10
G. Chaudhuri et al.
2.1 Introduction
The phenomenon of liquid–gas phase transition occurring in heavy ion collisions
at intermediate energies is a subject of contemporary interest [1–8]. The nature of
nucleon–nucleon strong interaction potential, which is an attractive one with a repulsive core is very similar to the van der Waals potential [4] except for the magnitude.
This type of interaction explains the phenomenon of phase transition in ordinary
liquid and hence similar observation is very much expected in nuclear systems also.
In ordinary liquids, when it is heated, the temperature rises till the boiling point is
reached after which it remains constant until the whole amount of liquid is converted
to gas. Similarly in order to observe phase transition in the nuclear system, one has to
pump energy to the system and the only possible way is by means of nucleus-nucleus
collision. In very high energy heavy-ion collision at high density and temperature,
hadronic matter transforms to the Quark–Gluon Plasma (QGP) phase. At the intermediate energy regime, nuclear multifragmentation is the dominant mechanism which
can be related to a liquid gas kind of transition at sub-saturation nuclear density.
Theoretical models of multifragmentation predict the existence of phase transition
in infinite nuclear matter. Experimental signatures also indicate the change of state
and this can be interpreted as finite-size counterpart of the first-order phase transition in nuclear matter. Different signatures of this transition have been studied
extensively both theoretically as well as experimentally [4, 5, 7–9]. The variation of
excitation energy and specific heat with temperature are two well-studied signatures
theoretically in order to detect the first-order phase transition [10–12].
Phase transition is usually characterized by the specific behavior of state variables
like pressure, density, energy, entropy, etc. [13, 14]. The order of phase transition,
according to Ehrenfest is determined by the lowest order derivative of free energy
that shows a discontinuity. In heavy-ion collisions, there is no direct way of accessing
these state variables and hence unambiguous detection of phase transition becomes
difficult. The present work is motivated by this limitation and aims at looking for signatures of phase transition that can be extracted from the observables which are easily
accessible in experiments. Ideally, phase transition exists in the thermodynamic limit
and for a first-order one, entropy should have a finite discontinuity and specific heat
a divergence at the phase transition temperature. In finite nuclei, the discontinuity or
divergence is replaced by sudden jump or maxima. The variation of total multiplicity
or size of the largest cluster (Z max ) with temperature is very much similar to that of
entropy or excitation energy (caloric curve) with temperature and this can be seen
from Fig. 2.1. Hence, the first-order derivative of these observables with temperature
is expected to behave in a similar way as those of entropy or energy. This observation
led to the investigation of the nature of the derivatives of these multifragmentation
observables which can be easily measured in experiments. Encouraging results have
been obtained from this study and it has been observed that first-order derivative of
the order parameters related to the total multiplicity, largest cluster size (produced
in heavy-ion collisions) exhibit similar behavior as that of the variation of specific
heat at constant volume C v which is an established signature of first-order phase
G. Chaudhuri et al.
2.1 Introduction
The phenomenon of liquid–gas phase transition occurring in heavy ion collisions
at intermediate energies is a subject of contemporary interest [1–8]. The nature of
nucleon–nucleon strong interaction potential, which is an attractive one with a repulsive core is very similar to the van der Waals potential [4] except for the magnitude.
This type of interaction explains the phenomenon of phase transition in ordinary
liquid and hence similar observation is very much expected in nuclear systems also.
In ordinary liquids, when it is heated, the temperature rises till the boiling point is
reached after which it remains constant until the whole amount of liquid is converted
to gas. Similarly in order to observe phase transition in the nuclear system, one has to
pump energy to the system and the only possible way is by means of nucleus-nucleus
collision. In very high energy heavy-ion collision at high density and temperature,
hadronic matter transforms to the Quark–Gluon Plasma (QGP) phase. At the intermediate energy regime, nuclear multifragmentation is the dominant mechanism which
can be related to a liquid gas kind of transition at sub-saturation nuclear density.
Theoretical models of multifragmentation predict the existence of phase transition
in infinite nuclear matter. Experimental signatures also indicate the change of state
and this can be interpreted as finite-size counterpart of the first-order phase transition in nuclear matter. Different signatures of this transition have been studied
extensively both theoretically as well as experimentally [4, 5, 7–9]. The variation of
excitation energy and specific heat with temperature are two well-studied signatures
theoretically in order to detect the first-order phase transition [10–12].
Phase transition is usually characterized by the specific behavior of state variables
like pressure, density, energy, entropy, etc. [13, 14]. The order of phase transition,
according to Ehrenfest is determined by the lowest order derivative of free energy
that shows a discontinuity. In heavy-ion collisions, there is no direct way of accessing
these state variables and hence unambiguous detection of phase transition becomes
difficult. The present work is motivated by this limitation and aims at looking for signatures of phase transition that can be extracted from the observables which are easily
accessible in experiments. Ideally, phase transition exists in the thermodynamic limit
and for a first-order one, entropy should have a finite discontinuity and specific heat
a divergence at the phase transition temperature. In finite nuclei, the discontinuity or
divergence is replaced by sudden jump or maxima. The variation of total multiplicity
or size of the largest cluster (Z max ) with temperature is very much similar to that of
entropy or excitation energy (caloric curve) with temperature and this can be seen
from Fig. 2.1. Hence, the first-order derivative of these observables with temperature
is expected to behave in a similar way as those of entropy or energy. This observation
led to the investigation of the nature of the derivatives of these multifragmentation
observables which can be easily measured in experiments. Encouraging results have
been obtained from this study and it has been observed that first-order derivative of
the order parameters related to the total multiplicity, largest cluster size (produced
in heavy-ion collisions) exhibit similar behavior as that of the variation of specific
heat at constant volume C v which is an established signature of first-order phase