Coulomb breakup of neutron-rich ${}^{29,30}$Na isotopes near the island of inversion

Abstract

First results are reported on the ground state configurations of the neutron-rich ${}^{29,30}$Na isotopes, obtained via Coulomb dissociation (CD) measurements as a method of the direct probe. The invariant mass spectra of those nuclei have been obtained through measurement of the four-momentum of all decay products after Coulomb excitation on a ${}^{208}Pb$ target at energies of 400-430 MeV/nucleon using FRS-ALADIN-LAND setup at GSI, Darmstadt. Integrated Coulomb-dissociation cross-sections (CD) of 89 $(7)$ mb and 167 $(13)$ mb up to excitation energy of 10 MeV for one neutron removal from ${}^{29}$Na and ${}^{30}$Na respectively, have been extracted. The major part of one neutron removal, CD cross-sections of those nuclei populate core, in its' ground state. A comparison with the direct breakup model, suggests the predominant occupation of the valence neutron in the ground state of ${}^{29}$Na$(3/2^{+})$ and ${}^{30}$Na$(2^{+})$ is the $d$ orbital with small contribution in the $s$-orbital which are coupled with ground state of the core. The ground state configurations of these nuclei are as ${}^{28}$Na$_{gs (1^+)\otimesν_{s,d}$ and ${}^{29}$Na${}_{gs}(3/2^{+})\otimes \hat{I}{½}_{s,d}$, respectively. The ground state spin and parity of these nuclei, obtained from this experiment are in agreement with earlier reported values. The spectroscopic factors for the valence neutron occupying the $s$ and $d$ orbitals for these nuclei in the ground state have been extracted and reported for the first time. A comparison of the experimental findings with the shell model calculation using MCSM suggests a lower limit of around 4.3 MeV of the sd-pf shell gap in ${}^{30}$Na.

Modified version of the manuscript is accepted for publication in Journal of Physics G, Jan., 2017