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Are there fingerprints of a tensor interaction ?

Are there fingerprints of a tensor interaction ?. How to adjust the parameters of tensor terms? Selected so splitting, on existing interactions? Full variation of all edf parameters to the same set of data?. M. Bender, V. Hellemans, T Duguet, K. Bennaceur, J. Meyer and T. Lesinski.

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Are there fingerprints of a tensor interaction ?

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  1. Are there fingerprints of a tensor interaction? • How to adjust the parameters of tensor terms? • Selected so splitting, on existing interactions? • Full variation of all edf parameters to the same set of data? M. Bender, V. Hellemans, T Duguet, K. Bennaceur, J. Meyer and T. Lesinski

  2. zero if good parity non zero zero at sphericity The Skyrme energy density functional:

  3. Several ways to write the tensor term, each time with different coupling constants If tensor interaction, all constants related to te and to If central part of the Skyrme functional is generated by a 2-body interaction, contributions to the tensor term. No ambiguity in this case to go beyond sphericity If Skyrme = purely an energy functional, fit at sphericity determines only CJt, t=0,1 How to choose the terms appearing for deformed nuclei???

  4. Fitting strategies for the introduction of a tensor term: • for each tensor parameters, full refit of the interaction: • TIJ interactions of Lesinski et al • take a known interaction (SLy5) and add a tensor force • Colot et al • stronger spin orbit • take known interactions and fit tensor and spin orbit • to specific data (SLy4T, …) • Zalewski et al • fit to distance between so partners in • 40Ca, 48Ca and 56Ni • weaker spin orbit

  5. 40Ca : N=Z, spin saturated for n and p, t=1 contributions are 0 no t=0 tensor (spin saturation) used to adjust t=0 so constant 56Nisame reasons, adjust t=0 tensor 48Ca adjust t=1 tensor 48Ni missing -> assumption on the ratio of t=0 and t=1 so Assumes that: same wf for so partners for n and p no pairing

  6. Tensor parameters adjusted on the energy difference g7/2-h11/2 in Sn isotopes for the protons and i13/2-h9/2for neutrons? Starting point: SLy5 parameterization no modification of the so term tensor parameters in the range suggested by Brink, Flocard and Stancu -> attractive -> stronger so than SLy5 Does one try to correct the so position of one member of the partners or the position of the centroïds of the g, h and I levels?

  7. What happens when going beyond sphericity? One has to define the extra terms of the functional: Colot et al: viewed as an interaction Zalewski et al.: viewed as an edf -> different possible options Main point to observe: so strength larger for SLy5T lower for SLy4+T Phys. Rev C80 064302 (2009)

  8. Are there better fingerprints for rotating nuclei? Many new terms in the edf when time reversal invariance is broken: Tensor terms: First problem: several time odd terms are responsible of divergence (in a larger range of parameters than determined by Landau parameters).

  9. Pairing Time odd terms

  10. Tensor interaction

  11. Some conclusions • Perturbative fitting of tensor not sufficient • Self consistency of the edf essential • There are probably other terms to add to the central part of the edf before to add a tensor interaction

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