Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of motion, which is
appropriate for highly dissipative evolutions, we discuss the physical justification for that treatment and investigate the sensitivity of the resulting mass yields to a variety of model ingredients, including in particular the dimensionality and discretization of the shape space and the structure of the dissipation tensor. The mass yields are found to be relatively robust, suggesting that the simple random walk presents a useful calculational tool. Quantitatively refined results can be obtained by including physically plausible forms of the dissipation, which amounts to simulating the Brownian shape motion in an anisotropic medium.
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for the fissio
n fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.
The spinodal amplification of density fluctuations is treated perturbatively within dissipative fluid dynamics for the purpose of elucidating the prospects for this mechanism to cause a phase separation to occur during a relativistic nuclear collisio
n. The present study includes not only viscosity but also heat conduction (whose effect on the growth rates is of comparable magnitude but opposite), as well as a gradient term in the local pressure, and the corresponding dispersion relation for collective modes in bulk matter is derived from relativistic fluid dynamics. A suitable two-phase equation of state is obtained by interpolation between a hadronic gas and a quark-gluon plasma, while the transport coefficients are approximated by simple parametrizations that are suitable at any degree of net baryon density. We calculate the degree of spinodal amplification occurring along specific dynamical phase trajectories characteristic of nuclear collision at various energies. The results bring out the important fact that the prospects for spinodal phase separation to occur can be greatly enhanced by careful tuning of the collision energy to ensure that the thermodynamic conditions associated with the maximum compression lie inside the region of spinodal instability.
Employing a recently developed Monte Carlo model, we study the fission of 240Pu induced by neutrons with energies from thermal to just below the threshold for second chance fission. Current measurements of the mean number of prompt neutrons emitted i
n fission, together with less accurate measurements of the neutron energy spectra, place remarkably fine constraints on predictions of microscopic calculations. In particular, the total excitation energy of the nascent fragments must be specified to within 1 MeV to avoid disagreement with measurements of the mean neutron multiplicity. The combination of the Monte Carlo fission model with a statistical likelihood analysis also presents a powerful tool for the evaluation of fission neutron data. Of particular importance is the fission spectrum, which plays a key role in determining reactor criticality. We show that our approach can be used to develop an estimate of the fission spectrum with uncertainties several times smaller than current experimental uncertainties for outgoing neutron energies up to 2 MeV.
The increased interest in more exclusive fission observables has demanded more detailed models. We present here a new computational model, FREYA, that aims to meet this need by producing large samples of complete fission events from which any observa
ble of interest can then be extracted consistently, including arbitrary correlations. The various model assumptions are described and the potential utility of the model is illustrated by means of several novel correlation observables.
We construct a simple two-phase equation of state intended to resemble that of compressed baryon-rich matter and then introduce a gradient term in the compressional energy density to take account of fintie-range effects in non-uniform configurations.
With this model we study the interface between the two coexisting phases and obtain estimates for the associated interface tension. Subsequently, we incorporate the finite-range equation of state into ideal or viscous fluid dynamics and derive the collective dispersion relation for the mechanically unstable modes of bulk matter in the spinodal region of the thermodynamic phase diagram. Combining these results with time scales extracted from existing dynamical transport simulations, we discuss the prospects for spinodal phase separation to occur in nuclear collisions. We argue that these can be optimized by a careful tuning of the collision energy to maximize the time spent by the bulk of the system inside the mechanically unstable spinodal region of the phase diagram. Our specific numerical estimates suggest cautious optimism that this phenomenon may in fact occur, though a full dynamical simulation is needed for a detailed assessment.
