Odd-even mass staggering with Skyrme-Hartree-Fock-Bogoliubov theory

Chen, W. J.; Bertulani, C. A.; Fang, Xu; Zhang, Y. N.

doi:10.1103/physrevc.91.047303

Cited by 14 publications

(5 citation statements)

References 24 publications

(39 reference statements)

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“…The odd-even staggering phenomena in nuclear radii and nuclear mass have attracted great interests in the past years and lots of efforts have been done, such as the works in Refs. [97][98][99][100][101][102][103].…”

Section: Resultsmentioning

confidence: 99%

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Huo¹,

Sun²,

Li³

et al. 2022

Preprint

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The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Sn isotopes are explored with the continuum Skyrme Hartree-Fock-Bogoliubov theory formulated with the Green's function method, in which the pairing correlation, the couplings with the continuum, and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated. In the ph channel, the SLy4 parameter set is taken for the Skyrme interaction, and in the pp channel, the DDDI is adopted for the pairing interaction. With those parameters, the available experimental two-neutron separation energies S2n and one-neutron separation energies Sn are well reproduced. Much shorter drip lines predicted by Sn are obtained compared with those by S2n. The systematic studies of the neutron pairing energies −Epair shown that values of the odd-A nuclei are much smaller in comparison with those of the neighboring even-even nuclei due to the absent contribution of pairing energy by the unpaired odd neutron. By investigating the single-particle structures, the rms radii and the density distributions, the possible halo structures in the neutron-rich Ca, Ni, and Sn isotopes are predicted, in which the sharp increases of rms radii with significant deviations from the traditional r ∝ A 1/3 rule and very diffuse spatial distributions in densities are observed. By analyzing the contributions of different partial waves to the total neutron density ρ lj (r)/ρ(r), the orbitals locating around the Fermi surface especially those with low angular momenta are found the main reason causing the extended nuclear density and large rms radii. Finally, the numbers of the neutrons N λ (N0) occupied above the Fermi surface λn (in the continuum) are discussed, the behaviors of which are basically consistent with those of pairing energy, supporting the key role of the pairing correlations in the halo phenomena.

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Section: Resultsmentioning

confidence: 99%

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Huo¹,

Sun²,

Li³

et al. 2022

Preprint

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“…To describe the system of fermions, the two-body Hamiltonian in terms of annihilation and creation operators [14] is often used, as,…”

Section: Theoretical Modelmentioning

confidence: 99%

“…where the density of the kinetic energy is , and the symbol means isoscalar and isovector, respectively [14].…”

Section: H(r)mentioning

confidence: 99%

Abnormal odd-even staggering behavior around ¹³²Sn studied by density functional theory *

Shi¹,

Wang²,

Dong³

et al. 2020

Chinese Phys. C

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In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around 132Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around 132Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around 132Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.

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“…Extensive works have been done recently on blocking calculations within the BCS and HFB frameworks for binding energy calculations of odd-A and odd-odd nuclei (see, e.g., Refs. [43,5,61]). Most of above calculations are done within the harmonic oscillator instead of the coordinate space.…”

Section: Theorymentioning

confidence: 99%

“…In those nuclei the spatial structure of the quasi-particle orbitals may be sensitive to both the single-particle energy and the pairing correlation. A related subject is the possible isospin dependence of the pairing force [40,41,42,45,43,44,47,46] and the OES of the binding energy [48], which has not been pinned down yet.…”

Section: Introductionmentioning

confidence: 99%

Odd–even staggering in neutron drip line nuclei

Changizi¹,

Qi²

2016

Nuclear Physics A

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We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-N isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in 120 Sn and globally to all available data on the OES of semi-magic nuclei with Z ≥ 8. In the former calculations, there is a noticeable difference between the neutron mean gaps in neutronrich O, Ca, Ni and Sn isotopes calculated with the surface pairing and those with the mixed and volume pairing. The difference gets much smaller if the globally optimized pairing strengths are employed. The heavier Pb isotopes show the opposite trend. Moreover, large differences between the mean gap and the OES may be expected in both calculations when one goes towards the neutron drip line.

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Odd-even mass staggering with Skyrme-Hartree-Fock-Bogoliubov theory

Cited by 14 publications

References 24 publications

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Abnormal odd-even staggering behavior around ¹³²Sn studied by density functional theory *

Odd–even staggering in neutron drip line nuclei

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Odd-even mass staggering with Skyrme-Hartree-Fock-Bogoliubov theory

Cited by 14 publications

References 24 publications

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

Abnormal odd-even staggering behavior around 132Sn studied by density functional theory *

Odd–even staggering in neutron drip line nuclei

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Abnormal odd-even staggering behavior around ¹³²Sn studied by density functional theory *