High-energy tail of H electron momentum distribution? 1/p^6?

In summary, the conversation discusses the momentum distribution of a single electron in the ground state of a hydrogen atom, with a focus on the high-energy tail (HTMD). Fock's 1935 non-relativistic quantum derivation predicts a 1/p^6 tail, but a 2001 paper by Eugene Oks and various experiments suggest a much lower power of 1/p^4 or lower. The unresolved question is which power accurately describes the real ground state of hydrogen. The use of a non-relativistic derivation is also questioned, as the relativistic solution of the Dirac equation for the hydrogen ground state is known in closed form.
  • #1
jarekduda
82
5
Kind of the basic question of atomic physics is momentum distribution of single electron of ground state hydrogen atom - especially the power in its high-energy tail (HTMD: high-tail momentum distribution), which should have strong impact especially on various scattering experiments.
Fock's 1935 non-relativistic quantum derivation leads to 1/p^6 tail.

However, I have recently found a 2001 Eugene Oks paper with a long list of references claiming that experiments suggest "heavier tails": much lower power, like 1/p^4 or even lower:
http://iopscience.iop.org/article/10.1088/0953-4075/34/11/315/pdf
e.g. "The point we are trying to make is that the above fundamental dispute still remains unresolved: the experiments seem to favour a HTMD of ∼1/p^k , where k is at least 1.5 times smaller than in the quantum HTMD."

So I wanted to ask which power should be used to describe the real ground state hydrogen atom?
 
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  • #2
So, why use a non-relativistic derivation? I assume the high energy tail in momentum space corresponds to or is driven by the region near the nucleus. Since the relativistic ground state of hydrogen (solution of the Dirac equation) is known in closed form, (Bojorkin and Drell Vol 1 page 55) I would think this is a solvable problem.
 

1. What is the High-energy tail of H electron momentum distribution?

The High-energy tail of H electron momentum distribution refers to the distribution of electron momentum in the hydrogen atom at high energies. It is a quantum mechanical phenomenon that describes the probability of finding an electron with a certain momentum in the atom.

2. Why is the high-energy tail of H electron momentum distribution important?

The high-energy tail of H electron momentum distribution is important because it provides valuable insights into the behavior of electrons in the hydrogen atom at high energies. It also has implications in various fields such as atomic physics, quantum mechanics, and nuclear physics.

3. How is the high-energy tail of H electron momentum distribution calculated?

The high-energy tail of H electron momentum distribution is calculated using mathematical equations derived from quantum mechanics. These equations take into account the energy levels and quantum states of the electron in the atom to determine the probability of finding the electron with a certain momentum at high energies.

4. What does the term "1/p^6" refer to in the high-energy tail of H electron momentum distribution?

The term "1/p^6" is a mathematical representation of the probability of finding an electron with a certain momentum in the high-energy tail of H electron momentum distribution. It is also known as the momentum distribution function and is used to calculate the probability of finding an electron with a specific momentum in the atom.

5. How does the high-energy tail of H electron momentum distribution relate to the uncertainty principle?

The high-energy tail of H electron momentum distribution is closely related to the uncertainty principle in quantum mechanics. This principle states that the more accurately we know the momentum of an electron, the less accurately we know its position, and vice versa. The high-energy tail of H electron momentum distribution reflects this uncertainty by describing the probability of finding the electron with a certain momentum at high energies.

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