Neutrino Reactions in Nuclear-Astrophysics (based on the Quasi-particle RPA) Myung-Ki Cheoun Soongsil University, Seoul, Korea K. S. Kim, E. Ha, W. Y. So, S. Y. Lee, C. Ryu… T. Kajino, T. Hayakawa, T. Maruyama … F. Simkovic, A. Faessler…

Contents 1. Motivation for the ν-process in Nucleosynthesis 2. Brief Introduction of QRPA 3. Indirect (Two-step or Compound nuclei) 4. Direct (One-step or Knock-out) Process and Strangeness contributions for ν-reactions 5. Results (12C,56Fe,56Ni,138Ba,139La) 6. Summary and Future works 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Depends on the transition matrix elements i.e. nuclear models Motivation 1 : Double Beta Decay Depends on the transition matrix elements i.e. nuclear models Based on the QRPA, which is one of the best choice to pin down the ambiguities from the nuclear structure 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Motivation 2 : Neutrino-12C in SN explosion Supernova n-Process & Key Reactions 7Li/11B - Ratio Yoshida, Kajino et al. ,2005, PRL94, 231101; 2006, PRL 96, 091101; 2006, ApJ 649, 319; 2008 ApJ 686, 448. 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Key Reactions for 138La, whose astronomical origin is still unknown Motivation 3 : Neutrino-138 La in SN explosion Key Reactions for 138La, whose astronomical origin is still unknown 139La(ν,ν'n)138La These excited states are of importance for this reaction. This state is populated in SNe of T9=1-3. The population ratio is calculated by T. E. N=82, Magic Number 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010 By Dr. Hayakawa

Motivation 4 : Neutrino-Nucleus Reactions on various energy region Cross Section Giant Resonance Delta Resonance Quasi Elastic Region Hadronic Region energy N* Resonance Dip Region Discrete Excited states Pion Threshold q Typical cross section by incident electron 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

How to describe the ground and excited states ? Motivation 5 : Neutrino-Nucleus Reactions via two-step rocess ν’(l) Indirect (Two-step) Processes ν W(+,-), Z0 p,n,… A* A B J ∏ How to describe the ground and excited states ? A* A 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010 B

Two Step Processes by Quasi-particle RPA (QRPA) Mean Fields (Hartree Fock, SM..) TDA, Random Phase Approximation (RPA) There remained short range correlations Our scheme is based on Quasi-particle Why Quasi-particle ?? 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Odd-even effects M (A: e-o) > [ M (A+1 : e-e) + M (A-1 : e-e) ] / 2 Quasi-particle RPA 3 Odd-even effects M (A: e-o) > [ M (A+1 : e-e) + M (A-1 : e-e) ] / 2 Proton-proton pairing correlations Even Neutron-neutron pairing correlations Even Proton-Neutron pairing correlations 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Pairing of Like and Unlike nucleons Quasi-particle RPA 4 Pairing of Like and Unlike nucleons neutron-neutron, proton-proton (T= 1) neutron-proton (T=1 and 0) couples J=L-1 and J=L+1 by tensor force. For example, 3S1 and 3D1 states play roles The np pairing could be vital for the exotic nuclei in the nucleo-synthesis with the deformations How to include the pairings in the nuclear structure ? 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Nuclei (gr.states) are presumed Quasi-particle RPA 5 (Deformed) BCS Cooper Pair in Nuclear Physics Nuclei (gr.states) are presumed as superfluid !! I =0 is more favorable 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Smearing of the Fermi Surface for Zr Quasi-particle RPA 8 Smearing of the Fermi Surface for Zr Fermi energy 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Description of Excited States By Haus Feshbach Theory Quasi-particle RPA 9 Description of Excited States Phonon Operator J ∏ By Haus Feshbach Theory or SMOKER Code A* A B 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Quasi-particle RPA 9-1 Cheoun et. al, JPG (2010) NC reactions cannot be described by the pn QRPA, which should be performed by pp+nn+pn QRPA by following the method for EM transition !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

QRPA Equation for A and B matrices Quasi-particle RPA 10 QRPA Equation for A and B matrices 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

FLOW of Computer Program Quasi-particle RPA 11 FLOW of Computer Program 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Weak currents and Cross sections 2 For a given transition operator Model Independent Model dependent 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Weak currents and Cross sections 3 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Results : Neutrino reactions (Exclusive and Inclusive) on12C, 56Fe and 56Ni 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Consider J^{pi} = 0(-,+) – 4(-,+) g_ph and g_pp are 1.0, which can be fined to adjust GTGR and beta decay data g_pp, g_nn, and g_np are adjusted to reproduce empirical pairing gaps. g_A = standard value. Coulomb corrections by Fermi ftn. or EMA Inclusive and exclusive reactions. CC and NC reactions for neutrino and anti- neutrino 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Calculate total cross sections given by the incident neutrino energy. Realistic Two Body Interaction is taken by Brueckner G-matrix by Bonn Potential !! Calculate total cross sections given by the incident neutrino energy. Calculate energy folded total c.s. by neutrino energy spectrum given by Fermi Dirac and Michel spectrum for supernovae and LSND neutrino, respectively. 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

