Interna'onal Nuclear Physics Conference Collec've neutrino flavor oscilla'ons and applica'on to supernova nucleosynthesis

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1 Interna'onal Nuclear Physics Conference 2016 Collec've neutrino flavor oscilla'ons and alica'on to suernova nucleosynthesis H. Sasaki 1,2, T. Kajino 1,2, T. Takiwaki 2, J. Hidaka 3, T. Maruyama 4, Y. Pehlivan 5, and A. B. Balantekin 6 1 Deartment of Astronomy, The University of Tokyo 2 Na'onal Astronomical Observatory of Jaan 3 Mechanical Engineering Deartment, Meisei University 4 College of Bioresource Sciences, Nihon University 5 Mimar Sinan Fine Arts University 6 Deartment of Physics, University of Wisconsin, Madison

2 Neutrino oscilla'ons Flavor eigenstates are mixing of energy eigenstates in vacuum Transi'on from a flavor state to another flavor state e µ = U α 1 2 β α,β = e, µ,τ =Mass eigenstates τ flavor 3 mass cos θ 23 sin θ 23 0 sin θ 23 cos θ 23 cos θ 13 0 sinθ 13 e iδ sin θ 13 e iδ 0 cos θ 13 cos θ 12 sin θ 12 0 sin θ 12 cos θ This matrix causes neutrino oscilla'ons PMNS matrix

3 Neutrino oscilla'ons in core collase suernovae (several seconds azer bounce) NC β 2 α Proto-neutron star r-rocess 92 Nb 180 Ta -rocess elements 7 Li θ 1 Vacuum oscilla'ons Collec've oscilla'ons (- forward sca_ering) 100km Duan, et al.,pr D74 (2006), MSW effect e e CC 138 La e e 11 B Contribute to nucleosynthesis e + n +e e + n +e +

4 Purose of our Research Collec've oscilla'ons will lay significant roles in suernova nucleosynthesis Study collec've oscilla'ons and their effects on nucleosynthesis What we did Calcultate 3 flavor collec've oscilla'ons and aly these results to network calcula'on in both mass hierarchy Δm 2 32 = m 2 2 Δm 2 3 m 32 > 0 2 Δm 2 32 < 0. Normal mass hierarchy. Inverted mass hierarchy

5 Our Model Model & Assum'on 15 M rogenitor (model s15s7b2 ), 1.2 s azer bounce S.E. Woosley and T.A.Weaver,1995,AJS,101,181 Sherical symmetric and steady state Neutrino shere: R = 20 km Assum'on Mixing arameters (θ ij, Δm ij2 ) from PDG Mean field - forward sca_ering term G. Sigl and G. Rafflet,1993,NP B406,423 H β q α Mean field β α α q β α, β = e, µ, τ α β

6 We calculate the evolu'on of 3 x 3 density matrix Formalism G. Sigl and G. Rafflet,1993,Nucl. Phys. B 406,423 a j ()a i( ) =(2π) 3 δ (3) ( )(ρ ) ij b i ()b j( ) =(2π) 3 δ (3) ( )(ρ ) ij Ensemble average of Heisenberg equa'on of ρ = i [H, ρ] ρ = i [H, ρ] ρ(t, r, ) ρ(t, r, ) )a i ( ). annihila'on oerator of i b j ( ). annihila'on oerator of j a j ()a i( ) b i ()b j( ) We solve these equa'ons!! H = H Vacuum + H MSW + H. Hamiltonian in flavor sace Mean field - forward sca_ering term -

7 Evolu'on of ρ ee ( e robability) Normal mass hierarchy Δm 32 2 > 0 Inverted mass hierarchy Δm 2 < 0 32 ρ ee MeV 30 MeV 5 MeV 270 km, the onset of collec've oscilla'ons 15 MeV MSW effect km, the onset of collec've oscilla'ons r (km) 5 MeV 30 MeV r (km)

8 Mass frac'on X i Mass frac'on of nucleus 4 He e + n +e Y e > 0.5 In Normal (Inverted) mass hierarchy, e + n +e + is enhanced by collec've oscilla'ons (MSW effect) r (km) n(normal) n(inverted) n(no oscilla'on)

9 rocess and onset of oscilla'ons T 9 10 Onset of collec've oscilla'ons (Normal) 145 km 3 2. T rocess.. e + n +e + 56 Ni 60 Zn 64 Ge (n,) β + 64 Ga (,γ) -nucleus 74 Se, 78 Kr, 84 Sr, 92 Mo, 96 Ru Onset of MSW effect (Inverted) 700 km rocess r (km)

10 Final mass frac'on Without oscilla'on r = 900 km, T 9 = 1.20 Inverted Normal 56 Ni 56 Co 56 Fe 64 Ge 64 Ga 64 Zn Mass frac'on Enhanced by rocess 2 10 'mes A (Mass number)

11 Future rosects Choose other trajectories and study oscilla'on effects on rocess elements Interret oscilla'on henomena analy'cally Beyond mean field Y. Pehlivan, et al., Phys. Rev. D, 84, , 2011 q q

12 Summary It seems that neutrino oscilla'ons esecially collec've oscilla'ons will lay significant roles towards nucleosynthesis in core collase suernovae 3 flavor collec've oscilla'ons were calculated and alied to the exlosive nucleosynthesis. In normal hierarchy, much free neutrons are created by collec've oscilla'ons before rocess, so abundance of -nucleus are enhanced. In inverted hierarchy, free neutrons are created by MSW effects but azer rocess, so the effect of oscilla'ons are negligible.