Abstract:
The properties of T=0 neutron-proton correlations are discussed within the frame work of different model calculations. Single-j shell calculations reveal that the T=0 correlations remain up to the highest frequencies. They are more complex and cannot be restricted to L=0 pairs only. Whereas it may be difficult to find clear evidence for T=0 pairing at low spins, T=0 correlations are found to induce a new excitation scheme at high angular momenta.

Abstract:
According to standard textbooks, the nuclear symmetry energy originates from the {\it kinetic} energy and the {\it interaction} itself. We argue that this view requires certain modifications. We ascribe the physical origin of the {\it kinetic} term to the discreteness of fermionic levels of, in principle arbitrary binary fermionic systems, and relate its mean value directly to the average level density. Physically it connects this part also to the isoscalar part of the interaction which, at least in self-bound systems like atomic nuclei, decides upon the spatial dimensions of the system. For the general case of binary fermionic systems possible external confining potentials as well as specific boundary conditions will contribute to this part. The reliability of this concept is tested using self-consistent Skyrme Hartree-Fock calculations.

Abstract:
A mean-field model with a generalized pairing interaction that accounts for neutron-proton pairing is presented. Both the BCS as well as number-projected solutions of the model are presented. For the latter case the Lipkin-Nogami projection technique was extended to encompass the case of non-separable proton-neutron systems. The influence of the projection on various pairing phases is discussed. In particular, it is shown that number-projection allows for mixing of different pairing phases but, simultanously, acts destructively on the proton-neutron correlations. The basic implications of proton-neutron pairing correlations on nuclear masses are discussed. It is shown that these correlations may provide a natural microscopic explanation of the Wigner energy lacking in mean-field models. A possible phase transition from isovector to isoscalar pairing condensate at high angular momenta is also discussed. In particular predictions for the dynamical moments of inertia for the superdeformed band in $^{88}$Ru are given.

Abstract:
A cranked mean-field model with two-body T=1 and T=0 pairing interactions is presented. Approximate projection onto good particle-number is enforced via an extended Lipkin-Nogami scheme. Our calculations suggest the simultaneous presence of both T=0 and T=1 pairing modes in N=Z nuclei. The transitions between different pairing phases are discussed as a function of neutron/proton excess, T$_z$, and rotational frequency, $\hbar\omega$. The additional binding energy due to the T=0 $np$-pairing correlations, is suggested as a possible microscopic explanation of the Wigner energy term in even-even nuclei.

Abstract:
The subtle interplay between the two nuclear superfluids, isovector T=1 and isoscalar T=0 phases, are investigated in an exactly soluble model. It is shown that T=1 and T=0 pair-modes decouple in the exact calculations with the T=1 pair-energy being independent of the T=0 pair-strength and vice-versa. In the rotating-field, the isoscalar correlations remain constant in contrast to the well known quenching of isovector pairing. An increase of the isoscalar (J=1, T=0) pair-field results in a delay of the bandcrossing frequency. This behaviour is shown to be present only near the N=Z line and its experimental confirmation would imply a strong signature for isoscalar pairing collectivity. The solutions of the exact model are also discussed in the Hartree-Fock-Bogoliubov approximation.

Abstract:
The $T$=2 excitations in even-even $N$=$Z$ nuclei are calculated within the isospin cranked mean-field approach. The response of pairing correlations to rotation in isospace is investigated. It is shown that whereas the isovector pairing rather modestly modifies the single-particle moment of inertia in isospace, the isoscalar pairing strongly reduces its value. This reduction of the moments of inertia in isospace with respect to its rigid body value is a strong indicator of collective isoscalar pairing correlations. Beautiful analogies between the role of isovector pairing for the case of spatial rotations and the role of isoscalar pairing for the case of iso-rotations are underlined.

Abstract:
The signature inversion in the \pi h11/2 \otimes \nu h11/2 rotational bands of odd-odd Cs and La isotopes and the \pi h11/2 \otimes \nu i13/2 bands of odd-odd Tb, Ho and Tm nuclei is investigated using pairing and deformation self consistent mean field calculations. The model can rather satisfactorily account for the anomalous signature splitting, provided that spin assignments in som of the bands are revised. Our calculations show that signature inversioncan appear already at axially symmetric shapes. It is found that this is due to the contribution of the \lambda\mu=22 component of the quadrupole pairing interaction to the mean field potential.

Abstract:
Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explore the competition between the normal monopole pair coupling and the spin-aligned coupling schemes. Such a coupling may be useful in elucidating the structure properties of $N=Z$ and neighboring nuclei.

Abstract:
The problem of the effective mass scaling in the single particle spectra calculated within the Skyrme energy density functional (EDF) method is studied. It is demonstrated that for specific pairs of orbitals the commonly anticipated isoscalar effective mass (m*) scaling of the single-particle level splittings is almost canceled by an implicit m*-scaling due to other parameters in the Skyrme EDF. This holds in particular for an indirect m*-scaling of the two-body spin-orbit strength making the theory essentially unpredictable with respect to single particle energies. It is argued that this unphysical property of the Skyrme EDF is a mere consequence of the strategies and datasets used to fit these functionals. The inclusion of certain single-particle spin-orbit splittings to fit the two-body spin-orbit and the tensor interaction strengths reinstates the conventional m*-scaling and improves the performance of the Skyrme EDF.

Abstract:
The superdeformed bands in 58Cu, 59Cu, 60Zn, and 61Zn are analyzed within the frameworks of the Skyrme-Hartree-Fock as well as Strutinsky-Woods-Saxon total routhian surface methods with and without the T=1 pairing correlations. It is shown that a consistent description within these standard approaches cannot be achieved. A T=0 neutron-proton pairing configuration mixing of signature-separated bands in 60Zn is suggested as a possible solution to the problem.