LSND : ne12C -> e- + 12Ngs M-K.Cheoun et.al, PRC (2010) 1- 1+ 2- Results for 12 C : I LSND : ne12C -> e- + 12Ngs 1- 1+ 2- O.K. !! M-K.Cheoun et.al, PRC (2010) 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Small uncertainties in Coulomb Corrections in CC Results for 12 C : II Small uncertainties in Coulomb Corrections in CC 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Results for 12 C : III In CC, effects of other multipole transitions as well as the GT could be important !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

In NC reaction, GT transition is dominant !! Results for 12 C : IV In NC reaction, GT transition is dominant !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Cross sections averaged by incident neutrino spectrum !! Results for 12 C : V Cross sections averaged by incident neutrino spectrum !! O.K. !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

A=12 triad Qb+= 16.32 MeV Qb-= 13.37 MeV Results for 12 C : VI A=12 triad Qb+= 16.32 MeV Our results : 21.26 and 10.33 (ms) O.K. !! Qb-= 13.37 MeV 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Hybrid Model (= SM + RPA) Results for 56 Fe and 56 Ni : I M-K.Cheoun et.al, JPG (2010) GT trans. IAS trans. Hybrid Model (= SM + RPA) 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Without Fermi correction : 0.79 (-40) !!!! Results for 56 Fe and 56 Ni : II Without Fermi correction : 0.79 (-40) !!!! Flux averaged C.S. for DAR Our results : 1.418 (-40) : Fermi Coulomb Correction With np pairing 1.735 (-40) !!!! O.K. !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Results for 56 Fe and 56 Ni : III GT strength 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

NCs are Dominated by 1+ similarly to 12C !! Results for 56 Fe and 56 Ni : IV NCs are Dominated by 1+ similarly to 12C !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Results : Neutrino Inclusive and Exclusive Reactions for 138Ba via CC and 139La via NC 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Key Reactions for 138La : Charged Current CC reactions for 138 La 1 Key Reactions for 138La : Charged Current GT transitions From the 0+ gs of 138Ba to an odd-odd nucleus 138La Low spin states (J=0-2) are strongly populated by this reaction. 3. Neutron Separation Energy is 7.4 MeV and Proton Separation E is 6.1 MeV Experimental Data 138Ba(3He,t)138La is available. Z=57,N=81 By Hayakawa 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

CC reactions for 138 La 2 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

We reproduce experimental (GT) strength distribution by the quenching factor !! (5.56,3.15) (3.88,4.5) 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Cross sections folded by Supernovae neutrinos 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

For NC reactions in odd-even nuclei, one cannot use the standard QRPA. NC reactions for even-odd nuclei 2 For NC reactions in odd-even nuclei, one cannot use the standard QRPA. We used the QSM (Quasi-particle Shell Model) Reproduce approximately low energy excitation spectrum for even-odd nuclei !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

NC reactions for even-odd nuclei 3 139La(ν,ν'n)138La Dominated by 2+ and 4+, and 0+!! N=82, Magic Number We need to separate cross sections for each excited state, which decays with emitting particles. 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

One-step Process 1 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Our Results and SM for 2 step Processes ! One step processes ! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Strangeness Contribution to neutrino reactions 2 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Summary 1 Free of parameters ! Quasi particle RPA was successfully applied to the beta and double beta decays. Weak transitions between ground and excited states are included in our (Deformed) QRPA code by using Donnelly's multipole operator method. Results for neutrino nucleus interactions (12C, 56Fe, 56Ni, 92Zr,93Nb,138Ba,139La), which are known to play very important roles in the ν and rapid proton processes for the nucleosynthesis in core collapsing SN, obtained by this method showed quite consistent results with available data. But there exists still muon anomaly problem in the exclusive reaction. Higher multipole states contributions may contribute for this problem. We are applying our method to the ν processes as well as other reactions in another nuclei. Free of parameters ! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

CSs increase with heavier nuclei CCs are larger than NC CCs are dominated by the GT, IAS and SDR NCs are dominated by the GT. 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Summary 2 Contribution by one step processes for BBN are smaller 2-4 times than those by Indirect Processes with Final state interactions. But, two step processes need to be multiplied by the decay processes into residual nuclei. One step reaction could be comparable to those by indirect processes. The ambiguities from the nuclear structure should be pinned down for more accurate information in the astronomical data. In specific, for the unstable nuclei necessary in NS, more refined theory including the deformation, Deformed Quasi-particle RPA (DQRPA), is under progress,. Neutrino reactions with nuclear matter under strong magnetic fields are also in progress. 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Transformation from Deformed to Spherical Basis Nillson Basis Spherical Basis 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

for the cordial hospitality Truly thanks for the cordial hospitality of LOC !! 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Form factors in the Weak Current JPG 35 (08) M.- K. Cheoun… Form factors in the Weak Current Vector Form Factor Strangeness E-M Form Factor Strangeness Axial Form Factor 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Cross sections Folded by Supernovae neutrinos 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

Strangeness Contribution to neutrino reactions 3 Total cross section (CC reaction) 2019-01-03 QCD2010, Kyoto, 28 Jan. 2010

2019-01-03 QCD2010, Kyoto, 28 Jan. 2010