arXiv:nucl-ex/0009004v1 6 Sep 2000
Effect of the intermediate velocity emissions
on the quasi-projectile properties for the
Ar+Ni system at 95 A.MeV
D. Dor´ ea,d 1, Ph. Bucheta, J.L. Charveta, R. Dayrasa,
L. Nalpasa, D. Cussolb, T. Lefortb, R. Legraina, C. Volanta,
G. Augerc, Ch.O. Bacrid, N. Bellaizeb, F. Bocageb,
R. Bougaultb, B. Bouriquetc, R. Broub, A. Chbihic, J. Colinb,
A. Demeyere, D. Durandb, J.D. Franklandc, E. Galichetd,h,
E. Genouin-Duhamelb, E. Gerlice, D. Guinete, S. Hudanc,
P. Lautessee, F. Lavaudd, J.L. Lavillec, J.F. Lecolleyb,
C. Leduce, N. Le Neindreb, O. Lopezb, M. Louvelb,
A.M. Maskaye, J. Normandb, M. Parlogf, P. Pawlowskid,
E. Plagnold, M.F. Rivetd, E. Rosatog, F. Saint-Laurentc 2,
J.C. Steckmeyerb, M. Sterne, G. Tabacarud, B. Tamainb,
L. Tassan-Gotd, O. Tirelc, E. Vientb, J.P. Wieleczkoc
aDAPNIA/SPhN, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
bLPC Caen (IN2P3-CNRS/ISMRA et Universit´ e), 14050 Caen Cedex , France
cGANIL (DSM-CEA/IN2P3-CNRS), B.P. 5027, 14076 Caen Cedex 5, France
dIPN Orsay (IN2P3-CNRS), 91406 Orsay Cedex, France
eIPN Lyon (IN2P3-CNRS/Universit´ e), 69622 Villeurbanne Cedex, France
fNuclear Institute for Physics and Nuclear Engineering, Bucharest, Romania
gDipartimento di Scienze Fisiche, Univ. di Napoli, 180126 Napoli, Italy
hConservatoire National des Arts et M´ etiers, 75141 Paris Cedex 03, France.
1DAPNIA/SPhN, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France, e-mail:
email@example.com, FAX : 33.1.69.08.75.84
2present address : CEA, DRFC/STEP, CE Cadarache, 13108 Saint-Paul-lez-
Preprint submitted to Elsevier Preprint8 February 2008
The quasi-projectile (QP) properties are investigated in the Ar+Ni collisions at 95
A.MeV taking into account the intermediate velocity emission. Indeed, in this re-
action, between 52 and 95 A.MeV bombarding energies, the number of particles
emitted in the intermediate velocity region is related to the overlap volume be-
tween projectile and target. Mean transverse energies of these particles are found
particularly high. In this context, the mass of the QP decreases linearly with the
impact parameter from peripheral to central collisions whereas its excitation energy
increases up to 8 A.MeV. These results are compared to previous analyses assuming
a pure binary scenario.
Key words: PACS Numbers ; 24.10.-i, 25.70.-z
The Quasi-Projectile deexcitation has been studied through a wide variety of
systems at intermediate energies - . In this energy domain a transition
from a binary process, leading to two main excited fragments (the quasi-
projectile (QP) and the quasi-target (QT)) in the exit channel, towards a
participant-spectator mechanism, is expected. From inclusive or semi exclu-
sive measurements it has not been possible to distinguish between these two
mechanisms. In some cases, the experimental data could be described equally
well either assuming a pure binary mechanism or a geometrical process ,.
With the improvement of experimental setups, namely the advent of 4π multi-
detectors allowing fully exclusive measurements, it should become possible to
reconstruct the QP and the QT from their decay products on an event by event
basis. However, this reconstruction process depends greatly on our ability to
identify unambiguously the origin of the detected products. Unfortunately, in
the intermediate energy range, the various sources of emission strongly over-
lap in the velocity space. Thus one has to rely on some assumptions on the
underlying mechanisms in order to unfold the various sources of emission. Al-
though it was generally admitted that below 100 AMeV, heavy ion collisions
have essentially a binary character, it has been shown since several years that
the decay products could not be fully imputed to the decay of excited quasi-
projectile and quasi-target -,- . Besides preequilibrium and direct
emissions already observed at low energies, processes like neck emission and
aligned fission had to be taken into account in order to explain the experi-
mental data. Indeed an excess of particles and fragments, not explained by
the statistical deexcitation of fully equilibrated QP and QT, is observed at
intermediate velocity with unusual kinematical properties.
