Added physics documentation

[RHanley1]

I have written a document which is intended to define all our conventions and has the useful derivations of electric dipole, magentic dipole, and electric quadrupole transition matrix elements and rates. This is not a final document and is intended to be dynamic as we refine the code-base.

I have also added to the .gitignore file so that LaTex build files are
not tracked.

[pathfinder49]

Could you define the notation rr used in equation 35.

[RHanley1]

Could you define the notation rr used in equation 35.

This is a dyadic/outer product of two vectors which makes a matrix. I'll add it in for more clarity.

[pathfinder49]

Your definition of the saturation intensity differs from that used in the code. GammaJ is in fact the tatal decay rate. These agree.

You have:

with:

The code defines this relative to gammaJ
https://github.com/OxfordIonTrapGroup/ion_phys/blob/53311d5dc568e6328a2558ffadd2a78c5658c9f7/ion_phys/common.py#L203-L221

[hartytp]

Isn't GammaJ just Gamma_{Tot}?

[pathfinder49]

Isn't GammaJ just Gamma_{Tot}?

Yes, edited my previous message. I had misread the GammaJ definition.

[hartytp]

But, I'll grant that the notation is maybe a bit unclear (GammaJ is Sum(i)Gamma_{ij} in my notation).

[dnadlinger]

What's holding up this getting merged?

[hartytp]

Someone doing a review to check style, consistency with the definitions we use elsewhere in the group, etc. It's been on my to do list for a while but I haven't managed it. I would happily delegate responsibility to a volunteer!

[hartytp]

Also, this feels like something that should be in sphinx or whatever so it auto-generates nice HTML docs that we can publish rather than being latex.