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Physicists have observed all the elementary particles predicted by the Standard Model. These particles, however, account for only 5% of the total mass-energy of the Universe. In the quest to solve the mystery of missing matter and to extend our knowledge about nature, a large number of experimental research programs are devoted to find a glimpse of New Physics. Table-top high precision measurements on molecules can contribute to these efforts in a manner complementary to high-energy experiments at colliders. In this thesis, we describe the operation of a traveling-wave Stark decelerator. This device is designed and constructed in order to slow down heavy polar molecules for various future explorations. Deceleration is achieved by manipulation of the molecules in controllable electric fields. We demonstrate in an experiment the successful operation of the Stark decelerator by slowing down a beam of SrF molecules to one-third of their initial velocity, thus removing almost 90% of the initial kinetic energy. We also reveal limiting conditions for this process. These results are of importance for many exciting experiments using heavy molecules in the near future. One relevant and promising example of such experiments is the search for a permanent electric dipole moment of the electron.

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecular properties of BaF is thus needed to plan the measurements and in particular to determine an optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require incorporation of both high-order correlation and relativistic effects in the calculations. In this work theoretical investigations of the ground and the lowest excited states of BaF and its lighter homologues, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster (FSCC) and multireference configuration interaction (MRCI) methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the $B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFs in this system. Special attention is given to the properties of the $A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and the excited states of the three molecules and the transition dipole moments (TDMs) between the different states., Comment: Minor changes; The following article has been submitted to the Journal of Chemical Physics. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/