From recent experimental data on the Ar+Ni reactions between 52 and 95
A.MeV obtained at GANIL with the 4π multidetector INDRA it was shown
 that it was not possible to reproduce the light particle rapidity spectra by
assuming only statistical emissions from excited QP and QT and that there
was an excess of high energy particles at mid- rapidity which increases as the
impact parameter decreases. In the present paper, we will concentrate on the
Ar+Ni reaction at 95 AMeV and we will show how the properties of the QP
that one can extract from the data are strongly affected by particle emission
around mid-rapidity. First the impact parameter classification and the event
selection will be presented. Then, the QP properties, mass and excitation en-
ergy, will be established according to two basic assumptions. i) Neglecting
mid- rapidity emission, following previous analysis -, a two source re-
construction will be performed in the frame of a purely binary scenario. ii) In
an attempt to take into account mid-rapidity emission (MRE) as evidenced
in  we will unfold the experimental light charged particle rapidity spectra
assuming three sources of emission, the QP, the QT and a third source of emis-
sion to simulate the mid-rapidity contribution. Thermal and shape equilibrium
are assumed in each source. Then the properties of the QP are extracted from
its decay products. In both cases, the mass and the excitation energy of the
QP thus obtained will be presented as a function of an experimental impact
parameter. Finally, results of both reconstruction methods will be compared
The experiment was performed at the GANIL facility which provided an36Ar
beam of 3-4 x 107pps at 95 A.MeV. After collision with a 193 µg/cm2self-
supporting58Ni target, reaction products were detected with the 4π charged
particle detector INDRA  with a minimum bias trigger requiring a four
fold event. Charge identification is achieved up to the projectile charge in the
forward hemisphere. Hydrogen and helium isotopes are separated for detection
angles from 30to 1760(rings 2 to 17).
Using the prescription of ref. , an impact parameter scale (bexp) is deduced
from the total transverse energy distribution (Etot
shown by the full line in Fig. 1(a). For the forthcoming analysis, we will retain
only events for which, at least the remnant of the QP has been detected. This
is done using the correlation between the total detected charge (Ztot) and the
pseudo total parallel momentum (P//tot= ΣZi× V//i) presented in Fig. 1(b).
Only events for which P//tot≥ 70%Pprojare kept. This condition selects events
with Ztotaround and larger than the projectile charge and represents ≈ 60% of
the estimated  total reaction cross section, σth
one amounts to 80% of σth
in Fig. 1(a)) still cover the whole range of Etot
tr) for all detected events as
r, whereas the total detected
r. We remark that the selected events (dashed line
Proton and alpha particle reduced rapidity spectra (Y/Ypwhere Ypis the pro-
jectile rapidity) show two components centered respectively around the target
and the projectile velocities as shown in Fig. 2 for protons at bexp=6 fm. This
strongly suggests evaporation from excited QP and QT. Then, assuming a
binary scenario and neglecting any non equilibrated emissions ,, all
particles and fragments are attributed to the QP or the QT event-by-event.
The reconstruction is based on a simplified version of the thrust method .
Both procedures roughly allocate all particles and fragments with a parallel
velocity smaller than the center-of-mass velocity to the QT and the others to
the QP. Charges, masses and velocities of both sources are then calculated.
Neutrons added in order to obtain the total mass of the system are distributed
between the QP and the QT according to the N/Z ratio (=1.04) of the system.
From simulations , the neutron kinetic energies are evaluated as the mean
kinetic energy of the protons minus 2 MeV to take into account the absence of
Coulomb barrier. Calorimetry is then used to calculate the excitation energy
(E∗) of the QP. Event by event we have E∗= Σi(mic2+ Ei) − msc2, where
miis the mass of each particle/fragment, Eitheir kinetic energy in the QP
frame and msthe mass of the source. The mass of the QP thus reconstructed
(around 34) is almost independent of the impact parameter. In contrast, the
excitation energy per nucleon increases almost linearly with decreasing impact
parameter to reach 18 A.MeV for central collisions. This value is in agreement
with the one obtained in  for violent collisions. These results are shown by
the full circles in Fig. 4 and will be further discussed in connection with the
results of the second assumption.
