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Diapositiva

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Title: Diapositiva


1
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 !
2
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).)

3
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

4
-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.
5
Schematic view
A(N-1,Z1)
A(N,Z)
A(N-2,Z2)
6
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
7
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

37
  • 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.
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