Isotopic Effects in Nuclear Reactions at Relativistic Energies
Temperature and Density in Heavy Ion Reactions at Intermediate Energies
ISOTOPIC EFFECTS IN NUCLEAR REACTIONS AT 
RELATIVISTIC ENERGIES 
C.Sfienti(1), M. De Napoli(2), S. Bianchin(1), A.S. Botvina(1)(6), J. Brzychczyk(4),  
A. Le Fèvre(1), J. Lukasik(1)(9), P. Pawlowski(4), W. Trautmann(1), P. Adrich(1),  
T. Aumann(1), C.O. Bacri(3), T. Barczyk(4), R. Bassini(5), C. Boiano(5), A. Boudard(7),  
A. Chbihi(8), J. Cibor(9), B. Czech(9), J.-E. Ducret(7), H. Emling(1), J. Frankland(8),  
M. Hellström(1), D. Henzlova(1), K. Kezzar(1), G. Immè(2), I. Iori(5), H. Johansson(1),  
A. Lafriakh(3), E. Le Gentil(7), Y. Leifels(1), W.G. Lynch(10), J. Lühning(1), U. Lynen(1),  
Z. Majka(4), M. Mocko(10), W.F.J.Müller(1), A. Mykulyak(11), H. Orth(1), A.N. Otte(1),  
R. Palit(1), A. Pullia(5), G. Raciti(2), E. Rapisarda(2), H. Sann(1)†, C. Schwarz(1), H. Simon(1), 
K. Sümmerer(1), C. Volant(7), M. Wallace(10), H. Weick(1), J. Wiechula(1), A. Wieloch(4) 
and B. Zwieglinski(11)
The ALADiN2000 Collaboration 
(1) Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany 
(2) Dipartimento di Fisica dell'Università and LNS-INFN, I-95126 Catania, Italy 
(3) Institut de Physique Nuclèaire, IN2P3-CNRS et Universitè, F-91406 Orsay, France 
(4) M. Smoluchowski Institute of Physics, Jagiellonian Univ., Pl-30059 Krakòw, Poland 
(5) Istituto di Scienze Fisiche, Università degli Studi and INFN, I-20133 Milano, Italy 
(6) Inst. Nucl. Res., Russian Accademy of Science, Ru-117312 Moscow, Russia 
(7) DAPNIA/SPhN, CEA/Saclay, F-91191 Gif-sur-Yvette, France 
(8) GANIL, CEA et IN2P3-CNRS, F-14076 Caen, France 
(9) H. Niewodniczanski Institute of Nuclear Physics, Pl-31342 Krakòw,Poland 
(10) Department of Physics and Astronomy and NSCL, MSU, East Lansing, MI 48824, USA 
(11) A. Soltan Institute for Nuclear Studies,Pl-00681 Warsaw, Poland 
Abstract 
A systematic study of isotopic effects in the break-up of projectile spectators at relativistic energies has 
been performed at the GSI laboratory with the ALADiN spectrometer coupled to the LAND neutron 
detector. Besides a primary beam of 124Sn, also secondary beams of 124La and 107Sn produced at the FRS 
fragment separator have been used in order to extend the range of isotopic compositions.  
The gross properties of projectile fragmentation are very similar for all the studied systems but specific 
isotopic effects have been observed in both neutron and charged particle production. The breakup 
temperatures obtained from the double ratios of isotopic yields have been extracted and compared with the 
limiting-temperature expectation.  
1. Introduction 
Challenging motivations for isotopic studies in nuclear multifragmentation are derived 
from the importance of the density dependence of the symmetry-energy term of the 
nuclear equation of state for astrophysical applications and for effects linked to the 
manifestation of the nuclear liquid-gas phase transition.  
Müller and Serot, in their seminal paper [1], have demonstrated that the two-fluid nature 
of nuclear matter has very specific consequences for the phase behavior in the coexistence 
region. Different isotopic compositions are predicted for the coexisting liquid and gas 
phases, with the gas being more neutron rich than the liquid in asymmetric (N ≠ Z) 
matter. This difference stems from the decrease in the symmetry energy in nuclear matter 
as the density is decreased. The expected magnitude of this density dependence, however, 
is model dependent and very poorly constrained by existing data [2]. 
