Multifragmentation, radial flow
and phase transitions for large nuclear systems.

Summary : Experiments performed at GSI for the Au+Au system between 100 and 1000 A.MeV show interesting evidences of a phase transition for nuclear matter. These observations are best seen at the highest energies and for mid-peripheral reactions. For the most central collisions and the lowest measured energy, the data indicate that i) the phase transition point could correspond to lower beam energies than 100 A.MeV and that ii) the radial flow energy may influence the decay schemes of these systems. A coherent scientific program with INDRA at GSI using heavy beams (Xe and Au) around and below 100 A.MeV will yield, simultaneously, high quality measurements of : i) the charge distributions, ii) the isotope ratio of the light ions (hence the thermodynamic temperature) and iii) the Z and qcm dependence of the radial flow. This consistent set of data should allow for a clear conclusion concerning the existence of the suggested critical behaviour in the case of central collisions.

At the lower energy, an important flow is deduced from the kinetic energy spectra of the charged products observed for qcm=90±10°. This flow is found to be decreasing with Z and values between 13.5 and 8.3 A.MeV are given 3] . At the higher energy, no significant flow has been found and the mean thermal energies are found to be consistent with those deduced from the 100 A.MeV data (those are estimated after subtracting the above mentioned flow).

The conclusion of these analysis is that at high incident energies (_1000 MeV) a number of experimental evidence (power law behaviour and caloric curve) point to the possible existence of a phase transition. At "low" energies (essentially 100 A.MeV) and for Au+Au central collisions it appears that, i) the observed exponential behaviour may point to the fact that an incident energy of 100 A.MeV is above a possible phase transition point, ii) the presence of radial flow due to compression has obviously a central role in determining the amount of energy that is left as "thermal excitation energy" and iii) that this flow could be also determinant for the decay pattern of the hot and compressed system formed and hence the charge distribution and isotopic ratio of light particles (see ref. 1,5,13]). Besides the fact that the discussed data have been obtained in very different conditions and with different devices, a number of significant questions are thus very much open.

Parallel to these studies, the analysis of data collected with the INDRA detector at GANIL for medium size systems (Xe+Sn for Ebeam=25-50 A.MeV ) is showing that, i) dynamical effects are very important for the production of IMFs and that, at least for mid-peripheral reactions, these come mainly from an intermediate zone between projectile and target, ii) for central collisions, the kinetic energy distributions show a significant qcm dependence and the flow values for Z=1 are significantly different from those of the heavier fragments (figure 3.). At the present time, a radial flow of 2.0 A.MeV is measured from the IMFs for these central collisions in the angular domain of qcm=90±30°.This value is compared to a systematic 12]  of measured radial flow values in figure 4. Obviously a detailed understanding of the nature of this flow, of the onset at which it appears and of its evolution with the size of the system as well with incident energy is necessary, especially below Ecm = 50A.MeV.

The study of a lighter systems at GANIL energies also show (Ar+Ni, Ar+Kcl for 32-95 A.MeV and ), that for energies close to 50 A.MeV events corresponding to nuclear vaporisation are observed 7]  (events with no Z>2 fragments : the onset for such events are said to have been seen for Au+Au at 400 A.MeV ). The study of these events between 50 and 95 A.MeV incident energy shows that considerable total excitation energies are reached (between 7 and 25 A.MeV) and that the isotope ratio are dependent on this excitation energy. A link with the above mentioned caloric curve will therefore be possible. The partition of this measured "total excitation energy" between its thermal and radial flow component is central to the present discussion.

The aim of the present proposal is to study around and below 100 A.MeV the multifragmentation of heavy systems by simultaneously measuring for central collisions i) the Z distribution, ii) the Z and q(cm) dependent flow and iii) the isotope ratios (hence TH,He and TLi,He). The combination of these three measurements should allow to draw coherent conclusions on the presence of a "phase transition" (1st or 2nd order ?) for these systems and to study with precision the value of radial flow and its influence on the decay mechanisms of these initially compressed hot systems.

For all these measurements, the INDRA detector is very well suited and has demonstrated the quality of its response in a very similar environment at GANIL. The charge resolution easily extends over the domain of ions produced in these violent collisions. The isotope identification for the light particles and ions is sufficient for a simultaneous measurement of TH,He and TLi,He. The granularity and energy resolution will allow for a precise measurement of the multiplicities and the radial flow. The results of simulations showing this are given below.

Following the conclusions drawn above, the scientific program of INDRA at GSI should include an extensive study of the Au+Au and Xe+Sn systems between the highest energies accessible to GANIL (Xe : 50 A.MeV , Ta (_Au) 40 A.MeV ) and the limit for which the qualities of INDRA are lost. The choice of the Au+Au system comes naturally form the data obtained from GSI. The study of the Xe+Sn will allow to complement the GANIL data, to study the influence of the coulomb field on the multifragmentation process and to look at the effect of system size on the radial flow values. It is also a system perfectly adapted to the INDRA detection efficiency. The joint study of both systems over such a large energy range (GANIL+SIS) will produce a unique and complete set of data.

As far as multiplicities are concerned, the granularity of INDRA should be sufficient for total multiplicities up to 100 (see simulations). The results of M.B.Tsang et al 2] . show that this corresponds to a Au beam energy of 400 A.MeV (for the Xe+Sn system the total charge is 104). The thickness of the light particle detectors are however limited at forward angles to proton energies of 250 MeV. It seems therefore, that incident energies should be limited to 150 A.MeV . This value representing also a good overlap with the complementary programs of the ALADIN and FOPI collaboration.

We therefore suggest to measure the following systems and energies :

Au+Au : 40, 60, 80, 100 and 150 A.MeV
Xe+Sn : 50, 60, 80, 100 and 150 A.MeV

The lower energies are absolutely necessary in order to calibrate the detector for the light particles (see below).

The target thickness that can be used with INDRA is limited by the requested energy detection threshold. The minimal INDRA threshold, with no target, is of the order of 1 MeV/A, we will limit the target thickness to obtain an effective threshold of 2 MeV/A. This yields an Au target of 2mg/cm2.

Taking a total cross section of 6 barn, a "central collision" cross section of 100 mbarn, a mean number of incident ions of 107 ions/sec (in an emittance of 3_.mm.mrad), and estimating that a number of 106 (per system and incident energy) central events are necessary to apply the various n-dimensional cuts one is led to make (Z, qcm, …) for the analysis and to extract radial flow values.

In these conditions the counting rates would be of 360evt/sec, for a minimal bias trigger (M_4) of which 6evt/sec correspond to central collisions. This would correspond to an average acquisition dead time of 30%, a low random coincidence rate and a reasonable flux for individual detectors.

The measurement time required for one measurement is then of 72 hours of data taking (72x3600x6=1.5 106 central events). A total of 10 system-energy measurements results in 30 days to which 3 days have to be added for beam tuning and detector set-up.

The different detectors present in INDRA are such that for heavy fragments (Z>2), the device is essentially self calibrating. The 300µm detectors at forward angles (q<45°), whose exact thickness is well known and whose pulse height defect have also been well studied are particularly useful. At backward angles (q>45°), each ring has an extra two-layer telescope (75µm and 2000µm) which by axial symmetry gives calibrated spectra for essentially all particles and nuclei.

For light particle at forward angles, the method consists in producing light particle secondary beams of known energy and using elastic scattering on a carbon target. As this will not be possible at GSI, we suggest to repeat, for each incident beam (Xe and Au) an energy which we have already measured at GANIL. In this manner, calibration for light particles and also for heavier ions will be obtained with precision. As the stability of the INDRA detectors has been observed to be very good even over long periods of time and as it is checked regularly by a laser pulse system, the calibration for the other incident energies will be obtained.

INDRA is a 4_ detector for charged particle and heavy ions designed primarily to satisfy the needs of a general multifragmentation program as can be defined in the GANIL energy range.

As most of the 4_ detector of its kind, it is designed with azimuthal symmetry around the beam direction. It is therefore made of a series of rings, each subtending a certain range of the polar angle q. Table 3. gives a brief geometrical description of the different rings. Each ring is divided into a number of detection cells, usually 24, containing different detection layers. The typical INDRA cell is shown in figure 6. In order to minimise the detection threshold for heavy ions, the first layer is an ionisation chamber (5 cm) with a field parallel to the direction of the incoming ions. Mechanically, an ionisation chamber covers 2 rings and is made of 12 independent cells. The gas, whose pressure is kept constant by a regular flow, is maintained in the chamber vessel by the cathode and the anode mylar foils. The chambers are usually filled with 50 mb of C3F8 gas, corresponding to an average threshold of 1 MeV/A for most heavy ion. It is important here to point out that INDRA operates under vacuum.

Behind this first detection layer, one finds, at forward angles (q _ 45°) 300 µm Silicon detectors. Each Silicon wafer has the same geometry as an ionisation chamber cell but is divided into 4 (3 for ring N° 2) independent detectors (cf. fig. 7 and table 3.). The _E-E information obtained when coupling the ionisation chamber (_E) to the silicon (E) allows to detect and identify the slowest heavy ions. Following the silicon detector, a Cesium Iodide (CsI) crystal with a similar geometry allows to detect the faster heavy ions when used in conjunction with the silicon and the light particles (p, d, t, 3He, a,…) when using the shape analysis (slow and fast signal) of the light signal of the crystal. The thickness of the CsI crystals depend on the ring number and are given in table 3. Beyond 45°, the detection modules are limited to the ionisation chamber and the CsI. Figure 7. shows ring N° 4-5 and figure 8. some views of the complete detector in different configurations.

Altogether the INDRA detector is made up of 96 independent ionisation chamber cells, 180 Silicon detectors, 324 CsI crystals, 12 phoswichs (NE102-NE115) and 8 telescopes (75µm and 3000 µm Silicon detectors) positioned on rings N° 10 to 17 for calibration purposes.

.

