A microscopic approach to nuclear dynamics. Cédric Simenel CEA/Saclay, France

Transcription

1 A microscopic approach to nuclear dynamics Cédric Simenel CEA/Saclay, France

2 Introduction Quantum dynamics of complex systems (nuclei, molecules, BEC, atomic clusters...) Collectivity: from vibrations to collisions Interplay with single-particle d.o.f. (Giant Resonance decay, Competition fusion/ transfer...) Quantum many-body problem

3 Microscopic, up to which scale?

4 Microscopic, up to which scale?

5 Microscopic, up to which scale? Ingredients of the model: nucleon-nucleon interaction approximations of the manybody problem

6 Hamiltonian Ĥ = ˆT + ˆV ˆT = N i=1 ˆp 2 ˆ(i) 2m ˆV = 1 2 N i j=1 ˆv(i, j) 4

7 Hamiltonian Separation into a mean field U and a residual interaction N i=1 ˆV = Û + ˆV res with Û = û(i) Mean-Field approximation: neglect Vres Each nucleon is assumed to evolve independently in the MF generated by the other nucleons. The interactions are «averaged» into a MF. Justified by the mean free path of a nucleon in the nucleus of the order of the size of the nucleus, thanks to the Pauli principle: All nucleon states with energy < EF are occupied E2-dE<EF E1<EF E1+dE E2<EF 5

8 Hamiltonian Separation into a mean field U and a residual interaction N i=1 ˆV = Û + ˆV res with Û = û(i) Mean-Field approximation: neglect Vres Each nucleon is assumed to evolve independently in the MF generated by the other nucleons. The interactions are «averaged» into a MF. Justified by the mean free path of a nucleon in the nucleus of the order of the size of the nucleus, thanks to the Pauli principle: All nucleon states with energy < EF are occupied E2-dE<EF E1<EF E1+dE E2<EF 5

9 Hamiltonian Separation into a mean field U and a residual interaction N i=1 ˆV = Û + ˆV res with Û = û(i) Mean-Field approximation: neglect Vres Each nucleon is assumed to evolve independently in the MF generated by the other nucleons. The interactions are «averaged» into a MF. Justified by the mean free path of a nucleon in the nucleus of the order of the size of the nucleus, thanks to the Pauli principle: All nucleon states with energy < EF are occupied E1<EF E1+dE E2-dE<EF already occupied E2<EF 5

10 Hartree-Fock Mean-field determined from the interaction û(i) = N j=1 Self-consistent mean-field HF equation ( ˆp 2 2m +û[ρ] ϕ j ˆ v(i, j) ϕ j û û[ϕ 1, ϕ 2, ϕ N ] û[ρ] ) ϕ i ĥ[ρ] ϕ i = e i ϕ i for i =1, 2 N

11 Practical aspects of HF calculations Imaginary time method for a ground state with no self-consistency ( ): i ϕ init = C i ϕ i e i h ˆ t e β h ˆ ϕ = C e βe i ϕ ( ( C e βe 0 init i i β ϕ 0 0 i h ˆ h ˆ [ρ]

12 Practical aspects of HF calculations HF calculations Start with Nilsson or harmonic oscillator w.f. Imaginary time method for a N lowest states of h[ρ]: iterative process (evolution with ) Δβ (Graham-Schmidt orthonormalization)

13 Practical aspects of HF calculations HF calculations Start with Nilsson w.f. Imaginary time method 16 O 1d3/2 2s1/2 1d5/2 1p1/2 1p3/2 1s1/2 ev8, P. Bonche et al., Comp. Phys. Com. 171, 49 (2005)

14 Practical aspects of HF calculations HF calculations Start with Nilsson w.f. Imaginary time method Occupied neutron w.f. 16 O ev8, P. Bonche et al., Comp. Phys. Com. 171, 49 (2005)

15 Ground-state density from HF calculations 16 O

16 Ground-state density from HF calculations

17 Ground-state density from HF calculations filling of 3s1/2 shell

18 Excited states single-particle excitations Low-lying collective vibrations Giant resonances

19 Interpretation of 130 Sn (Z=50, N=80) spectrum

20 Interpretation of 130 Sn (Z=50, N=80) spectrum neutrons

21 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

22 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

23 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

24 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

25 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

26 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

27 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

28 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

29 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

30 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 2d3/2 neutrons

31 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 Ψ(2 + ) = aψ(νh 11/2 νh 11/2 ) +bψ(νd 3/2 νd 3/2 ) +cψ(νd 3/2 νs 1/2 ) +... neutrons 2d3/2

32 Interpretation of 130 Sn spectrum 1h11/2 3s1/2 Ψ(2 + ) = aψ(νh 11/2 νh 11/2 ) +bψ(νd 3/2 νd 3/2 ) +cψ(νd 3/2 νs 1/2 ) neutrons 2d3/ => low-lying collective vibration HF eigenstate