Particle-number fluctuations and neutron-proton pairing effects on proton and neutron radii of even-even N≈Z nuclei

2012 ◽  
Author(s):  
M. Douici ◽  
N. H. Allal ◽  
M. Fellah ◽  
N. Benhamouda ◽  
M. R. Oudih
Keyword(s):  
Particle Number ◽  
Proton Pairing

NEUTRON–PROTON PAIRING EFFECT ON ONE-PROTON AND TWO-PROTON SEPARATION ENERGIES IN RARE-EARTH PROTON-RICH NUCLEI

2012 ◽  
Vol 21 (12) ◽  
pp. 1250100 ◽  
Author(s):  
F. HAMMACHE ◽  
N. H. ALLAL ◽  
M. FELLAH
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Particle Number ◽  
Good Description ◽  
Mean Field ◽  
Pairing Effect ◽  
Pairing Correlations ◽  
The One ◽  
Proton Pairing ◽  
Realistic Choice

The one-proton and two-proton separation energies are studied for "ordinary" and rare-earth proton-rich nuclei by including the isovector neutron–proton (np) pairing correlations using the BCS approximation. Even–even as well as odd nuclei are considered. In the latter case, the wave function is defined using the blocked-level technique. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the np isovector pairing effects on the one-proton and two-proton separation energies are non-negligible. However, the only isovector BCS approximation seems to be inadequate for a good description of these quantities when including the np pairing effects: either a particle-number projection or the inclusion of the isoscalar pairing effect seems to be necessary. Another possible improvement would be a more realistic choice of the pairing strengths.

THE HIGHER TAMM–DANCOFF APPROXIMATION: THEORETICAL CONTEXT AND PHENOMENOLOGICAL ASPECTS

2008 ◽  
Vol 17 (01) ◽  
pp. 228-239 ◽  
Author(s):  
PHILIPPE QUENTIN ◽  
HOUDA NAIDJA ◽  
LUDOVIC BONNEAU ◽  
JOHANN BARTEL ◽  
HA THUY LONG
Keyword(s):  
Shell Model ◽  
Quadrupole Interaction ◽  
Particle Number ◽  
Proton Proton ◽  
Hartree Fock ◽  
Pairing Correlations ◽  
Key Aspects ◽  
Proton Pairing ◽  
Theoretical Foundations ◽  
Model Approach

We present the key aspects of the theoretical foundations of the Higher Tamm–Dancoff Approximation which can be interpreted as a truncated shell-model approach based on a Hartree–Fock solution, ensuring the conservation of the particle number. Then we discuss some phenomenological aspects of the residual interactions used, namely the delta interaction to describe the neutron–neutron and proton–proton pairing correlations and the quadrupole–quadrupole interaction to describe vibrational correlations.

Moment of inertia of even–even proton-rich nuclei using a particle-number conserving approach in the isovector neutron–proton pairing case

2016 ◽  
Vol 25 (06) ◽  
pp. 1650032 ◽  
Author(s):  
Faiza Hammache ◽  
N. H. Allal ◽  
M. Fellah ◽  
M. R. Oudih
Keyword(s):  
Particle Number ◽  
Mean Field ◽  
Moment Of Inertia ◽  
Second Step ◽  
Nuclear Moment ◽  
Pairing Effect ◽  
Picket Fence ◽  
Projection Effect ◽  
The One ◽  
Proton Pairing

An expression of the particle-number projected nuclear moment of inertia (MOI) has been established in the neutron–proton (np) isovector pairing case within the cranking model. It generalizes the one obtained in the like-particles pairing case. The formalism has been, as a first step, applied to the picket-fence model. As a second step, it has been applied to deformed even–even nuclei such as [Formula: see text] and of which the experimentally deduced values of the pairing gap parameters [Formula: see text], [Formula: see text], are known. The single-particle energies and eigenstates used are those of a deformed Woods–Saxon mean-field. It was shown, in both models, that the np pairing effect and the projection one are non-negligible. In realistic cases, it also appears that the np pairing effect strongly depends on [Formula: see text], whereas the projection effect is practically independent from the same quantity.

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.

EFFECT OF THE PARTICLE-NUMBER SYMMETRY RESTORATION ON ROOT MEAN SQUARE RADII OF EVEN–EVEN NEUTRON-DEFICIENT NUCLEI IN THE ISOVECTOR PAIRING CASE

2012 ◽  
Vol 21 (04) ◽  
pp. 1250046 ◽  
Author(s):  
M. DOUICI ◽  
N. H. ALLAL ◽  
M. FELLAH ◽  
N. BENHAMOUDA ◽  
M. R. OUDIH
Keyword(s):  
Experimental Data ◽  
Root Mean Square ◽  
Single Particle ◽  
Particle Number ◽  
Mean Field ◽  
Second Step ◽  
Mean Square ◽  
The One ◽  
Proton Pairing

The effect of the particle-number symmetry restoration on the root mean square (rms) proton and neutron radii of neutron-deficient nuclei is studied in the isovector pairing case. As a first step, an expression of the nuclear radii which includes the neutron–proton pairing effects and which strictly conserves the particle-number has been established using the SBCS (Sharp BCS) method. It is shown that this expression generalizes the one obtained in the pairing between like-particles case. As a second step, the proton and neutron rms radii are numerically evaluated for even–even nuclei such as 16⩽Z⩽56 and 0⩽(N-Z)⩽4 using the single-particle energies of a Woods–Saxon mean-field. The results are compared with experimental data when available and with the results obtained when one considers only the pairing between like-particles.

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 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.

scholarly journals Evaluation of theβ+-decay logftvalue with inclusion of the neutron-proton pairing and particle-number projection

2016 ◽  
Vol 107 ◽  
pp. 04002
Author(s):  
S. Kerrouchi ◽  
N.H. Allal ◽  
M. Fellah ◽  
M.R. Oudih
Keyword(s):  
Particle Number ◽  
Proton Pairing
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