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

zero if good parity

non zero

zero at sphericity

The Skyrme energy density functional:

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???

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

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

56Ni same 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

Tensor parameters adjusted on the energy difference g7/2-h11/2in 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 ofthe partners or the position of the centroïds of the g, h and I levels?

What happens when going beyond sphericity?

One has to define the extra terms of the functional:Colot et al: viewed as an interactionZalewski 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)

Are there better fingerprints for rotating nuclei?Many new terms in the edf when time reversal invariance is broken:

First problem: several time odd terms are responsible of divergence (in a larger range of parameters than determined by Landau parameters).

Tensor terms:

Pairing Time odd terms

Tensor interaction

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