The calculations of Müller and Serot are restricted to infinite matter with no Coulomb 
force included. In addition, the isotopic composition, in the calculations, is typically 
varied within a range of proton fractions ρp/ρ = 0.3 to 0.5 whose limits are not easily 
accessible in experiments with heavy nuclei.  
Theoretical studies for finite systems also indicate that the sequential decay of excited 
reaction products has a tendency to reduce some of the expected effects [3]. 
If the phase transition for asymmetric nuclei still manifests itself as a plateau in the 
caloric curve [5] (i.e. the correlation between the temperature of the system and its 
excitation energy), this could be influenced by the degree of asymmetry as well as by the 
mass of the system undergoing the fragmentation. 
Figure 1. Location of the four studied projectiles in the plane of atomic number Z versus 
neutron number N. The contour lines represent the limiting temperatures according to [4] , the 
dashed line gives the valley of stability, and the full line corresponds to the N/Z = 1.49 of 197Au.
It has been shown [4] that, due to the Coulomb pressure, there exists a limiting 
temperature which represents the maximum temperature at which nuclei are found to exist 
as self-bound objects in Hartree-Fock calculations. The dependence of the breakup 
temperature on the excitation energy could therefore be governed by the limiting 
temperature. Figure 1 shows the calculated limiting temperature as a function of the 
neutron and proton number [4]. As it is possible to see from the picture, in case of proton-
rich nuclei, the phenomenon of vanishing limiting temperature is predicted, the limiting 
temperature decreasing with increasing proton fraction. 
Clearly, new experiments exploring such phenomena are mandatory for having a better 
knowledge of the thermodynamics of a finite nucleus and its decay.  
Recently a systematic investigation of projectile-spectator fragmentation has been 
undertaken at the ALADiN spectrometer at the GSI [6,7]: four different projectiles, 124Sn, 
197Au, 124La and 107Sn, all with an incident energy of 600 AMeV on 116Sn and 197Au 
targets, have been studied. The two latter beams have been delivered by the FRagment 
Separator (FRS) of the GSI as products of the fragmentation of a primary 142Nd beam at 
890 AMeV on a 9Be production target [7].  
The necessity of low beam intensities for the best operational condition of the ALADiN 
setup (≅2000 particles/sec), and the possibility of using a thick target in order to achieve 
high interaction rates are indeed conditions compatible with radioactive-ion-beam 
experiments. Moreover, the inverse kinematics offers the possibility of a threshold-free 
detection of all heavy fragments and residues and thus gives a unique access to the 
breakup dynamics. 
The measurement of the charge and the momentum vector of all projectile fragments with 
Z≥2 has been performed, with high efficiency and high resolution, with the TP-MUSIC 
IV detector [8]. Using the reconstructed values for the rigidity and pathlength, the charge 
of the particle measured by the TP-MUSIC IV, and the time-of-flight given by the TOF-
Wall, the velocity and the momentum vector can be calculated for each detected charged 
particle. The knowledge of velocity and momentum allows then the calculation of the 
particle's mass.  
Neutrons emitted in directions close to θlab = 0
o , are detected with the Large-Area 
Neutron Detector (LAND) which covers about half of the solid angle required for 
neutrons from the spectator decay. 
2. Gross Properties of multifragment decay 
The gross properties of projectile fragmentation are very similar for all the studied 
systems. 
The fragments emerging from the decay of the projectile spectators are well localised in 
rapidity. The distributions are peaked around a rapidity value very close to be beam 
rapidity and become narrower with increasing mass of the fragment. 
The observed independence of the Rise and Fall, i.e. of the correlation between the 
multplicity of intermediate mass fragments with Zbound, also for the unstable systems [6], 
confirms the hypothesis of equilibrium at freeze-out. 
