Effect of single-particle splitting in the exact wave function of the isovectorial pairing Hamiltonian

H., S. Lerma

doi:10.1103/physrevc.82.014302

Cited by 4 publications

(1 citation statement)

References 20 publications

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“…General expression can be found in [22]. Here we only signal that, for the simplest non-trivial case of N = Z = 4 = M , it was shown that the wave function can be approximated by…”

Section: Exact Solution Of the Isovectorial Pairing Plus Spin-orbit Imentioning

confidence: 82%

Isovectorial pairing in solvable and algebraic models

Lerma

Vargas

Hirsch

2011

J. Phys.: Conf. Ser.

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Isovectorial pairing in solvable and algebraic modelsToAbstract. Schematic interactions are useful to gain some insight in the behavior of very complicated systems such as the atomic nuclei. Prototypical examples are, in this context, the pairing interaction and the quadrupole interaction of the Elliot model. In this contribution the interplay between isovectorial pairing, spin-orbit, and quadrupole terms in a harmonic oscillator shell (the so-called pairing-plus-quadrupole model) is studied by algebraic methods. The ability of this model to provide a realistic description of N=Z even-even nuclei in the fpshell is illustrated with 44 Ti. Our calculations which derive from schematic and simple terms confirm earlier conclusions obtained by using realistic interactions: the SU(3) symmetry of the quadrupole term is broken mainly by the spin-orbit term, but the energies depends strongly on pairing.

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“…General expression can be found in [22]. Here we only signal that, for the simplest non-trivial case of N = Z = 4 = M , it was shown that the wave function can be approximated by…”

Section: Exact Solution Of the Isovectorial Pairing Plus Spin-orbit Imentioning

confidence: 82%

Isovectorial pairing in solvable and algebraic models

Lerma

Vargas

Hirsch

2011

J. Phys.: Conf. Ser.

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Number-Projected Electric Quadrupole Moments of Even–even Proton-Rich Nuclei in the Isovector Pairing Case

Douici

Allal

Fellah

et al. 2013

Int. J. Mod. Phys. E

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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.

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Charge, proton and neutron systems and matter radii of N ≈ Z odd-mass nuclei using a particle-number projection approach in the T = 1 pairing case

Allal

Fellah

Douici

et al. 2016

Int. J. Mod. Phys. E

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The charge radii, the proton and neutron systems radii, as well as the matter radii of [Formula: see text] odd-mass nuclei are studied using a particle-number projection approach in the neutron–proton (np) isovector ([Formula: see text]) pairing case. Expressions of the proton and neutron systems quadratic radii are first established within a projection after variation method (i.e., of PBCS type) using a recently proposed wave function for odd-mass nuclei. It is checked that they reduce to the ones obtained in the like-particles pairing case. The new expressions are then used to study numerically the various radii of nuclei such as [Formula: see text] and [Formula: see text], using the single-particle energies of a Woods–Saxon mean-field. It is shown that the few available experimental data are satisfactorily described by means of the present work approach. Furthermore, it appears that the np pairing and projection effects on the various radii are small on average in the case of odd-mass nuclei. However, the relative discrepancies with the values when only the pairing between like-particles is taken into account or the values obtained before the projection may reach up to 3% or 4% for some nuclei.

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Effect of single-particle splitting in the exact wave function of the isovectorial pairing Hamiltonian

Cited by 4 publications

References 20 publications

Isovectorial pairing in solvable and algebraic models

Isovectorial pairing in solvable and algebraic models

Number-Projected Electric Quadrupole Moments of Even–even Proton-Rich Nuclei in the Isovector Pairing Case

Charge, proton and neutron systems and matter radii of N ≈ Z odd-mass nuclei using a particle-number projection approach in the T = 1 pairing case

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