Structure of potassium isotopes studied with collinear laser spectroscopy

By exploring the structure of different nuclei, one can learn about the interaction between the nucleons, their building blocks. In this field of research, there is a strong interplay between experiment and theory. In particular, theory has a crucial role in the interpretation of the experimental results, while new experimental results provide testing ground and directions for theorists. In the light- and mid-mass regions of the nuclear chart, the shell model is very successful and widely used for calculations of the ground- as well as excited- states properties. It is based on associated larger energy gaps between single particle energy levels for isotopes with certain proton (Z) and neutron (N) numbers, which are called "magic numbers". It was believed that these numbers (8, 20, 28, ...) are preserved for all nuclei throughout the nuclear chart. However, during the last decades studies of the isotopes with an unbalanced number of protons and neutrons revealed that in these isotopes the shell gaps could change when compared to the stable isotopes. This effect is known as the shell evolution. In general, the potassium isotopes with 19 protons are excellent probes for the shell-model theory. In the region below Ca (Z < 20), the inversion of the ground- and the first-excited states (3/2$^{+}$ and 1/2$^{+}$, respectively) for isotopes with 20 ≤ N ≤ 28 was discovered. In the Cl chain (Z = 17), it happens at N = 24, while for K isotopes, the inversion takes place at N = 28. This has drawn appreciable attention in the last decade from both experimentalists and theorists. The effect is the consequence of the degeneracy (or even inversion) of the $\pi 2s_{1/2}$ and $\pi 1d_{3/2}$ orbitals when the $\nu 1f_{7/2}$ orbit is being filled. "What will happen with this particular gap when the next neutron orbit, $\nu 2p_{3/2}$, is being filled?" and "What are the forces responsible for this?" were open questions which we addressed in our studies. The experiment was carried out on the COLLAPS beam-line located at CERN- ISOLDE, where collinear laser spectroscopy was performed on a bunched beam of the radioactive K atoms. The hyperfine structure of the potassium isotopes from N = 19 up to N = 32 was measured and the analysis yielded the nuclear spins, magnetic moments and the mean square charge radii. In addition, shell- model calculations with different effective interactions were carried out, where only one of them predicted the correct ground-state spin for $^{49}$K (I = 1/2) and all agreed for $^{51}$K (I = 3/2). The evolution of the $\pi (2s_{3/2} − 1d_{3/2})$ gap was investigated in more detail using the spin-tensor decomposition method. Moreover, the evolution of the energy gap was also investigated using ab initio calculations where 3N forces were included. The obtained results are in a reasonable agreement with experimental data, considering the fact that this interaction was fitted only to data up to mass A = 4. Magnetic moments (g factors) are sensitive to the occupation of particular single particle orbits and the configuration of the wave function. Thus, the discussion based on the comparison between the experimental results and the shell-model calculations is reported. It is shown that only $^{48}$K and $^{49}$K have a more fragmented ground-state wave function. Additionally, the ground-state spin of $^{48,50}$K was established firmly for the first time, to be I = 1 and I = 0, respectively. The directly measured isomer shift between the ground state (I$^{\pi} = 3^{+}$) and isomeric state (I$^{\pi} = 0^{+}$) in $^{38}$K resulted in a significant difference in the mean square charge radius, contradicting the previous conclusion based on an indirect measurement. The shell-model calculations, which accounted for the excitation of protons and neutrons across Z and N = 20 shell gaps, were performed in order to support the intuitive interpretation of this increase of the charge radius.