How to simulate an isotope shift measurement

• A
• Malamala
In summary, the conversation is discussing how to measure transitions in a paper about King plot non-linearities in order to determine a sensitivity for a new physics parameter. The speaker suggests generating data using equation 5 and using the error propagation method mentioned below equation 9 to get the error on ##\alpha_{NP}##. They also mention using a Monte Carlo simulation for more accuracy.
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!

It's not clear to me why you will need a simulation to do this calculation. If you assume a non-zero value of ##\alpha_{NP}##, don't you just need to calculate the derivatives of ##\frac{\partial \alpha_{NP}}{\partial \nu_i}## for ##i = 1,2## being the two transition frequencies, and perform standard propagation of error?

Alternatively, for more accuracy, just run a simple monte carlo. Some algebra will let you derive an expression like ##\nu_2 = f(\nu_1,\alpha_{NP})## by solving the equation for ##\alpha_{NP}## for ##\nu_2##. Then introduce some measurement noise by adding uncorrelated random numbers to both ##\nu_1## and ##\nu_2##, with equal variance (assuming you measure both transitions with equal uncertainty). Then just find the scatter on your observed values of ##\alpha_{NP}##. Was that clear?

BillKet

1. What is an isotope shift measurement?

An isotope shift measurement is a technique used in scientific research to determine the difference in energy levels between isotopes of the same element. This is typically done by measuring the atomic transition frequencies of the isotopes, which can provide information about the nuclear structure and properties of the element.

2. Why is it important to simulate an isotope shift measurement?

Simulating an isotope shift measurement allows scientists to understand and predict the behavior of isotopes in different environments, without having to conduct an actual experiment. This can save time and resources, and also provide insight into the underlying mechanisms and factors that influence the measurement.

3. What factors need to be considered when simulating an isotope shift measurement?

Some important factors to consider when simulating an isotope shift measurement include the energy levels and transitions of the isotopes, the effects of external factors such as temperature and pressure, and the accuracy and precision of the measurement instruments.

4. What tools or software are commonly used to simulate an isotope shift measurement?

There are various tools and software available for simulating an isotope shift measurement, such as MATLAB, Python, and specialized software like Hyperfine. These programs typically use mathematical models and algorithms to simulate the behavior of isotopes and their interactions with different environments.

5. What are some potential applications of simulating an isotope shift measurement?

Simulating an isotope shift measurement can have a wide range of applications, including in nuclear physics research, materials science, and even in medical imaging and diagnostics. By understanding the behavior of isotopes, scientists can also develop new technologies and techniques that utilize these properties for various purposes.

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