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Add quadratic Zeeman shift #85

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hartytp opened this issue Jan 6, 2025 · 0 comments
Open

Add quadratic Zeeman shift #85

hartytp opened this issue Jan 6, 2025 · 0 comments

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@hartytp
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hartytp commented Jan 6, 2025

There is a quadratic AC Zeeman shift, which arises from mixing between fine-structure states with the same parity [1]. This is currently not accounted for in atomic_physics but is relevant, for examples, in the D-levels of calcium.

The treatment in [1] is pretty nice. The shift goes like B^2 * C_2 (todo check the definition of C_2 for signs and factors of 1/2) where C_2 is calculated from

image

Here \Gamma is essentially a place holder for any quantum numbers like F which are used to identify states. NB since we work in the high-field basis where the nuclear spin is decoupled from the electron we do not need to worry about 6-j symbols (that's all handled by state_vectors).

The calculation of the reduced matrix elements are quite involved and not something we should get into in atomic_physics, but it's worth supporting a means of calculating the shifts on each state. My proposal is as follows:

  1. We add a new LevelData.quadratic_shift_matrix_element field, defaulting to 0, which stores the reduced matrix element
  2. In the constructor of Atom we use equation (9) above to apply a correction to the energy of each state to account for this shift

[1] https://arxiv.org/pdf/2201.02843

@hartytp hartytp changed the title Add quadratic AC Zeeman shift Add quadratic Zeeman shift Jan 30, 2025
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