A list of lectures by Abdou CHBIHI
Nuclear Reactions in the Fermi Energy Domain – Experiments with Large Arrays
Conception of 4 detectors : example of INDRA detector
and future detectors
Introduction
The construction of any detector has, first to be motivated by the physics case, second
to identify the relevant quantities to be measured, third to choose the adequate detectors and
finally to build it. The example that I will give is the conception of the INDRA detector.
Some physics case which motivated the construction of INDRA (some of them will be
developed in these series of lectures) are briefly :
 Formation and decay of hot nuclei, multifragmentation process (central
collisions)
o Temperature limit ?
o If the nuclei reach this temperature it drives the system into the
multifragmentation ?
o Thermal or dynamical origin of multifragmentation
 Projectile fragmentation (peripheral to semi-peripheral collisions)
o Few nucleons transfer, followed by sequential decay of the quasi –
projectile
o Massive transfer
o Inelastic excitation of the projectile/ target involving a collective
excitation modes (GDR)
 Determination of the freeze-out volume by means of the correlation function
techniques (interferometry), either particle-particle or fragment-fragment
correlations.
 Unexpected physics case : resonance spectroscopy in order to study exotic
nuclei.
Heavy ion collisions at intermediate energies (energies > Cb) can produce very
dissipative reactions where the structure of the participants is modified. Within these reactions
it is possible to study the nuclear matter under extreme condition of temperature and density
(and asymmetry) far from stability (different from the ground-state).
Several transport and statistical (or hybrid) model calculations in the way to explain
the reaction mechanism of such collisions predict the production of large variety of particles.
During the collision different particles can be emitted, neutral particles: gamma, neutron, light
charged particles (LCP): proton, deuteron, triton, 3He, alpha, 6He as well as copious number
of intermediate mass fragments with charge Z>2 (IMF).
1) Gross NPA553 (1993) 175c.
Figure 1: Statistical multi-fragmentation calculations MMMC: fraction of events
corresponding to different decay channels of 197Au as a function of excitation energy.
Experimentally, to study this type of reaction, it is necessary to detect the whole
reaction products (LP and IMF) in order to reconstruct the event hoping to assess the initial
state of the reaction. If one wants to achieve this reconstruction with a good accuracy, one
have to use an experimental device able to detect, identify, measure the kinetic energy and the
position of all products. The use of an experimental device with a large angular coverage (4
sr), high granularity and low threshold is therefore essential.
General characteristics
Granularity and spatial coverage
At least three points have to be considered:

The number of particles to detect for a given event and their spatial repartition

The multiplicity resolution needed

The fraction of multi-hit allowed.
To detect a maximum of particles produced in the collision, the detector must
be divided onto a number of cells. Thus defines the granularity of the detector. The number
of cells must be much higher than the number of particles produced in the event in order to
avoid multi-hits.
To estimate an optimal granularity probability calculations are needed. We first
consider a reaction where an isotropic emission of particles is assumed, the energy threshold
is 0, the effect of diffusion of particle from a cell to cell is negligible, the counting rate is
M is the number of particles
emitted during the reaction, the probability to have p detectors fired among N detectors is
given by:
p
N  N M 
 p
PNM, p      k (1  N ) M k (1) p  x  x k
 p k  p  k 
 x
x 0


Three recurrence relations are needed in order to resolve the above equation:
PNM, p  1  ( N  p) PNM, p1  ( N  p  1)PNM, p11 for p  M
PNM, p  
PNM, p 
N 1 p M
N
PN , p 1  PNM1, p 1
p
p
p 1 M
N 1 p M
PN 1, p1 
PN 1, p
N 1
N 1
Particular cases: i) probability to have M detectors fired among N detectors for an
event with multiplicity M:
PNM,M 
N!
M
( N  M )!
ii) probability to not detect any particle in N detectors for an event with multiplicity M
PNM, 0  (1  N ) M
For more details about this formalism see :
2) G.B. Hagemann et al., Nucl.Phys. A245 (1975) 166,
3) S.Y. Van der Werf NIM A153 (1978) 221
4) L. Westerberg et al. NIM A145 (1977) 295
5) Tutorial : program mult prepared by Gopal.
Figure 2 shows the average number of fired detectors as a function of multiplicity for a
variable number of cells. Whatever the number of cells involved, Nt cannot exceed the
product .M . Thus shows the importance of space coverage.
Figure 2 : Average number of fired detectors as function of multiplicity for
different granularities (number of cells). In this calculation 


Figure 3 : Probability of multi –hit in the same cell as function of ratio of
available number of detection cells to the event multiplicity. In this calculation 
The probability of detecting all particles increases with the number of available
detection cells. However this probability is limited by the total efficiency, Nt cannot exceed
 M The increase of number of cells increases also the dead zone of cells making the
efficiency decreasing. Therefore a compromise between the angular coverage and granularity
of the detector has to be found. For the INDRA detector the probability of multi-hit is limited
at 5% which corresponds to Nd/M = 8.
For the intermediate energy regime the maximum average multiplicity is around 40
LCP and 10 IMF, on the other hand if one limits the probability of multi-hit at 5% one may
need 320 cells for LCP and 80 cells for IMF.