Study of the nuclear spin-orientation in incomplete fusion reactions. Measurement of the magnetic moment of the 2$^{+}$ states in $^{22}$Ne and $^{28}$Mg

Knowledge of the nuclear magnetic moments is of great importance to get a clear understanding of nuclear structure. The magnetic moment is sensitive to the single-particle nature of the valence nucleons. The development of radioactive beam facilities allows nowadays studying nuclear spins and moments of exotic nuclei which are far from the stability line. However, the measurement of magnetic moments of exotic nuclei produced as radioactive beams requires the development of reliable methods. Successful development of such methods would open up the possibility to discover new nuclear structure phenomena. The study outlined in this thesis is formed by two experiments. The first experiment was performed at ALTO facility in Orsay, France. One of the main requirements in order to measure a nuclear magnetic moment is to produce a spin-oriented ensemble. The latter can be produced by suitable reaction mechanism and nuclear spin interaction with the surrounding environment. The degree of the orientation depends on the formation process and reaction mechanism. The aim of this first experiment was investigating the level of nuclear spin orientation in incomplete fusion reaction mechanism. Two reaction channels were studied, the isomeric states in ⁶⁵mNi (I = 9/2$^{+}$, Eₓ = 1017 keV, T$_{1/2}$ = 26 ns), and ⁶⁶mCu (I = 6⁻, Eₓ = 563 keV, T₁/₂= 600 ns) with Time-Dependent Perturbed Angular Distribution (TDPAD) method. The result of the experiment demonstrates the possibility of obtaining spin alignment in incomplete fusion reaction of an order of 20%. This reaction mechanism, with such an important amount of spin alignment has potential near radioactive beam facilities to study the neutron-rich region with inverse kinematics reactions. The second experiment, and the main part of the thesis was performed at HIE-ISOLDE at CERN. This experiment aimed to obtain high precision g-factor information on a short-lived picosecond state. A new Time Differential Recoil-In-Vacuum (TDRIV) method was applied for the first time using post-accelerated radioactive beams. The g-factor measurement was performed for the first-excited state in ²⁸Mg nucleus (Eₓ = 1474(1) keV, T$_{1/2}$ = 1.2(1) ps). Since the lifetime of the state is of the order of picoseconds, its g-factor can be measured only via the spin precession of the nucleus in an extremely strong magnetic field (kT). Such fields can only be produced at the nucleus by hyperfine interactions. In order to obtain a high precision on a g-factor measurement, a TDRIV calibration experiment was performed with a stable ²²Ne beam. This run allowed testing the system under the same conditions as with radioactive²⁸Mg beam. In addition, using the known g-factor of the first-excited state in ²²Ne allows to determine the absolute target-to-degrader distance so that to decrease the uncertainty and obtain a high precision g-factor measurement. The obtained calibration parameters from the ²²Ne data will be used in the determination of g-factor of $^{28}$Mg.