It was shown in  that isotropic evaporation from excited QP and QT was
not sufficient to explain the measured light products (Z ≤ 6) rapidity spectra.
In particular, there is an excess of particles emitted around mid-rapidity which
cannot be explained by a simple overlap of the QP and QT emission spheres.
This mid-rapidity contribution increases with decreasing bexp. Furthermore,
the average transverse energy (< Etr>) of these particles (fig. 3(a) full cir-
cles) is much higher than expected from evaporation. The same behaviour is
observed for all products of Z ≤ 6, suggesting that the excess of particles at
intermediate velocity has peculiar kinematical properties. It has to be noted
that due to detection thresholds, the < Etr> values around the target rapidity
are artificially increased.
In order to take into account this intermediate velocity component, besides
the two evaporating sources, emission from a third source around mid-rapidity
was assumed. A fit procedure, widely used to modelize differential cross sec-
tions [27–29], is performed supposing three thermalized sources. The labora-
tory energy spectra are fitted with the sum of three Maxwellian distributions
assuming volume emission :
El exp[−(El+ Esi− 2
are respectively the energy, the angle and the mass of the emitted parti-
cle in the laboratory. The number of parameters (9) can be reduced with
the following assumptions : 1) the temperatures of the QP and of the QT
are the same , 2) assuming that non equilibrium particles are emitted
symmetrically around 900in the center of mass, from momentum conser-
vation, the QP and QT parallel velocities are linked through the relation
VQT= (Mproj/Mtarget)(Vproj− VQP).
source, Tibeing adjustable parameters and El, θland Mpart
Due to statistics, only energy spectra of light particles (p,d,t,3He,4He) are
fitted. For each particle type, the detection energy thresholds are adjusted in
order to have the same value for all rings (independently of the experimental
thresholds which may fluctuate slightly from one detector to the other). For a
given impact parameter bin and a given particle type, all energy spectra from
ring 2 to ring 17 are fitted simultaneously . As ring 1 (2-30) does not provide
isotopic separation, it is not included in the fit. Thus, a set of parameters
is obtained for each light particle type and each impact parameter bin. As
shown in Fig. 3(b), the overall quality of the fits is quite good. Distribution
irregularities are due to experimental biases. Solid angles are different from
one ring to the other. The average angle of a ring being used to calculate the
rapidity, the distributions are slightly distorted. For protons, at bexp=3 fm,
it is found that the mid-rapidity component contributes significantly to the
total proton rapidity distribution and covers the whole rapidity range. Direct
emissions evaluated with intranuclear cascade calculations give similar results
-. One notes also that the average transverse energies, < Etr > as a
function of Y/Ypare well reproduced (Fig. 3(a)).
The fit parameters for protons and alpha particles evolve rather smoothly with
bexpfrom central to peripheral collisions (see Table 1). The proton source re-
duced rapidities are rather constant from central to peripheral collisions for the
QP (0.91<YQP/Yp<0.93) and the mid-rapidity source (0.46<YMRE/Yp<0.49).
For other particles, both rapidities increase with impact parameter. The ap-
parent temperature of the QP increases significantly from peripheral to cen-
tral collisions (Table 1). At a given impact parameter, different particle types
yield different temperatures in contradiction with the equilibrium hypothesis.
In , similar deviations were observed and their possible origin discussed. It
has been shown  that introducing nucleon-alpha scattering could improve
significantly the fit for the alpha particle rapidity spectra. Thus, nucleon-
cluster collisions in the region of overlap between projectile and target may be
in part responsible for the discrepancies between the temperature parameters
and source rapidities obtained in our simple three source fits for different par-
ticle types. For all particles, the apparent temperatures of the mid-rapidity
source are large (Table 1) and increase strongly from peripheral to central col-
lisions where they reach ≃25-30 MeV. These variations with impact parameter
can be explained in part by the fact that the total transverse energy is used as
impact parameter selector. In effect, for instance, the temperature parameter
is linked to the mean transverse energy through the relation < Etr>= T for
volume emission, thus establishing a correlation between the impact parameter
selection and the temperature (see below).