The shape of the charge distributions are as well similar for all the systems. For larger 
values of Zbound, the charge distribution exhibits a U-shape. The heavy fragments are the 
residues of the lowly-excited projectile-spectators after the evaporation of light fragments 
and nucleons. In semi-central reactions, i.e. smaller values of Zbound, the distribution 
broadens and flattens over nearly the full charge distribution. For still lower values of 
Zbound, the charge distribution becomes steep. This is consistent with the system 
disassembling into predominantly lighter fragments. 
The charge distributions have been fitted with a power-law parameterization, σ(Z) ∝ Z-τ, 
in the charge range 3≤Z≤15. The power-law parameters τ (Figure 2 – left panel) allow to 
follow the transition from the U-shape to a pure exponential spectrum and reach the 
minimum value in the Zbound range which corresponds to the maximum production of 
IMF, i.e. in the multifragmentation region. They follow a nearly universal curve almost 
independent of the isotopic composition of the original spectator system. 
Figure 2. (Left Panel) The extracted τ  parameters as a function of normalized Zbound for 
124La, 124Sn and 107Sn at 600 AMeV, compared with earlier data for 197Au obtained at the 
same energy. (Right Panel) Neutron multiplicities as obtained from the LAND detector for 
all the studied systems (colored symbols are SMM predictions). 
Specific isotopic effects, even though small, can nevertheless be observed: in particular, 
the hierarchy of τ for the neutron-poor 124La and 107Sn and neutron-rich 124Sn and 197Au 
systems for Zbound/Zproj>0.5 is opposite to the standard predictions of the Statistical 
Multifragmentation Model SMM [9]. It can, however, be explained with a weak isotopic 
dependence of the surface-term coefficient in the liquid-drop description of the fragment 
masses at low excitation energy which gradually disappears with increasing excitation of 
the fragmenting system [10]. 
Specific isotopic effects are as well found in the reconstructed neutron multiplicities 
measured with the LAND detector [11] (Figure 2 - right panel). For peripheral collisions 
the values of the multiplicity depend on the number of available neutrons in the entrance 
channel. Going towards central collisions the number of emitted neutrons is progressively 
determined by the N/Z in the entrance channel. In a preliminary comparison with SMM 
calculation (colored points in Figure 2) a promising agreement has been observed.  
Neutrons will be important for establishing the mass and energy balance and in particular 
for calorimetry. In this respect it is crucial to identify the spectator neutrons and to 
distinguish them from the fireball ones. From a preliminary analysis of their rapidity 
distributions, the corresponding spectator sources have been identified. They are 
characterized by temperatures up to 4 MeV, possibly caused by large contributions from 
evaporation. 
2. Structure and Memory Effects in particle production 
The mass resolution obtained for projectile fragments entering into the acceptance of the 
ALADiN spectrometer is about 3% for fragments with Z=3 and decreases to 1.5% for 
Z≥6 [7]. Masses are thus individually resolved for fragments with atomic number Z≤10. 
The elements are resolved over the full range of atomic numbers up to the projectile Z 
with a resolution of ΔZ≤0.2 obtained with the TP-MUSIC IV detector. The mean N/Z of 
the mass distributions of light fragments in the range 3 ≤Z ≤ 13 for two different Zbound 
cuts is presented in Figure 3. 
Figure 3. Mean values <N>/Z of light fragments with 3 ≤ Z ≤ 13 produced in the 
fragmentation of 124Sn and 124La at 600 A MeV for two different bins in Zbound.
The values obtained for 124Sn are larger than those for 124La or 107Sn (not shown) as 
expected from the different N/Z of the original projectiles. Their odd-even variation is, 
however, much more strongly pronounced for the neutron-poor cases. The strongly bound 
α-type nuclei (even-even N=Z) attract a large fraction of the product yields during the 
secondary evaporation stage. This effect is, apparently, larger if already the hot fragments 
are close to N=Z symmetry, as it is expected for the fragmentation of 124La and 107Sn [12]. 
