Electro-Weak Reactions on light nuclei* in supernovae Doron Gazit progress report talk March 2007...

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


Supernova IISupernova II- The death of a massive star

Crab Nebula


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


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


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


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


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.


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).


Equilibrium n,p,t,3He, Abundances

i ii

Pb

q nY

n


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.


Calculating the cross-section


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


Nuclear Neutral Current

Isovector

Axial

Vector

Isoscalar

Vector

0 2 20 0 5 11 2 sin 2 sin

2 2 2W WJ JJJ


Nuclear Charged Current

Isovector

Axial

Vector

5

2 2JJ J


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.


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


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


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


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


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.


Advantages

• No free parameters.• dependence gives error estimation

due to higher degrees of freedom.


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]


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)


– 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


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.


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


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


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)


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.


4-body system with4-body system with MT-V nucleon-MT-V nucleon-

nucleon potentialnucleon potential

EIHHBARE

Binding Energy

Matter Radius


Eexp=28.296 MeV


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.


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


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)


Neutrino scattering on A=3,4 Neutrino scattering on A=3,4 nucleinuclei

Results


Convergence of the calculation


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).


Inelastic neutral neutrino reactions on 4He

Woosley et. al, ApJ 356, 272 (1990)

Haxton, PRL 60, 1999 (1988)


Energy transfer in reaction on 4He and A=3


Energy transfer near the neutrinosphere


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.


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.


storage


Cutoff dependence of 3H cross-section


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



• 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



• 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

Electro-Weak Reactions on light nuclei* in supernovae Doron Gazit progress report talk March 2007...

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