Chapter 3
Statistical and Dynamical Bimodality
in Multifragmentation Reactions
S. Mallik, G. Chaudhuri, F. Gulminelli, and S. Das Gupta
Abstract The bimodal behavior of the order parameter is studied in the framework
of Boltzmann–Uehling–Uhlenbeck (BUU) transport model. In order to do that, simplified yet accurate method of BUU model is used which allow calculation of fluctuations in systems much larger than what was considered feasible in a well-known
and already existing model. It is observed that depending on the projectile energy
and centrality of the reaction, both entrance channel and exit channel effects can
be at the origin of the experimentally observed bimodal behavior. Both dynamical
and statistical bimodality mechanisms are associated with the theoretical model to
different time scales of the reaction, and to different energy regimes.
3.1 Introduction
The bimodal behavior of the order parameter is an important signature of first order
phase transition [1–3]. Phase transitions occur in very large systems, but in nuclear
physics, practical theoretical calculations (and heavy-ion reaction experiments) need
to be done with finite systems.
The largest cluster is an important order parameter for studying nuclear liquid–gas
phase transition in intermediate energy heavy-ion reactions. For an infinite system,
the normalized order parameter is 1 in the liquid phase and it suddenly drops to 0
when the system crosses the transition temperature. From, statistical point of view,
bimodality is a result of the singularity (infinite system) being replaced by the smearing (finite system). At low temperature, the largest cluster probability peaks at the
liquid side, whereas at high temperature, it is limited to the gas side only. But in
a small range of intermediate temperature, one can expect a double-humped distriS. Mallik (B) · G. Chaudhuri
Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India
e-mail: swagato@vecc.gov.in
F. Gulminelli
LPC, CNRS/EnsiCaen et Universite, Caen IN2P3, France
S. Das Gupta
Physics Department, McGill University, Montréal H3A 2T8, Canada
© Springer Nature Singapore Pte Ltd. 2021
R. K. Puri et al. (eds.), Advances in Nuclear Physics, Springer Proceedings
in Physics 257, https://doi.org/10.1007/978-981-15-9062-7_3
27
Statistical and Dynamical Bimodality
in Multifragmentation Reactions
S. Mallik, G. Chaudhuri, F. Gulminelli, and S. Das Gupta
Abstract The bimodal behavior of the order parameter is studied in the framework
of Boltzmann–Uehling–Uhlenbeck (BUU) transport model. In order to do that, simplified yet accurate method of BUU model is used which allow calculation of fluctuations in systems much larger than what was considered feasible in a well-known
and already existing model. It is observed that depending on the projectile energy
and centrality of the reaction, both entrance channel and exit channel effects can
be at the origin of the experimentally observed bimodal behavior. Both dynamical
and statistical bimodality mechanisms are associated with the theoretical model to
different time scales of the reaction, and to different energy regimes.
3.1 Introduction
The bimodal behavior of the order parameter is an important signature of first order
phase transition [1–3]. Phase transitions occur in very large systems, but in nuclear
physics, practical theoretical calculations (and heavy-ion reaction experiments) need
to be done with finite systems.
The largest cluster is an important order parameter for studying nuclear liquid–gas
phase transition in intermediate energy heavy-ion reactions. For an infinite system,
the normalized order parameter is 1 in the liquid phase and it suddenly drops to 0
when the system crosses the transition temperature. From, statistical point of view,
bimodality is a result of the singularity (infinite system) being replaced by the smearing (finite system). At low temperature, the largest cluster probability peaks at the
liquid side, whereas at high temperature, it is limited to the gas side only. But in
a small range of intermediate temperature, one can expect a double-humped distriS. Mallik (B) · G. Chaudhuri
Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India
e-mail: swagato@vecc.gov.in
F. Gulminelli
LPC, CNRS/EnsiCaen et Universite, Caen IN2P3, France
S. Das Gupta
Physics Department, McGill University, Montréal H3A 2T8, Canada
© Springer Nature Singapore Pte Ltd. 2021
R. K. Puri et al. (eds.), Advances in Nuclear Physics, Springer Proceedings
in Physics 257, https://doi.org/10.1007/978-981-15-9062-7_3
27