for it allowed us to extract for the first time the critical exponent in the analysis of Au Cat1A GeV 6,7. InAu Au inclusive individual yields, with which this work is concerned, the shift in the location of the maximum appears to be, again, independent of the beam energy along with the well-known rise and fall of the fragment production versus the centrality of the collision. C. Moments of charge distributions Moments of the charge distribution, M k M bin (z) z z k n(z) M bin, vs multiplicity bin, where n(z) is the measured yield, are given in Fig. 7. The second moment is shown in Figs. 7 a 7 d for four different beam energies. Correlations between different moments are shown in Figs. 7 e and 7 f. One can easily recognize that a maximum appears at M bin 3. This is the first multiplicity bin for which we observe the power law for peripheral collisions, as seen in Fig. 3. In particular, as expected, the second moment is characterized by a maximum which tends to soften when a mass cutoff is applied 30. In our case this softening comes in a natural way due to the detector cut at charge Z 8. A correlation between different moments, third versus second, Fig. 7 e, and fifth versus second, Fig. 7 f, is nicely seen, in agreement with percolation model calculations The slopes of these correlations are consistent with the exponent which best fits the yields for M bin 3,4,5,6 in Fig. 3. III. CONCLUDING REMARKS In conclusion, we have shown that EOS data for the inclusive yields of fragments (Z 1 7) in Au Au, from E beam 400A MeV up to E beam 1150A MeV, show a typical power law distribution when selecting peripheral collisions in agreement with previous model calculations as well as with other experimental data. The data at E beam 250A MeV show somehow a different trend. The exponent required to fit with a power law the IMF for peripheral collisions, at E beam 250A MeV, is smaller than 2. We have found that, for a given beam energy, the location of the maximum in the individual yields of different charged frag

6 A. INSOLIA et al. PHYSICAL REVIEW C ments shifts towards lower multiplicity as the fragment charge increases from Z 3 toz 7. This trend is also common to all six energies. In addition to these universal features, the second moment of the charge distribution shows a maximum at the M bin 3 for all considered beam energies. We think that the universal features of Au Au data at all six beam energies, presented in this work, are consistent with previous experimental findings on multifragmentation. ACKNOWLEDGMENTS Two of the authors A.I. and C.T. thank Andrea Rapisarda for many useful discussions. 1 EOS Collaboration, J.A. Hauger et al., Phys. Rev. C 57, J.E. Finn et al., Phys. Rev. Lett. 49, A.S. Hirsch, A. Bujak, J.E. Finn, L.J. Gutay, R.W. Minich, N.T. Poule, R.P. Scharenberg, B.C. Stringfellow, and F. Turkot, Phys. Rev. C 29, For a recent overview of phase transitions in nuclei see, for example, Critical Phenomena and Collective Observables, Proceedings of the International Conferance CRIS 96, Acicastello, Italy, 1996, edited by S. Costa, S. Albergo, A. Insolia, and C. Tuvé World Scientific, Singapore, EOS Collaboration, M. Gilkes et al., Phys. Rev. Lett. 73, EOS Collaboration, J.B. Elliott et al., Phys. Lett. B 381, EOS Collaboration, J. B. Elliott et al., Phys. Rev. C submitted. 8 B. Farizon et al., Phys. Rev. Lett. 81, G. Rai et al., IEEE Trans. Nucl. Sci. 37, EOS Collaboration, E. Hjort et al., inproceedings of the 9th Winter Workshop on Nuclear Dynamics, Advances in Nuclear Dynamics, edited by B. B. Back, W. Bauer, and J. Harris World Scientific, Singapore, 1993, pp W. Christie et al., Nucl. Instrum. Methods Phys. Res. A 255, Transport Collaboration, C. Tuvè et al., Phys. Rev. C 56, Transport Collaboration, C. Tuvè et al., Phys. Rev. C 59, S. Albergo et al., Nucl. Instrum. Methods Phys. Res. A 311, Transport Collaboration, J. Engelage et al., Radiat. Meas. 27, ALADIN Collaboration, J. Pochodzalla et al., incritical Phenomena and Collective Observables, Proceedings of the International Conference CRIS 96, Acicastello, Italy, 1996, edited by S. Costa, S. Albergo, A. Insolia, and C. Tuvé World Scientific, Singapore, J. Pochodzalla, Prog. Part. Nucl. Phys. 39, H.H. Gutbrod, A.M. Poskanzer, and H.G. Ritter, Rep. Prog. Phys. 52, W. Bauer and W.A. Friedman, Phys. Rev. Lett. 75, W. Bauer and A. Botvina, Phys. Rev. C 52, R M.L. Gilkes et al., Phys. Rev. Lett. 75, G.J. Kunde et al., Phys. Rev. Lett. 74, P.F. Mastinu et al., Phys. Rev. Lett. 77, M.E. Fisher, Rep. Prog. Phys. 30, M. Baldo, G.F. Burgio, and A. Rapisarda, Phys. Rev. C 51, V. Latora, M. Belkacem, and A. Bonasera, Phys. Rev. Lett. 73, M. Belkacem, V. Latora, and A. Bonasera, Phys. Rev. C 52, D. Stauffer and A. Aharony, Introduction to Percolation Theory Taylor & Francis, London, L. Phair et al., Phys. Rev. Lett. 79, W. Bauer, Phys. Rev. C 38, X. Campi, J. Phys. A 19, L X. Campi, Phys. Lett. B 208,