PowerPoint-Pr

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International Workshop on Fundamental Symmetries
From Nuclei and Neutrinos to the Universe ECT,
Trento, 25-29. June 2007
Charged-Current Neutrino-Nucleus Reactions in the
Relativistic QRPA
N. Paar Physics Department Faculty of
Science University of Zagreb Croatia www.phy.hr/
npaar
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NEW HIGHWAY TO NEUTRINO-NUCLEUS CROSS-SECTIONS
A(?e,e-)B A(?µ,µ-)B
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NEUTRINO-NUCLEUS REACTIONS
neutrino nucleus charged current reactions
neutrino-nucleus cross section
Hamiltonian for the weak interaction
transition nuclear matrix elements (assuming
plane waves for leptons)
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NEUTRINO-NUCLEUS CROSS SECTION
Extreme relativistic limit final lepton energy
El gtgt mlc2
Walecka, Donnely
Transverse magnetic Transverse electric
multipole operators
Coulomb longitudinal multipole operators
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multipole operators are given in terms of
spherical Bessel functions, spherical harmonics,
and vector spherical harmonics
? Coulomb multipole operator
?Longitudinal multipole operator
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? transverse electric multipole operator
? transverse magnetic multipole operator
? nucleon form factors
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? 7 fundamental operators
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NEUTRINO-NUCLEUS REACTIONS IN OPEN-SHELL NUCLEI
Reduced matrix elements for various transition
operators include the details of the nuclear
structure (nuclear ground state and excitations)
Recent microscopic studies improved significantly
description of weak interaction rates, however,
there are several problems
1. SHELL MODEL ? accurate in description of the
ground state wave functions, description of
high-lying states necessitates a large
model space which is problematic to treat
numerically Different interactions in various
mass regions employed, only lower mass nuclei can
be studied
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2. (Continuum) Random Phase Approximation ?
includes high lying particle-hole configurations,
but configuration mixing was included by putting
by hand the fractional occupancies of
single-particle states
GROUND STATE Woods-Saxon potential fitted to
single-particle energies
RPA RESIDUAL INTERACTION G-matrix from Bonn
potential or zero-range Landau Migdal force
PARTIAL OCCUPATION OF ORBITS (12C) determined in
shell model (e.g. OXBASH with Cohen Kurath
interaction)
adjustment factor to rescale the neutrino cross
section
Kolbe, Langanke, Vogel, Nucl. Phys. A 652, 91
(1999).
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3. HYBRID MODEL
SHELL MODEL Strasbourg-Madrid codes by Caurier
et al. ?Gamow-Teller strength (with quenching
factor) ( rescaled by a factor to account
finite momentum transfer)
Occupation numbers
CONTINUUM RPA ? forbidden transitions
GROUND STATE Woods-Saxon potential fitted to
single-particle energies
RPA RESIDUAL INTERACTION G-matrix from Bonn
potential or zero-range Landau Migdal force
Kolbe, Langanke, Martinez-Pinedo, Phys. Rev. C
60, 052801 (1999).
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4. Skyrme Hartree-Fock Quasiparticle RPA ?
towards a consistent description of weak
interaction rates along the nuclide chart
GROUND STATE based on Skyrme energy density
functional, BCS pairing
RPA RESIDUAL INTERACTION Derived from the same
Skyrme functional, renormalized strength in the
pairing channel (0.7)
Volpe, Auerbach, Colò, Suzuki, Van Giai, Phys.
Rev. C 62, 015501
QRPA for neutrino capture by r-process
waiting-point nuclei (includes Gamow-Teller and
first forbidden transitions)
Surman, Engel, Phys. Rev. C 58, 2526 - 2530
(1998)
Different transtion operators are employed in
different approaches
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NEW ? Neutrino-nucleus cross sections based on
self-consistent Relativistic Quasiparticle
Random Phase Approximation (RQRPA)
RELATIVISTIC HARTREE-BOGOLIUBOV MODEL (RHB)
RELATIVISTIC QUASIPARTICLE RPA (RQRPA) BOTH THE
GROUND STATE EQUATIONS RESIDUAL QRPA
INTERACTION ARE DERIVED FROM THE SAME EFFECTIVE
LAGRANGIAN DENSITY PAIRING CORRELATIONS ARE
DESCRIBED BY THE FINITE RANGE GOGNY FORCE
RHB ? Vretenar, Afanasjev, Lalazissis, Ring,
Phys. Rep. 409, 101 (2005). RQRPA ? Paar, Ring,
Niksic, Vretenar, Phys. Rev. C 67, 034312 (2003).
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RELATIVISTIC MEAN FIELD THEORY
system of Dirac nucleons coupled to the exchange
mesons and the photon field through an effective
Lagrangian.
(J?,T)(0,0)
(J?,T)(1-,0)
(J?,T)(1-,1)
Sigma-meson attractive scalar field
Omega-meson short- range repulsive field
Rho-meson isovector field
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LAGRANGIAN DENSITY
the Lagrangian of the free nucleon
the Lagrangian of the free meson fields and the
electromagnetic field
minimal set of interaction terms
with the vertices
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MODELS WITH DENSITY DEPENDENT COUPLINGS
the meson-nucleon couplings g?, g?, g? -gt
functions of vector density
Density-dependent meson-nucleon couplings
connection to Dirac-Brueckner calculations based
on realistic NN interactions
The parameters are determined from properties of
nuclear matter and bulk properties of finite
nuclei (binding energies, charge radii, neutron
radii, surface thickeness ...)
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RELATIVISTIC HARTREE-BOGOLIUBOV MODEL (RHB)
Unified description of mean-field and pairing
correlations
Dirac hamiltonian
Pairing field
RMS CHARGE RADII
DIFFERENCES rn-rp
BINDING ENERGIES
Sn
Sn
sRMS0.9 MeV
Accurate description of ground state properties
along nuclide chart
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PROTON-NEUTRON RELATIVISTIC QUASI-PARTICLE RPA
(RQRPA)
Paar, Niksic, Vretenar, Ring, Phys. Rev. C 69, 1
(2004)
Derived from the time-dependent RHB equation in
the limit of small oscillations around the RHB
ground state generalized density
p and ?-meson exchange generate the spin-isospin
dependent interaction terms
The ?-nucleon and p-nucleon interaction
Lagrangian (
)
plus the Landau-Migdal zero-range force in the
spin-isospin channel
PN-RQRPA
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RQRPA DESCRIPTION OF COLLECTIVE EXCITATIONS IN
NUCLEI
MONOPOLE EXCITATIONS
DIPOLE EXCITATIONS
208Pb
Exp. 13.3 MeV
Paar, Vretenar, Ring, Phys. Rev. Lett. 94, 182501
(2005). Paar, Papakonstantinou, Ponomarev,
Wambach, Phys. Lett. B 624, 195 (2005).
Paar, Nikšic Vretenar, Ring, Phys. Lett. B 606,
288 (2005). Paar, Vretenar, Nikšic, Ring, Phys.
Rev. C 74, 037303 (2006).
Exp. 7.37 MeV
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EXOTIC MODES IN NUCLEI AWAY FROM THE VALLEY OF
STABILITY
PYGMY DIPOLE RESONANCE
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EXOTIC MODES IN NUCLEI AWAY FROM THE VALLEY OF
STABILITY
REVIEW PAPER Paar, Vretenar, Khan, Colo "Exotic
modes of excitation in atomic nuclei far from
stability", Rep. Prog. Phys. 70, 691 (2007).
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ISOBARIC ANALOG AND GAMOW-TELLER RESONANCES
(RQRPA)
ISOSPIN-FLIP EXCITATIONS
S0 T1 J? 0
S1 T1 J? 1
SPIN-FLIP ISOSPIN-FLIP EXCITATIONS
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RHBRQRPA NEUTRINO-NUCLEUS CROSS SECTIONS
Back to reduced matrix elements for the
neutrino-nucleus cross section ?
RQRPA amplitudes
RHB occupation probabilities
? single-particle reduced matrix elements
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RHBRQRPA NEUTRINO-NUCLEUS (12C) CROSS SECTION
Coulomb correction from numerical solution of the
Dirac equation for an extended nuclear charge
Effective momentum approximation
RHBRQRPA
Engel, Phys. Rev. C 57, 2004 (1998)
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RHBRQRPA NEUTRINO-NUCLEUS (208Pb) CROSS SECTION

