Nuclear structure symmetries and double beta decay'

1
Nuclear structure symmetriesand double beta
decay.
2
Subjects

• Basic Notions about symmetries
• Isospin and gauge symmetries
• The enlargement of the Hilbert Space
• Some examples
• Pairing-isospin problem
• Double Fermi and Gamow-Teller Decays
• Coulomb isospin breaking
• Conclusions

3
Scheme

• The strategy is based on a trade-off of
  constraints (like usual Lagrange multiplier) by
  operators (fields) and by the corresponding
  enlargement of the Hilbert space (BRST
  super-symmetry).
• Alternatively, one may introduce counter-terms to
  restore symmetries which are violated by the
  interactions or by the mean field approximations

4
Examples

• Treatment of nuclear interactions beyond the mean
  field approximation and the associated symmetry
  breaking
• -Pairing (Isospin, Gauge)
• -Center of mass motion (Galilean and
  translational invariance)
• -Nuclear deformations (Rotational invariance)
• -Coulomb effects (Isospin)

5
Relevance for DBD studies

• Symmetry breaking effects and spurious
• effects in RPA and QRPA calculations
• (like the mode instabilities in the QRPA and
  spurious effects in 0,1-,0 and 1
• channels, ad-hoc attempts to go beyond the
  RPA or QRPA approaches).

6
Pairing-isospin

• The treatment of the pairing interaction, in a
  fully symmetric way, must obey the invariance
  against gauge (particle number) and isospin
  transformations. This is not the case of the
  standard approach (either BCS or Shell Model in
  truncated valence spaces). The formal steps (to
  fulfill the symmetries) are
• a)transformation of the Hamiltonian to the
  intrinsic frame
• b)separation of collective and intrinsic
  components of the operators and wave functions

7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
conclusions

• The observance of symmetries is crucial to
  calculate correctly nuclear observables (like DBD
  ones)
• The collective treatment of DBD transitions is
  feasible, like it was in the case of nuclear
  rotations (Copenhagen Unified Model).
• The use of the formalism fixes without
  ambiguities the value of all the involved
  couplings.