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Register a new userTransfer probabilities for the reactions $^{14,20}$O+$^{20}$O in terms of multiple time-dependent Hartree-Fock-Bogoliubov trajectories
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The transfer reaction between two nuclei in the superfluid phase is studied with the Time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In order to restore the symmetry of the relative gauge angle a set of independent TDHFB evolutions is done. Then the transfer probability is computed using a triple projection method. This method is first tested to determine the transfer probabilities on a toy model and compared to the exact solution. It is then applied to the reactions $^{20}$O+$^{20}$O and $^{14}$O+$^{20}$O in a realistic framework with a Gogny interaction.
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Background: The Density-constraint Time-dependent Hartree-Fock method is currently the tool of choice to predict fusion cross-sections. However, it does not include pairing correlations, which have been found recently to play an important role. Purpose: To describe the fusion cross-section with a method that includes the superfluidity and to understand the impact of pairing on both the fusion barrier and cross-section. Method: The density-constraint method is tested first on the following reactions without pairing, $^{16}$O+$^{16}$O and $^{40}$Ca+$^{40}$Ca. A new method is developed, the Density-constraint Time-dependent Hartree-Fock-Bogoliubov method. Using the Gogny-TDHFB code, it is applied to the reactions $^{20}$O+$^{20}$O and $^{44}$Ca+$^{44}$Ca. Results: The Gogny approach for systems without pairing reproduces the experimental data well. The DC-TDHFB method is coherent with the TDHFB fusion threshold. The effect of the phase-lock mechanism is shown for those reactions. Conclusions: The DC-TDHFB method is a useful new tool to determine the fusion potential between superfluid systems and to deduce their fusion cross-sections.
Time-dependent Hartree-Fock (TDHF) theory has achieved a remarkable success in describing and understanding nuclear many-body dynamics from nucleons degrees of freedom. We here report our investigation of multinucleon transfer (MNT) processes employing the TDHF theory. To calculate transfer probabilities for channels specified by the number of protons and neutrons included in reaction products, a particle-number projection (PNP) method has been developed. The PNP method is also used to calculate excitation energies of reaction products. Combined use of the PNP method with a statistical model, we can evaluate MNT cross sections taking account of effects of particle evaporation. Using these methods, we evaluate MNT cross sections for $^{40,48}$Ca+$^{124}$Sn, $^{40}$Ca+$^{208}$Pb, and $^{58}$Ni+$^{208}$Pb reactions. From systematic analyses, we find that cross sections for channels with a large reaction probability are in good agreement with experimental data. However, the agreement becomes less accurate as the number of transferred nucleons increases. Possible directions to improve the description are discussed.
We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps $delta_{2n(p)}$. Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.
The variational Hartree-Fock-Bogoliubov (HFB) mean-field theory is the starting point of various (ab initio) many-body methods dedicated to superfluid systems. While taking the zero-pairing limit of HFB equations constitutes a text-book problem when the system is of closed-(sub)shell character, it is typically, although wrongly, thought to be ill-defined whenever the naive filling of single-particle levels corresponds to an open-shell system. The present work demonstrates that the zero-pairing limit of an HFB state is mathematically well-defined, independently of the closed- or open-shell character of the system in the limit. Still, the nature of the limit state strongly depends on the underlying shell structure and on the associated naive filling reached in the zero-pairing limit for the particle number A of interest. All the analytical findings are confirmed and illustrated numerically. While HFB theory has been intensively scrutinized formally and numerically over the last decades, it still uncovers unknown and somewhat unexpected features. From this general perspective, the present analysis demonstrates that HFB theory does not reduce to Hartree-Fock theory even when the pairing field is driven to zero in the HFB Hamiltonian matrix.
Background: Multinucleon transfer (MNT) and quasifission (QF) processes are dominant processes in low-energy collisions of two heavy nuclei. They are expected to be useful to produce neutron-rich unstable nuclei. Nuclear dynamics leading to these processes depends sensitively on nuclear properties such as deformation and shell structure. Purpose: We elucidate reaction mechanisms of MNT and QF processes involving heavy deformed nuclei, making detailed comparisons between microscopic time-dependent Hartree-Fock (TDHF) calculations and measurements for the $^{64}$Ni+$^{238}$U reaction. Methods: Three-dimensional Skyrme-TDHF calculations are performed. Particle-number projection method is used to evaluate MNT cross sections from the TDHF wave function after collision. Results: Fragment masses, total kinetic energy (TKE), scattering angle, contact time, and MNT cross sections are investigated for the $^{64}$Ni+$^{238}$U reaction. They show reasonable agreements with measurements. At small impact parameters, collision dynamics depends sensitively on the orientation of deformed $^{238}$U. In tip (side) collisions, we find a larger (smaller) TKE and a shorter (longer) contact time. In tip collisions, we find a strong influence of quantum shells around $^{208}$Pb. Conclusions: It is confirmed that the TDHF calculations reasonably describe both MNT and QF processes in the $^{64}$Ni+$^{238}$U reaction. Analyses of this system indicates the significance of the nuclear structure effects such as deformation and quantum shells in nuclear reaction dynamics at low energies.
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