You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
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
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:
We add a new LevelData.quadratic_shift_matrix_element field, defaulting to 0, which stores the reduced matrix element
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
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 ofC_2
for signs and factors of 1/2) whereC_2
is calculated fromHere
\Gamma
is essentially a place holder for any quantum numbers likeF
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 bystate_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:LevelData.quadratic_shift_matrix_element
field, defaulting to 0, which stores the reduced matrix elementAtom
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
The text was updated successfully, but these errors were encountered: