2 New Signatures of Phase Transition from Models of Nuclear Multifragmentation
23
Fig. 2.12 Dependence of the
peak position of -da max /dT ,
-da 2 /dT , dM/dT, and C v on
fragmenting system size (a)
and freeze-out volume (b)
maxima in da max /dT , da 2 /dT , dM/dT, and C V . The transition temperatures obtained
from all the four observables give consistent results. Small differences between them
can be attributed to the finiteness of the fragmenting system.
2.4 Summary
This work introduces some new signatures of nuclear liquid–gas phase transition
which can be measured easily and more accurately in experiments. The observables
chosen were the total multiplicity, average largest cluster size a max , and a normalized
variable a 2 which assume distinctly different values in liquid and the gas phases thus
serving as order parameters of the transition. The variation of these observables
with temperature is very much similar to that of entropy or excitation energy and
hence the temperature derivatives behave as specific heat at constant volume (C v )
which is an established signature of phase transition. Transition temperature can be
identified from the position of the maxima of these derivatives analogous to that
of C v . Multiplicity derivative (d M/dT ) serves as a robust signal with very good
performance even in the presence of Coulomb interaction which is long range and
thereby suppresses signatures of phase transition. This signature not only persists
but gets enhanced after secondary decay of the primary hot fragments and thus can
be easily detected in experiments which measure total multiplicity. This signal was
proposed using the canonical thermodynamical model and was later confirmed by us
using the lattice gas model. This was very recently verified in other theoretical models
as well as in experiment. The other two observables concerning the derivatives of the
largest and second largest clusters also peak at the same temperature as that of C v and
can be considered as signals of first-order phase transition in one component system
switching off the Coulomb interaction. It is sometimes easier to measure the size
of the largest cluster than to count the total multiplicity covering all the fragments
produced in the experiment. The effect of source size and freeze-out volume on the
transition temperature is also studied using the one-component model. The extension
of this study for real nuclei will be a part of our future work.
23
Fig. 2.12 Dependence of the
peak position of -da max /dT ,
-da 2 /dT , dM/dT, and C v on
fragmenting system size (a)
and freeze-out volume (b)
maxima in da max /dT , da 2 /dT , dM/dT, and C V . The transition temperatures obtained
from all the four observables give consistent results. Small differences between them
can be attributed to the finiteness of the fragmenting system.
2.4 Summary
This work introduces some new signatures of nuclear liquid–gas phase transition
which can be measured easily and more accurately in experiments. The observables
chosen were the total multiplicity, average largest cluster size a max , and a normalized
variable a 2 which assume distinctly different values in liquid and the gas phases thus
serving as order parameters of the transition. The variation of these observables
with temperature is very much similar to that of entropy or excitation energy and
hence the temperature derivatives behave as specific heat at constant volume (C v )
which is an established signature of phase transition. Transition temperature can be
identified from the position of the maxima of these derivatives analogous to that
of C v . Multiplicity derivative (d M/dT ) serves as a robust signal with very good
performance even in the presence of Coulomb interaction which is long range and
thereby suppresses signatures of phase transition. This signature not only persists
but gets enhanced after secondary decay of the primary hot fragments and thus can
be easily detected in experiments which measure total multiplicity. This signal was
proposed using the canonical thermodynamical model and was later confirmed by us
using the lattice gas model. This was very recently verified in other theoretical models
as well as in experiment. The other two observables concerning the derivatives of the
largest and second largest clusters also peak at the same temperature as that of C v and
can be considered as signals of first-order phase transition in one component system
switching off the Coulomb interaction. It is sometimes easier to measure the size
of the largest cluster than to count the total multiplicity covering all the fragments
produced in the experiment. The effect of source size and freeze-out volume on the
transition temperature is also studied using the one-component model. The extension
of this study for real nuclei will be a part of our future work.