The nuclear two-photon, or double-gamma decay is a rare decay mode in atomic nuclei whereby a nucleus in an excited state emits two gamma rays simultaneously. This second-order electromagnetic process, well known in atomic physics, has been little studied for the atomic nucleus due to the largely predominant first-order processes. Even-even nuclei with a first excited 0+ state are favorable cases to search for a double-gamma decay branch, since the emission of a single gamma ray is strictly forbidden for 0+ to 0+ transitions by angular momentum conservation. The double-gamma decay still remains a very small decay branch (<1E-4) competing with the dominant (first-order) decay modes of atomic internal-conversion electrons (ICE) or internal positron-electron (e+-e-) pair creation (IPC).

The thesis project has two distinct experimental parts: First, we store bare (fully-stripped) ions in their excited 0+ state in the heavy-ion storage ring (ESR) at the GSI facility to search for the double-gamma decay in several nuclides. For neutral atoms the excited 0+ state is a rather short-lived isomeric state with a lifetime of the order of a few tens to hundreds of nanoseconds. At relativistic energies available at GSI, however, all ions are fully stripped of their atomic electrons and decay by ICE emission is hence not possible. If the state of interest is located below the pair creation threshold the IPC process is not possible either. Consequently, bare nuclei are trapped in a long-lived isomeric state, which can only decay by double-gamma emission to the ground state. The decay of the isomers is identified by so-called time-resolved Schottky Mass Spectroscopy. This method allows to distinguish the isomer and the ground state by their (very slightly) different revolution time in the ESR, and to observe the disappearance of the isomer peak in the mass spectrum with a characteristic decay time. Successful experiment establishing the double-gamma decay in several nuclides (72Ge, 98Mo, 98Zr) were already performed and a new experiment to study the nuclide 194Pb has been accepted by the GSI Programme Committee and its realization is planned for 2027.

The second part concerns the direct observation of the emitted photons using gamma-ray spectroscopy. While the storage ring experiments allow to measure the partial lifetime for the double gamma decay, further information on the nuclear properties can be only be achieved by measuring the photon themselves. A test experiment has been performed to study its feasibility and the plans a more detailed study should be developed with the PhD project.

The theoretical description from first principles, i.e. in a so-called ab initio manner, of atomic nuclei containing more than 12 nucleons has only recently become possible thanks to the crucial developments in many-body theory and the availability of increasingly powerful high-performance computers. These ab initio techniques are successfully applied to study the structure of nuclei, starting from the lightest isotopes and now reaching all medium-mass nuclei containing up to about 80 nucleons. The extension to even heavier systems requires decisive advances in terms of storage cost and computation time induced by available many-body methods. In this context, the objective of the thesis is to develop the dimensionality reduction method based on the factorization of tensors involved in the non-perturbative many-body theory known as deformed coupled cluster (dCC). The proposed work will exploit the latest advances in nuclear theory, including the use of nuclear potentials from chiral effective field theory and renormalization group techniques, as well as high-performance computing resources and codes.