Laser-assisted decay and optical spectroscopy studies of neutron-deficient thallium isotopes

The neutron-deficient thallium isotopes with one proton less than the Z = 82 shell closure, are situated in an interesting region of the nuclear chart, notorious for intruder states and shape coexistence. Shape coexistence is the remarkable phenomenon in which two or more distinct types of deformation occur at low energy in the same atomic nucleus. Shape coexistence has been studied intensively, experimentally as well as theoretically in different nuclei in the light-lead region and the isomerism in the thallium isotopes was among the first indications of this phenomenon. Different shapes, whose structure has been linked to specific proton orbitals above and below the Z = 82 shell closure, are present at low energy in the neutron-deficient odd-mass thallium nuclei. In the odd-odd nuclei, the coupling of an unpaired proton and unpaired neutron gives rise to multiplets of low-lying states from which some can be isomeric. Since thallium has one proton missing in the major proton shell, and when approaching neutron mid-shell at N = 104, the structure of these isotopes manifests itself by the interplay between shape coexistence phenomena as well as single-particle properties. In this thesis, the structure of a number of neutron-deficient thallium isotopes is studied with laser-assisted decay and optical spectroscopy performed at the ISOLDE facility in CERN (Geneva, Switzerland). This dual approach was essential to identify the different decay branches and disentangle the decay schemes of the different long-lived states in the thallium isotopes. The decay products were detected with the Windmill system and two HPGe detectors surrounding the Windmill chamber. A study of the internal decay of the (10$^{−}$) intruder state in $^{184}$Tl revealed an excitation energy of 506.1(1) keV, extending the (10$^{−}$)$\rightarrow$(7$^{+}$) energy systematics beyond neutron mid-shell and confirming the parabolic behavior of the excitation energy as a function of neutron number. Using the extracted half-life of the (10$^{−}$) state, the retardation factors of the depopulating E3 and M2 transitions were determined and compared with retardation factors in neighboring odd-mass and even-mass thallium isotopes. Combined with the information on the published reduced $\alpha$-decay widths of the bismuth isotopes populating levels in neighboring thallium nuclei, a confirmation of the proton 1p-2h intruder character of the (10$^{−}$) isomer and an interpretation of the levels in $^{184}$Tl fed in the isomeric decay in terms of [$\pi$3s$_{1/2}$ $\otimes$ $\nu$1i$_{13/2}$] and [$\pi$2d$_{3/2}$ $\otimes$ $\nu$1i$_{13/2}$] configurations could be obtained. From the results of the laser-spectroscopy study, it was observed that the magnetic moment of the (7$^{+}_{1}$) state shows increased importance of the [$\pi$d$_{3/2}$ $\otimes$ $\nu$1i$_{13/2}$] configuration, compared to respective magnetic moments in the heavier odd-odd thallium isotopes. The similarity of the charge radius of the (10$^{−}$) isomeric state with the charge radii of the $\pi$h$_{9/2}$-based intruder states in heavier odd and odd-odd thallium isotopes supports the proton intruder character of this state in $^{184}$Tl. Through the observation of hindered and unhindered $\alpha$ decay, low-lying states, possibly intruders, in the daughter nuclei can be selectively studied and identified, yielding direct information on the excitation energy, decay pattern and possible configurations involved. In this thesis, the results of an $\alpha$ decay of $^{182,184}$Tl are presented. New fine-structure $\alpha$ decays have been observed for both isotopes and previous observed $\alpha$-decay lines were confirmed. Using a purification procedure on the singles $\alpha$-decay energy spectra, $\alpha$-decay branching ratios could be determined for the three long-lived (10$^{−}$), (7$^{+}$) and (2$^{−}$) states in $^{184}$Tl. Also for $^{182}$Tl new $\alpha$-decay lines have been identified and a lower limit of the $\alpha$-decay branching ratio could be determined. Using $\alpha$-$\gamma$-coincidence analysis, multiple $\gamma$ rays were observed de-exciting levels in $^{178,180}$Au fed by $^{182,184}$Tl $\alpha$ decays. The $\gamma$ transitions connecting these low-lying states in $^{178,180}$Au are essential to sort the data and possibly identify bands from in-beam studies in these isotopes. Owing to the complex fine-structure $\alpha$ decays and limited knowledge about the structure of the daughter nuclei, only partial level schemes could be constructed for both gold isotopes in the present work. Reduced $\alpha$-decay widths have been calculated, using the determined $\alpha$-decay branching ratios and half-lives of the different isomeric states, and are compared with values obtained in neighboring odd- and even-mass thallium isotopes. Except for the allowed $\alpha$ decay of the $^{184}$Tl (10$^{−}$) state, the other fine-structure $\alpha$ decays observed in this study are hindered. This points to strong structural changes between parent thallium and daughter gold isotopes. In laser-spectroscopy studies, the nuclear states themselves are probed, providing model-independent information on ground and isomeric states through the measurement of the hyperfine structure patterns in long chains of isotopes. In this work, $^{179−184}$Tl has been studied using the in-source laser spectroscopy technique with the aim to extend the previously known isomeric chain beyond neutron mid-shell at N = 104. The deduced magnetic moments point to a smooth isotopic change in nuclear structure at neutron mid-shell and beyond. A similar smooth behavior has been observed for the extracted charge radii testifying to the persistence of the near-spherical shape of the ground state, comparable to the previously observed trend in the lead isotopes. The newly measured charge radii of the thallium isomeric states involving the $\pi$h$_{9/2}$ intruder orbital are significantly larger than those of the ground states.