Fine structure of nuclear spin-dipole excitations in covariant density functional theory

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1 1 o3iø(œ April 12 16, 2012, Huzhou, China Fine structure of nuclear spin-dipole excitations in covariant density functional theory ùíî (Haozhao Liang) ŒÆÔnÆ 2012 c 4 13 F ÜŠöµ Š # Ç!Nguyen Van Giai Ç!ë+ Æ

2 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

3 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

4 Nuclear spin-isospin resonances Nuclear charge-exchange excitations β-decay charge-exchange reactions These excitations play important roles in spin and isospin properties of the in-medium nuclear interaction neutron skin thickness Krasznahorkay:1999PRL, Vretenar:2003PRL, Yako:2006PRC β-decay rates of nuclei in r-process path Engel:1999PRC, Borzov:2006NPA ββ-decay rates Ejiri:2000PhysRep, Avignone:2008RMP inclusive neutrino-nucleus cross sections Kolbe:2003JPG, Vogel:2006NPA isospin corrections for superallowed β deacys Towner & Hardy:2010RPP, HZL:2009PRC... Nuclear spin-isospin resonances become one of the central topics in nuclear physics, particle physics, and astrophysics.

5 SD excitations and resolving different J π components Spin-dipole (SD) excitations with S = 1 and L = 1 have attracted more and more attentions due to their connection with neutron-skin thickness Krasznahorkay:1999PRL cross section of neutrino-nucleus scattering Kolbe:2003JPG, Vogel:2006NPA ββ-decay rates Ejiri:2000PhysRep Different from Gamow-Teller (GT) excitations having single J π = 1 + component, SD excitations are composed of three collective components with spin-parity J π = 0, 1 and 2. Resolving the J π = 0, 1, 2 components is crucial to understand strengths of the nucleon-nucleon effective tensor interactions Bai:2010PRL,2011PRC multipole-dependent effects on the neutrino-nucleus scattering Lazauskas:2007NPA and the 0νββ decays Šimkovic:2008PRC, Fang:2011PRC

6 Microscopic theories for SD excitations Shell models (A 60) Caurier:2005RMP Random Phase Approximation (RPA) based on density functional theories traditional (non-relativistic) density functional Auerbach:1984PRC, Bai:2010RPL,2011PRC covariant (relativistic) density functional RHF+RPA Excellent agreement with the GT resonances data was obtained without any readjustment of the covariant density functional. HZL, Giai, Meng, PRL 101, (2008)

7 In this work In this work Self-consistent RPA approach based on the RHF theory will be applied to investigate the SD excitations. Results will be compared to the fine structure provided by the most up-to-date experiments in 16 O. RH+RPA results will be also shown to present the effects of the exchange terms.

8 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

9 Relativistic Hartree-Fock theory Covariant density functional theory RHF theory Effective Lagrangian density Bouyssy:1987PRC, Long:2006PLB ( L = [iγ ψ µ µ M g σ σ γ µ g ω ω µ + g ρ τ ρ µ + e 1 τ ) 3 A µ f ] π γ 5 γ µ µ π τ 2 m π µ σ µ σ 1 2 m2 σσ Ωµν Ω µν m2 ωω µ ω µ 1 4 R µν R µν m2 ρ ρ µ ρ µ µ π µ π 1 2 m2 π π π 1 4 F µν F µν (1) ψ Energy functional of the system E = Φ 0 H Φ 0 = E k + E D σ + E D ω + E D ρ + E D A +E E σ + E E ω + E E ρ + E E π + E E A (2)

10 Random Phase Approximation Random Phase Approximation RPA equations Ring & Schuck:1980 A B B A X Y = ω ν X Y (3) where the matrix elements of particle-hole residual interactions read A = (E A E a )δ AB δ ab (E α E a )δ αβ δ ab + f Af b V f B f a f a f B f A f b V f β f a f a f β, f α f b V f B f a f a f B f α f b V f β f a f a f β B = f Af B V f b f a f a f b f A f β V f b f a f a f b f α f B V f b f a f a f b f α f β V f b f a f a f b (4a) (4b) Particle-hole (ph) residual interactions in self-consistent RPA derived from the second derivative of the energy functional with rearrangement terms, if the meson-nucleon couplings are density-dependent

11 RHF+RPA RHF+RPA in charge-exchange channel Particle-hole residual interactions σ-meson: V σ (1, 2) = [g σ γ 0 ] 1 [g σ γ 0 ] 2 D σ (1, 2) (5a) ω-meson: V ω (1, 2) = [g ω γ 0 γ µ ] 1 [g ω γ 0 γ µ ] 2 D ω (1, 2) (5b) ρ-meson: V ρ (1, 2) = [g ρ γ 0 γ µ τ] 1 [g ρ γ 0 γ µ τ] 2 D ρ (1, 2) (5c) pseudovector π-n coupling: V π (1, 2) = [ f π m π τγ 0 γ 5 γ k k ] 1 [ f π m π τγ 0 γ 5 γ l l ] 2 D π (1, 2) (5d) zero-range counter-term of π-meson: V πδ (1, 2) = g [ f π m π τγ 0 γ 5 γ] 1 [ f π m π τγ 0 γ 5 γ] 2 δ(r 1 r 2 ), g = 1/3 (5e) π-meson is included naturally. g = 1/3 in the zero-range counter-term of π-meson is maintained for the sake of self-consistency.

