Abstract
Existing mean-field models, namely the Hartree-Fock (HF) and time-dependent Hartree-Fock (TDHF) approaches, can be used to determine the expectation values for one-body observables, such as fragment mass, in nuclear reactions and decays but are known to underestimate the fluctuations in these values. This is due to their assumption that each nucleon moves independently in a mean-field generated by the interactions between the nucleons neglecting important two-body correlations. Balian and Veneroni considered the variational determination of expectation values and fluctuations and obtained an improved formula for these fluctuations which can be implemented using existing TDHF codes. This approach has previously been implemented in a small number of test cases but symmetries and simplified interactions were used due to computational limitations. In this work we first review the Balian-Veneroni approach. We then present calculations of the mass distributions for the decay of giant resonances in32S, 40ca and 132Sn and in deep-inelastic and fusion-evaporation reactions for 160+160 and 40Ca+40Ca using a three-dimensional TDHF code with the full Skyrme interaction comparing with the previous calculations and/or experimental data as appropriate. We find that the Balian-Veneroni approach consistently produces fluctuations that exceed the TDHF values but that the numerical problems inherent in running prolonged TDHF calculations, particularly due to emitted nucleons being reflected back from the boundaries of our spatial box, cause significant numerical difficulties for longer nuclear' processes. We are consistently able to obtain converged results for giant resonance calculations but encounter difficulties for the deep-inelastic scattering reactions and are unable to obtain reliable results for the fusion- evaporation reactions. Our results differ from those obtained previously. We discuss the sources of these discrepancies.