Post on 21-Dec-2015
Electro-Weak Electro-Weak Reactions on light Reactions on light
nucleinuclei**in supernovaein supernovae
Doron GazitDoron Gazitprogress report talkprogress report talk
March 2007
Supervisor: Prof. Nir BarneaSupervisor: Prof. Nir Barnea..
Electro-Electro-Weak Weak Reactions on light Reactions on light
nucleinuclei**in supernovaein supernovae
PhD. Progress report2
Neutrino reactions with nuclei play major role in various fields of Physics.
Astrophysics, particle physics…
Open questions in Astrophysics:
Core collapse Supernovae explosion mechanism.
Nucleosyntesis in Supernovae.
Introduction
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Supernova IISupernova II- The death of a massive star
Crab Nebula
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The death of a massive star“the nuclear physicist paradigm”
After millions of years of evolving… •Iron peak nuclei don’t burn to
heavier nuclei no support to the core mass.
•The core becomes gravitationally unstable collapses.
•Nuclear forces halt the collapse, and drive an outgoing shock.
•The shock loses energy due to dissociation, neutrino radiation.
•The shock stalls…
~1 sec
~100 msec
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Schematic structure
Proto-Neutron Stare
e
NeutrinosphereT~4MeV
~1011-1012 g/cc
shock
“Hot Bubble”T~1-2MeV
~107-109 g/cc
Envelope layers: Si, O, C, He…
~ 10% A=3, 4 nuclei
~70% A= 4 nuclei
nucleosynthesis
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wind from the newly born PNS
• Carry 99% of the explosion energy.• Produced almost in flavor equilibrium
inside the hot collapsed core (proto-neutron star).
• Due to charged current reactions on electrons:
, ,,e e
~
10 MeV
~
15 MeV
~20 MeV
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wind from the newly born PNS
• Influence all the important processes:– Deposit energy in matter below the shock,
to determine shock radius.– Set neutron richness in the hot bubble, to
initiate the r process. It also fragments synthesized heavy nuclei.
These processes can be affected by These processes can be affected by the existence of nuclei in the the existence of nuclei in the
shocked regionshocked region
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Nuclei below the shock
• The Hot Bubble:– Low density, high temperature.– Favors the creation of 4He: “Alpha effect”
• Inelastic -4He reactions can diminish the effect.
– Composition: 4He, nucleons and electrons.– Haxton [1988]:
• Inelastic -nuclei reactions release a substantial amount of energy.
• Sufficient amount of have enough energy to dissociate 4He (~20 MeV).
• Near the newly born star, the temperature and density increases.
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Abundances of A=3,4 nuclei near the neutrinosphere
• The neutrinosphere is too dense to use simple NSE.
• Virial expansion extends NSE and includes the inter-particle scatterings.
• We wrote a virial EOS which includes: p, n, t, 3He, .
• The abundances are then derived from the EOS.
““Neutrino Breakup of A=3 Nuclei in Supernova”, Neutrino Breakup of A=3 Nuclei in Supernova”, E. O’Connor, E. O’Connor, D. GazitD. Gazit, C. J. Horowitz, A. Schwenk, N. Barnea, PRC , C. J. Horowitz, A. Schwenk, N. Barnea, PRC (submitted for publication).(submitted for publication).
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Equilibrium n,p,t,3He, Abundances
i ii
Pb
q nY
n
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Neutrino nucleosynthesis in the Helium layer
• Neutrino inelastic interactions with nuclei above the shock is a seed to nucleosynthesis.
• These neutrinos dissociate 4He in the He layer.• The A=3 nuclei fuse with 4He to create 7Li, through
the chain of reactions:
and
• Only neutral current reactions with 4He are important, because of 4He binding energy.
• Current knowledge of the neutrino sector indicates 1-3 neutrino flavor oscillations in the O/C layers.– Increases e energy, and increases nucleosynthesis through
charged reactions.
