Global nuclear structure aspects of
tensor interaction Wojciech Satuła in collaboration with
J.Dobaczewski, P. Olbratowski, M.Rafalski, T.R. Werner, R.A. Wyss, M.Zalewski Kazimierz Dolny 2008 + NNN + .... tens of MeV ab initio Principles of low-energy nuclear physics effective theories Coupling constants & fitting strategies Single-particle fingerprints of tensor interaction - SO splittings & magic gaps Influence of tensor fields on: - nuclear deformability - the total binding energy
Global nuclear structure aspects of
tensor interaction Wojciech Satuła in collaboration with
J.Dobaczewski, P. Olbratowski, M.Rafalski, T.R. Werner, R.A. Wyss, M.Zalewski Kazimierz Dolny 2008 + NNN + .... tens of MeV ab initio Principles of low-energy nuclear physics effective theories Coupling constants & fitting strategies Single-particle fingerprints of tensor interaction - SO splittings & magic gaps Influence of tensor fields on: - nuclear deformability - the total binding energy & S2n - high-spin (terminating) states Summary
Modern Mean-Field Theory º Energy Density Functional
®
j,
r, t,
J,
« ®
T,
®
s,
®
F,
Hohenberg-Kohn-Sham Effective theories for low-energy nuclear physics:
Fourier local
correcting
potential hierarchy of scales: 2roA1/3 ro ~ 2A1/3 is based on a simple and very intuitive assumption that low-energy
nuclear theory is independent on high-energy dynamics ~ 10 The nuclear effective theory Long-range part of the NN interaction (must be treated exactly!!!) where regularization Coulomb ultraviolet
cut-off denotes an arbitrary Dirac-delta model Gogny interaction przykład There exist an „infinite” number
of equivalent realizations
of effective theories
lim da a 0 Skyrme interaction - specific (local) realization of the
nuclear effective interaction: spin-orbit density dependence 10(11) parameters Y | v(1,2) | Y Slater determinant
(s.p. HF states are equivalent to the Kohn-Sham states) Spin-force inspired local energy density functional local energy density functional relative momenta spin exchange
Symmetric NM: - saturation density ( ~0.16fm-3) - energy per nucleon (-16 0.2MeV) - incompresibility modulus (210 20MeV) + - isoscalar effective mass (0.8) + Asymmetric NM: isovector effective mass
(GDR sum-rule enhancement)
- symmetry energy ( 30 2MeV) + neutron-matter EOS
(Wiringa, Friedmann-Pandharipande) Finite, double-magic nuclei
[masses,radii, rarely sp levels]: surface properties ZOO– 20 parameters are fitted to: density rg
dependent CC Skyrme-inspired functional
is a second order expansion
in densities and
currents: tensor spin-orbit
150 160 170 180 190 0.7 0.8 0.9 1 m*/m W0 SLy4 SLy5 SkP SkXc SkM* SIII SkO 5.5 6.5 7.5 8.5 140 150 160 170 180 190 experiment std. so 90% so SkP SkO SkXc SkM* MSk1 SLy5 SLy4 SkI1 SIII De(f7/2-f5/2) [MeV] W0 W0 120 130 140 150 160 170 De(d3/2-f7/2) [MeV] SkP SkM* SkXc SLy4 SkI1 SIII SkO MSk1 5 6 7 experiment * std. so 90% so scales with Wo
(two-body SO interaction) Binding energy-dictated fit:
superficial m* dependence
in the spin-orbit strength: and contradicting scalings
in the single-particle splittings scales with Wo*
(Wo* = Wo) m mo *
Fitting strategies of the tensorial coupling constants (I) De(f5/2-f7/2) [MeV] 5 6 7 8 5 6 7 8 40Ca 48Ca 56Ni a) b) neutrons protons bare SkO spectra
SkPT T0=-39(*5);T1=-62(*-1.5);SO*0.8 C1 J C0 J 1 3 5 7 0.7 0.8 0.9 1 40Ca 1 3 5 7 -40 -30 -20 -10 0 56Ni f7/2-f5/2 p3/2-p1/2 f7/2-d3/2 2 4 6 8 -80 -60 -40 -20 0 f7/2-f5/2 f7/2-d3/2 from binding energies 48Ca f7/2-f5/2 f7/2-d3/2 f7/2-p3/2 p3/2-p1/2 Single-particle energies [MeV] Fitting strategies of the tensorial coupling constants (II) 1) Fit of the isoscalar SO strength 48Ca 56Ni 40Ca 2) Fit of the isoscalar tensor strength: 3) Fit of the isovector tensor strength
or, more precisely, C1J/C1 j< j> F j> F j< - the details - D J 48Ni or 78Ni are needed
in order to fix SO-tensor sector f7/2 f5/2 splittings around
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