Investigating the nuclear structure of the neutron-rich odd-mass Fe isotopes, in the $\beta$-decay of their parent - Mn

For many years the shell structure of the nucleus, originally proposed by Mayer and Haxel, predicting certain energy gaps at specific proton and/or neutron numbers, has been consistent with the experimental findings at or near the line of stability. These nuclei exhibit a sequence of magic numbers – 2, 8, 20, 28, 50, 82, which is different from the one calculated using only a Harmonic Oscillator potential: 2, 8, 20, 40, 70... The strong spin-orbit term, added to the latter potential by Mayer and Haxel, is a necessary requirement for a successful description of these quantum systems, which lowers the energy orbitals with higher spins directly affecting the l = 4 (1$g_{9/2}$) orbit by reducing the gap at N = 40 and creating the N = 50 one. With the development of more exotic radioactive beams, however, it has been observed that for nuclei away from the stability line the traditional shell gaps have weakened, while new energy gaps have emerged instead. It has been further realized that the residual nucleon- nucleon interaction can lead to significant shifts in the single-particle energies, such that phenomena like the appearance of new shell gaps can be explained. Thus, understanding how shell structure in nuclei develops is a major goal in nuclear physics research. The region around proton number Z = 28 and neutron number N = 40 is interesting owing to the experimental evidences, that the neutron-rich iron (Fe) and chromium (Cr) isotones exhibit increasingly collective behaviour (N > 34), rather than the semi-magic one expected if the N = 40 gap were to be robust. While the spherical $^{68}$Ni isotope shows features of a doubly-closed nucleus – 28 40 high 2$^{+}_{1}$ excitation energy and low $B(E2; 2^{+}_{1} \rightarrow 0^{+}$) value – the nature of the high excitation energy of the 2$^{+}_{1}$ state could be explained as due to the presence of the opposite-parity ν1$g_{9/2}$ orbital across the N = 40 energy gap and the negative-parity $pf$ shell. The latter orbital is necessary in order to form a 2$^{+}$ state, as the neutrons in the $p_{1/2}$ orbital of the full pf shell cannot. Furthermore, the development of collectivity as Z decreases from 28, is seen as a result of enhanced quadrupole collectivity when promoting neutron pairs across N = 40. Stated another way, by removing protons from the 1$f_{7/2}$ orbital, the attractive central and tensor terms of the monopole proton-neutron interaction between the proton-holes in the $f_{7/2}$ orbital and the neutrons in the 1$g_{9/2}$ and the 2$d_{5/2}$ orbitals brings the neutron single-particle states down in energy. At the same time the repulsive tensor interaction between the proton-holes in the $f_{7/2}$ orbital and the neutrons in the 1$_{f5/2}$ orbital pushes the latter up, further reducing the N = 40 closure.The quadrupole collectivity is then enhanced as a result of the presence of the $\Delta$j = 2 orbitals ($1g$ and $2d$), close to the $pf$ shell, making it energetically more favorable to excite pairs of neutrons. The shape-driving, unique-parity ν$1g_{9/2}$ orbital is also facilitating spin isomerism in the region of the odd-A iron isotopes. This thesis presents the experimentally deduced information on excited states, $\gamma$-transitions and $\beta$-decay branches in the consecutive decays of the odd- A $^{61−67}$Mn, $^{63−67}$Fe and $^{63−67}$Co. The radioactive source of manganese isotopes were produced in a proton-induced fission reaction experiment at ISOLDE, CERN. After selective laser ionization, acceleration and mass separation the ions of interest were implanted on a movable tape station, surrounded by several types of detectors. The $\gamma$- and $\beta$-particles in the decays were detected with two triple HPGe MINIBALL detectors (three single crystals mounted in one cryostat) and three $\Delta$E plastic scintillators in close geometry, respectively, and recorded on an event-by-event basis using digital electronics. The analysis of the decay data reveals a wealth of new information. New excited and isomeric states have been given tentative spin and parity assignments, while the half-lives of the isomeric levels and the ground states of the mother - manganese - could be determined in many cases for the first time or with a greater than the previously measured precision. The energy of the isomeric positive-parity states in iron can now be traced up to $^{67}$Fe, completing the systematic of the metastable states in those isotopes, including a newly discovered ms-isomeric state in $^{63}$Fe. The available information for the cobalt and nickel nuclei is also again greatly enhanced with respect to the ‘a priori’ existing data with the addition of new excited states and thus $\gamma$-transitions.In the decay of $^{65}$Fe the experimental statistics allowed for the assignment of a $\gamma$-transition connecting the previously constructed two separate decay schemes. A pair of states in each investigated odd-mass iron isotope, have been observed to have a strong direct $\beta$-decay branch. The states are fed much stronger than all other observed levels, concentrating together more than half of the $\beta$-decay strength. The pair of states, with an energy separation of about 650 keV, has been observed to move up in excitation energy with the addition of neutrons: from the ground state and the 629-keV excited state in $^{61}$Fe to the 942- and the 1570-keV state in the heaviest investigated $^{67}$Fe isotope. Finding these same states in each one of the odd-mass iron isotopes indicates that the spin and parity and possibly the configuration of the ground state of the $\beta$-decaying manganese mother isotope remains the same throughout the isotopic chain, up to A = 67.