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V. V. A.TsakstaraA.TsakstaraDivision of Theoretical Physics Division of Theoretical Physics
University of University of IoanninaIoannina
GreeceGreece
Investigating the nuclear response of Te Investigating the nuclear response of Te isotopes to SN neutrinosisotopes to SN neutrinos
MEDEX MEDEX --09 Prague, Czech Republic, June 1509 Prague, Czech Republic, June 15--18, 200918, 2009
OutlineOutline•• IntroductionIntroduction
i. Neutrino Production Sources
ii. Supernova Neutrino production
iii. SN- νν detection by terrestrial experiments ( COBRA)
iv. Neutrino-nucleus reaction cross sections at low energies
•• Nuclear Response to SNNuclear Response to SN-- νν SpectraSpectrai. Response of Te, Zn - isotopes to SN- ν spectraii. Convolution (folding) method for:
Differential cross sections <d<dσσ/d/dωω>>Double differential cross sections <d<d22σσ/d/dΩΩddωω>>
iii. Low energy beam neutrinos in SN- ν searchesReactor neutrino spectraBeta - beam neutrino spectra
•• Summary Summary -- Conclusions Conclusions -- OutlookOutlook
Neutrino SourcesNeutrino Sources1) 1) Astrophysical Neutrino SourcesAstrophysical Neutrino Sources
i. Solar Neutrinos
ii. Supernova Neutrinos
iii. Atmospheric Neutrinos
iv. Cosmological Neutrinos
2) 2) Laboratory Neutrino SourcesLaboratory Neutrino Sources
At the end of hydrostatic burning a massive star ~ 8 Msun consists of concentric shells that are the relics of its previous burning phases
When the mass of the iron core exceeds the MCh =1.4 Msun, the gravitational pull > thermal pressure
Star evolution and Star evolution and νν--production production mechanismmechanismss
FeS,Si FeO S, Si
C Ne, Mg
He C, O
H He
The coreThe core--collapse collapse supernovasupernova is is started!!!started!!!
CoreCore--collapse simulation resultscollapse simulation results
H. Th. H. Th. JankaJanka, K. , K. LangankeLanganke et al, astroet al, astro--ph/0612072 v1, 2006ph/0612072 v1, 2006
The main stages of stellar evolution (for massive stars) according to Janka et al., are:
Initial phase of collapse
Neutrino trappingBounce and shock formation
Shock propagation and neutrino burst
Shock stagnation and neutrino heating
Neutrino cooling and neutrino driven wind
neutrinos neutrinos of all flavorsof all flavorsare producedare produced!!!!!!
Average energy of SNAverage energy of SN--νν spectraspectra
Average energy of emitted neutrinos reflects the temperature of matter around the neutrinosphere.
,e e xE E Eν ν ν ν< <
3 , 5e
T M e Vν ≈ 5e
T M e Vν ≈ 8x
T M eVν ≈
ev
11 2516
eν
xνxv
( ) ( ) ( ),d dd
d dnν
ν νω
σ ω σ ε ωε ε
ω ω
∞
= ∫
The differential ν-nucleus cross-section ddσσ ((εενν ,,ωω)/)/ddωω is folded by using the expression to study the nuclear response to SNSN--ννspectra:
ωω = = ΕΕii -- ΕΕf f == εεii –– εεff :: excitation energy of the nucleus
The Convolution Method in SNThe Convolution Method in SN--νν SearchesSearches
The nn((εενν)) is a specific ν –energy distribution normalized to unity as:
( ) 1v vdn ε ε =∫
Energy Energy distribution for SNdistribution for SN--νν
Boosted betaBoosted beta--beam neutrino spectrabeam neutrino spectra
Reactor neutrino Reactor neutrino spectrumspectrum
Fermi Fermi -- DiracDirac
Power Power -- llawaw
e
e e e
2ν
ν ν μ ν4μ
96ε(ε ) = (m -2ε )
mn
( ) ( ) ⎡ ⎤⎛ ⎞⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
2v
eff v 3eff v
eff
ε1[T,n ] ε =FD F n T εExp -n +1T
n
( )⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
ν
ν
α ε- a+1εν
ν νν
ε1ε ,a ε = ePL c ε[ ]( )n
FermiFermi--DiracDiracPowerPower--lawlaw
Michel Michel spectraspectra Boosted beta Boosted beta -- beambeam
Low – energy betabeta--beams beams can provide information about SN-νinteractions the interpretation of a SN –ν signal in a terrestrial detector.
