Diapositiva

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Congratulations to Frank and Ettore for many
years of efforts and for given motivations to
many of us (fights included, e.g a near
technical KO in Frank vs Hans). Sincere hopes
for many more years of contributions to DBD and
neutrino physics. Hope both of you cash some of
the nordic gold !
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Further Test of the QRPA calculation of DBD-NME

• Osvaldo Civitarese
• University of La Plata (Argentina)
• (in collaboration with Jouni Suhonen, University
  of Jyvaskyla (Finland).)

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Topics and Motivations

• Nuclear matrix elements in the QRPA
• Parameters and dependence upon them
• Approximations beyond the QRPA
• Short Range Correlations
• Spectroscopic Information about q.p.states
• Conclusions

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-Nuclear structure effects on the matrix elements
governing the mass sector of the neutrinoless
double beta decay (g_pp-dependence) -Effective
parameters single-beta decay and double beta
decay? two-neutrino or zero-neutrino
modes? -Effective operators (from first
principles) -Universality (if any) of the matrix
elements as a rule Test the
approximations in a simple model before applying
them in realistic cases.
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Schematic view
A(N-1,Z1)
A(N,Z)
A(N-2,Z2)
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2-neutrino mode
A(N,Z) A(N-2,Z2)2 electrons
2 neutrinos
a) Lepton number is conserved b) Suppressed by
kinematics (four leptons in the final state) c)
Independent of neutrino properties
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0-neutrino mode
A(N,Z) A(N-2,Z2)2 electrons

• lepton number is not conserved
• not suppresed by kinematics (two leptons in the
  final state)

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Basic Spectroscopic Information (consistency test)

• Single beta decay and EC transitions
• Energy spectra, electromagnetic transitions
• Particle transfer ((p,t)) and charge exchange
  ((3He,t),(p,n)) data.
• Practical rule The information obtained by
  theoretical reproducing a single DBD transition
  does not mean anything, unless related
  observables are also reproduced.

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G_pp dependence

• Transformation from the single-particle to the
  quasi-particle basis (particle number is lost,
  isospin symmetry is lost).
• In open shells the Inclusion of pair terms of the
  residual proton-neutron interaction induces
  attractive pairing-like effects which compite
  with repulsive spin-dependent terms. This effect
  is also present in shell model results.
• The renormalization of the particle-particle
  interactions may induced a symmetry breaking,
  which invalidates the qrpa approach
• Mean field terms and residual interactions (they
  do not talk to each other)

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Beyond the QRPA

• -Inclusion of terms which go beyond the
  quasi-boson approximation the procedure is not
  supported by self-consistency requirements and it
  introduces spurious effects.
• -Among the attempts fully renormalized qrpa

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Symmetries

• Isospin violations (mean field effects)
• 1)Mean field approximations (like BCS) break
  isospin and number symmetries.
• 2)The QRPA also break these symmetries,
• but in a different way.
• 3)Both mechanisms are not coupled.

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Finite size and Short Range Correlations

• Effects due to the finite size of the nucleons,
  with reference to q (the neutrino momentum)
• Since q is or the order of 150-200 MeV/c short
  range correlation effects are expected to be
  operative at distances of the order of 1fm
• Large corrections (40 percent reductions) have
  been reported in the literature (Jastrow method),
  in contrast to smaller effects (about 5 percent)
  found with the UCOM

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• Jastrow
• f(r)1-exp(-ar)(1-b r2)
• ltFO(bare)Igt is replaced by ltFO(correlated)Igt
• O(correlated)f(r)Of(r)
• UCOM
• correlated stategtCuncorrelatedgt
• O(correlated) C O C
• The operator C minimizes the matrix element of
  the
• Hamiltonian, then the choice of the two-body
• interaction affects the form of the operator C

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SUMMARY

• - Results of the extensions of the QRPA (like
  the RQRPA, FRQRPA) are not comparable.
• -The bulk of the NME, for the neutrinoless mode,
  is nearly insensitive to g_pp
• -Single beta decay, particle transfer, (3He,t)
  and (p.n) data are proper tools to extract g_pp
  values, indeed.
• -It may be that g_pp is enterely fixed by
  symmetry, i.e. not need of ad-hoc procedures
  which go beyond the mean field qrpa approach.