Evaluation of the β+ decay log ft value with inclusion of the neutron–proton pairing and particle number conservation

2015 ◽  
Vol 24 (02) ◽  
pp. 1550014 ◽  
Author(s):  
S. Kerrouchi ◽  
N. H. Allal ◽  
M. Fellah ◽  
M. R. Oudih
Keyword(s):  
Particle Number ◽  
Transition Probabilities ◽  
Bcs Theory ◽  
Nuclear Deformation ◽  
Β Decay ◽  
Deformation Effect ◽  
Particle Number Conservation ◽  
Fluctuation Effects ◽  
Proton Pairing ◽  
Gamow Teller

The particle number fluctuation effects, which are inherent to the Bardeen–Cooper–Schrieffer (BCS) theory, on the beta decay log ft values are studied in the isovector case. Expressions of the transition probabilities, of Fermi as well as Gamow–Teller types, which strictly conserve the particle number are established using a projection method. The probabilities are calculated for some transitions of isobars such as N ≃ Z. The obtained results are compared to values obtained before the projection. The nuclear deformation effect on the log ft values is also studied.

Particle-number conservation in odd mass proton-rich nuclei in the isovector pairing case

2015 ◽  
Vol 24 (06) ◽  
pp. 1550042 ◽  
Author(s):  
M. Fellah ◽  
N. H. Allal ◽  
M. R. Oudih
Keyword(s):  
Ground State ◽  
State Energy ◽  
Particle Number ◽  
Mean Field ◽  
Expectation Values ◽  
Deformation Effect ◽  
Pairing Effect ◽  
Projection Effect ◽  
Particle Number Conservation ◽  
The One

An expression of a wave function which describes odd–even systems in the isovector pairing case is proposed within the BCS approach. It is shown that it correctly generalizes the one used in the pairing between like-particles case. It is then projected on the good proton and neutron numbers using the Sharp-BCS (SBCS) method. The expressions of the expectation values of the particle-number operator and its square, as well as the energy, are deduced in both approaches. The formalism is applied to study the isovector pairing effect and the number projection one on the ground state energy of odd mass N ≈ Z nuclei using the single-particle energies of a deformed Woods–Saxon mean-field. It is shown that both effects on energy do not exceed 2%, however, the absolute deviations may reach several MeV. Moreover, the np pairing effect rapidly diminishes as a function of (N - Z). The deformation effect is also studied. It is shown that the np pairing effect, either before or after the projection, as well as the projection effect, when including or not the isovector pairing, depends upon the deformation. However, it seems that the predicted ground state deformation will remain the same in the four approaches.

NUMBER-PROJECTED BETA TRANSITION PROBABILITIES WITHIN A NEUTRON–PROTON PAIRING FRAMEWORK

2010 ◽  
Vol 19 (07) ◽  
pp. 1383-1409 ◽  
Author(s):  
S. KERROUCHI ◽  
N. H. ALLAL ◽  
M. FELLAH ◽  
M. DOUICI
Keyword(s):  
Particle Number ◽  
Transition Probabilities ◽  
Mean Field ◽  
Linearization Method ◽  
Beta Transition ◽  
Quasi Particle ◽  
Pairing Strength ◽  
Level Model ◽  
Pairing Correlations ◽  
Proton Pairing

Particle-number fluctuations effects on the beta transition probabilities are studied in the neutron–proton pairing framework. The Hamiltonian of the system has been considered in its most general form and has been diagonalized by means of the linearization method. However, since the generalized Bogoliubov–Valatin transformation obtained in this way leads to a quasi-particle Hamiltonian which is still nondiagonal, a rediagonalization has been performed. The corresponding wave functions have been projected on both the good neutron and proton numbers using a recently proposed method. Expressions of the beta transition probabilities which strictly conserve the particle-number have then been established. As a first step, the model has been numerically tested within the framework of the schematic one-level model. As a second step, nuclei such as N = Z has been studied using the single-particle energies and eigenstates of the Woods–Saxon deformed mean field. It has thus been shown the necessity of: (i) including the isovector pairing correlations, (ii) performing a rediagonalization of the Hamiltonian, (iii) performing a particle-number projection, (iv) carefully choice the pairing-strength values, when calculating the transition probabilities.

Particle-number conservation in quasiparticle representation in the isovector neutron–proton pairing case

2015 ◽  
Vol 24 (12) ◽  
pp. 1550097 ◽  
Author(s):  
M. Fellah ◽  
N. H. Allal ◽  
Faiza Hammache ◽  
M. R. Oudih
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Number Operator ◽  
Expectation Values ◽  
Total Particle Number ◽  
Total Particle ◽  
Level Model ◽  
Particle Number Conservation ◽  
The One ◽  
Proton Pairing

Until now, the Sharp-Bardeen–Cooper–Schrieffer (SBCS) particle-number projection method, in the isovector neutron–proton pairing case, has been developed in the particle representation. However, this formalism is sometimes complicated and cumbersome. In this work, the formalism is developed in the quasiparticle representation. An expression of the projected ground state wave function is proposed. Expressions of the energy as well as the expectation values of the total particle-number operator and its square are deduced. It is shown that these expressions are formally similar to their homologues in the pairing between like-particles case. They are easier to handle than the ones obtained using the particle representation and are more adapted to numerical calculations. The method is then numerically tested within the schematic one-level model, which allows comparisons with exact results, as well as in the case of even–even nuclei within the Woods–Saxon model. In each case, it is shown that the particle-number fluctuations that are inherent to the BCS method are completely eliminated by the projection. In the framework of the one-level model, the values of the projected energy are clearly closer to the exact values than the BCS ones. In realistic cases, the relative discrepancies between projected and unprojected values of the energy are small. However, the absolute deviations may reach several MeV.

Gamow—Teller strength distribution near 100Sn: The β decay of 102In

2003 ◽  
pp. 336-336
Author(s):  
M. Gierlik ◽  
A. Płochocki ◽  
M. Karny ◽  
W. Urban ◽  
Z. Janas ◽  
...  
Keyword(s):  
Strength Distribution ◽  
Β Decay ◽  
Gamow Teller

scholarly journals Two-phonon structures for beta-decay theory

2018 ◽  
Vol 194 ◽  
pp. 02008
Author(s):  
A.P. Severyukhin ◽  
N.N. Arsenyev ◽  
I.N. Borzov ◽  
R.G. Nazmitdinov ◽  
S. Åberg
Keyword(s):  
Random Matrix ◽  
Single Particle ◽  
Ground State ◽  
Matrix Theory ◽  
Decay Rates ◽  
Total Probability ◽  
Phonon Coupling ◽  
Skyrme Interaction ◽  
Β Decay ◽  
Gamow Teller

The β-decay rates of 60Ca have been studied within a microscopic model, which is based on the Skyrme interaction T45 to construct single-particle and phonon spaces. We observe a redistribution of the Gamow–Teller strength due to the phonon-phonon coupling, considered in the model. For 60Sc, the spin-parity of the ground state is found to be 1+. We predict that the half-life of 60Ca is 0.3 ms, while the total probability of the βxn emission is 6:1%. Additionally, the random matrix theory has been applied to analyze the statistical properties of the 1+ spectrum populated in the β-decay to elucidate the obtained results.

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