arXiv subjects
Publications and source records attributed to C. B. Das.
Isotopic spin dependent lattice gas model is used to examine if it produces the isoscaling behaviour seen in intermediate energy heavy ion collisions. Qualitative features are reproduced but quantitative agreement with experiments is lacking.
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and number of particles in the system are kept fixed), canonical ensemble (temperature and number of particles are kept fixed) or grand canonical ensemble (fixed temperature and a variable number of particles but with an assigned average). This paper deals with calculations with canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in intermediate energy heavy ion collision, to study the caloric curves for nuclei and to explore the possibility of negative specific heat because of the finiteness of nuclear systems. The model can also be used for detailed calculations of other observables not connected with phase transitions, such as populations of selected isotopes in a heavy ion collision. The model also serves a pedagogical purpose. For the problems at hand, both the canonical and grand canonical solutions are obtainable with arbitrary accuracy hence we can compare the values of observables obtained from the canonical calculations with those from the grand canonical. Sometimes, very interesting discrepancies are found. To illustrate the predictive power of the model, calculated observables are com$data from the central collisions of Sn isotopes.
The Lattice Gas Model was extended to incorporate the effect of radial flow. Contrary to popular belief, radial flow has little effect on the clusterization process in intermediate energy heavy-ion collisions except adding an ordered motion to the particles in the fragmentation source. We compared the results from the lattice gas model with and without radial flow to experimental data. We found that charge yields from central collisions are not significantly affected by inclusion of any reasonable radial flow.
The grand canonical ensemble has been used to make predictions for composite yields using simple models for nuclear fragmentation. While this gives correct model prediction for high energy collisions, it can give very inaccurate results at intermediate energy.
A thermodynamic model for multifragmentation which is frequently used appears to give very different values for specific heat at constant volume depending upon whether canonical or grand canonical ensemble is used. The cause for this discrepancy is analysed.
We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. In this model $c_v$ is always positive but for finite nuclei $c_p$ can be negative for some temperatures and pressures. Furthermore, negative values of $c_p$ can be obtained in canonical treatment. One does not need to use the microcanonical ensemble. Negative values for $c_p$ can persist for systems as large as 200 paticles but this depends upon parameters used in the model calculation. As expected, negative specific heats are absent in the thermodynamic limit.
We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. We draw a p-V diagram for the model and compare with a p-V diagram obtained from a mean-field theory. We investigate the question of chemical instability in the multifragmentation model. Phase transitions in the model are discussed.
For transport model simulations of collisions between two nuclei which have $N/Z$ significantly different from unity one needs a one-body potential which is both isospin and momentum dependent. This work provides sets of such potentials.
In efforts to determine phase transitions in the disintegration of highly excited heavy nuclei, a popular practice is to parametrise the yields of isotopes as a function of temperature in the form $Y(z)=z^{-τ}f(z^σ(T-T_0))$, where $Y(z)$'s are the measured yields and $τ, σ$ and $T_0$ are fitted to the yields. Here $T_0$ would be interpreted as the phase transition temperature. For finite systems such as those obtained in nuclear collisions, this parametrisation is only approximate and hence allows for extraction of $T_0$ in more than one way. In this work we look in detail at how values of $T_0$ differ, depending on methods of extraction. It should be mentioned that for finite systems, this approximate parametrisation works not only at the critical point, but also for first order phase transitions (at least in some models). Thus the approximate fit is no guarantee that one is seeing a critical phenomenon. A different but more conventional search for the nuclear phase transition would look for a maximum in the specific heat as a function of temperature $T_2$. In this case $T_2$ is interpreted as the phase transition temperature. Ideally $T_0$ and $T_2$ would coincide. We invesigate this possibility, both in theory and from the ISiS data, performing both canonical ($T$) and microcanonical ($e=E^*/A$) calculations. Although more than one value of $T_0$ can be extracted from the approximate parmetrisation, the work here points to the best value from among the choices. Several interesting results, seen in theoretical calculations, are borne out in experiment.
We consider a model where, for a finite disintegrating system, yields of composites can be calculated to arbitrary accuracy. An analytic answer for yields is also known in the thermodynamic limit. In the range of temperature and density considered in this work, the model has a phase transition. This phase transition is first order. The analytic expression for yields of composites, in the thermodynamic limit, does not conform to the expression $ =a^{-τ}f(a^σ (T-T_c))$ where, the usual identification would be that $T_c$ is the critical temperature and $τ,σ$ are critical exponents. Nonetheless, for finite systems, we try to fit the yields with the above expression. A minimisation procedure is adopted to get the parameters $T_c,τ$ and $σ$. While deviations from the formula are not negligible, one might believe that the deviations are consistent with the corrections attributable to finite particle number effects and might then conclude that one has deduced at least approximately the values of critical parameters. This exercise thus points to difficulties of trying to extract critical parameters from data on nuclear disintegration. An interesting result is that the value of $T_c$ deduced from the ``best'' fit is very close to the temperature at which the first order phase transition occurs in the model. The yields calculated in this model can also be fitted quite well by a parametrisation derived from a droplet model.
We consider extensions of the lattice gas model to incorporate radial flow. Experimental data are used to set the magnitude of radial flow. This flow is then included in the Lattice Gas Model in a microcanonical formalism. For magnitudes of flow seen in experiments, the main effect of the flow on observables is a shift along the $E^*/A$ axis.
Calculations for a set of nuclear multifragmentation data are made using a Canonical and a Grand Canonical Model. The physics assumptions are identical but the Canonical Model has an exact number of particles, whereas, the Grand Canonical Model has a varying number of particles, hence, is less exact. Interesting differences are found.
Different statistical multifragmentation models have been used to study isoscaling, i.e. the factorization of the isotope ratios from two reactions, into fugacity terms of proton and neutron number, R21(N,Z)=Y2(N,Z)/Y1(N,Z)=C*exp(a*N+b*Z). Even though the primary isotope distributions are quite different from the final distributions due to evaporation from the excited fragments, the values of a and b are not much affected by sequential decays. a is shown to be mainly sensitive to the proton and neutron composition of the emitting source and may be used to study isospin-dependent properties in nuclear collisions such as the symmetry energy in the equation of state of asymmetric nuclear matter.
For pedagogical reasons we compute the caloric curve for 11 particles in a $3^3$ lattice. Monte-Carlo simulation can be avoided and exact results are obtained. There is no back-bending in the caloric curve and negative specific heat does not appear. We point out that the introduction of kinetic energy in the nuclear Lattice Gas Model modifies the results of the standard Lattice Gas Model in a profound way.
Microcanonical calculations are no more difficult to implement than canonical calculations in the Lattice Gas Model. We report calculations for a few observables where we compare microcanonical model results with canonical model results.
Realistic caloric curves are obtained for $^{197}Au + ^{197}Au$ reaction with incident energy ranging from 35 to 130 MeV/nucleon in the dynamic statistical multifragmentation model. It is shown that for excitation energy 3 to 8 MeV/nucleon, the temperature remains constant in the range 5 to 6 MeV, which is close to experiment. The mechanism of energy deposition through the tripartition of colliding system envisaged in this model together with inter-fragment nuclear interaction are found to play important role. A possible signature of liquid-gas phase transition is seen in the specific heat distribution calculated from these caloric curves, and the critical temperature is found to be $\sim$ 6 to 6.5 MeV.