- #1
Malamala
- 309
- 27
Hello! I am trying to make some predictions for an experiment in which we have a first ##E_2## transition in an atom driven by a laser, and then we have a second laser that is ionizing the molecule only if the first laser was resonant (i.e. if the atom was excited). For the purpose of the question we can assume that the ionization efficiency is 100% i.e. if the atoms gets excited, it will get ionized, too. I found this formula for the probability per second of the ##E_2## transition:
$$A_{E_2} = \frac{32\pi^5\alpha c a_0^4}{15 \lambda g'}S_{E_2} = \frac{1.11995 \times 10^{18}}{\lambda g'}S_{E_2}$$
where ##\lambda## is the transition wavelength in angstroms, ##g'## is the degeneracy of the excited state and ##S_{E_2}## is the E2 line strength in atomic units. ##S_{E_2}## is known theoretically to be 1.43 and in the end I get ##A_{E_2} \sim 2\times 10^{-4} s^{-1}##. I also have the (pulsed) laser power which is 100 mW and beam area which is 1mm##^2##. Using the Plank's formula, I get that the number of photons per unit second per mm##^2## is ##\sim 10^{18}##. If I have a given atom, interacting with such a pulse, I would like to know the probability of being excited. However, it seems like I would need to plug in some sort of area of the atom. Basically the formula I would use is:
$$2 \times 10^{18} \times 10^{-4} \times A_{atom} \times mm^{-2}$$
But I am not sure what to use for that. I guess I can use ~##10^{-10}##m for the atomic radius, but that seems like a classical approximation. I was wondering if I am doing something wrong. Why do I get this extra area in the formula and how do I deal with it? Thank you!
$$A_{E_2} = \frac{32\pi^5\alpha c a_0^4}{15 \lambda g'}S_{E_2} = \frac{1.11995 \times 10^{18}}{\lambda g'}S_{E_2}$$
where ##\lambda## is the transition wavelength in angstroms, ##g'## is the degeneracy of the excited state and ##S_{E_2}## is the E2 line strength in atomic units. ##S_{E_2}## is known theoretically to be 1.43 and in the end I get ##A_{E_2} \sim 2\times 10^{-4} s^{-1}##. I also have the (pulsed) laser power which is 100 mW and beam area which is 1mm##^2##. Using the Plank's formula, I get that the number of photons per unit second per mm##^2## is ##\sim 10^{18}##. If I have a given atom, interacting with such a pulse, I would like to know the probability of being excited. However, it seems like I would need to plug in some sort of area of the atom. Basically the formula I would use is:
$$2 \times 10^{18} \times 10^{-4} \times A_{atom} \times mm^{-2}$$
But I am not sure what to use for that. I guess I can use ~##10^{-10}##m for the atomic radius, but that seems like a classical approximation. I was wondering if I am doing something wrong. Why do I get this extra area in the formula and how do I deal with it? Thank you!