# Tunnel ionization rates; question on atomic units

1. Apr 8, 2010

### dnic12345

1. The problem statement, all variables and given/known data

First of all, this is my first post here, so I apologize if I format things incorrectly.

I'm working on a Matlab script to evaluate the tunnel ionization rates via the PPT model given the correct set of input parameters. The rate equation I am using contains equations 1-11 of A. Talebpour, et al. "Semi-empirical model for the rate of tunnel ionization..." from Opcits Communications 163, (1999) 29-32.

The paragraph leading up to the formula gives "In this model the rate of the TI from a state of an atom with ionization potential Ei, quantum numbers l and m and effective charge Zeff, in a laser field with frequency w and peak electric field F, in atomic units is given by..."

My rate calculations are giving me answers that are many orders of magnitudes off and I think its due to my use of atomic units. I know I have l,m, and Zeff in my equations correct, but I am unsure on the ionization potentials, frequencies, and electric fields in atomic units. The values I have in other units are:

w = 2.8986e+014 Hz (1035 nm wavelength)
Ei = 15.58 eV (N2)
E-field = 1.5e10 V/m

2. Relevant equations

There are way too many to type out for this formula; my main question is about atomic units. See the above-referenced paper for the actual equations.

3. The attempt at a solution
I've read about atomic units meaning that many constants (like h, hbar, etc) are identically set to 1, but I can't see how to apply this in my situation. I have found several different conversion factors online, but I can't convince myself that any of them are right.

Thanks

2. Apr 8, 2010

3. Apr 8, 2010

### dnic12345

Yea, I read through that and a number of other pages/pdfs. I did end up using values that are identical to what's on the wikipedia page. I believe I found my problem: the conglomeration of the eqs 1-11 spits out the tunnel ionization rate that I assumed to be in units of Hz. It makes more sense for the TI rate to be atomic units, given that all the inputs are in AU. When I convert the rate I calculate from AU to Hz, I get rates that are much closer to the reference values I have.

Now I think my work is just to make sure I have input and evaluated everything else correctly. I did use an approximation to an infinite sum that may be the key to my error.

Thanks for the response.

4. Apr 8, 2010

### nickjer

No problem, and good luck.