Calculate the energy of the electron in a non-H like atom

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Discussion Overview

The discussion revolves around calculating the energy of an electron in non-hydrogen-like atoms, specifically those with more than one electron. Participants explore various approaches to this problem, including numerical and approximate methods, and consider scenarios involving Rydberg energy levels and the influence of other electrons on the energy calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the calculation of electron energy levels in non-hydrogen-like atoms, particularly in higher energy states and in the presence of other electrons.
  • Another participant notes that the problem does not have an exact solution due to the complexity of multiple interacting bodies.
  • A request for numerical calculations and approximate methods is made, with an emphasis on obtaining the most precise approach possible.
  • One participant suggests that if an electron is at a greater average distance from the nucleus, it may perceive the nucleus as a point charge due to screening effects from other electrons.
  • Another participant mentions the concept of a "quantum defect" in relation to accounting for the core's influence on electron energy levels.
  • A reference to perturbation calculations in quantum chemistry is made, discussing the effect of the finite size of the nucleus on potential calculations.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the methods for calculating electron energy levels, with no consensus reached on a definitive approach or solution. The discussion remains open-ended with multiple competing ideas presented.

Contextual Notes

Participants acknowledge the limitations of their approaches, including the lack of exact solutions and the complexities introduced by multiple electrons and their interactions.

jorgeha
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Hello mates. I was doing some research about Rydberg atoms, and I came up with this question: what's the energy of an electron in n energy level in an atom which is NOT hydrogen-like, that is, an atom with more than 1 electron? How can we calculate it?
What if the electron we are studying is in a much higher energy level (Rydberg energy level) and the others are in the lowest posible? What if we have an excited electron apart of the one we are studying?

Thank you in advance.
 
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jorgeha said:
How can we calculate it?

Numerically or approximately. It does not have an exact solution. Note that you have 3 or more bodies here, and that doesn't even have a classical solution.
 
Vanadium 50 said:
Numerically or approximately. It does not have an exact solution. Note that you have 3 or more bodies here, and that doesn't even have a classical solution.
I was asking for a numerical calculation. I guessed it could only be an approximate answer but I didn't know to what extent. I'd like the most exact approach possible, if you could lead me to some articles or books about these calculations I would be grateful. Thanks.
 
If one of the electrons has a position distribution where it's at a much longer average distance from the nucleus than the others, I think it will effectively see the nucleus as a point charge of +1e because of the screening by the other electrons. Another way to obtain the same effect is to make a "helium atom" where one of the orbiting particles is an electron and the other a muon (the muon will have a much smaller "orbit radius" because of its large mass compared to the electron).
 
hilbert2 said:
If one of the electrons has a position distribution where it's at a much longer average distance from the nucleus than the others, I think it will effectively see the nucleus as a point charge of +1e because of the screening by the other electrons. Another way to obtain the same effect is to make a "helium atom" where one of the orbiting particles is an electron and the other a muon (the muon will have a much smaller "orbit radius" because of its large mass compared to the electron).
Yes, the core is taken into account then via some "quantum defect": https://en.wikipedia.org/wiki/Quantum_defect
 
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I remember some perturbation calculations in a quantum chemistry homework where we had to estimate the effect of the finite size of the nucleus by assuming that the nucleus is a small sphere that contains a constant positive charge density. Then the potential inside the nucleus was calculated with Gauss's law. A core that contains both positive and negative charge is probably not very different.
 

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