EPJA

[paper] The energy-weighted sum rule and the nuclear radius

The energy-weighted sum rule and the nuclear radius

Hans Peter Schröder

doi: 10.1140/epja/i2015-15109-9

The energy-weighted integrated cross-section for photon absorption –known as sum rule σ−1 — is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at σ−1 . Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated σ−1 and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of σ−1 differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections g(A) and the uncorrelated function f(A) as a ratio it shows that g(A)/f(A) tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)).

Oct 2, 2015 by Theo radii theory 0

[paper] Magnetic moments of K isomers as indicators of octupole collectivity

Magnetic moments of K isomers as indicators of octupole collectivity

N. Minkov and P. M. Walker

doi: 10.1140/epja/i2012-12080-y

The relation between the quadrupole-octupole deformation and the structure of high-K isomers in heavy even-even nuclei is studied through a reflection asymmetric deformed shell model including a BCS procedure with constant pairing interaction. Two-quasiparticle states with K^π=4⁻, 5⁻, 6⁻, 6⁺ and 7⁻ are considered in the region of actinide nuclei (U, Pu and Cm) and rare-earth nuclei (Nd, Sm and Gd). The behaviour of two-quasiparticle energies and magnetic dipole moments of these configurations is examined over a wide range in the plane of quadrupole and octupole deformations (&betal₂ and β₃. In all considered actinide nuclei, the calculations show that there is pronounced sensitivity of the magnetic moments to the octupole deformation. In the rare-earth nuclei, the calculations for ^154,156Gd show stronger sensitivity of the magnetic moment to the octupole deformation than in the other considered cases.

Jun 10, 2012 by Theo theory 0

[paper] Quadrupole moments of spherical semi-magic nuclei within the self-consistent Theory of Finite Fermi Systems

Quadrupole moments of spherical semi-magic nuclei within the self-consistent Theory of Finite Fermi Systems

S.V. Tolokonnikov et al.

doi: 10.1140/epja/i2012-12070-1

The quadrupole moments of odd neighbors of semi-magic lead and tin isotopes and N=50, N=82 isotones are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. Two sets of published functionals are used to estimate systematic errors of the present self-consistent approach. They differ by the spin-orbit and effective tensor force parameters. The functional DF3-a leads to quadrupole moments in reasonable agreement with the experimental ones for most, but not all, nuclei considered.

May 27, 2012 by Theo g factor 0

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