The contribution of each source to the rapidity distribution depends upon the
impact parameter and the particle type. The multiplicities of particles emitted
by the QP and the QT follow the same evolution. The proton multiplicity for
the QP (Table 1) stays constant around 1.5 from peripheral to mid-central
collisions and then decreases to reach 0.5 in central collisions. For alpha par-
ticles, the multiplicity starts at a value of 0.5 in peripheral collisions to reach
a maximum around 1.2 in mid-central collisions and then decreases to reach a
value of 0.6 in central collisions. This behavior can be understood if the size of
the source decreases with decreasing impact parameter while the temperature
increases. For other particles the evolution is intermediate between that of
protons and alpha particles. By contrast the multiplicity of particles emitted
near mid-rapidity increases strongly as the impact parameter decreases what-
ever the particle type. This evolution suggests a geometrical effect as we will
In order to evaluate the robustness of these results, several tests have been
performed. Using different prescriptions to fit the data, constraining some of
the parameters, adding Coulomb barriers, assuming surface emission instead
of volume emission, lead essentially to the same evolution of the parameters
(velocities, temperatures and multiplicities) with impact parameter. Assuming
a surface emission for QP and QT, their source temperatures are found slightly
lower but the fits are in poorer agreement with the experimental data. Using
the heaviest fragment in the forward hemisphere, Zmax, as an indicator of
the impact parameter (the closer to the charge of the projectile the fragment
charge is, the larger is the impact parameter) avoids the correlation between
the temperature and the impact parameter . This procedure yields lower
QP and QT temperatures but does not affect the relative contributions of each
source. In , another global variable, related to the dissipated energy in the
forward hemisphere, was used to select events according to the violence of the
collision and emissions between 75oand 105oin the mid-rapidity frame were
studied. In this case, the temperature parameters of the mid-rapidity evolved
from 17 to 20 MeV for protons with the centrality of the collision. The event
selection and the angular cut explain the differences between these results and
those presented here. However, we remark that these values are located inside
our limits (see Table 1).
The next step is the reconstruction of the QP as a function of impact param-
eter. The mean multiplicity and energy of each particle emitted by the QP at
each impact parameter bin are used. Because the projectile has N=Z, neutrons
are added assuming that neutron multiplicity is equal to proton multiplicity
(< multn>=< multp>). The contribution of fragments at mid-rapidity be-
ing small, those are shared between the QP and the QT as in the two source
analysis previously described. For a given impact parameter, the mass of the
QP is calculated as,
< AQP>= Σi< multi> ×Ai+ Σf< multf> × < Af>
+ < multn> ×An
and its excitation energy is estimated through calorimetry,
QP>= Σi< multi> ×(mic2+3
2Ti)+Σf< multf> ×(< mf> c2+ < Ef>)
+ < multn> ×(mnc2+3
2Tp)− < mQPc2> (3)
where i, n, f are the index for light charge particles, neutrons and fragments
and QP refers to the emitting source. A’s are the atomic masses, m’s, the
masses, < Ef > are the fragment mean kinetic energies. Neutron tempera-
ture (Tn) is assumed to be equal to proton temperature (Tp). One can note
that fragments have an important contribution in (2) due to their masses and
a small one in (3) due to their low kinetic energies. All this reconstruction
assumes that particles originate from the same source even if the velocities
obtained with the fits are different. This difference being larger for small im-
pact parameter, values below 3 fm are less significant.
The QP masses and excitation energies thus obtained, are presented (stars)
in Fig. (4) as a function of the impact parameter, together with the results
(circles) of the previous two source analysis. Whereas a two source analy-
sis yielded QP masses independent of impact parameter, in contrast, for the
three source approach, one notes in fig. 4 (a) a linear increase with impact
parameter of the QP mass : from 10 for central collisions to 32 for periph-
eral ones. For peripheral collisions containing few mid-rapidity particles, both
scenarii lead to nearly identical results. The linear mass increase with impact
parameter suggests a geometrical dependence. In fig. 4(a) the curve represents
the QP mass predicted in a calculation  where the geometrical overlap of
projectile and target is considered as the intermediate source and the non
interacting volumes are taken as QP and QT. Although the general trend
with impact parameter is similar to the three source result, the predicted QP
mass decreases more rapidly with decreasing bexpthan obtained from the three
source analysis. This discrepancy at low impact parameter may be imputed,
in part, to the bexpdetermination. One can also argue that at 95 A.MeV the
participant-spectator regime is not fully reached.
Dynamical calculations for small systems ,- present a similar relation
between the QP mass and the impact parameter if particles emitted before the
re-separation time of QP and QT are not included in the QP reconstruction.