Figure 6 : The typical detection cell of INDRA for q_45°. beyond this angle, the silicon detector is removed

CsI						Si		Ionisation Chamber
Ring N°	qmin ( ° )	qmax ( ° )	N	Df ( ° )	e (cm)		DW (msr)		e (µm)	Df ( ° )	N	n CsI	d (cm)	DW (msr)
2	3	4.5	12	30	14		0.82		300	30	12	3	65.5	3.4
3	4.5	7	24	15	14		1.29		300
4	7	10	24	15	14		2.10		300	30	12	4	31.5	11.4
5	10	14	24	15	14		3.59		300
6	14	20	24	15	10		8.00		300	30	12	4	25	40.4
7	20	27	24	15	10		12.2		300
8	27	35	24	15	10		18.7		300	30	12	4	12	96.0
9	35	45	24	15	10		29.3		300
10	45	57	24	15	8		41.7		No	30	12	4	12	187
11	57	70	24	15	8		52.0		No
12	70	88	24	15	6		79.8		No	30	12	2	12	160
13	92	110	24	15	5		79.8		No	45	8	3	12	239
14	110	126	16	22.5	5		93.5		No	45	8	4	12	340
15	126	142	16	22.5	5		76.6		No
16	142	157	8	45	5		99.1		No	45	8	2	12	159
17	157	176	8	45	5		59.5		No

Associated to these detectors, a completely new electronic scheme has been developed. Its main characteristics are :

As noted above, the INDRA detector was constructed to work in the GANIL energy range. In this sense, the nature and the thickness of its detectors are well adapted to the energies suggested for the GSI program. The charge identification for the fast projectile like fragments should allow for a good identification (qlab>3°, see lower) of the heaviest ions even if charge separation is not quite obtained for the heaviest beams. At Ganil, separation of Z=64 was obtained in the forward region except for ring n° 1.

Since the multiplicities involved in an Au+Au reaction at 100 A.MeV are significantly higher that those measurable in the GANIL energy range, It is necessary to study in detail the efficiency of INDRA with respect to the these multiplicities and to the total charge collection. To do this we have used the GENEVE event generator 10]  associated with the INDRA simulator. In figure 9, we show the prediction of this generator compared to the results of the Xe + Sn system @ 50 MeV/A. The overall conclusion that can be obtained is that for this system, the generator gives "realistic" predictions even if it overestimates the light charge particle multiplicity. Of course, being based on classical "deep inelastic" mechanisms as well as standard fusion and statistical decay for the small impact parameters, it does not contain the effects that we have described above (flow, neck formation,...). However, for efficiency evaluations, it suffices to give a correct estimate of the multiplicities and charge distributions, which is the case.

We have therefore used this code to generate collisions between Au+Au at 50 and 100 MeV/A. The figure 10 shows the multiplicity distributions, the total charge collected as a function of this multiplicity and the fragment multiplicity versus the light charge particle multiplicity. Again, these results show a realistic behaviour, although, when compared to the data of reference 1] , the simulated data for 100 A.MeV Shows features relevant to higher incident energy data, namely a characteristic bending of the IMF multiplicity as a function of the LCP multiplicity because full damping is assumed for the most central collisions. This should not affect the conclusions on the adaptability of INDRA to the suggested program. Table 2 gives for various ring and for central collisions (the worst possible case), the percentage of double hits (IMF-LCP and LCP-LCP) observed for a number of suggested systems.

We also show in fig. 11 the charge collected per ring. This measures well the problems associated with the detection of multiple ions in a single detector : These multiple detection problems do exist, but because of the multi-layer nature of the INDRA detection cells, many of the situations encountered can be resolved, thus reducing greatly the effect of the large numbers seen in table 2 to levels of _10-20 % (see fig. 11). This explains why INDRA will be in a much better position as compared to other previous measurement done with comparable detectors 2].

Another problem that we will indeed face with the SIS beams and energies is the poor Z-resolution obtained from ring N°1 (the only INDRA ring made with Phoswich (NE102-NE115) detectors). This is a concern for the most peripheral reactions which produce a projectile like nucleus below 3°. To solve this , we suggested to replace this ring with a higher quality device based on Silicon and CsI detectors (comparable to the other rings of INDRA). This device has not been included in the present simulations and will obviously improve the performance of the detector.

The present status of the analysis of the data both at GSI and INDRA shows, that for central collisions, the region around and below 100 A.MeV should be searched for the possible existence of a phase transition such as has been postulated for higher energy data (caloric curve and power law charge distribution). The INDRA detector is ideally suited to simultaneously measure the different quantities which taken jointly should allow for a definite conclusion to be drawn : Z distributions, isotope identification for the lighter ions and a complete measurement of the flow. Two systems would be studied between 40 and 150 A.MeV : Xe+Sn and Au+Au. The amount of beam requested for these measurements is 33 days (99 shifts).

The combination of SIS beams and energies with the INDRA detector offers therefore a unique possibility to cover in the near future, with a "state of the art" configuration (accelerator+detector), a remarkable domain of heavy ion physics.