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)