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We study the role of the tensor term of the Skyrme effective interactions on the spin-orbit splittings in the N=82 isotones and Z=50 isotopes. The different role of the triplet-even and triplet-odd tensor forces is pointed out by analyzing the spin-orbit splittings in these nuclei. The experimental isospin dependence of these splittings cannot be described by Hartree-Fock calculations employing the usual Skyrme parametrizations, but is very well accounted for when the tensor interaction is introduced. The capability of the Skyrme forces to reproduce binding energies and charge radii in heavy nuclei is not destroyed by the introduction of the tensor term. Finally, we also discuss the effect of the tensor force on the centroid of the Gamow-Teller states.PACS numbers:

Our paper aims at providing an answer to the question whether one can reliably describe the properties of the most important spin-isospin nuclear excitations, by using the available nonrelativistic Skyrme energy functionals. Our method, which has been introduced in a previous publication devoted to the Isobaric Analog states, is the self-consistent Quasiparticle Random Phase Approximation (QRPA). The inclusion of pairing is instrumental for describing a number of experimentally measured spherical systems which are characterized by open shells. We discuss the effect of isoscalar and isovector pairing correlations. Based on the results for the Gamow-Teller resonance in 90 Zr, in 208 Pb and in few Sn isotopes, we draw definite conclusions on the performance of different Skyrme parametrizations, and we suggest improvements for future fits. We also use the spin-dipole resonance as a benchmark of our statements.

The nuclear time-dependent Hartree-Fock model formulated in the three-dimensional space, based on the full standard Skyrme energy density functional complemented with the tensor force, is presented for the first time. Full self-consistency is achieved by the model. The application to the isovector giant dipole resonance is discussed in the linear limit, ranging from spherical nuclei ( 16 O, 120 Sn) to systems displaying axial or triaxial deformation ( 24 Mg, 28 Si, 178 Os, 190 W , 238 U). Particular attention is paid to the spin-dependent terms from the central sector of the functional, recently included together with the tensor. They turn out to be capable of producing a qualitative change on the strength distribution in this channel. The effect on the deformation properties is also discussed. The quantitative effects on the linear response are small and, overall, the giant dipole energy remains unaffected. Calculations are compared to predictions from the (quasi)-particle random phase approximation and experimental data where available, finding good agreement.

Background: It is generally acknowledged that the time-dependent Hartree-Fock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavy-ion reactions. The TDHF method is also known in nuclear physics in the small amplitude domain, where it provides a useful description of collective states, and is based on the mean-field formalism which has been a relatively successful approximation to the nuclear many-body problem. Currently, the TDHF theory is being widely used in the study of fusion excitation functions, fission, deep-inelastic scattering of heavy mass systems, while providing a natural foundation for many other studies.Purpose: With the advancement of computational power it is now possible to undertake TDHF calculations without any symmetry assumptions and incorporate the major strides made by the nuclear structure community in improving the energy density functionals used in these calculations. In particular, time-odd and tensor terms in these functionals are naturally present during the dynamical evolution, while being absent or minimally important for most static calculations. The parameters of these terms are determined by the requirement of Galilean invariance or local gauge invariance but their significance for the reaction dynamics have not been fully studied. This work addresses this question with emphasis on the tensor force. Method:The full version of the Skyrme force, including terms arising only from the Skyrme tensor force, is applied to the study of collisions within a completely symmetry-unrestricted TDHF implementation. Results:We examine the effect on upper fusion thresholds with and without the tensor force terms and find an effect on the fusion threshold energy of the order several MeV. Details of the distribution of the energy within terms in the energy density functional is also discussed.Conclusions: Terms in the energy density functional linked to the tensor force can play a non-negligible role in dynamic processes in nuclei.

A microscopic model aimed at the description of charge-exchange nuclear excitations along isotopic chains which include open-shell systems is developed. It consists of the quasiparticle random phase approximation (QRPA) made on top of Hartree-Fock-Bardeen-Cooper-Schrieffer (HF-BCS). The calculations are performed by using the Skyrme interaction in the particle-hole channel and a zero-range, density-dependent pairing force in the particle-particle channel. At variance with the (many) versions of QRPA which are available in the literature, in our work special emphasis is put on the full self-consistency. Its importance, as well as the role played by the charge-breaking terms of the nuclear Hamiltonian, like the Coulomb interaction, the charge symmetry and charge independence breaking (CSB-CIB) forces and the electromagnetic spin-orbit, are elucidated by means of numerical calculations of the isobaric analog resonances (IAR). The theoretical energies of these states along the chain of the Sn isotopes agree well with the experimental data in the stable isotopes. Predictions for unstable systems are presented.

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Abstract. This contribution to the "Open Problems in Nuclear Structure Theory" special edition looks at some issues with using Time-Dependent Hartree Fock and related techniques to study structural phenomena in nuclear physics. We limit the discussion to structures like giant resonances and discuss some open questions regarding the interpretation of TDHF calculations.