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Microscopic description of neutron emission rates in compound nuclei

The neutron emission rates in thermal excited nuclei are conventionally described by statistical models with a phenomenological level density parameter that depends on excitation energies, deformations and mass regions. In the microscopic view of hot nuclei, the neutron emission rates can be determined by the external neutron gas densities without any free parameters. Therefore the microscopic description of thermal neutron emissions is desirable that can impact several understandings such as survival probabilities of superheavy compound nuclei and neutron emissivity in reactors. To describe the neutron emission rates microscopically, the external thermal neutron gases are self-consistently obtained based on the Finite-Temperature Hartree-Fock-Bogoliubov (FT-HFB) approach. The results are compared with the statistical model to explore the connections between the FT-HFB approach and the statistical model. The Skyrme FT-HFB equation is solved by HFB-AX in deformed coordinate spaces. Based on the FT-HFB approach, the thermal properties and external neutron gas are properly described with the self-consistent gas substraction procedure. Then neutron emission rates can be obtained based on the densities of external neutron gases. The thermal statistical properties of $^{238}$U and $^{258}$U are studied in detail in terms of excitation energies. The thermal neutron emission rates in $^{238, 258}$U and superheavy compound nuclei $_{112}^{278}$Cn and $_{114}^{292}$Fl are calculated, which agree well with the statistical model by adopting an excitation-energy-dependent level density parameter. The coordinate-space FT-HFB approach can provide reliable microscopic descriptions of neutron emission rates in hot nuclei, as well as microscopic constraints on the excitation energy dependence of level density parameters for statistical models.