RHBRQRPA
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RHBRQRPA
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RHBRQRPA
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DISTRIBUTION OF CROSS SECTIONS OVER
MULTIPOLARITIES
RHBRQRPA
?talk Lazauskas
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CONTRIBUTIONS FROM ALLOWED AND FORBIDDEN
TRANSITIONS
RHBRQRPA
CROSSING BETWEEN THE CROSS SECTIONS WITH ALLOWED
AND FORBIDDEN TRANSITIONS !
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RHBRQRPA CROSS SECTION AVERAGED OVER NEUTRINO
FLUX
Flux averaged cross section
(?µ,µ-) ltsgt(10-40cm2) (?e,µ-) ltsgt(10-42cm2)
RPA(Volpe et al.) 19.23 55.10
QRPA(Volpe et al.) 20.29 52.0
CRPA(Kolbe) 18.18 19.28
PN-RQRPA 19.59 12.14
EXP.(LSND) 120.31.8 14.11.6
EXP.(KARMEN) 14.01.2
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CROSS SECTIONS AVERAGED OVER SUPERNOVA NEUTRINO
FLUX
Supernova neutrino flux is given by Fermi-Dirac
spectrum
Cross section averaged over Supernova neutrino
flux
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CROSS SECTIONS AVERAGED OVER SUPERNOVA NEUTRINO
FLUX
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CHARGED CURRENT NEUTRINO-NUCLEUS CROSS SECTIONS
IN RQRPA
The same effective interactions can be employed
in a systematic way to evaluate reduced
transition matrix elements, for nuclei throughout
the nuclide chart
Relativistic framework for nuclear
charge-exchange excitations provides consistent
description of neutrino-nucleus charged current
reactions
Better knowledge on spin-dipole and excitations
of higher multipolarities can improve description
of neutrino-nucleus reactions

• CONSISTENT DESCRIPTION OF NEUTRINO-NUCLEUS
  REACTIONS AT THE LIMITS OF STABILITY
• Relevance for nuclear astrophysics
• NEUTRINO NUCLEOSYNTHESIS

• NEUTRINO-NUCLEUS CROSS SECTIONS FOR NEUTRINO
  DETECTORS, BETA BEAMS

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COLLABORATORS
T. Marketin T. Nikšic P. Ring D. Vretenar
www.phy.hr/npaar