m. girod, f.chappert, cea bruyères-le-châtel neutron matter and binding energies with a new gogny...
TRANSCRIPT
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
Coulomb
.rr.W.i
2
rrrrPx1t
PPMPHPBW.exp
rrV
21122112ls
212100
2,1jjjjj
rr
21
2
j
2
21
�
14 parameters (Wi, Bi, Hi, Mi, i) for i=1,2; t0, x0, Wls
14 parameters 14 parameters 14 equations
• B.E. and radii: 16O et 90Zr G.S. properties• 2 pairing matrix elements pairing properties
• 48Ca: sym=2sN - 2s
P N-P asymmetry
• ………….
14 parameters determined
parameter « sym » Neutron Matter ?
Test of the interaction: 0 , E0, K, Esurf, meff, Esym….
Link between the parameter symand the Neutron Matter EOS?
sym=2sN - 2s
P in 48Ca
Results in neutron matter: D1S, D1N
Results in nuclear matter with D1N?
Nuclear matter properties D1S-D1N
D1S D1N
0 (fm-3) 0.163 0.159
E0/A (MeV) -15.93 -15.96
K (MeV) 210 229
Esurf (MeV) 20.0 19.3
meff 0.70 0.75
Esym (MeV) 32.0 32.9
Wls (MeV) 130 115
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
A1A1A B
2
BBB
, A odd
correlations
Pairing gap (Satula et al.)
Pairing energy in Sn isotopes
2
1E pair
HFB
Moment of Inertia in 244Pu
II) Properties of D1N in nuclei
2) Binding energies
Binding Energies: Sn isotopesE=EHFB-Eexp
D1S
D1N
Neutron Matter fit Drift of Binding Energies?
Binding Energies: more precise study
Binding Energies: Sm isotopesE=EHFB-Eexp
D1S
D1N
Binding EnergiesB=BHFB-Bexp
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:
18.50 fm Experimental value13.51 fm D1 12.12 fm D1S 10.51 fm D1N
Experiment: pairing force ~ bare force (Paris, AV18, ….)
Semi-empirical (Weiszäcker) mass formula
Empirical values:
av=-15.68, as=18.56, ac=0.717, aI=28.1 [MeV]
energysymmetry
2
I
energyCoulomb
3/12c
energysurface
3/2s
energyvolume
v A
)ZN(a
4
1AZaAaAa)Z,N(E
Calculation of the coefficients (av,as,aI)with the built interaction?
Pairing propertiesFull 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 propertiesFull 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 232Th1
Inertia momenta in 232Th
1 12 2
Neutron Matter EOS:the variational method
non interacting WF
Trial wave-function:
A
jiijrfF F
kfkf
k
f(rij)f(rij)
f(rij) is varied until Evar is minimum
FF
HFFHEvar
Variational procedure:
f(rij) f(rij)
FF
HFFHE
rfF,F
var
A
jiij
Pairing properties: D1N
A1A1A B
2
BBB
, A odd
~200 keV
Binding Energies: D1S
B=BHFB-Bexp
Binding EnergiesB=BHFB-Bexp
Binding Energies: D1S
B=BHFB-Bexp
Binding EnergiesB=BHFB-Bexp
Binding EnergiesB=BHFB-Bexp
Results in neutron matter: D1S, D1N
Neutron Matter EOS with Gogny forces:
Pairing properties: D1
A1A1A B
2
BBB
, A odd
~300 keV
Pairing gap (Satula et al.)
Pairing properties
GS energy
HFB
correlations
Exp.?
Beyond HFB
Odd nucleus
Ecorr
Kuo et al. D1 D1S D1N
corr[keV] Few ~100 ~300 ~200 ~200
Corr.
HFB
GS
1st excited states
Eoddeven odd
Eeven
ST sub-spaces