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Register a new userCranked shell model and isospin symmetry near N=Z
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A cranked shell model approach for the description of rotational bands in $Napprox Z$ nuclei is formulated. The isovector neutron-proton pairing is taken into account explicitly. The concept of spontaneous breaking and subsequent restoration of the isospin symmetry turns out to be crucial. The general rules to construct the near yrast-spectra for rotating nuclei are presented. For the model case of particles in a j-shell, it is shown that excitation spectra and the alignment processes are well described as compared to the exact shell model calculation. Realistic cranked shell model calculations are able to describe the experimental spectra of $^{72,73}$Kr and $^{74}$Rb isotopes.
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Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all superallowed transitions A,I^pi=0^+,T=1,T_z rightarrow A,I^pi=0^+,T=1,T_z+1 with T_z =-1,0 and A ranging from 10 to 74.
We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to vario
For natural parity states of several odd-A nuclei a comparison of shell model calculations in the full pf configuration space with the Nilsson diagram and particle-rotor predictions shows that prolate strong coupling applies at low excitation energy, revealing multi-quasiparticle rotational bands and, in some cases, bandcrossings. Moreover, ground state bands experience a change from collective to non-collective regime, approaching the termination. Similar features are observed in the even-even nuclei. In the even-even N=Z nuclei evidence of the vibrational gamma-band is found. A review of non-natural parity structures is furthermore presented.
Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=frac12$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets. Relative strengths of the obtained isospin-symmetry-breaking terms {em are not} consistent with the differences in the $NN$ scattering lengths, $a_{nn}$, $a_{pp}$, and $a_{np}$. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.
Experimentally observed ground state band based on the $1/2^{-}[521]$ Nilsson state and the first exited band based on the $7/2^{-}[514]$ Nilsson state in the odd-$Z$ nucleus $^{255}$Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations being performed on these rotational bands. Both the experimental kinematic and dynamic moment of inertia ($mathcal{J}^{(1)}$ and $mathcal{J}^{(2)}$) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia $mathcal{J}^{(1)}$ with the experimental ones extracted from different spin assignments, the spin $17/2^{-}rightarrow13/2^{-}$ is assigned to the lowest-lying $196.6(5)$ keV transition of the $1/2^{-}[521]$ band, and $15/2^{-}rightarrow11/2^{-}$ to the $189(1)$ keV transition of the $7/2^{-}[514]$ band, respectively. The proton $N=7$ major shell is included in the calculations. The intruder of the high$-j$ low$-Omega$ orbitals $1j_{15/2}$ $ (1/2^{-}[770])$ at the high spin leads to the band-crossing at $hbaromegaapprox0.20$ ($hbaromegaapprox0.25$) MeV for the $7/2^{-}[514]$ $alpha=-1/2$ ($alpha=+1/2$) band, and at $hbaromegaapprox0.175$ MeV for the $1/2^{-}[521]$ $alpha=-1/2$ band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.
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