defineBasis (for DynamicPolarizability) double counts extraLevels if nMin < ground state n

[jagerber48]

The defineBasis method within DynamicPolarizability class double counts energy levels depending on nMin and nMax passed in as a result of the extraLevels check.

It appears that extraLevels for an atom finds any levels that have principle quantum number smaller than the ground state, but, which nonetheless have energy higher than the ground state and are dipole coupled to the ground state. These extraLevels are always added into the basis for DynamicPolarizability calculation. This check is useful and has helped us avoid missing coupling to some states in the past. For the case of Rubidium87 the ground state has n=5 but there are some n=4 levels included in extraLevels. If one passes in nMin=4 to defineBasis then these states are double counted. This has led to incorrect values for calculations.

from arc import Rubidium87, DynamicPolarizability
atom = Rubidium87()
n = 5
l = 1
j = 3/2
calc = DynamicPolarizability(atom, 5, 1, 3/2)
print('with nMin = 5:')
calc.defineBasis(5, 6)
print(calc.basis)

print('with nMin = 4:')
calc.defineBasis(4, 6)
print(calc.basis)

gives

with nMin = 5:
[[5, 0, 0.5, 0.5], [5, 2, 1.5, 0.5], [5, 2, 2.5, 0.5], [6, 0, 0.5, 0.5], [6, 2, 1.5, 0.5], [6, 2, 2.5, 0.5], [4, 2, 2.5], [4, 2, 1.5]]
with nMin = 4:
[[4, 0, 0.5, 0.5], [4, 2, 1.5, 0.5], [4, 2, 2.5, 0.5], [5, 0, 0.5, 0.5], [5, 2, 1.5, 0.5], [5, 2, 2.5, 0.5], [6, 0, 0.5, 0.5], [6, 2, 1.5, 0.5], [6, 2, 2.5, 0.5], [4, 2, 2.5], [4, 2, 1.5]]

This issue could be resolved by checking if the existing state is already included in the basis whenever adding new states to the basis.

I have not checked if this issue occurs anywhere else in the code but it may be likely.

[nikolasibalic]

Hi @jagerber48 ,

Many thanks for reporting this! It should be fixed now (202447b) in version 3.0.19 available on PyPI.

I had to switch to new CI pipeline also, so if you have any problems with new installation, let me know. What I tested locally worked fine.

[jagerber48]

Hello @nikolasibalic, thank you for working on and maintaining this great package!

Your fix looks good. I'll let you know if I have issues with the new install, though not sure when I'll try it.

This fix solves the issues in my eyes. Am I the one who closes the issue?