The theoretical description of nuclear fission remains one of the major challenges of quantum many-body dynamics. The motion through the fission barrier is followed by a fast, nonadiabatic descent of the potential between the fragments. The latter stage is crucial as it generates most of the excitation energy in the fragments. The superfluid dynamics in the latter stage of fission is obtained from the time-dependent Hartree-Fock theory including BCS dynamical pairing correlations. The fission modes of the 258 Fm nucleus are studied. The resulting fission fragment characteristics show good agreement with experimental data. Quantum shell effects are shown to play a crucial role in the dynamics and formation of the fragments. The importance of quantum fluctuations beyond the independent particle and quasiparticle picture is emphasized and qualitatively studied.

The effect of pairing correlation on transfer reaction below the Coulomb barrier is investigated qualitatively and quantitatively using a simplified version of the Time-Dependent Hartree-Fock + BCS approach. The effect of particle number symmetry breaking on the description of reaction and dedicated methods to extract one and two-nucleon transfer probabilities (P1n and P2n) in a particle number symmetry breaking approach are discussed. Influence of pairing is systematically investigated in the 40 Ca+ 40,42,44,46,48,50 Ca reactions. A strong enhancement of the two-particle transfer probabilities due to initial pairing correlations is observed. This enhancement induces an increase of the ratio of probabilities P2n/(P1n) 2 compared to the case with no pairing. It is shown that this ratio increases strongly as the center of mass energy decreases with a value that could be larger than ten in the deep sub-barrier regime. An analysis of the pair transfer sensitivity to the type of pairing interaction, namely surface, mixed or volume, used in the theory is made. It is found that the pair transfer is globally insensitive to the type of force and mainly depends on the pairing interaction strength.

Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass-splits. 1 Without quantum shells, which can give extra binding energy to these mass-asymmetric shapes, the nuclei would fission symmetrically. The strongest shell effects are in spherical nuclei, so naturally the spherical "doubly-magic" 132 Sn nucleus (Z = 50 protons), was expected to play a major role. However, a systematic study of fission has shown that the heavy fragments are distributed around Z = 52 to 56, 2 indicating that 132 Sn is not the only driver. Reconciling the strong spherical shell effects at Z = 50 with the different Z values of fission fragments observed in nature has been a longstanding puzzle. 3 Here, we show that the final mass asymmetry of the fragments is also determined by the extra stability of octupole (pear-shaped) deformations which have been recently confirmed experimentally around 144 Ba (Z = 56), 4, 5 one of very few nuclei with shellstabilized octupole deformation. 6 Using a modern quantum many-body model of superfluid fission dynamics, 7 we found that heavy fission fragments are produced predominantly with 52 − 56 protons, associated with significant octupole deformation acquired on the way to fission. These octupole shapes favouring asymmetric fission are induced by deformed shells at Z = 52 and 56. In contrast, spherical "magic" nuclei are very resistant to octupole deformation, which hinders their production as fission fragments. These findings may explain surprising observations of asymmetric fission of lighter than lead nuclei. 8 Atomic nuclei are usually found in a minimum of energy "ground-state" which may be deformed due to quantum correlations. Elongation beyond the ground-state costs potential energy until a maximum is reached at the fission barrier. Increasing the elongation beyond the fission barrier decreases the potential energy and the system follows a fission valley in the "potential energy surface" until it breaks into two fragments (scission). In the absence of quantum shell effects, all heavy nuclei preferentially fission into two fragments of similar mass (mass-symmetric fission). However, quantum shells in the fissioning nucleus can result in several valleys to scission. These may be mass-symmetric or mass-asymmetric.Although recent progress has been made in describing fission fragment mass distributions with stochastic based approaches, 9, 10 theoretical description of the first stage of fis-

The modelling of nuclear reactions and radioactive decays in astrophysical or earth-based conditions requires detailed knowledge of the masses of essentially all nuclei. Microscopic mass models based on nuclear energy density functionals (EDFs) can be descriptive and used to provide this information. The concept of intrinsic symmetry breaking is central to the predictive power of EDF approaches, yet is generally not exploited to the utmost by mass models because of the computational demands of adjusting up to about two dozen parameters to thousands of nuclear masses. We report on a first step to bridge the gap between what is presently feasible for studies of individual nuclei and large-scale models: we present a new Skyrme-EDF-based model that was adjusted using a three-dimensional coordinate-space representation, for the first time allowing for both axial and triaxial deformations during the adjustment process. To compensate for the substantial increase in computational cost brought by the latter, we have employed a committee of multilayer neural networks to model the objective function in parameter space and guide us towards the overall best fit. The resulting mass model BSkG1 is computed with the EDF model independently of the neural network. It yields a root mean square (rms) deviation on the 2457 known masses of 741 keV and an rms deviation on the 884 measured charge radii of 0.024 fm.

The density profiles of around 750 nuclei are analyzed using the Skyrme energy density functional theory. Among them, more than 350 nuclei are found to be deformed. In addition to rather standard properties of the density, we report a non-trivial behavior of the nuclear diffuseness as the system becomes more and more deformed. Besides the geometric effects expected in rigid body, the diffuseness acquires a rather complex behavior leading to a reduction of the diffuseness along the main axis of deformation simultaneously with an increase of the diffuseness along the other axis. The possible isospin dependence of this polarization is studied. This effect, that is systematically seen in medium- and heavy-nuclei, can affect the nuclear dynamical properties. A quantitative example is given with the fusion barrier in the $^{40}$Ca+ $^{238}$U reaction.Comment: 8 pages, 13 figure

We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of TDHF+BCS, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in TDHF+BCS, but there are other problems with the BCS that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the U and V Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schrödinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schrödinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.

Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is the first step to bridge microscopic and macroscopic approaches. The method is versatile and can be applied to study a large class of nuclear processes. An illustration is given here with the fission of 258 Fm. Using the quadrupole moment and eventually higher-order multipole moments, the associated collective masses are estimated along the microscopic mean-field evolution. When more than one collective variable are considered, it is shown that the off-diagonal matrix elements of the inertia play a crucial role. Using the information on the quadrupole moment and associated momentum, the collective evolution is studied. It is shown that dynamical effects beyond the adiabatic limit are important. Nuclei formed after fission tend to stick together for longer time leading to a dynamical scission point at larger distance between nuclei compared to the one anticipated from the adiabatic energy landscape. The effective nucleus-nucleus potential felt by the emitted nuclei is finally extracted.

The systematic study of isoscalar (IS) and isovector (IV) giant quadrupole responses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D. Lacroix, Phys. Rev. C 88, 044310 (2013)] is extended to the case of axially deformed and triaxial nuclei. The static and dynamical energy density functional based on Skyrme effective interaction are used to study static properties and dynamical response functions over the whole nuclear chart. Among the 749 nuclei that are considered, 301 and 65 are respectively found to be prolate and oblate while 54 do not present any symmetry axis. For these nuclei, the IS-and IV-GQR response functions are systematically obtained. In these nuclei, different aspects related to the interplay between deformation and collective motion are studied. We show that some aspects like the fragmentation of the response induced by deformation effects in axially symmetric and triaxial nuclei can be rather well understood using simple arguments. Besides this simplicity, more complex effects show up like the appearance of non-trivial deformation effects on the collective motion damping or the influence of hexadecapole or higher-orders effects. A specific study is made on the triaxial nuclei where the absence of symmetry axis adds further complexity to the nuclear response. The relative importance of geometric deformation effects and coupling to other vibrational modes are discussed.