3 74He , 'p H , Li 3 7 74He , 'n He , Be n,p Li
Energy dependent, accurate
Energy dependent, accurate
cross-sections are needed.
cross-sections are needed.
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Calculating the cross-section
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Neutrino-nucleus interaction
XAZ
1X, XA AZ Z
, l
0Z
iP,EP iμ i
μP E ,Pf f f
1k,kk 1μ1
2k,kk 2μ2
qω,qμ lepton current Nuclear
current W
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Nuclear Neutral Current
Isovector
Axial
Vector
Isoscalar
Vector
0 2 20 0 5 11 2 sin 2 sin
2 2 2W WJ JJJ
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Nuclear Charged Current
Isovector
Axial
Vector
5
2 2JJ J
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Construction of the nuclear currents
• The leading operators are one-body operators.
• It is well known that Mesonic degrees of freedom influence the scattering process.
• Conservation of Vector currents means that in low momentum transfer the vector one body operators include Meson exchange currents.
• Axial MEC should be calculated explicitly.• Effective Field Theory – a modern
perturbative way to construct the many body currents.
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EFT systematics• Identify Q – the energy scale of the process.
(for SN – few 10’s of MeV)
• In view of Q -Identify the relevant degrees of freedom. (I use pions and nucleons).
• Choose – the theory cutoff. (400-800 MeV)
• Write all the possible operators which agree with the symmetries of the underlying theory (QCD).
2
nd
DerivativesDerivativesor pion massesor pion masses
nucleonsnucleons
order of interactionorder of interaction
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Chiral Lagrangian (NLO)
5
2 2 2† †
1 5 2
Tr Tr U+U 24 4
4, Tr a
EFT A N
N
N i iv g a M N
f f mU U
i N a a N NN aM M
D N a NNN iD N iv NNN
L -N basic interaction
Lagrangian
N of order 3
2N contact terms
Calibrated using 3H life
time
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Leading 1-body transition operators• The closed shell
character of 4He, suppresses the usually leading:– Gamow-Teller
operator.– Fermi operator.
• The leading operators are proportional to the momentum transfer.
• Higher multipoles, relativistic corrections, contribute less than 1%.
A1E
V1C
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MEC – back to configuration space
• Usually we would use Fourier transform.
• But, operators are valid only up to a certain cutoff .
• We use the same approach as Park et al:
2
3
32
ik rf r k f k
d k e S
Gaussian cutoff function
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Remarks• This approach gives the same
scattering operators as in Park et. al. (PRC 67(2003), 055206).
• We are left with one unknown parameter: dr.
• This parameter is calibrated using the experimental triton half life.
Transition operators – done.
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Advantages
• No free parameters.• dependence gives error estimation
due to higher degrees of freedom.
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Disadvantages
• In order to correctly describe light nuclei spectra, one has to expand the Hamiltonian at least to N3LO.
• The phenomenological Hamiltonians of SNPA are successful in doing so.
• Thus, MEEFT… [Rho 2006]
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Hybrid EFT-SNPA
• We use a hybrid approach:– Nuclear Hamiltonian –
phenomenological.• Standard nuclear physics (SNPA) WF.
– MEC transition operators – EFT.• This approach was used to calculate:
and gave same results as standard nuclear physics.
e
e
p p d e
p e
3 4He He
Park et. al., PRC 67, 055206 (2003)
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– realistic NN potential: AV8’ or AV18.– realistic NNN potential: UIX (combined
with AV18)
The Nuclear Hamiltonian
1
HA
i NN NNNi i j i j k
t v v
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Cross-section calculation
Where the response functions,
ˆ ˆ 0 1 2 0 0ˆ ˆ
1 2f f fO ,O f
R ω Ψ O Ψ Ψ O Ψ E E
The initial and final states should be calculated using a model for the 4He
nucleus.
