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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