12
G. Chaudhuri et al.
solved in the canonical ensemble where the number of particles in the nuclear system
is finite (as it would be in experiments). The study is done for different nuclear
sizes, freeze-out volumes, and temperatures. Since Coulomb interaction is long range
and suppresses the signatures of phase transition, hence, we have switched off the
Coulomb force in some part of our study in order to have a better idea of the signatures.
In such cases, we have considered symmetric nuclear matter and no distinction is
made between neutron and proton. In addition to CTM, we have also used the lattice
gas model [22] recently developed in our group in order to study the multiplicity
derivative signal. This model uses geometry similar to the percolation model but is
much more elaborate with the insertion of a Hamiltonian. Both the thermodynamic
and the lattice gas models confirmed the multiplicity derivative as the signature of
first-order phase transition in nuclear multifragmentation.
We have given a brief description of the models used in our calculation in the next
section. After that, the results displaying the new signatures are proposed in detail.
The last section gives the summary of our work.
2.2 Brief Description of Models
2.2.1 The Canonical Thermodynamical Model
In this section, we describe briefly the canonical thermodynamical model which
is briefly designated as CTM. We assume that a system with A 0 nucleons and Z 0
protons at temperature T has expanded to a higher than normal volume and the
partitioning into different composites can be calculated according to the rules of
equilibrium statistical mechanics. In a canonical model, the partitioning is done
such that all partitions have the correct A 0 , Z 0 (equivalently N 0 , Z 0 ). Details of the
implementation of the canonical model can be found elsewhere [21]; here, we give
the essentials necessary to follow the present work.
The canonical partition function is given by
Q N 0 ,Z 0 =
ω
n I,J
I,J
n I,J !
.
(2.1)
Here, the sum is over all possible channels of breakup (the number of such channels
is enormous) which satisfy N 0 =
I × n I,J and Z 0 =
J × n I,J ; ω I,J is the
partition function of one composite with neutron number I and proton number J ,
respectively, and n I,J is the number of this composite in the given channel. The
one-body partition function ω I,J is a product of two parts: one arising from the
translational motion of the composite and another from the intrinsic partition function
of the composite:
G. Chaudhuri et al.
solved in the canonical ensemble where the number of particles in the nuclear system
is finite (as it would be in experiments). The study is done for different nuclear
sizes, freeze-out volumes, and temperatures. Since Coulomb interaction is long range
and suppresses the signatures of phase transition, hence, we have switched off the
Coulomb force in some part of our study in order to have a better idea of the signatures.
In such cases, we have considered symmetric nuclear matter and no distinction is
made between neutron and proton. In addition to CTM, we have also used the lattice
gas model [22] recently developed in our group in order to study the multiplicity
derivative signal. This model uses geometry similar to the percolation model but is
much more elaborate with the insertion of a Hamiltonian. Both the thermodynamic
and the lattice gas models confirmed the multiplicity derivative as the signature of
first-order phase transition in nuclear multifragmentation.
We have given a brief description of the models used in our calculation in the next
section. After that, the results displaying the new signatures are proposed in detail.
The last section gives the summary of our work.
2.2 Brief Description of Models
2.2.1 The Canonical Thermodynamical Model
In this section, we describe briefly the canonical thermodynamical model which
is briefly designated as CTM. We assume that a system with A 0 nucleons and Z 0
protons at temperature T has expanded to a higher than normal volume and the
partitioning into different composites can be calculated according to the rules of
equilibrium statistical mechanics. In a canonical model, the partitioning is done
such that all partitions have the correct A 0 , Z 0 (equivalently N 0 , Z 0 ). Details of the
implementation of the canonical model can be found elsewhere [21]; here, we give
the essentials necessary to follow the present work.
The canonical partition function is given by
Q N 0 ,Z 0 =
ω
n I,J
I,J
n I,J !
.
(2.1)
Here, the sum is over all possible channels of breakup (the number of such channels
is enormous) which satisfy N 0 =
I × n I,J and Z 0 =
J × n I,J ; ω I,J is the
partition function of one composite with neutron number I and proton number J ,
respectively, and n I,J is the number of this composite in the given channel. The
one-body partition function ω I,J is a product of two parts: one arising from the
translational motion of the composite and another from the intrinsic partition function
of the composite: