How to work in the |F,m_F> states in hyperfine structure

In summary, the conversation discusses the interaction between two atoms with one proton and one electron each. The states for the electrons are classified as singlet (S=0) and triplet (S=1) states. The question is whether the nuclear spin of the protons should be kept parallel when writing the states. The answer is that if there are two protons, the spin state must also be written in terms of singlet and triplet states. However, this would result in 16 states in the uncoupled basis and a 9x9 matrix in the coupled basis. The author of the paper being discussed mentions 8 eigenvalues of the hyperfine Hamiltonian, suggesting that they assume the proton spins to be parallel. A reference
  • #1
lelouch_v1
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TL;DR Summary
A little confused about the notation in the coupled and uncoupled basis
Suppose that we have two atoms with one proton one electron each, and these electrons interact with each other. The states for the electrons are the singlet(S=0) and the triplet states(S=1). My question is if i have to keep the nuclear spin of the protons parallel when i write the states, for example $$\frac{1}{\sqrt{2}}(|+-\rangle-|-+\rangle)_e\otimes|\Uparrow\rangle_p$$
for the singlet state, and if so, can i use the fact that F=S+I, which in this case whould yield the state |1,1?> ?(S=0,I=1/2+1/2=1,ms=0,mI=1)
 
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  • #2
If you have two protons, then you also have to write the spin state of the protons in term of singlet and triplet states.
 
  • #3
DrClaude said:
If you have two protons, then you also have to write the spin state of the protons in term of singlet and triplet states.
Thank you for your answer. I thought of that as well, but that would lead to having 16 states in the uncoupled basis, and in the coupled basis we would have $$|2,M_F\rangle \ \ \ , \ \ \ |1,M_F\rangle \ \ \ , \ \ \ |0,0\rangle$$ which yields a 9X9 matrix. The problem with that is that the author of the paper that i am reading (it's on the radical pair mechanism) states that there are 8 eigenvalues of the hyperfine hamiltonian, meaning an 8X8 matrix, so i suppose that he always takes the proton spins to be parallel (either both spins up or both down).
 
  • #4
Can you give the reference?
 

1. What are the |F,m_F> states in hyperfine structure?

The |F,m_F> states in hyperfine structure refer to the energy levels of an atom's nucleus in the presence of an external magnetic field. These states are characterized by the total angular momentum F and its projection on the z-axis, m_F. They play a crucial role in understanding the behavior of atoms in magnetic fields.

2. How do I work in the |F,m_F> states in hyperfine structure?

To work in the |F,m_F> states in hyperfine structure, you will need a strong understanding of quantum mechanics, specifically in the context of atomic physics. You will also need to be familiar with the relevant equations and principles, such as the Zeeman effect and the Landé g-factor. Additionally, you will need access to specialized equipment, such as high-resolution spectroscopy instruments, to study these states experimentally.

3. What is the significance of the |F,m_F> states in hyperfine structure?

The |F,m_F> states in hyperfine structure are important because they provide insight into the behavior of atoms in magnetic fields. They also play a crucial role in precision measurements, such as atomic clocks, and in applications such as magnetic resonance imaging (MRI).

4. How are the |F,m_F> states in hyperfine structure experimentally observed?

The |F,m_F> states in hyperfine structure can be observed through spectroscopy techniques, such as laser spectroscopy or microwave spectroscopy. These techniques involve shining a specific frequency of light or microwaves onto the atom, causing transitions between the different energy levels. By measuring the frequencies at which these transitions occur, we can determine the energy levels and thus observe the |F,m_F> states.

5. What are some real-world applications of the |F,m_F> states in hyperfine structure?

The |F,m_F> states in hyperfine structure have many practical applications, such as in atomic clocks, which use the precise energy levels of these states to measure time. They also play a crucial role in magnetic resonance imaging (MRI), which uses the behavior of atoms in magnetic fields to create detailed images of the human body. Additionally, these states are used in precision measurements and tests of fundamental physics theories.

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