In the article "tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field" (ADK ionization model) it is written: "...to derive an equation for the probability of tunnel ionization of complex atoms or atomic ions, and in arbitrary states... it is necessary ... to obtain the sought-for equation, in which the states of the complex atoms are characterized by effective principal and orbital quantum numbers n* and l* that take into account the quantum effects "
I'll appreciate it if someone can explain to me what is the physical meaning of these effective quantum numbers and what's the meaning by the "quantum effect" ?
Thanks in advance
Quantum effect means here simply a non-classic effect, that can't be explained by classic physics. In this sense tunelling is a quantum effect, since it's an experimental fact that can't be explained on the grounds of classical mechanics.
Explaining what do n and l quantum numbers mean requires at least a short course in quantum mechanics/chemistry: please check any modern book on this topic (I'd recommend Modern Quantum Chemistry by Atilla Szabo or Introduction to Quantum Chemistry by Linus Pauling).
I'm aware of the phrase quantum effect in relation to a non-classical phenomena, and I know what the quantum numbers n and l mean. My question was regarding the effective quantum numbers n* and l* (as I explained in the question!). In Eq. (4) of the cited article the effective principal quantum number n* is defined as n*=n-delta_l , where delta_l is phrased the quantum effect. My question was and still is: what is this quantum effect quantity, and what physical meaning does it have ?
I'll appreciate if someone can refer me to a scientific source explaining this quantity and it's physical meaning.
Sorry, I misread your post.
The effective n (n*) is a number that tries to take into account the screening of nucleus by other electrons (just like the effective nuclear charge, which is always equal to or lower than the true nuclear charge). It was developed by Slater hich also gave an euqation to calculate (actually estimate) it. Slater defined n* by the rule that for n = 1, 2, 3, 4, 5, 6 respectively; n* = 1, 2, 3, 3.7, 4.0 and 4.2.
The number can be used to derive a very simple formula to estimate the total energy of the mutlielectron system: see http://en.wikipedia.org/wiki/Slater's_rules
The effective orbital number l* comes from all electrons occupying non-complete shells, for which the orbital momenta are coupled.
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