In the aims to increase the precision of the isotope shift measurements in the collinear ion beams, in order to probe new physics, three hypothetical experimental setups were modelled and characterised. The current state of the art measurements are done in trapped ion setups reaching 0.1MHz precision. Ion beam experiments like the ones at ISOLDE offer a much wider range of possible isotopes and isomers but in the past also had poorer performances precision-wise. Two of these aim to implement Ramsey type measurement. Ramsey type measurements were attempted in the past, but these attempts failed due to lack of understanding of the line shapes, which were now successfully modelled in this work. The base setup was improved and now promises a precision of less than a 1kHz (100x better than the state of the art) giving us the best of both worlds.