Collective excitations in nuclei away from the valley of stability

Transcription

1 Collective excitations in nuclei away from the valley of stability A. Horvat 1, N. Paar , CSSP 14, Sinaia, Romania 1 Institut für Kernphysik, TU Darmstadt, Germany (for the R3B-LAND collaboration) Physics Department, Faculty of Science, University of Zagreb, Croatia HGS-HIRe Helmholtz Graduate School for Hadron and Ion Research

2 Contents 1 e fm /MeV 6 4 ISOVECTOR 13 Sn -1 3 e fm 6 /MeV ISOSCALAR 13 Sn E[MeV] D.M. Rossi et al., Phys. Rev. Lett. 111, 453 (13) Mechanism behind the pygmy dipole strength (PDS) in the framework of relativistic energy density functional with density dependent meson - nucleon coulplings Observables correlated with and sensitive to the symmetry energy at saturation density Which nuclei are best suited to constrain the symmetry energy at saturation from measured strength related quantities? Experimental study of the E1 response of neutron rich nuclei by means of Coulomb excitation by high Z target in inverse kinematics

3 The relativistic mean field description of the nuclear ground state L = Ψ(iγ µ µ m)ψ + 1 ( σ) 1 m σσ 1 4 Ω µνω µν + 1 m ωω 1 4 R µν R µν + 1 m ρ ρ 1 4 F µνf µν g σ ΨσΨ g ω Ψγ µ ω µ Ψ g ρ Ψγ µ ρ µ τψ e Ψγ µ (1 + τ 3 ) A µ Ψ Phenomenological description - m σ, m ω, m ρ, g σ, g ω, g ρ - adjustable parameters + pairing part of the Gogny interaction + parametrization of density dependence coupling parameters DD-ME interaction Solving Euler-Lagrange equations in a quasiparticle basis relativistic Hartree-Bogoliubov (RHB) T. Nikšić, D. Vretenar, P. Finelli and P. Ring, Phys. Rev. C ()

4 Relativistic mean field model - RHB DD-ME parametrization* mezon m(mev ) g(ρ sat) a b c d σ ω ρ *G. A. Lalazissis, T. Nikšić, D. Vretenar, P. Ring, Phys. Rev. C (5).4 tin isotopes.4 nickel isotopes g σ,ω(x) = g σ,ω(ρ sat ) f σ,ω(x), r skin [fm].3. r skin [fm] bσ,ω(x + dσ,ω) g σ,ω(x) = g σ,ω(ρ sat ) a σ,ω 1 + c σ,ω(x + d σ,ω), A A g ρ(x) = g ρ(ρ sat )Exp[ a ρ(x 1)], x = ρ ρ sat.

5 Excitations - Relativistic Quasiparticle Random Phase Approximation (RQRPA) RPA approximation built upon a RHB ground state Response to an externally applied field (small amplitude limit) ˆF (t) = ˆF e iωt + h.c. discrete RPA energies, corresponding transition probabilities 1 B(EJ; J i J f ) = J i + 1 J f ˆQ J J i B(E1) [e fm ] B(E1) [1 3 e fm 6 ] ISOVECTOR Sn J π =1, Τ=1 J π =1, Τ= ISOSCALAR E [MeV] For a spherically symmeteric nucleus in the ground state (J Π = + ) the (J, Π, T ) of excitation determined by j, π, τ of the quasipaticle pairs involved E(J) selection rules j κ j κ J j κ + j κ π κ π κ = ( 1) J

6 Structure of J=1, T=1 RPA states in tin isotopes Example 13 Sn E RPA = 15.5MeV E RPA = 7.75MeV 1 i 13/ 3g 9/ neutrons 3f 4p 5/ 3/ 1i 13/ 1 protons 1 i 13/ 3g 9/ neutrons 3f 4p 5/ 3/ 1i 13/ 1 protons E [MeV] f 5/ 1h 3p 9/ 3p 1/ 3/ f 7/ f 1h 7/ 9/ E [MeV] f 5/ 1h 3p 9/ 3p 1/ 3/ f 7/ f 7/ 3s 1h 11/ 1h 1/ 11/ d5/ 3s 1h 11/ 1h 1/ 11/ d5/ -1 3s d 1/ d 3/ 1g 5/ 7/ -1 d 3/ 1g 7/ -1 3s d 1/ d 3/ 1g 5/ 7/ -1 d 3/ 1g 7/ - 1g 9/ p 1/ p 3/ 5 1g 9/ 5 p - p 1/ 3/ - 1g 9/ p 1/ p 3/ 5 1g 9/ 5 p - p 1/ 3/ f 5/ 1f 5/ 1f 7/ 1f 7/ s 1/ -3 s 1/ 1d 3/ f 5/ 1f 5/ 1f 7/ 1f 7/ s 1/ -3 s 1/ 1d 3/ 1d 5/ 1d 3/ 1d 5/ 1d 3/ p 1p 1/ 3/ 1s 1/ d 5/ 1p 1p 1/ 3/ 1s 1/ p 1p 1/ 3/ 1s 1/ d 5/ 1p 1p 1/ 3/ 1s 1/ -6 B T (EJ, ω ν) = M T,J,ν κ,κ κ,κ -6

