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The neutron and proton odd-even mass differences are studied with Hartree-Fock+BCS (HFBCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction, which is recently derived from a microscopic nucleon-nucleon interaction. To this end, we perform HFBCS calculations for even and odd semi-magic Tin and Lead isotopes together with even and odd Z isotones with N = 50 and 82. The filling approximation is applied to the last unoccupied particle in odd nuclei. Comparisons with the experimental data show a clear manifestation of the isospin dependent pairing correlations in both proton and neutron pairing gaps. It has been known that pairing correlations play an important role in finite and also infinite nuclear systems [1][2][3]. Recently, the theory of nuclear masses or binding energies has attracted renewed interest with the advent of self-consistent mean field theories, and also density functional theories (DFT) [4,5]. A global feature of the nuclear binding energies is the odd-even mass staggering (OES) phenomenon. Several theoretical studies have been made to attribute this phenomenon to the BCS superfluidity in the nuclear ground states. It has been pointed out that other effects also contribute the OES effect [6,7].Recently, global calculations of nuclear masses became feasible by using modern computational resources. A goal of these global calculations is to improve the reliability of theories and to establish universal energy density functionals for nuclear masses. In this respect, the pairing correlations should be carefully examined by using microscopic methods such as Hartree-Fock(HF)+BCS or Hartree-Fock-Bogoliubov (HFB) theories. Indeed, first studies in this direction have been carried out and a possible isospin dependence of the effective pairing interaction has been discussed in the literature [8,9].The nuclear interaction may conserve the isospin at a fundamental level, but core polarization can induce isospin dependence when the core has a neutron excess. Another contribution may come from the Coulomb interaction. Recently, an effective isospin dependent pairing interaction was proposed from the study of nuclear matter pairing gaps calculated by realistic nucleon-nucleon interactions. In ref.[8], the density−dependent pairing interaction was defined bywhere ρ = ρ n + ρ p is the nuclear density and β is the asymmetry parameter β = (ρ n − ρ p )/ρ. The isovector dependence is introduced through the density-dependent term g τ . The function g τ is determined by the pairing gaps in nuclear matter and its functional form is given bywhere ρ 0 =0.16 fm −3 is the saturation density of symmetric nuclear matter. We choose f s (βτ z ) = 1 − f n (βτ z ) and f n (βτ z ) = βτ z = [ρ n (r) − ρ p (r)] τ z /ρ(r). The parameters for g τ are obtained from the fit to the pairing gaps in symmetric and neutron matter obtained by the microscopic nucleon-nucleon interaction. The pairing strength V 0 will be adjusted to give the best fit to odd-even staggering of nuclear masses.

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. As an example, the potential energy surfaces of 208 Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till very deformed region, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.

Cochlear implant (CI) listeners typically perform poorly on tasks involving the pitch of complex tones. This limitation in performance is thought to be mainly due to the restricted number of active channels and the broad current spread that leads to channel interactions and subsequent loss of precise spectral information, with temporal information limited primarily to temporal-envelope cues. Little is known about the degree of spectral resolution required to perceive combinations of multiple pitches, or a single pitch in the presence of other interfering tones in the same spectral region. This study used noise-excited envelope vocoders that simulate the limited resolution of CIs to explore the perception of multiple pitches presented simultaneously. The results show that the resolution required for perceiving multiple complex pitches is comparable to that found in a previous study using single complex tones. Although relatively high performance can be achieved with 48 channels, performance remained near chance when even limited spectral spread (with filter slopes as steep as 144 dB/octave) was introduced to the simulations. Overall, these tight constraints suggest that current CI technology will not be able to convey the pitches of combinations of spectrally overlapping complex tones.