Inclusive data obtained with the FRS fragment separator at GSI for 238U [13] and 56Fe 
[14] fragmentations on titanium targets at 1 A GeV bombarding energy confirm that the 
observed patterns are very systematic, exhibiting at the same time nuclear structure 
effects characteristic for the isotopes produced and significant memory effects of the 
isotopic composition of the excited system by which they are emitted. This has the 
consequence that, because of its strong variation with Z, the neutron-to-proton ratio 
<N>/Z is not a useful observable for studying nuclear matter properties. For this purpose, 
techniques, such as the isoscaling [7], will have to be used which cause the nuclear 
structure effects to cancel out. A precise modeling of these secondary processes is, 
therefore, necessary for quantitative analyses. 
Another interesting feature of the mass distributions predicted by SMM is their 
dependence, in the case of the proton-rich systems, on the excitation energy of the system 
[10]. This difference arises from the dependence of the number of neutrons in light 
fragments on the Z spectrum. For the neutron-rich 124Sn system, on the other hand, the 
distributions should be independent of the excitation energy. From a first qualitative 
comparison with the model prediction of the mass distributions for different Zbound cuts, 
however, we have not observed any noticeable variation in the mean N/Zs for the 124La 
system (Figure 3). Also in this case it will be crucial to precisely model the sequential 
decay in order to clarify whether it has washed out the expected effect.  
3. Limiting temperature 
As previously mentioned, for proton-rich systems a rapid drop of the limiting temperature 
has been theoretically predicted (Figure 1) because of the increasing Coulomb pressure 
[4]. On the other hand, SMM calculations predict nearly isospin-invariant temperatures 
for the coexistence region [10]. Therefore, in order to distinguish whether the breakup 
temperature is determined by the binding properties of the excited hot nuclear system or 
by the phase space accessible to it by fragmentation we have analyzed the temperature for 
the studied neutron-poor and neutron-rich systems.  
The temperatures used in the caloric curve studies [5,15] were deduced from a double 
ratio of isotopic yields. Under the assumptions of low density and chemical equilibrium a 
grand canonical treatment [16] yields for the double ratio: 
ZAZA exp
),(),(
),(),(
with ΔB being the double difference of the binding energies of the chosen isotopes and a 
a statistical factor containing spin and mass terms. Furthermore, for best sensitivity the 
binding energy difference ΔB should be comparable or larger than the temperatures to be 
measured [17]. 
The thermometry with the 3,4He isotope pairs used in the nuclear caloric curve [5] benefits 
from the large difference ∆B = 20.6 MeV of the binding energies of these two nuclei but 
it is not the only choice. There are also other combinations of isotopes which can be 
expected to provide the necessary sensitivity for the measurement of temperatures in the 
MeV range. In a recent systematic study of different isotopic thermometers for spectator 
fragmentation [18] TBeLi, TCLi, and TCC have been analyzed in detail. In particular, it has 
been found that the rise at small Zbound, i.e. high excitation energy, previously observed 
with THeLi is well reproduced by most thermometers, including TBeLi which is derived 
from the 7,9Be and 6,8Li isotope ratios. This is an indication that the rise is not necessarily 
related to a particular behavior of either 3He or 4He. An overall good agreement between 
the different temperature observables has been obtained with the exception of those 
containing carbon isotopes. In the latter cases, the apparent temperature values remain 
approximately constant with values between 4 and 5 MeV.  
Measured isotope ratios as a function of Zbound for the 
124Sn, 124La and 107Sn systems are 
shown in Figure 4. A very interesting dependence on the isotopic composition of the 
Figure 4. Measured isotopic yield ratios as a function of Zbound/Zproj for the neutron-rich 
124Sn and the neutron-poor 124La and 107Sn systems. 
spectator is observed for all analyzed ratios with the exception of the 3He/4He ratio, 
exhibiting a reduced difference between the neutron-rich and neutron-poor systems. The 
strong sequential decay into α particles could explain the difference between these two 
behaviors. Therefore, also in this case, the structure effects responsible for the observed 
odd-even variation in the N/Z/s of intermediate-mass fragments (Figure 3) play the major 
role. 
