Radial equation for atoms that are not hydrogen?

[pbeierle]

So I've seen radial equations for Hydrogen out there (eg http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydrad.html), where can I find one for more any arbitrary atom?

admitedly, I realize that the equations become more and more complicated the larger the atom is. This is especially problematic considering that i need to calculate radii for electrons in Am-241, Np-237 etc, but unless there is an easier way to calculate the frequencies of these electrons, I don't have much of an option ^_^

 

[Amok]

There are no analytical solutions for the SE for atoms other than hydrogen. What are you trying to solve?

 

[pbeierle]

I need to find the characteristic xray frequencies from the emitted electrons as they move from their original orbits in Am-241 to their lower energy orbits in Np-237. My thought was I can calculate the wavelengh of these electrons knowing their radial equations, and calculate the frequency difference from there to calculate the xray frequencies. Obviously If I know the orbital energies this problem will be even easier, but I could not find such expressions either.

 

[Amok]

Wait, wait, wait. What phenomenon is this? Electrons are going from an Americum atom to a Neptunium atom?

 

[pbeierle]

sorry, i guess I was not very clear. As Am-241 undergoes alpha decay to Np-237, x-rays are emitted and can be detected. These xrays are not gamma rays that come from the nucleus as one might initially think.

The electrons in the Am atom have a certain energy whose wavefunction depends on the nucleus (because the nucleus provides a potential). when the nucleus suddenly drops 2 protons, the potential of the wavefunctions of the electrons will also change one would expect for the electrons to drop down to lower energy states as a result, which is how the xrays are produced.

my job is to calculate the frequency of the xrays that are produced and compare this to the spectrum that I have detected (in order to calibrate the detector). again though, i don't know how to calculate the orbital energy or radial equation for electrons that are this low on the periodic table

 

[Amok]

I know quite a bit about spectroscopy, but not very much about nuclear physics. But I'm going to take a wild guess and say that this is not the kind of calculation that you can do accurately without a computer program.