12 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

13 RHF+RPA for Gamow-Teller resonances Gamow-Teller resonances in 48 Ca, 90 Zr, and 208 Pb GTR excitation energies can be reproduced in a fully self-consistent way HZL, Giai, Meng, PRL 101, (2008)

14 Physical mechanisms of GTR RH+RPA no contribution from isoscalar mesons (σ, ω), because exchange terms are missing. π-meson is dominant in this resonance. g has to be refitted to reproduce the experimental data RHF+RPA isoscalar mesons (σ, ω) play an essential role via the exchange terms. π-meson plays a minor role. g = 1/3 is kept for self-consistency. HZL, Giai, Meng, PRL 101, (2008)

15 Spin-dipole resonances Main peak can be reproduced by RHF+RPA exp. Yako:2006PRC Energy hierarchy RHF+RPA: E(2 ) < E(1 ) < E(0 ) agree with SHF+RPA Fracasso:2007PRC RH+RPA: E(2 ) < E(0 ) < E(1 ) Separating experimentally the different components from the total transition strength would be helpful to evaluate the theoretical predictive power, e.g., SDR in 208 Pb Wakasa:2010arXiv and 16 O Wakasa:2011PRC

16 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

17 Fine structure of GT and SD excitations in 16 O A most recent 16 O( p, n) 16 F experiment Wakasa et al., PRC 84, (2011) SHF+RPA calculations: Bai et al., PRC 84, (2011)

18 Spin-dipole excitations by RHF+RPA HZL, Zhao, Meng, arxiv: [nucl-th] SDR in T channel by RHF+RPA, the lowest RPA state as the reference of E x. exp. Wasaka:2011PRC In general, the 0, 1, and 2 excitations are well reproduced. The 0 1, 1 1, and 2 1 triplets are found at E x 0 MeV. The shoulder at E x 6 MeV and giant resonance at E x 7.5 MeV are nicely reproduced. In particular, the shoulder state cannot be described by shell model calculations.

19 Spin-dipole excitations by RHF+RPA HZL, Zhao, Meng, arxiv: [nucl-th] SDR in T channel by RHF+RPA, the lowest RPA state as the reference of E x. exp. Wasaka:2011PRC The broad resonances at E x 9.5 and MeV are understood as the mixture of the J π = 1 and 2 excitations, and the former one is dominant by 2 component, whereas the latter one is dominant by 1 component. The 0 resonances are predicted to be fragmented at MeV with the peak at E x 14.5 MeV.

20 SD excitations by RHF+RPA and RH+RPA RH+RPA results The general pattern of 2 excitations are similar to that of RHF+RPA calculations, except the peak at E x 9.5 MeV is missing. The 1 resonances are predicted at MeV, somehow too high in energy by comparing to data. The 0 resonances are predicted to be centralized at MeV, but not seen in experiments yet. Conclusion By comparing with the experimental date, it is found that the self-consistent RHF+RPA calculations are more favored.

21 Unperturbed and collective excitations R - (fm 2 /M e V ) R - (fm 2 /M e V ) R - (fm 2 /M e V ) P K O 1 H a r tr e e -F o c k R P A J = 0 - J = J = E x ( M e V ) D D - M E 2 H a r tr e e R P A J = 0 - J = 1 - J = E x ( M e V ) HZL, Zhao, Meng, arxiv: [nucl-th]

22 Diagonal matrix elements of ph interactions d i a g o n a l m a t r i x e l e m e n t s ( M e V ) J = 0-1 /2 πs 1 /2 J = 1-1 /2 πs 1 /2 J = 2-1 /2 πd 5 /2 P K O 1 3 /2 πd 3 /2 3 /2 πd 5 /2 3 /2 πd 5 /2 3 /2 πd 3 /2 3 /2 πs 1 /2 J = 0-1 /2 πs 1 /2 J = 1-1 /2 πs 1 /2 J = 2-1 /2 πd 5 /2 D D -M E 2 3 /2 πd 3 /2 3 /2 πd 5 /2 3 /2 πd 5 /2 t o t a l σ + ω ρ π P V π Z R 3 /2 πd 3 /2 3 /2 πs 1 /2 HZL, Zhao, Meng, arxiv: [nucl-th]

23 Spin-dipole excitations in T + channel by RHF+RPA HZL, Zhao, Meng, arxiv: [nucl-th] SDR in T + channel by RHF+RPA, the lowest RPA state as the reference of E x. exp. Hicks:1991PRC The 0 1, 1 1, and 2 1 triplets are found at E x = 0 2 MeV. The main resonance at E x 8.3 MeV is nicely reproduced, where the 2 component is predicted as the dominant component. A shoulder structure at E x 6.5 MeV is mainly formed by the 2 excitations.

24 Spin-dipole excitations in T + channel by RHF+RPA HZL, Zhao, Meng, arxiv: [nucl-th] SDR in T + channel by RHF+RPA, the lowest RPA state as the reference of E x. exp. Hicks:1991PRC Giant resonances at E x = MeV are also reproduced. It is predicted that these resonances mainly consist of 1 and 2 excitations, and the 1 component is the dominant component. The 0 resonances are predicted to be fragmented at E x = MeV.

25 Outline 1 Introduction 2 Theoretical Framework Relativistic Hartree-Fock theory Random Phase Approximation RHF+RPA 3 GT and SD Resonances 4 Fine structure of SD excitations in 16 O 5 Summary

26 Summary SD excitations have been investigated with the fully self-consistent RPA based on the covariant density functional theory. The fine structure of SD excitations in the most up-to-date 16 O( p, n) 16 F experiment is excellently reproduced without any readjustment in the functional. The characteristics of SD excitations are understood with the delicate balance between the σ- and ω-meson fields via the exchange terms. The fine structure of SD excitations for 16 O(n, p) 16 N channel has also been predicted for future experiments.