Paschen-Back and Zeeman in different base

In summary, the Zeeman and Paschen-Back effect can produce different results when using different base sets.
  • #1
Dreak
52
0
Hello,

In the image below, we see the result of the Zeeman and Paschen-Back effect in a magnetic field which we worked out, together with the exact result, described in different basesets (coupled J,mj and uncoupled mlms).


fe8_zeemanpaschenback.png


I understand that each effect can be better described in a different set, but I don't understand how that the result can be so 'wrong' compared to the exact result by using this different base.

I thought it was possible to go from coupled to uncoupled and visa versa, doesn't this also mean that an effect has to give the same results in a different base? Where does these errors come from?


I hope my question is clear enough :X
 
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  • #2
How exactly did you "work it out"? Do you refer to a perturbational treatment?
 
  • #3
DrDu said:
How exactly did you "work it out"? Do you refer to a perturbational treatment?

yes.

For example PB:

H(0) = H_Bohr + H_Zeeman
H(1) (perturbation Hamiltonian) = H_SO (spin orbit coupling)

with H_Zeeman = b(l_z = g_e.s_Z

and H_SO = l.s = 1/2(l_+s_- + l_-s_+) + l_z.s_z
 
  • #4
What you probably did was not using different bases but different zeroth order hamiltonians which have the corresponding basefunctions as eigenstates.
The perturbation series obtained starting from different zeroth order hamiltonians may differ dramatically. Using one H_0 already a first order correction may be sufficient to obtain a very good approximation to the exact eigenstates and energies while with another H_0 the perturbation series may be highly divergent.
 
  • #5
DrDu said:
What you probably did was not using different bases but different zeroth order hamiltonians which have the corresponding basefunctions as eigenstates.
The perturbation series obtained starting from different zeroth order hamiltonians may differ dramatically. Using one H_0 already a first order correction may be sufficient to obtain a very good approximation to the exact eigenstates and energies while with another H_0 the perturbation series may be highly divergent.


Ah yes, seems a fitting explanation, thanks! :)
 

1. What is the Paschen-Back effect?

The Paschen-Back effect is a phenomenon in atomic physics where the energy levels of an atom are altered in the presence of a strong magnetic field. This effect occurs when the spin-orbit coupling of an atom is stronger than the interaction between the electron's spin and the magnetic field.

2. How does the Paschen-Back effect differ from the Zeeman effect?

The Paschen-Back effect and the Zeeman effect both involve the splitting of energy levels in the presence of a magnetic field. However, the Paschen-Back effect occurs when the spin-orbit coupling is strong, while the Zeeman effect occurs when the spin-orbit coupling is weak. In the Paschen-Back effect, the energy levels are split into several fine structure levels, while in the Zeeman effect, the energy levels are only split into two levels.

3. What is the importance of studying Paschen-Back and Zeeman effects in different bases?

Studying Paschen-Back and Zeeman effects in different bases allows us to gain a deeper understanding of the behavior of atoms in the presence of a magnetic field. It also helps us to better understand the underlying physical principles behind these effects and their potential applications in various fields, such as astrophysics, quantum computing, and materials science.

4. Can Paschen-Back and Zeeman effects be observed in all atoms?

Yes, Paschen-Back and Zeeman effects can be observed in all atoms. However, the strength of these effects may vary depending on the atomic structure and the strength of the applied magnetic field.

5. How do Paschen-Back and Zeeman effects impact spectroscopy?

The Paschen-Back and Zeeman effects play a crucial role in spectroscopy as they cause the energy levels of atoms to split, resulting in a more complex spectrum. This allows for more precise measurements of atomic energy levels and can provide valuable information about the atomic structure and the environment in which the atom is located.

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