For the 124Sn projectile spectator, moreover, the ratios, with the exception of 3He/4He, are 
almost independent of Zbound. For the mentioned ratio the decrease between the most 
central and the most peripheral collisions is about a factor 4 whereas for example, for the 
9Be/8Li ratio the total variation amounts hardly to a factor of 2. There seems to be a clear 
correlation between the difference of the binding energies of the involved isotopes and 
Zbound, i.e. excitation energy of the system [18]: the higher the first the stronger the 
variation of the corresponding ratio with Zbound.  
On the other hand, in the case of the proton-rich systems all ratios exhibit a strong 
dependence on the excitation energy deposited in the system.  
From the measured ratios the isotopic temperatures have been extracted and an overall 
agreement with the previous systematics [18] have been obtained for the THeLi, TBeLi, TCLi, 
and TCC thermometers. 
In Figure 5 in particular, the apparent THeLi and TBeLi temperatures for the 
124Sn and 124La, 
Figure 5. Isotopic temperatures THeLi and TBeLi as a function of Zbound/Zproj for 124Sn and 
124La, 107Sn projectile spectators. 
107Sn spectator systems are reported. By comparing the two systems with the same mass 
but different isospin-content, the average difference of the obtained THeLi temperatures is 
0.7±0.1 MeV whereas almost no difference (hardly 0.1 MeV in average) between the two 
systems is observed in the case of the TBeLi thermometer. The small difference observed in 
the case of THeLi is caused by the fact that the dependence of the 
6Li/7Li ratio (Figure 4) on 
the isotopic composition of the system is not compensated by the weak dependence of the 
3He/4He ratio. In the case of TBeLi both isotopic ratios 
7,9Be and 6,8Li exhibit a dependence 
on the N/Z of the original projectiles, which cancels out in the double ratio. The 
invariance of the isotopic temperature with the isotopic composition of the system is 
inconsistent with the limiting temperature predictions [4] of 2 MeV for the 124Sn and 124La 
systems (Figure 1) and seems to favor a statistical interpretation [10]. 
4. Conclusions 
Isotopic effects in the break-up of projectile spectators at relativistic energies have been 
reported. The gross properties of projectile fragmentation are very similar for all the 
studied systems. Specific isotopic effects, even though small, can nevertheless be 
observed: in particular, the inversion in the hierarchy of the τ exponential parameter of 
the charge distribution can be explained with a weak isotopic dependence of the surface-
term coefficient of the nuclear equation of state [10]. 
The mean N/Zs of the isotope distributions of light fragments exhibit as well specific 
isotopic effects. In particular, the observed odd-even variation is much more strongly 
pronounced for the neutron-poor cases and could be explained in terms of a simultaneous 
concurrence of both structure effects characteristic for the isotopes produced and memory 
effects of the isotopic composition of the excited system from which they are emitted.  
From the double ratios of Z≤4 isotopes, the isotopic temperatures have been determined. 
The small dependence (of about 0.7 MeV) observed in the THeLi thermometer could be 
due to the influence of structure effects in the sequential decay. The invariance with the 
isotopic composition in the entrance channel is inconsistent with the limiting-temperature 
predictions and seems to favors the statistical interpretation. On the other hand, the 
limiting-temperature concept reproduces nicely the mass dependence of the caloric curves 
[15] and only seems to fail when applied to the isospin degree of freedom.  
It should be noted that most of the limiting-temperature calculations are made for beta 
stable nuclei [19] while it was not explicitly tested whether the studied systems are still 
near the stability at breakup.  
The weak N/Z dependence of the breakup temperatures measured in this experiment 
shows that this is not a major point of concern. The same observation, on the other hand, 
is not compatible with the strong Coulomb effect predicted by Besprosvany and Levit [4]. 
This open point in the connection between limiting temperatures for heavy nuclei and 
breakup temperatures of fragmenting nuclear systems will require an improved 
understanding. 
C.Sf. acknowledges the receipt of an Alexander-von-Humboldt fellowship. This work was 
supported by the European Community under contract No. RII3-CT-2004-506078 and 
HPRI-CT-1999-00001 and by the Polish Scientific Research Committee under contract 
No. 2P03B11023. 
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