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Skyrme N2LO
functionals: first results
on finite nuclei
Skyrme N2LO functionals: first results on
finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Introduction
Infinite matter
calculations
D. Davesne, P. Becker, A. Pastore, J. Navarro
Application to
astrophysics LYVA1
Application to spherical
nuclei
Orsay, October 2017
First results
Conclusion and
perspectives
n
N2LO/N3LO extensions : physical motivation
n
Results in infinite matter
n
Extension of Gogny interaction
n
Application in astrophysics
n
Application to finite nuclei: first results
n
Conclusion
Linear response
formalism
N2LO/N3LO extensions : physical motivation
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Introduction
Infinite matter
calculations
n Construction of new effective interactions necessary!
Application to
astrophysics LYVA1
n Instabilities experienced with popular interactions (Skyrme,
Application to spherical
nuclei
Gogny)
n Initial idea (Skyrme) : expansion in powers of momentum (k2 )
→ systematic expansion up to kn ... which n???
n N2LO : n = 2 ; N3LO : n = 3 ; ...
2 2
n Gogny: e−r /µ , M3Y : e−µr /µr, ... : SAME kind of expansion
[F. Raimondi et al., Phys.Rev. C84 (2011) 064303]
First results
Conclusion and
perspectives
Linear response
formalism
N2LO/N3LO extensions : physical motivation
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Finite-range interaction D1S: infinite sum of partial waves.
Introduction
80
E/A [MeV]
60
Infinite matter
calculations
D1S
S-wave
S+P-wave
S+P+D-wave
S+P+D+F-wave
Application to
astrophysics LYVA1
Application to spherical
nuclei
First results
40
Conclusion and
perspectives
Linear response
formalism
20
0
-20
0
0.1
0.2
0.3
0.4
0.5
-3
ρ [fm ]
Only S, P, D and F (` < 4) waves necessary → N3LO good enough
Skyrme pseudo-potential N2LO/N3LO
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Introduction
1
V(r1 , r2 ) = t0 (1 + x0 Pσ ) + t3 (1 + x3 Pσ )ρα (R)
6
Skyrme (N1LO)
i
h 0
0
1
2
2
+ t1 (1 + x1 Pσ ) k + k + t2 (1 + x2 Pσ ) k · k
2
h
i
1
+ t1(4) (1 + x1(4) Pσ ) (k2 + k0 2 )2 + 4(k0 · k)2
4
Skyrme N2LO
(4)
(4)
0
2
02
+ t2 (1 + x2 Pσ )(k · k)(k + k )
i
0
h 0
1
+ t1(6) 1 + x1(6) Pσ (k 2 + k2 ) (k 2 + k2 )2 + 12(k0 · k)2
2
Skyrme N3LO
h
i
0
0
02
(6)
(6)
2 2
2
+ t2 1 + x2 Pσ (k · k) 3(k + k ) + 4(k · k)
n D and F partial waves included
n Gauge invariance
n Also includes:
n spin-orbit term W0
n tensor terms
Infinite matter
calculations
Application to
astrophysics LYVA1
Application to spherical
nuclei
First results
Conclusion and
perspectives
Linear response
formalism
Infinite matter: (S , T ) channels N2LO
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
n Used as a preliminary test before dealing with finite nuclei
n First step: (S , T ) channels
Introduction
n Results compared to BHF calculations from Baldo and al.
Infinite matter
calculations
Application to
astrophysics LYVA1
15
10
5
0
-5
-10
-15
0
BHF
SLy5
NLO
N2LO
-5
-5
-10
-10
-15
-15
-20
-20
-25
-25
-30
-30
0
0.1
0.2
ρ [fm-3]
0.3
0
0.1
0.2
ρ [fm-3]
0.3
Application to spherical
nuclei
First results
(S=1,T=1)
15
10
5
0
-5
-10
-15
0
(S=0,T=1)
(S=1,T=0)
(S=0,T=0)
(1997)
Conclusion and
perspectives
Linear response
formalism
Infinite matter: (S , T ) channels N3LO
Skyrme N2LO
functionals: first results
on finite nuclei
40
35
30
25
20
15
10
5
0
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
BHF
N1LO
N2LO
N3LO
0
0.2
0.4
0.6
0.8
0
0.2
ρ [fm-3]
n Agreement up to ρ = 0.8 fm−3
n Exploration of a new parameter space
0.4
0.6
ρ [fm-3]
0.8
Introduction
Infinite matter
calculations
(S=1,T=1)
40
35
30
25
20
15
10
5
0
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
Application to
astrophysics LYVA1
Application to spherical
nuclei
First results
Conclusion and
perspectives
(S=0,T=1)
(S=1,T=0)
(S=0,T=0)
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Linear response
formalism
Infinite matter: (S , T ) channels M3Y
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Introduction
30
Infinite matter
calculations
20
20
10
10
0
0
0
0
(S=1,T=1)
40
30
-10
-10
-20
-20
-30
-30
-40
0
0.2
0.4
0.6
0
0.2
-3
ρ [fm ]
0.4
0.6
-40
0.8
n M3Y takes into account nuclei and (S , T ) channels: both are not
incompatibles
Application to
astrophysics LYVA1
Application to spherical
nuclei
(S=0,T=1)
(S=1,T=0)
(S=0,T=0)
M3Y
40
First results
Conclusion and
perspectives
Linear response
formalism
Infinite matter: (S , T ) channels Gogny
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Not possible...
Introduction
20
3 Gaussians
D1M-fit
D1M
30
20
10
10
(S=1,T=1)
(S=0,T=0)
30
Infinite matter
calculations
40
40
-10
-20
-20
-30
-30
-40
0
0.2
0.4
0.6
... except with a third gaussian
0
0.2
-3
ρ [fm ]
0.4
0.6
-40
0.8
(S=0,T=1)
(S=1,T=0)
0
-10
Application to spherical
nuclei
First results
Conclusion and
perspectives
0
0
0
Application to
astrophysics LYVA1
Linear response
formalism
Determination of the three ranges
Skyrme N2LO
functionals: first results
on finite nuclei
D. Davesne, P. Becker,
A. Pastore, J. Navarro
Physical meaning of a range :
n Yukawa potential: related to masses (770, 490, 140 MeV)
n Gaussian potential??? → definition via the self-energy
Introduction
Infinite matter
calculations
Application to
astrophysics LYVA1
Application to spherical
nuclei
First results
Conclusion and
perspectives
0.25
0.2
Example:
RF/H Yukawa
mρ = 770 MeV
→ µ−1
Y =0.256 fm
RF/H Gogny
RF/H
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
3
→ R(µ−1
Y )=0.228 =R(µG )
→ µG = 0.475 fm
x
→ ranges: µ1 = 0.475 fm, µ2 = 0.746 fm , µ3 = 1.964 fm
Linear response
formalism
Davesne.pdf (PDF, 1.37 MB)
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