M. Girod, F.Chappert, CEA Bruyères-le-Châtel Neutron Matter and Binding Energies with a New Gogny Force

Purpose of our study,  0 =0.16 fm -3 D1S Gogny force does not reproduce the EOS for neutron matter Fit NM with Skyrme forces: PhD E. Chabanat Sly4

I) The fit to Neutron Matter EOS New Gogny force: D1N II) Properties of D1N in nuclei Contents

I) The fit to Neutron Matter EOS New Gogny force: D1N

The Gogny force 14 parameters (Wi, Bi, Hi, Mi,  i ) for i=1,2; t 0, x 0,  W ls

14 parameters 14 parameters 14 equations B.E. and radii: 16 O et 90 Zr G.S. properties 2 pairing matrix elements pairing properties 48 Ca: sym=  2s N -  2s P N-P asymmetry …………. 14 parameters determined parameter « sym » Neutron Matter ? Test of the interaction:  0, E 0, K, E surf, m eff, E sym ….

Link between the parameter sym and the Neutron Matter EOS? sym=  2s N -  2s P in 48 Ca

Results in neutron matter: D1S, D1N Results in nuclear matter with D1N?

Nuclear matter properties D1S-D1N D1SD1N  0 (fm -3 ) E 0 /A (MeV) K (MeV) E surf (MeV) m eff E sym (MeV) W ls (MeV) Results in nuclei with D1N?

II) Properties of D1N in nuclei 1) Pairing properties 2) Binding energies

II) Properties of D1N in nuclei 1) Pairing properties

Pairing properties: D1, D1S, D1N, A odd correlations Pairing gap (Satula et al.)

Pairing energy in Sn isotopes

Moment of Inertia in 244 Pu

II) Properties of D1N in nuclei 2) Binding energies

Binding Energies: Sn isotopes  E=E HFB -E exp D1S D1N Neutron Matter fit Drift of Binding Energies ?

Binding Energies: more precise study

Binding Energies: Sm isotopes  E=E HFB -E exp D1S D1N

Binding Energies  B=B HFB -B exp

Conclusion Aim: build a new Gogny force which fits Neutron Matter EOS D1N Properties in nuclei: Same pairing properties as D1S if not better (moments of inertia) The drift of B.E. with N has disappeared I) PAIRING II) BINDING ENERGIES (B.E.) Other calculations are being done: beyond mean-field D1N should be soon validated: D1S D1N

Acknowledgements Nuclear Structure Theory group: J.F. Berger, M.Girod B.Ducomet, H.Goutte, S.Peru, N.Pillet, V.Rotival

Results in neutron matter: D1S, D1N Neutron Matter EOS with Gogny forces:

Pairing properties Scattering lengths S=0, T=1: fm Experimental value fm D fm D1S fm D1N Experiment: pairing force ~ bare force (Paris, AV18, ….)

Semi-empirical (Weiszäcker) mass formula Empirical values: a v =-15.68, a s =18.56, a c =0.717, a I =28.1 [MeV] Calculation of the coefficients ( a v,a s,a I ) with the built interaction?

Pairing properties Full HFB calculation Odd A: blocking approximation is used Deviation with experiment: Blocking approximation B.E. of odd nuclei under-estimated when quasi-particle- vibration coupling present Kuo et al: few hundred keV correction

Pairing properties Full HFB calculation Odd A: blocking approximation is used Deviation with experiment: Blocking approximation B.E. of odd nuclei under-estimated when quasi-particle-vibration coupling present Kuo et al: few hundred keV correction

Inertia momenta in 232 Th  1

Inertia momenta in 232 Th 11 11 22 22

Neutron Matter EOS: the variational method  non interacting WF Trial wave-function: kf  f(r ij ) f(r ij ) is varied until E var is minimum Variational procedure:

 f(r ij )

Pairing properties: D1N, A odd ~200 keV

Binding Energies: D1S  B=B HFB -B exp

Binding Energies  B=B HFB -B exp

Binding Energies: D1S  B=B HFB -B exp

Binding Energies  B=B HFB -B exp

Binding Energies  B=B HFB -B exp

Results in neutron matter: D1S, D1N Neutron Matter EOS with Gogny forces:

Pairing properties: D1, A odd ~300 keV Pairing gap (Satula et al.)

Pairing properties GS energy HFB correlations Exp. ? Beyond HFB Odd nucleus  E corr Kuo et al.D1D1SD1N  corr [keV] Few ~100~300~200 Corr. HFB GS 1 st excited states  E odd even odd  E even

ST sub-spaces