Structure and dynamics from the time-dependent Hartree-Fock model E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR March 2010

Structure and dynamics from the time-dependent Hartree-Fock model Outline Motivation Mean-field theory The Skyrme effective interaction The tensor terms Spin-orbit splitting in superheavy nuclei The time-odd terms Fusion properties in TDHF Summary & Outlook E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Motivation Self-consistent mean-field approaches provide a useful tool for studying structure and dynamics across the full nuclear landscape There are several improvements that can be made to the energy density functionals employed within the models The tensor terms have previously been neglected but proved successful for describing spin-orbit splitting in exotic nuclei Also have an impact on deformation and in dynamics The time-odd fields are not well understood but are important for the description of odd-A nuclei and time-dependent phenomena Several terms appear in EDF which are poorly constrained by existing fits We will explore time-odd and tensor densities in our 3D TDHF code E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Mean-field theory Hartree-Fock wavefunction approximated by a single Slater determinant Built from basis of single-particle states Fermi statistics of nucleons accounted for Ground state determined by minimising expectation value of Hamiltonian with respect to single-particle wavefunctions or densities All static properties determined from local density (Hohenberg-Kohn theorem) TDHF equations solved by evolving 1-body density matrix in time E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Local densities Constructed from non-local densities Each density has either scalar, vector or tensor structure and is even or odd with respect to time-reversal E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

The Skyrme effective interaction Structure and dynamics from the time-dependent Hartree-Fock model The Skyrme effective interaction Approximates the N-N interaction by density matrix expansion of zero- range terms in momentum space (k) up to second order Contains local term, central and exchange non-local terms, density dependence, spin-orbit interaction and tensor terms Tensor terms previously neglected from Skyrme force fits until recently E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

The energy density functional Structure and dynamics from the time-dependent Hartree-Fock model The energy density functional Skyrme EDF calculated from Total energy Pairing etc may also be included Minimisation of total energy gives rise to the Hartree-Fock equations that are solved iteratively Densities often recoupled into isoscalar and isovector components E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

The energy density functional Structure and dynamics from the time-dependent Hartree-Fock model The energy density functional EDF from Skyrme’s interaction Bilinear combinations of time-even and time-odd terms conserve Galilean invariance of overall functional Coupling constants either fitted to nuclear data directly or as combinations of Skyrme interaction parameters E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Philosophy Skyrme effective interaction can provide rigid framework for determining EDF coupling constants Time-odd fields may be studied without further fits Most Skyrme parameter sets have been fitted exclusively to static properties in even-even nuclei Time-even fields are reflected in many properties and are well understood Time-odd fields become active when intrinsic time-reversal invariance broken E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model The tensor force Originates from pion-exchange processes and induces correlations between single-nucleon orbitals with different isospin T. Otsuka et al., Phys. Rev. Lett. 95, 232502 (2005) This results in a contribution to binding energy and spin-orbit splitting In mean-field models the effect on spin-orbit splitting dominates E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Skyrme’s tensor terms Tensor contribution to the energy density in the most general case is Several studies have been performed under assumptions of spherical symmetry or axial deformation Spin-orbit potential has simplified form in this case B.A. Brown et al., Phys. Rev. C 74, 061303 (2006) G. Colò et al., Phys. Lett. B 646, 227-231 (2007) M. Zalewski et al., Eur. Phys. J A 42, 577 (2009) M. Bender et al., Phys. Rev. C 80, 064302 (2009) E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Role of the tensor terms in superheavy nuclei Structure and dynamics from the time-dependent Hartree-Fock model Role of the tensor terms in superheavy nuclei E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Role of the tensor terms in superheavy nuclei Structure and dynamics from the time-dependent Hartree-Fock model Role of the tensor terms in superheavy nuclei 2p across Z=138 isotopes E. B. Suckling and P. D. Stevenson, Eur. Phys. Lett. 2010 Tensor terms modify single- particle structure in SHEs Some forces predict a Z=138 shell closure Nucleon number dependence a consequence of high level density Large asymmetry in protons and neutrons Performance in terms of the density dependence of each force in asymmetric matter is important E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Effect of time-odd and tensor terms in collisions Structure and dynamics from the time-dependent Hartree-Fock model Effect of time-odd and tensor terms in collisions 16O+16O head-on collision @ Ecm = 100 MeV in 3D TDHF E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Effect of time-odd and tensor terms in collisions Structure and dynamics from the time-dependent Hartree-Fock model Effect of time-odd and tensor terms in collisions SLy5 + perturbative tensor terms E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Effect of time-odd and tensor terms in collisions Structure and dynamics from the time-dependent Hartree-Fock model Effect of time-odd and tensor terms in collisions E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Effect of time-odd and tensor terms in collisions Structure and dynamics from the time-dependent Hartree-Fock model Effect of time-odd and tensor terms in collisions Force Threshold (MeV) Fusion X-Section @ C.O.M 34MeV (mb) Exp. 1075 SLy5 75 -- SLy5 + Juv2 68 SLy5 + time-odd 67 1347 SLy5 + tensor 64 T22 63 1306 T24 74 1378 E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Effect of time-odd and tensor terms in collisions Structure and dynamics from the time-dependent Hartree-Fock model Effect of time-odd and tensor terms in collisions J2 energy contribution @ Ecm=34 MeV Time-odd energy @ Ecm=34 MeV, b=6.65 E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Summary The time-odd and spin-current tensor densities have been added and tested in our 3D TDHF code The effects of the tensor terms have been studied in the case of spherical symmetry on the single particle structure in superheavy nuclei Tensor terms are shown to modify the spin-orbit splittings around this region However predictions are sensitive to the details of the parameterisation Further fits that include single-particle and established properties in superheavy nuclei are required Preliminary studies of the effects of time-odd and tensor terms of the Skyrme EDF have been studied for the 16O+16O collision Fusion threshold is lowered as a result of the spin-current tensor density Fusion cross-section is overestimated by ~20% after inclusion of the terms Time-odd densities have non-negligable contributions to the total energy E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR

Structure and dynamics from the time-dependent Hartree-Fock model Outlook Further calculations including collisions between deformed systems will be investigated Time-odd and tensor terms are likely to have larger contributions in these cases Improved interactions/EDFs that include time-odd and tensor terms within the fits will provide a better description of static and dynamic properties in the future Thank You E.B. Suckling, S. Fracasso and P.D. Stevenson Nordic Winter Meeting on Physics @ FAIR