We introduce a natural and simple way to implement the regularization scheme of the Hartree-Fock-Bogoliubov equations with zero range pairing interaction. The renormalization scheme proves to be equivalent to a simple energy cutoff with a position dependent running coupling constant.

We show that within the framework of a simple local nuclear energy density functional (EDF), one can describe accurately the one-and two-nucleon separation energies of semimagic nuclei. While for the normal part of the EDF we use previously suggested parameterizations, for the superfluid part of the EDF we use the simplest possible local form compatible with known nuclear symmetries.PACS numbers: 21.60. Jz, 21.30.Fe A steady transition is taking place during the last several years from the mean-field description of nuclear properties in terms of effective forces to an energy density functional approach (EDF). A significant role is played in this transition process by the fact that an EDF approach has a strong theoretical underpinning [1]. The effective forces used to derive the EDF are nothing else but a vehicle, since in themselves they have no well-defined physical meaning. For example, the effective Skyrme two-particle interaction is neither a particle-hole nor a particle-particle interaction. The particle-hole interaction (or the Landau parameters) is defined only as the second order functional derivative of the total EDF with respect to various densities, while the particle-particle interaction responsible for the pairing correlations in nuclei has to be supplied independently and with no logical connection to the Skyrme parameters.We shall not attempt to even mention various meanfield approaches suggested so far, in this respect see Refs.[2], but we shall concentrate instead on a single aspect of the nuclear EDF, namely its pairing properties. Only recently it became clear that a theoretically consistent local EDF formulation of the nuclear pairing properties is indeed possible [3][4][5]. Even though the crucial role of the pairing phenomena in nuclei has been established firmly, it is surprising to realize how poor the quality of our knowledge still is. Phenomenologically, one cannot unambiguously decide whether the pairing correlations in nuclei have a volume or/and a surface character [6][7][8][9][10][11][12][13]. The isospin character of the nuclear pairing correlations requires further clarification as well. These questions become even sharper in the language of a local EDF.There is also the largely practical issue of whether one should use a zero-range or a finite-range effective pairing interaction. The only reason for the introduction of a finite-range was to resolve the formal difficulty with divergences in calculating the anomalous densities [10]. The majority of practitioners favor a much simpler approach, which embodies essentially the same physics, the introduction of an explicit energy cut-off. The best example are perhaps the works of the group [11,12], which so far is the leader in describing all known nuclear masses. An explicit finite-range of the pairing interaction r 0 (which can be translated into an energy cut-off E c ≈h 2 /mr 2 0 ) and a zero-range with an explicit energy cut-off E c in the final analysis are equivalent. Both approaches, however, are a poor's man solution to the r...

We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.

We show that in a dilute fermionic superfluid, when the fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in fermionic superfluids possible.

The adsorption of water at 100 K on an ordered film of MgO͑100͒ prepared on Mo͑100͒ is studied by low energy electron diffraction, HREELS ͑high resolution electron energy loss spectroscopy͒, and UPS ͑ultraviolet photoelectron spectroscopy͒. The appearance of the loss of OH species from HREELS and the 3 valence features of the hydroxyl from UPS indicate that the water can be partially dissociated on MgO͑100͒/Mo͑100͒ at the initial coverages. The experimental results are in good agreement with the theoretical calculations.