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.

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.

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.

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.

ISOVECTOR PAIRING EFFECT ON NUCLEAR MOMENT OF INERTIA AT FINITE TEMPERATURE IN N = Z EVEN–EVEN SYSTEMS

2011 ◽  
Vol 20 (09) ◽  
pp. 1947-1959 ◽  
Author(s):  
I. AMI ◽  
M. FELLAH ◽  
N. H. ALLAL ◽  
N. BENHAMOUDA ◽  
M. BELABBAS ◽  
...  
Keyword(s):  
Single Particle ◽  
Finite Temperature ◽  
Mean Field ◽  
Moment Of Inertia ◽  
Numerical Calculations ◽  
Nuclear Moment ◽  
Temperature Dependent ◽  
Moments Of Inertia ◽  
Pairing Effect ◽  
Rotating Nuclei

Expressions of temperature-dependent perpendicular (ℑ⊥) and parallel (ℑ‖) moments of inertia, including isovector pairing effects, have been established using the cranking method. They are derived from recently proposed temperature-dependent gap equations. The obtained expressions generalize the conventional finite-temperature BCS (FTBCS) ones. Numerical calculations have been carried out within the framework of the schematic Richardson model as well as for nuclei such as N = Z, using the single-particle energies and eigenstates of a deformed Woods–Saxon mean-field. ℑ⊥ and ℑ‖ have been studied as a function of the temperature. It has been shown that the isovector pairing effect on both the perpendicular and parallel moments of inertia is non-negligible at finite temperature. These correlations must thus be taking into account in studies of warm rotating nuclei in the N ≃ Z region.

NEUTRON-PROTON ISOVECTOR PAIRING EFFECT ON THE NUCLEAR MOMENT OF INERTIA

2008 ◽  
Vol 17 (04) ◽  
pp. 655-667 ◽  
Author(s):  
D. MOKHTARI ◽  
I. AMI ◽  
M. FELLAH ◽  
N. H. ALLAL
Keyword(s):  
Rare Earth ◽  
Moment Of Inertia ◽  
Nuclear Moment ◽  
Pairing Effect ◽  
Analytical Expression ◽  
Rare Earth Nuclei ◽  
Theoretical Predictions ◽  
The Moment ◽  
Experimental Values

The neutron-proton (n-p) isovector pairing effect on the nuclear moment of inertia has been studied within the framework of the BCS approximation. An analytical expression of the moment of inertia, that explicitly depends upon the n-p pairing, has been established using the Inglis cranking model. The model was first tested numerically for nuclei such as N = Z and whose experimental values of the moment of inertia are known (i.e. such as 16 ≤ Z ≤ 40). It has been shown that the n-p pairing effect is non-negligible and clearly improves the theoretical predictions when compared to those of the pairing between like particles. Secondly, predictions have been established for even-even proton-rich rare-earth nuclei. It has been shown that the n-p pairing effect is non-negligible when N = Z and rapidly decreases with increasing values of (N-Z).

NUMBER-PROJECTED ELECTRIC QUADRUPOLE MOMENTS OF EVEN–EVEN PROTON-RICH NUCLEI IN THE ISOVECTOR PAIRING CASE

2013 ◽  
Vol 22 (05) ◽  
pp. 1350029 ◽  
Author(s):  
M. DOUICI ◽  
N. H. ALLAL ◽  
M. FELLAH ◽  
N. BENHAMOUDA ◽  
M. R. OUDIH
Keyword(s):  
Quadrupole Moment ◽  
Mean Field ◽  
Electric Quadrupole ◽  
Variation Method ◽  
Quadrupole Moments ◽  
Electric Quadrupole Moment ◽  
Pairing Effect ◽  
Before And After ◽  
Projection Effect ◽  
Gap Parameter

An expression of the number-projected electric quadrupole moment Q2 has been established in the isovector pairing case using the SBCS discrete projection before variation method. It has been verified that this expression reduces to the pairing between like-particles one at the limit when the np pairing gap parameter Δ np goes to zero. The convergence of the projection method has been numerically tested and a fast convergence has been observed. The electric quadrupole moment has been numerically calculated for some even–even proton-rich nuclei such as 16 ≤ Z ≤ 56 and 0 ≤ (N-Z) ≤ 4. The single-particle energies and eigen-states used are those of a Woods–Saxon mean-field. The np pairing effect on Q2 has been studied either before and after the projection; it seems that it is somewhat small since the relative discrepancies do not exceed 12%. Moreover, the np pairing effect is roughly the same in both situations. However, it has been shown that this effect diminishes with increasing values of (N-Z). The projection effect on Q2 has also been studied when including, or not, the np pairing correlations. It appears that this effect is slightly less important in the np pairing case than when only the pairing between like-particles is considered.

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.

scholarly journals Neutron-proton pairing effect on the proton-rich nuclei moment of inertia

2007 ◽  
Author(s):  
D. Mokhtari ◽  
I. Ami ◽  
M. Fellah ◽  
N. H. Allal
Keyword(s):  
Moment Of Inertia ◽  
Pairing Effect ◽  
Proton Pairing
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