7 Assessing the Collectivity of Particular RPA States Two-quasiparticle contributions to transition probabilities M κ, κ [fm] M κ,κ [fm] f 7/ -> 1g 9/ 1f 7/ -> 1g 9/ Isovector 6 protons 13 Ni neutrons Sn 1f 7/ -> 1g 9/ 1d 3/ -> 1f 5/ 1f 5/ -> 1g 7/ E RPA =9.6 MeV E RPA =1.79 MeV 1d 3/ -> 1f 5/ 1f 7/ -> 1g 9/ 1f 5/ -> 1g 7/ 1h 11/ -> 1i 13/ 1g 9/ -> 1h 11/ 1f5/ 1h 11/ -> 1i 13/ 1g 9/ -> 1h 11/ 1f 5/ -> 1g 7/ 1g 7/ -> 1h 9/ E RPA =7.75 MeV E RPA =15.5 MeV -> 1g7/ 1g 7/ -> 1h 9/ M κ, κ [fm] Ni Isoscalar E RPA =9.6 MeV -> same low E qp neutron pairs contribute to IS and IV PDS E qp [MeV] protons neutrons 13 Sn E RPA =7.75 MeV 1 15 E qp [MeV] 1 E qp [MeV] 1 E qp [MeV] E qp (κ, κ ) = κκ + (E κκ λ) + κ κ + (E κ κ λ) Proton and neutron pairs with similar E qp contribute coherently in the case of an IVGDR state and cancel out for the PDS state. Same result for other neutron rich nuclei

8 E1 Strength Related Observables, Symmetry Energy and Neutron Skin Thickness same EDF in the description of nuclear matter properties and within the RHB+QRPA approach direct link between nuclear matter properties (symmetry energy at saturation density (J) and its slope L) and E1 excitation strength related observables and neutron skin thickness (r np) C AB = DDME-min1 J L K m*/m E(GMR) E(PDR) E(GDR) EWS(PDR) B(E1)(PDR) α D (PDR) EWS (all) B(E1) (all) α D (all) A B A B r np ( Pb) DDME-min c AB Distribution moments m k (T, J) = ν ω k νb T (J, ω ν) Thomas-Reiche-Kuhn sum rule m 1 (T = 1, J = 1) = 9 e NZ 4π m A (1+κ TRK ) Dipole polarizability α D = e ν ν ˆD = π E ν E 9 e m 1

9 E1 Strength Related Observables, Symmetry Energy and Neutron Skin Thickness same EDF in the description of nuclear matter properties and within the RHB+QRPA approach direct link between nuclear matter properties (symmetry energy at saturation density (J) and its slope L) and E1 excitation strength related observables and neutron skin thickness (r np) C AB = A B A B Non-relativistic Skyrme (SV-min) Distribution moments m k (T, J) = ωνb k T (J, ω ν) ν Thomas-Reiche-Kuhn sum rule m 1 (T = 1, J = 1) = 9 e NZ 4π m A (1+κ TRK ) Dipole polarizability P.-G. Reinhard and W. Nazarewicz, Phys. Rev. C (1) model dependence α D = e ν ν ˆD = π E ν E 9 e m 1

10 Constraining the Symmetry Energy - Sensitivity of Observables A family of effective DD-ME interactions with J = 3, 3, 34, 36, 3 MeV* total low total low R[e fm MeV -1 ] Sn J=3, L=3. MeV J=3, L=46.5 MeV J=34, L=6.1 MeV J=36, L=5.5 MeV J=3, L=11. MeV α D [fm 3 ] m [fm ] a) 3 b) 14 c) 3 d) Sn 1 Sn 14 Sn 1 Sn 13 Sn 136 Sn 1 3 E [MeV] J (MeV) J (MeV) R np [fm] R np [fm] overall quantities - α D - most sensitive low-lying moments are more sensitive to changes in J and r np all low-lying moments exhibit the same sensitivity to J since the PDS energy is independent of J constraining J sensitivity grows with neutron number constraining r np with PDS 14 Sn better than 13 Sn, tin isotopes heavier than 13 Sn are most sensitive *D. Vretenar, T. Nikšić, P. Ring, Phys. Rev. C 6, 431 (3)

11 Constraining the Symmetry Energy - Sensitivity of Observables Sn increase in r np by filling the 1h 11/ orbital no increase in PDS due to selection rules transitions to and from 1h 11/ lie in the high energy decoherent E qp region 16 Sn E [MeV] 1i 13/ + f 5/ 3p 1/ 3p 3/ 1h 9/ f 7/ h 11/ 3s 1/ + d 3/ + d 5/ + 1g 7/ + 1g 9/ + J. Piekarewicz, Phys. Rev. C (6)

12 Systematic Experimental Study of the Dipole Response for the Tin Isotope Chain - S41 Cross section for Coulomb induced nuclear breakup reactions v~c b dσ(e ) N1, Z1 de N, Z = 16π 3 9~c ne 1 (E ) db de (E 1, J, E ) Invariant mass method E = X P i mproj c i Image taken from Fabia Schindler, Master Thesis