1. 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…

2. 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
QCD2010, Kyoto, 28 Jan. 2010

3. 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
QCD2010, Kyoto, 28 Jan. 2010

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

5. 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
QCD2010, Kyoto, 28 Jan. 2010
By Dr. Hayakawa

6. 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
QCD2010, Kyoto, 28 Jan. 2010

7. 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
QCD2010, Kyoto, 28 Jan. 2010 B

8. 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 ??
QCD2010, Kyoto, 28 Jan. 2010

9. 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
QCD2010, Kyoto, 28 Jan. 2010

10. 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 ?
QCD2010, Kyoto, 28 Jan. 2010

11. 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
QCD2010, Kyoto, 28 Jan. 2010

12. Smearing of the Fermi Surface for Zr
Quasi-particle RPA 8
Smearing of the Fermi Surface for Zr
Fermi energy
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13. 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
QCD2010, Kyoto, 28 Jan. 2010

14. 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 !!
QCD2010, Kyoto, 28 Jan. 2010

15. QRPA Equation for A and B matrices
Quasi-particle RPA 10
QRPA Equation for A and B matrices
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16. FLOW of Computer Program
Quasi-particle RPA 11
FLOW of Computer Program
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17. Weak currents and Cross sections 2 For a given transition operator
Model Independent
Model dependent
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18. Weak currents and Cross sections 3
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19. Results : Neutrino reactions (Exclusive and Inclusive) on12C, 56Fe and 56Ni
QCD2010, Kyoto, 28 Jan. 2010

20. 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
QCD2010, Kyoto, 28 Jan. 2010

21. 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.
QCD2010, Kyoto, 28 Jan. 2010

22. 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)
QCD2010, Kyoto, 28 Jan. 2010

23. Small uncertainties in Coulomb Corrections in CC
Results for 12 C : II
Small uncertainties in Coulomb Corrections in CC
QCD2010, Kyoto, 28 Jan. 2010

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

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

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

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

28. 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)
QCD2010, Kyoto, 28 Jan. 2010

29. 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 : (-40) : Fermi Coulomb Correction
With np pairing (-40) !!!!
O.K. !!
QCD2010, Kyoto, 28 Jan. 2010

30. Results for 56 Fe and 56 Ni : III
GT strength
QCD2010, Kyoto, 28 Jan. 2010

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

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

33. 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
QCD2010, Kyoto, 28 Jan. 2010

34. CC reactions for 138 La 2
QCD2010, Kyoto, 28 Jan. 2010

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

36. Cross sections folded by Supernovae neutrinos
QCD2010, Kyoto, 28 Jan. 2010

37. 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 !!
QCD2010, Kyoto, 28 Jan. 2010

38. 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.
QCD2010, Kyoto, 28 Jan. 2010

39. One-step Process 1
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40. Our Results and SM for 2 step Processes ! One step processes !
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41. Strangeness Contribution to neutrino reactions 2
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42. 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 !
QCD2010, Kyoto, 28 Jan. 2010

43. 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.
QCD2010, Kyoto, 28 Jan. 2010

44. 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.
QCD2010, Kyoto, 28 Jan. 2010

45. Transformation from Deformed to Spherical Basis
Nillson Basis
Spherical Basis
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46.
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47. for the cordial hospitality
Truly thanks
for the cordial hospitality
of LOC !!
QCD2010, Kyoto, 28 Jan. 2010

48. 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
QCD2010, Kyoto, 28 Jan. 2010

49. Cross sections Folded by Supernovae neutrinos
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50. Strangeness Contribution to neutrino reactions 3
Total cross section (CC reaction)
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51.
QCD2010, Kyoto, 28 Jan. 2010