# How to simulate an isotope shift measurement

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• Malamala

#### Malamala

Hello! My questions are based on this paper talking about King plot non-linearities. Assuming I have 3 isotopes and 2 transitions, I would like to know how well I should measure the transitions (i.e. what uncertainty on the transition value) in order to reach a given sensitivity for the new physics parameter. What I am thinking of doing is to generate data using equation 5 (i.e. without any new physics, assuming I know the masses and changes in charge radii), which of course if I plug in equation 9 will give me ##\alpha_{NP} = 0##. However, even if ##\alpha_{NP} = 0##, I can still use the error propagation mentioned below equation 9 to get the error on ##\alpha_{NP}##. So basically I will get ##\alpha_{NP} = 0 \pm d\alpha_{NP}## and from here I can set an upper bound on ##\alpha_{NP} < d\alpha_{NP}## at 1 sigma level. And based on the value of ##d\alpha_{NP}## I am aiming for, I can get the needed uncertainty on the transitions frequencies. However, in practice, ##\alpha_{NP}## won't be zero. It will be smaller than ##d\alpha_{NP}##, but not zero and the upper limit will be ##\alpha_{NP} + d\alpha_{NP}##, which in principle can be up to 2 times bigger than ##d\alpha_{NP}## alone. Given that I know what upper bound I aim for, how can I get the needed uncertainty on the transitions in this general case? Thank you!

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