These calculations also show that these ”early” particles are distributed over
the whole range of parallel velocity as deduced from the three source fits. To
obtain a realistic estimation of the QP emissions, it is important to subtract
the mid-rapidity component over the whole rapidity range.
Excitation energies deduced from both analyses are compared in fig. 4 (b). The
Zmaxsorting (open symbols) has also been tested in order to roughly evaluate
the effect of the event sorting. The Zmax value is the one corresponding to
the more abundant QP residue in the considered bexpbins. As observed, the
obtained values are close to those of the three source fit method based on the
bexpsorting, indicating that the sorting has only small effect on the results. In
all cases the excitation energies increase with decreasing impact parameter.
However, except for the most peripheral collisions where mid-rapidity emission
is negligible, the three source fit method yields excitation energies about a
factor of two smaller than the two source analysis. As bexp decreases, the
mid-rapidity component carries an increasing amount of the deposited energy,
limiting the excitation energy imparted to the QP and the QT.
Preliminary analyzes between 32 and 95 A.MeV  show that beyond 52
A.MeV the yields of the different sources become independent of the bom-
barding energy. The mean transverse energy of the mid-rapidity component
increases linearly with bombarding energy while it is constant for the QP and
QT contributions. Above ∼ 50 A.MeV, most of the energy is deposited into
the overlap region between projectile and target and is evacuated by the mid-
Quasi-projectiles produced in the reaction36Ar +58Ni at 95 A.MeV have
been reconstructed from their decay products under two basic assumptions,
i) purely binary collisions, ii) additional emission from the overlapping zone
between projectile and target. The properties (mass and excitation energy) of
the QP thus reconstructed depend strongly upon these assumptions. Indeed,
for mid-central collisions, there is a factor of 1.71 between QP masses and
1.76 between excitation energies, the assumption ii) leading to the lowest
estimation. It has been shown that the properties of particles emitted at mid-
rapidity are incompatible with an evaporation process from fully equilibrated
quasi-projectiles and quasi-targets which made the assumption i) unrealistic.
Based upon results of ii), these particles cover the whole rapidity range and
mix in part with particles evaporated from the excited quasi-projectile and
quasi-target. The unfolding procedure presented in this work is an important
step in order to reconstruct sources with precision. The additional source in
assumption ii) includes many processes and it will be necessary to disentangle
them to go further in the interpretation.
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RapidityTemp.Mult RapidityTemp. Mult
b (fm)0-1 7-80-17-80-14-5 7-8 0-17-8 0-17-8 0-14-57-8
proton0.910.938.4 5.00.51.6 1.50.460.49 25.5 15.06.3 2.6 0.3
alpha 0.820.95 14.46.9 0.61.2 0.5 0.460.71 30.18.4 2.9 0.8 0.2
Fit parameters for protons and alpha particles in the quasi-projectile (QP) and the
mid-rapidity component (MRE).
0 100200 300400500600700800
E tr tot (MeV)
Yield (arb. units)
Pseudo P//tot (MeV/c)
Fig. 1. (a) Total transverse energy distributions for all (full line) and selected events
(dashed line). Estimated impact parameter values (in fm) corresponding to different
trintervals are indicated.(b) Total charge versus pseudo total parallel momentum.
Only events with a total momentum larger than 70 % of Pprojare selected (vertical
line). There is a factor two between contour levels.
dσ / d( Y/Yp ) (arb. units)
Fig. 2. Proton reduced rapidity distributions at b=6 fm. The hole at Y/Yp=0 is
due to the target shadow.
< Etr > (MeV)
dσ / d( Y/Yp ) (arb. units)
Fig. 3. Data and fit results for bexp=3 fm. (a) Average transverse energy < Etr>
of protons vs reduced rapidity. The experimental data (full circles) are compared
with the result of a three source fit (open circles). (b) Proton reduced rapidity
distribution. The experimental data are indicated by the dark histogram and fit
result by the grey line. The fit contributions of the QP, QT (grey lines) and the
MR (dashed line) are drawn. The arrow labelled Ynnindicates the nucleon-nucleon
reduced rapidity. For experimental and calculated spectra, an energy threshold of 2
MeV was imposed.
0 Download full-text
QP excitation energy (A.MeV)
Fig. 4. Average QP mass (a) and excitation energy (b) as a function of the experi-
mental impact parameter. The line in (a) is the result of a geometrical calculation
(see text). Open symbols show the effect of the different event sortings.