Cranked shell model and isospin symmetry near N = Z

Frauendorf, S.; Sheikh, J. A.

doi:10.1016/s0375-9474(98)00624-1

Cited by 72 publications

(77 citation statements)

References 39 publications

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“…For this N = Z nucleus, there has been an open question of whether the protonneutron pair correlation plays a role in the structure discussions. It has been shown that with the renormalized pairing interactions within the like-nucleons in an effective Hamiltoinan, one can account for the T = 1 part of the protonneutron pairing [29]. However, whether the renormalization is sufficient for the complex region that exhibits the phenomenon of band crossings, in particular when both neutron and proton pair alignments occur at the same time is an interesting question to be investigated.…”

Section: The First Experimental Information On Transitions Inmentioning

confidence: 99%

Projected shell model study for the yrast-band structure of the proton-rich mass-80 nuclei

et al. 2001

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A systematic study of the yrast-band structure for the proton-rich, even-even mass-80 nuclei is carried out using the projected shell model approach. We describe the energy spectra, transition quadrupole moments and gyromagnetic factors. The observed variations in energy spectra and transition quadrupole moments in this mass region are discussed in terms of the configuration mixing of the projected deformed Nilsson states as a function of shell filling.

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Section: The First Experimental Information On Transitions Inmentioning

confidence: 99%

Projected shell model study for the yrast-band structure of the proton-rich mass-80 nuclei

et al. 2001

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“…It is well known that the lowest τ = 0 and τ = 1 states compete for the ground state changing the sign of the energy difference E τ =1 − E τ =0 in odd-odd N = Z nuclei, while all even-even N = Z nuclei have the τ = 0 ground states. Several authors [1,2,3,4,5,6,7] already pointed out that this degeneracy in odd-odd N = Z nuclei reflects the delicate balance between the symmetry energy and the like-nucleon neutron-neutron (nn) (or proton-proton (pp)) pairing energy. On the other hand, it has recently been shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing energies [9,10, 25].…”

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confidence: 99%

“…Several authors [1,2,3,5,6,7] discussed that this degeneracy is attributed to the delicate balance between the symmetry energy a(A)τ (τ + 1)/A and pairing gap ∆ and that the energy difference δB = B(Z, N )…”

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Proton-neutron pairing energies inN=Znuclei at finite temperature

Kaneko

Hasegawa

2005

Phys. Rev. C

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Thermal behavior of isoscalar (τ =0) and isovector (τ =1) proton-neutron (pn) pairing energies at finite temperature are investigated by the shell model calculations. These pn pairing energies can be estimated by double differences of "thermal" energies which are extended from the double differences of binding energies as the indicators of pn pairing energies at zero temperature. We found that the delicate balance between isoscalar and isovector pn pairing energies at zero temperature disappears at finite temperature. When temperature rises, while the isovector pn pairing energy decreases, the isoscalar pn pairing energy rather increases. We discuss also the symmetry energy at finite temperature. The proton-neutron (pn) pairing energies have become one of hot topics in the study of the nuclear structure for proton-rich nuclei. In particular, interests are increasing in studying isovector (τ =1) and isoscalar (τ =0) pn pairing energies in medium mass N = Z nuclei produced at the radioactive nuclear beam facilities. The study of pn pairing energies is also important in the astrophysical context. These nuclei lie along the explosive rp-process nucleosynthesis path and the nuclear properties such as masses, halflives, and isomers have a strong influence on modeling the rp-process and identifying possible nucleosynthesis sites. Odd-odd N = Z nuclei are an ideal experimental laboratory for the study of pn pairing energies. It is well known that the lowest τ = 0 and τ = 1 states compete for the ground state changing the sign of the energy difference E τ =1 − E τ =0 in odd-odd N = Z nuclei, while all even-even N = Z nuclei have the τ = 0 ground states. Several authors [1,2,3,4,5,6,7] already pointed out that this degeneracy in odd-odd N = Z nuclei reflects the delicate balance between the symmetry energy and the like-nucleon neutron-neutron (nn) (or proton-proton (pp)) pairing energy. On the other hand, it has recently been shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing energies [9,10, 25].It has been recently reported [11,12] that the canonical heat capacities extracted from observed level densities in 162 Dy, 166 Er and 172 Yb display the S shape with a peak around T ≈ 0.5 MeV, which is interpreted as the breaking of like-nucleon J = 0 pairs because the BCS critical temperature corresponds to T c ≈ 0.57∆ n (T = 0) ≈ 0.5 MeV, where the like-nucleon pairing gap ∆ n (T = 0) is calculated at zero temperature by the BCS theory. Thus it seems that the S shape is a signature of pairing transition at the critical temperature. For the finite Fermi system like a nucleus, however, since the nuclear radius is much smaller than the coherence length of the Cooper pair, statistical fluctuations beyond the mean field in the BCS theory become large. The fluctuations smooth out the sharp phase transition, and then the like-nucleon pairing gap ∆ n does not quickly become zero at the BCS critical temperature but decreases with increasing temperature. There are many approaches to treat...

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“…The usual techniques used in order to remedy this shortcoming are those already used for the study of pairing correlations between likeparticles, i.e. the Quasiparticle Random Phase Approximation (QRPA) (cf., e.g., [9,10,11,12,13,14,15,16,17]), the Lipkin-Nogami (LN) method [18] or the Generator Coordinate Method (GCM) [19]. However, in these methods, the particle-number symmetry is only approximately restored.…”

Section: Introductionmentioning

confidence: 99%

Effects of the particle-number projection on the isovector pairing energy

Allal¹,

Fellah²,

Oudih³

et al.

The 2nd International Conference on Nuclear Physics in Astrophysics

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Abstract. The usual neutron-proton BCS wave function is simultaneously projected on both the good neutron and proton numbers using a discrete projection operator. The projected energy of the system is deduced as a limit of rapidly convergent sequence. It is numerically studied for the N = Z nuclei of which "experimental" pairing gaps may be deduced from the experimental odd-even mass differences. It then appears that the particle-number fluctuation effect is even more important than in the case of pairing between like-particles.PACS. 21.60.-n Nuclear structure models and methods -21.30.Fe Forces in hadronic systems and effective interactions

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Cranked shell model and isospin symmetry near N = Z

Cited by 72 publications

References 39 publications

Projected shell model study for the yrast-band structure of the proton-rich mass-80 nuclei

Projected shell model study for the yrast-band structure of the proton-rich mass-80 nuclei

Proton-neutron pairing energies inN=Znuclei at finite temperature

Effects of the particle-number projection on the isovector pairing energy

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