# Hyperfine structure transition of Cs-133: calculation?

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• Marco Masi
In summary, the hyperfine structure transition of Cs-133 is a specific energy level transition in the cesium atom that is important for the official definition of the second in the SI system. It is calculated using the relativistic Dirac equation and the hyperfine structure constant, which represents the strength of the interaction between the electron and the nucleus. The accuracy of the calculation can be affected by factors such as experimental measurements and relativistic effects. However, advancements in technology and theoretical methods have led to increasingly accurate calculations, with the most recent one having an uncertainty of only 0.3 parts per trillion.
Marco Masi
I'm looking for the theoretical calculation of the hyperfine structure transition frequency of Ca-133 which is used in atomic clocks to define the second according to SI-Units. Google, Google... there is a lot about the hyperfine Hamiltonian of hydrogen, but couldn't find none about that of Ca-133. I would like to see how that famous 9,192,631,770 Hz frequency which defines our earthly time standard is calculated through theory. Can anyone help?

I think it should be Caesium not Calsium.

blue_leaf77 said:
I think it should be Caesium not Calsium.

Opss... You are right, Cs-133... not Ca. Thanks.

## 1. What is the hyperfine structure transition of Cs-133 and why is it important?

The hyperfine structure transition of Cs-133 is a specific energy level transition in the cesium atom. It is important because it serves as the basis for the official definition of the second, the unit of time in the International System of Units (SI).

## 2. How is the hyperfine structure transition of Cs-133 calculated?

The hyperfine structure transition of Cs-133 is calculated using the relativistic Dirac equation, which takes into account the spin and magnetic interactions of the electrons and the nucleus. The calculation involves solving this equation and obtaining the energy levels of the atom.

## 3. What is the significance of the hyperfine structure constant in the calculation?

The hyperfine structure constant is a dimensionless quantity that represents the strength of the interaction between the magnetic moments of the electron and the nucleus. It is an important parameter in the calculation of the hyperfine structure transition of Cs-133.

## 4. What factors affect the accuracy of the calculation of the hyperfine structure transition?

The accuracy of the calculation of the hyperfine structure transition of Cs-133 can be affected by factors such as the precision of the experimental measurements used to determine the hyperfine structure constant and the relativistic effects that may be neglected in the calculation.

## 5. How has the calculation of the hyperfine structure transition changed over time?

The calculation of the hyperfine structure transition of Cs-133 has improved over time due to advancements in technology and theoretical methods. The most recent calculation, using a combination of experimental and theoretical values, has an uncertainty of only 0.3 parts per trillion, making it the most accurate determination to date.

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