We construct linear combinations of boosted beta beam spectra nnγγii:
1
( ) ( )i
N
N ii
an nγ ν γ νε ε
=
= ∑
The expansion coefficients aaii = 1,2,= 1,2,……,N ,N for the boost factors γγi = 1,2,i = 1,2,……,N,N are obtained by minimizing the expression
( ) ( )N SNd n nγ
νν ν νεε ε ε−∫
LowLow--energy betaenergy beta--beams in SNbeams in SN--νν physicsphysics
N.JachowiczN.Jachowicz and and G.C.McLauyhlinG.C.McLauyhlin, Phys. Review C 77,2008 , Phys. Review C 77,2008
PowerPower--law fitting with 3law fitting with 3--5 boost components5 boost components
128,130 ' 128,130 *( , )e eTe v v Te
Nuclear response to SNNuclear response to SN--νν of COBRA targetof COBRA target
64,68 ' 64,68 *( , )e e
The aim of this work is to study the response to SN-ν of the nuclear isotopes ZnZn, TeTe, contained in the COBRACOBRA detector, through the neutral current reactions
Zn v v Zn
νν ν΄ν΄(u)(u)
(d)(d)(d)(d) (d)(d)
(d)(d)
(u)(u)ZZ00
* '( , ) ( , )v Z A Z A v+ → + '*( , ) ( , )v Z A Z A ν+ → +
K. K. ZuberZuber, , PhysPhys. . LettLett. B 519, 1. B 519, 1––7 (2001); 7 (2001); ProgProg. . PartPart. . NuclNucl. . PhysPhys. 57, 235. 57, 235––240 (2006);240 (2006);
Results of the convolution for Results of the convolution for 6464ZnZn
Convoluted differential cross-section using Fermi-Dirac (left) and power-law (right)
Results of the convolution for Results of the convolution for 6464ZnZn
Convoluted differential cross-section using Fermi-Dirac (left) and power-law (right)
Results of the convolution for Results of the convolution for 130130TeTe
Convoluted double differential cross-section using Fermi-Dirac (left) and power-law (right)
Results of the convolution for Results of the convolution for 130130TeTe
Convoluted double differential cross-section using Fermi-Dirac
Results of the convolution for Results of the convolution for 130130TeTe
Results of the convolution for Results of the convolution for 128128TeTe
Summary Summary –– CConclusionsonclusionsWe study the response of Zn Zn andand TeTe isotopes to the SN- ν spectra by
evaluating the folded: 1)1) differential cross-sections ddσσ//ddωω2)2) double deferential cross-sections <d<d22σσ/d/dΩΩddωω>>
We used the convolution method and employed(i)(i) FermiFermi--DiracDirac neutrino energy distribution (ii)(ii) PowerPower--lawlaw neutrino energy distribution (iii)(iii) ReactorReactor neutrino energy distribution(iv)(iv) Linear-combination of boosted betaboosted beta--beambeam neutrinos
They are appropriate for neutrinos produced in Supernova explosions.
We found that there are not dramatical differences between the above distributions. However, shows very interesting characteristics.
Acknowledgments:Acknowledgments: I wish to I wish to acknowledge financial support from acknowledge financial support from the the ΠΕΝΕΔΠΕΝΕΔ--03/80703/807, Hellenic GSRT , Hellenic GSRT ProjectProject
Thank you!!!Thank you!!!
Supervision:Supervision:T.S.KosmasT.S.Kosmas University University IoanninaIoannina (Greece)(Greece)CollaboratorsCollaborators::P.C. Divari TEI Peireas (Greece)
J. Sinatkas TEI Western Makedonia (Greece)