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ˆ ˆ
ˆ ˆ 2 2
1 2
1 2
O ,O
O ,OR I
Rd
LWe define the LIT of R() as
0 1 2 0
ˆ ˆ 2 2
ˆ ˆ( , )
( )1 2
f f
R IO ,O ff i R I
O O
E E
L
0 1 2 0
1 1ˆ ˆ( ) ( )f ff
f i R I f i R I
O OE E i E E i
0 1 2 0
1 1ˆ ˆ( ) ( )f ff
f i R I f i R I
O OE E i E E i
ˆ ˆ 0 1 2 0 0ˆ ˆ
1 2f f fO ,O f
R ω Ψ O Ψ Ψ O Ψ E E
LIT method
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0 1 2 0
1 1ˆ ˆ( ) ( )f ff
i R I i R I
O OH E i H E i
The LIT methodsubstituting:
0 1 2 0 1 2
1 1ˆ ˆ( ) ( )i R I i R I
O OH E i H E i
using closure:
f fH fE
0 1 2 0
1 1ˆ ˆ( ) ( )f ff
i R I i R I
O OH E i H E i
where:
0
1 ˆ( )i i
i R I
OH E i
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0 0ˆH E R I i ii O
Therefore we have to solve the Schroedinger like equations:Therefore we have to solve the Schroedinger like equations:
Few Remarks:• There is no solution to the homogeneous
equation. • The boundary conditions are of a bound state.• Assures full final state interaction.
HOW DO WE SOLVE FOR WFs?
Efros, Leidemann & Orlandini, PLB 408, 1 (1994)
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Effective Interaction in the Hyperspherical Harmonics method
• The HH - eigenfunctions of the kinetic energy operator, with quantum number K.
• We expand the WF in (anti) symmetrized HH.
• Use Lee-Suzuki transformation to replace the bare potential with an effective one.
Barnea, Leidemann, Orlandini, PRC, 63 057002 (2001); Nucl. Phys. A, 693 (2001) 565.
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4-body system with4-body system with MT-V nucleon-MT-V nucleon-
nucleon potentialnucleon potential
EIHHBARE
Binding Energy
Matter Radius
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Eexp=28.296 MeV
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General remarks about the nuclear calculation
• The calculation is ab-initio:
– frame work of non-relativistic QMnon-relativistic QM.– explicit degrees of freedom: A NucleonsA Nucleons.– only inputs are the nuclear potentialnuclear potential and the
excitation operatorsexcitation operators.
• As a check: – We reproduce dr() from Park et. al.– We reproduce half-life calculations for 6He, with AV18.
• The combination of EIHHEIHH and LITLIT methods had been used to for calculating photo-disintegration and electron scattering processes for A=3,4,6,7.
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Photoabsorption on 4He
• The scattering operator at low energy is:
• Due to Siegert Theorem, at low energy it includes MEC contribution:– Model independent check of underlying
degrees of freedom.– Test of Nuclear Hamiltonian in the
continuum.
3
1 1
ˆ2
Z Ai i
ii i
rD r
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Berman et al. (,n) 1980 Feldman et al. (,p) 1990Wells et al. 1992Nilsson et al. 2005Shima et al. 2005
4He total photoabsorption cross-section with the realistic forces AV18+UIX.
Gazit et. al., PRL 96, 112301 (2006)
Gazit et. al., PRC 74, 061001R (2006)
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Neutrino scattering on A=3,4 Neutrino scattering on A=3,4 nucleinuclei
Results
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Convergence of the calculation
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MEC contribution• Has quantitative effect only for GT (E1
A) due to symmetry relations.
• 4He:– GT is suppressed due to closed shell character of .– Without MEC, GT contributes less than 1% of CRS in case of
AV18+UIX calculation. GT triples due to MEC.– MEC contribution to CRS: 1.5%.– Cutoff dependence of CRS: 0.5% (error estimation).
