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A new method of extracting the g-ray intensities necessary to perform lifetime measurements using the differential decay curve method (DDCM) is presented in this work, the unresolved Doppler-shifted components method (UDCM). The UDCM allows for a DDCM analysis to be performed using a g-ray transition for which the fully Doppler-shifted and degraded components are unresolvable in energy and so are detected as a single peak. This technique was used to measure the known lifetime of the yrast 2+1 state in 50Mn with a depopulating transition that does not have resolvable fully Doppler-shifted and degraded components. The lifetime measured through applying the UDCM was consistent with the standard DDCM measurement of the 2+1 state. Use of the UDCM allows for DDCM lifetime measurements to be made using transitions of smaller g-ray energies, smaller recoil velocities and, in some cases, with a smaller uncertainty. In contrast to a standard DDCM analysis, a UDCM analysis is also independent of the widths of the fully Doppler-shifted and degraded components and as a result they do not need to be determined.

To describe the nuclear structure of one or a group of nuclei several observables should be consulted. The excitation energies of states with given spin and parity is often known and gives a good first impression. Nevertheless transition strengths of excited states are a much better probe, since they depend quadratically on the wavefunction. These can be determined in a model-independend way from the corresponding level lifetime. Within this work a total of four experiments were performed to measure the lifetime of excited states in 180Pt and 178Hg. In the neutron-deficient mass region close to the shell closure at lead (Z=82) interesting phenomena such as shape coexistence and shape transitions are observed. The most prominent example is 186Pb, which exhibits three different shapes. The ground state as well as two excited 0+ states together with the corresponding rotational bands are associated to multiparticle-multihole excitations resulting in the different shapes. A similar situation is established for the Hg isotopes near the neutron N=104 midshell, where the lightest isotope for which transition strengths are known is 180Hg. Going further away from the shell closure the 176,178,180Os isotopes are good candidates for the X(5) symmetry, i.e. the transition from spherical to axially deformed. Two questions arise: How can the Pt isotopes just between Os and Hg be described and what is the evolution of shape coexistence in the Hg isotopes leaving neutron midshell? Both questions are addressed within this thesis. 180Pt shows no remains of a X(5) like shape transition and multiparticle-multihole excitations are evident. This structure reaches the ground state and a new so-called island of inversion is found. This simultaneously answers the longlasting question whether configuration mixing is needed to describe the Pt isotopes or not. From the excitation energies 178Hg is expected to be at the edge of the shape-coexistence region. The measured transition strengths confirm the shift of the structure with different shape to higher-lying states, but also a new phenomenon of intermediate deformation (between normal and superdeformation) shows up with decreasing neutron number. The interpretation is given by comparison to several existing calculations as well as particular calculations using geometrical models and the interacting boson model. The experiments were carried out at different accelerator facilities employing the recoil distance Doppler-shift (RDDS) method, except one experiment when electronic-timing techniques were used to measure long lifetimes. Further a dedicated plunger apparatus was commissioned during one experiment. The GALILEO -ray spectrometer is the successor of GASP, which necessitated a completely new mechanical design of the plunger. This fragile device newly allows the combination with charged-particle detectors, e.g. EUCLIDES.

Lifetimes of the T = 1 isobaric analog Ip = 2+ states in 50Mn and 50Cr were measured simultaneously by employing the recoil distance Doppler-shift (RDDS) technique. The states were populated in a fusion-evaporation reaction with a ¹²C beam on a 40Ca target. An analysis of the data and the calculations from the present work, together with the available B(E2 : 2+ RT 0+) data of the isobaric analog states in 50Fe and 50Cr, were used to study isospin symmetry in the three A = 50 isobaric nuclei. Shell-model calculations reproduce the magnitudes as well as the increasing trend of the B(E2) data with increasing Z. To draw a firm conclusion on the level of isospin mixing in the triplet, a new precision measurement of the 2+ RT 0+ transition rate in 50Fe will be required.

The lifetimes of the 21+ , the 22+ and the 31- states of ²¹0Po have been measured in the ²08Pb(¹²C,¹0Be)²¹0Po transfer reaction by the Doppler-shift attenuation method. The result for the lifetime of the 21+ state is about three times shorter than the adopted value. However, the new value still does not allow for a consistent description of the properties of the yrast 21+ , 41+ , 61+ , and 81+ states of ²¹0Po in the framework of nuclear shell models. Quasi-particle Phonon Model (QPM) calculations also cannot overcome this problem thus indicating the existence of a peculiarity which is neglected in both theoretical approaches.

The lifetime of the 21+ state of ²¹²Po was measured in the ²08Pb(¹²C,8Be)²¹²Po transfer reaction by g-ray spectroscopy employing the recoil distance Doppler shift (RDDS) method. The derived absolute B(E2) value of 2.6(3) W.u. indicates a low collectivity and contradicts previous claims of a-cluster components in the structure of the 21+ state. It is demonstrated that a consistent description of the properties of the 21+− 41+− 61+− 81+ sequence in ²¹²Po cannot be achieved in the framework of a single- j shell-model calculation, either. This puzzle is traced to the properties of the seniority-2 configurations in ²¹0Pb and ²¹0Po.