Magnetic dipole moments, electric quadrupole moments, and electron scattering form factors of neutron-rich sd−pf cross-shell nuclei

Abstract

Magnetic dipole and electric quadrupole moments are calculated for neutron-rich sd-pf cross-shell nuclei. These nuclei include open shell isotopes with the number of protons less than 20 and neutrons greater than 20, for which experimental data are available. Shell model calculations are performed with full $sd$ shell model space for $Z$\ensuremath{-}8 valence protons and full $pf$ shell model space for $N$\ensuremath{-}20 valence neutrons, where the remaining 20 neutrons are frozen in $s$, $p$ and $sd$-shells. Also, magnetic and Coulomb electron scattering form factors are calculated for some of these nuclei. Excitation out of major shell space are taken into account through a microscopic theory which allows particle-hole excitation from the core and model space orbits to all higher orbits with $2\ensuremath{\hbar}\ensuremath{\omega}$ excitation. Effective charges are obtained for each isotope. Core polarization (CP) is essential for obtaining a reasonable description of the electric quadrupole moments and enhance the Coulomb form factors but has no effect on the dipole magnetic moments but squeezes the magnetic form factors. The magnetic static and dynamic properties can be described by free $g$ factors for the model space nucleons without introducing CP effect, on the contrary to the electric static and dynamic properties, which cannot be described properly by the model space nucleons without taking into account CP effects.