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What happens on un-ionized electrons after ionization?

  1. Jan 22, 2014 #1

    I'm now working in the spectroscopy and I'm wondering in one instantaneous moment of ionization.

    Let's have an atom with multiple bound electrons.

    The external energy (like in form of photon) is introduced on the atom such that outer bound electron is ionized and the question emerges.

    What happens on un-ionized bound electrons?

    One electron is now missing and the Hamiltonian of the system have to be modified such that new bound states according to new Hamiltonian should be established.

    Just before ionization, all electrons were occupying the old bound state which were determined by the old Hamiltonian, the Hamiltonian before ionization.

    Does that mean there is instantaneous transition from old states to new states for the remaining electrons?

    It doesn't make sense the energy levels of new states are higher than old states. It is also impossible that new states are identical to the old states since the new Hamiltonian differs from old one.

    The only way for bound electrons to go is to transition to the new states which energy levels are lower than one ones and there must be additional energy release from this transition.

    Am I right? If that is true, we can capture the moment of the ionization by observing spectrum coming from such a instantaneous transition just after ionization.
  2. jcsd
  3. Jan 23, 2014 #2


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    1. The Hamiltonian does not change. It depends only on the external potential (nuclear attraction), and the electron interactions [ one-particle (kinetic energy) and two-particle (coulomb repulsion)]. What changes is a *mean field* one-particle approximation to the Hamiltonian, e.g., the Fock operator. However, this is an approximation implying the validity of the mean-field picture. Orbital energies (the eigenvalues of such a mean-field Hamiltonian) are not real!

    2. Electrons do not have individual levels. What happens is that you go from the initial N-electron wave function, which is an eigenstate of the interacting Hamiltonian, to an (N-1)-electron wave function, which is also an eigenfunction of the same interacting Hamiltonian. This transition involves all electrons; the (N-1) electron eigenstate is not simply the N-electron eigenstate with one electron removed. The remaining (N-1) electrons also undergo a change in electronic structure to relax to the absence of the previous electron.

    If you now create a 1-particle mean-field approximation of the Hamiltonian using the mean-field of the N-1 electron wave function, you will see that this mean field has changed, and with it its associated "orbital energies". However, this is a consequence of the change in the wave function, not its cause.
  4. Jan 23, 2014 #3
    Answer looks complocated to understand. Thus..the states of the N-1 bound electrons are different from N electron case right?
  5. Jan 23, 2014 #4


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    Unionized electrons? Not many of those left. A lot of employers in the U.S. are outsourcing their electron needs to right-to-work states.
  6. Jan 25, 2014 #5


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    You can think classically: you had an electrically neutral system consisting of a positive nucleus with orbiting electrons. The ionization event occurs when you have cast off a charged particle.

    The remaining, movable charges will be drawn in closer because of the net charge imbalance. These correspond to higher energy states.

    This process is very fast, taking place in the attosecond time domain: http://www.nature.com/nature/journal/v449/n7165/abs/nature06229.html

    The measurements indicate that the rearrangement is very fast, but measurable: 100 attoseconds.

    Note: 1 attosecond = 0.001 femtoseconds = 10^-18 seconds.
  7. Jan 25, 2014 #6
    Okay. It looks definitely true that the remaining electrons should go to occupy new bound states according to new Hamiltonian after ionization but..to occupy new states which enery level is higher than old? It is possible? It looks the violation of the energy! How it is possible?
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