• A=3:– GT contributes 50% for T=1MeV,
and decreases quickly to 5% for T=10 MeV.– MEC contribution to CRS: 16% for T=1 MeV. Decreases
gradually…– MEC contribution to CRS: 1% for T=10 MeV.– Cutoff dependence of CRS: 1% (error estimation).
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Inelastic neutral neutrino reactions on 4He
Woosley et. al, ApJ 356, 272 (1990)
Haxton, PRL 60, 1999 (1988)
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Energy transfer in reaction on 4He and A=3
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Energy transfer near the neutrinosphere
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Conclusions• A complete microscopic calculation of the neutral
and charged neutrino scattering on 4He, 3H, 3He
was accomplished:– Full final state interaction (via LIT).– Different realistic potentials were considered, including
modern 3NF.– Axial MEC, EFT* based, were included.– The numerical accuracy is less than 1%.– We estimate CRS to be accurate to 5%:
• Small cutoff dependence – EW model is accurate to 1%.• Sensitivity to nuclear potential.
• We find that A=3 nuclei can be important in the neutrinosphere area.
• The work makes an important step towards a more robust and reliable microscopic description of the area below the shock, in which 4He is the most abundant nuclei.
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Publication summary (refereed journals)
1. “Photoabsorption on 4He with a realistic nuclear force”, Doron Gazit, Sonia Bacca, Nir Barnea, Winfried Leidemann, Giuseppina Orlandini, PRL, PRL, 96 (2006) 112301.96 (2006) 112301.
2. “Photonuclear sum-rules and the tetrahedral configuration of 4He””,,Doron Gazit, Nir Barnea, Sonia Bacca, Winfried Leidemann, Giuseppina Orlandini, PRC 74 (2006) 061001.PRC 74 (2006) 061001.
3. “Neutrino neutral reaction on 4He, effects of final state interaction and realistic NN force “, Doron Gazit, Nir Barnea, PRC 70 (2004) 048801.PRC 70 (2004) 048801.
4. “Low energy neutrino reactions on 4He”, Doron Gazit, Nir Barnea, January 2007, PRL (Submitted for publication).
5. “Few-body calculation of neutrino neutral inelastic scattering on 4He “,Doron Gazit, Nir Barnea, October 2007, Nucl. Phys. A (Submitted for publication).
6. “Neutrino Breakup of A=3 Nuclei in Supernova", E. O'Connor, Doron Gazit, C. J. Horowitz, A. Schwenk, N. Barnea, February 2007, PRC (submitted for publication).
7. “Low energy inelastic neutrino reactions on light nuclei”, Doron Gazit, Nir Barnea, in preparation.
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storage
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Cutoff dependence of 3H cross-section
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Choose (400-700 MeV) to calibrate the half life.
calculations in this method
2
2 22
/1 V
R
V A A
K Gt
f f g
F GT
1,
2i i i
i i
F GT
1 F 1.657 0.005GT experimentally
AV18 + UIX1.599GT
Get dr().
Use dr() to calculate MEC contribution in other reactions.
3H half life
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Effective Interaction in the Hyperspherical Harmonics method
• 1st step: remove center of mass
• 2nd step: introduce hyperspherical coordinates:
• 3rd step: rewrite KE in hyperspherical coordinates:
},...,,,...,{,... 1211322
122
21 AAA
1 2 . 1 2 1, ,.., , , ,...,A c m Ar r r R
2
2
2
2 ˆ43
KA
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Effective Interaction in the Hyperspherical Harmonics method
• HH functions are eigen-functions of the hyperspherical angular momentum operator K2
• 4th step: transform the HH basis into (anti) symmetric basis
• Expand WF in HH
• In many situations this expansion converges very slow.• 5th step: replace bare potential with an effective one,
through the Lee-Suzuki similarity transformation:
)()( ...... 1
AAYKLMKLM YY
ji
ijeffeffji
ij rVTHrVTH )()(
)(1][
AAYKLMnKn YRC