Hello.
The famous ADK (Ammosov, Delone, and Krainov) tunnel-ionization model (M. V Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP, vol. 64, pp. 1191–1194, 1986.) depends on several parameters and the orbital quantum number l and magnetic quantum number m are among them.
As we know electronic configuration of each atom, l is not problem. However, how can I choose proper m? For example, nitrogen N in ground state has electronic configuration of 1s22s22p3. In order to calculate tunneling-ionization of this N, I need to know m for outer electron.
How can I know m of outer electron in atom or ion? Is there any rule to order m in each subshell?
Read "Electron Configurations, the Aufbau Principle, Degenerate Orbitals, and Hund's Rule" in
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html#aufbau
the 2p3 subshell electrons of N have m=-1 m=0 and m=1
and the electron with m=0 has a much higher detachment (tunnelling ionization) probability than for electrons with m = |1|, see after (14) in
http://www.jetp.ac.ru/cgi-bin/dn/e_064_06_1191.pdf
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html#aufbau
http://www.jetp.ac.ru/cgi-bin/dn/e_064_06_1191.pdf
Hello Koen,
Thanks to reply my question.
Ok. For N atom, m = 0 electron will be ionized first since the tunneling-ionization rate with m = 0 is much higher than |m| = 1 electrons as you pointed out. For N1+ ion, there are two electrons in 2p subshell. Does they stay m = +1, -1 state or transition into m = 0 state? If they stay, I can simply calculate the ionization rate with |m| = 1 for this ion and I don't need to ask further quesiton as order of ionization of electrons in the subshell can be simply following the order of the ionization rate for each m.
If one assumes that the N1+ ion has its n,l,m=2,p,0 electron missing, since this electron has the highest probability of detachment via tunnelling (or are there other detachment mechanisms other than tunneling??), then one should calculate ionization probability for an electron with m=|1|, which depends on the external electric field amplitude. Are avalanche effects also present in the situation that you consider? I am not an expert in this field, however, it is a very interesting subject, since nitrogen is a large portion of our atmosphere, and complicated natural electric discharges are frequently present. Part of the Ethergy research is exactly this.
Oh...I see. So, basically the ionization rates for all possible m for a given electronic configuration are calculated first then statistically the order of the ionizations over m follows the order of magnitude of calculated ionization rates (ex: If m = 1 electron has 2nd highest ionization rate, this electron should be ionized in 2nd).
I do not know if |m|=1 electrons may change quantum state to |m|=0, in case the |m|=0 is already missing in the N atom (the N1+ ion). This might be possible, I am not an expert in QM. Does the tunnel-ionization model by ADK describe this possibility? I suppose it doesn't. The energy of the orbital electrons depends on the n and l quantum numbers, and does not depend on the m quantum number. In case only the m quantum number changes, this electron state transition does not involve photon emission/absorption, so it might be possible spontaneously. It is a good suggestion anyway, however, even if an |m=1| electron transits to the m=0 state in a N1+ ion, the probability of this electron to tunnel away from the N1+ ion maybe much lower than the tunnelling probability of the 'first' electron that tunnelled away from the N atom, since the potential energy for the m=0 electron is different, comparing the N atom with the N1+ ion.
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