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qsa
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What is the relativitic correction to the e^2/r coulomb law without spin between two electrons.second order is enough.
dextercioby said:Second order in what ? Standard references mention a correction proportional to the 4th power of momentum, if the electron's and the proton's spin are neglected.
Vanadium 50 said:Why would electron-electron have a different functional form than electron-proton?
What is the relativistic correction to the e^2/r coulomb law?
Bill_K said:To the next order, V(r) = -(Ze2/4π)1/r - (Ze4/60π2m2) δ(r)
I know the delta function looks weird, like it was something just stuck in by hand. But that's really the result. It looks more sensible in momentum space, where
V(k) ~ k-2 (1 - (e2/60π2m2) k2 + ...)
and the Fourier transform of the second term is the Fourier transform of 1, which is a delta function.
unusualname said:I think you're looking for something like this qsa
Effective Field Theory of Gravity: Leading Quantum Gravitational Corrections to Newtons and Coulombs Law
where the first order correction is shown to be an additional
3G(m1+m2)/(r*c^2)
(multiplied by the classical coloumb term)
(obviously m1=m2 for the electron, and r is the separation)
But, personally, I would give up running naive random models in the hope of getting physical laws, you'll go crazy. If your new model matches this formula it's still not a big deal, especially not if you don't explain how it's constrained in a coherent and simple manner.
qsa said:This is another story for another time since these corrections are out of reach of experiment. Bill_K gave the correct answer. As for my model ,you know I cannot talk about it here, I will send you an email soon with the latest results(maybe alpha up to eight digits).
The two electron relativistic corrections to PE, or potential energy, are important because they account for the relativistic effects of the interactions between two electrons in a system. These corrections are necessary for accurate calculations of energy levels and properties of atoms and molecules.
The most commonly used method for calculating two electron relativistic corrections is through the use of the Breit-Pauli Hamiltonian, which includes terms for the spin-orbit interaction and the relativistic mass correction. These corrections can also be calculated using other methods such as the Douglas-Kroll-Hess approach or the fully relativistic Dirac equation.
One electron relativistic corrections only take into account the effects of a single electron in an atom or molecule, while two electron relativistic corrections consider the interactions between two electrons. One electron corrections are typically used for lighter elements, while two electron corrections are necessary for heavier elements with more complex electronic structures.
Two electron relativistic corrections can have a significant impact on the energy levels of atoms and molecules, particularly for heavier elements. These corrections can shift energy levels and alter the relative energies of different electronic states, which can affect the properties and behavior of chemical systems.
No, two electron relativistic corrections cannot be neglected in calculations as they are necessary for accurate predictions of energy levels and properties of atoms and molecules. Neglecting these corrections can lead to significant errors and inaccuracies in calculations, particularly for heavier elements.