In quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product of two relativistic effects: the apparent magnetic field seen from the electron perspective and the magnetic moment of the electron associated with its intrinsic spin. A similar effect, due to the relationship between angular momentum and the strong nuclear force, occurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model. In the field of spintronics, spin–orbit effects for electrons in semiconductors and other materials are explored for technological applications. The spin–orbit interaction is one cause of magnetocrystalline anisotropy and the spin Hall effect.
For atoms, energy level splitting produced by the spin–orbit interaction is usually of the same order in size as the relativistic corrections to the kinetic energy and the zitterbewegung effect. The addition of these three corrections is known as the fine structure. The interaction between the magnetic field created by the electron and the magnetic moment of the nucleus is a slighter correction to the energy levels known as the hyperfine structure.
I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment...
For an electron in the orbital characterized by ##l=0## we have ##j=0\pm1/2## and so ##J^2=j(j+1)## gives ##J^2=3/4## and ##-1/4## (normalized to ##\hbar^2##). Finally, ##L.S=1/2(J^2-L^2-S^2)## results in ##L.S=0## and ##-1##. However, according to ##L.S=l_xs_x+l_ys_y+l_zs_z## we find ##L.S=0##...
The set of quantum numbers for the 4p orbital is: 4, 1, {-1,1}, +-1/2 (n,l,m,s)
The set of quantum numbers for the 4d orbital: 4,2,{-2,2},+-1/2
Hence we can calculate DeltaE for the 4p sub levels for j=1+- 1/2
And for the 4d sub levels as j=2+-1/2.
Giving four total values for Delta E as:
C_4p...
Homework Statement
Consider an electron in a hydrogen atom in the presence of a constant magnetic field ##B##, which we take to be parallel to the ##z##-axis. Without the magnetic field and ignoring the spin-orbit coupling, the eigenfunctions are labelled by ##\vert n, l, m, m_s \rangle##...
Homework Statement
Considering the atom made of an electron and a positron. The spin-orbit Hamiltonian is:
$$H=\frac{e^2}{4\nu^2c^2r^34\pi\epsilon_0}\vec{L}\cdot\vec{S}$$
with ##\vec{L}## the relative angular momentum, with ##\vec{S}## the total spin and ##\mu## the reduced mass. Finding the...
sorry I am going slightly off the topic. <<Moderator's note: split off from this thread.>>
I asked this question because I'm studying a paper concerning the presence of spin orbit coupling at the interface between two metals.
This is the part of the paper I'm studying:
"Our aim is to...
Hi guys!
For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential.
Schrodinger equation can be written in this form:
$$[-\frac{\hbar^2}{2m}(\frac{\partial...
Homework Statement
I am given the Rashba Hamiltonian which describes a 2D electron gas interacting with a perpendicular electric field, of the form
$$H = \frac{p^2}{2m^2} + \frac{\alpha}{\hbar}\left(p_x \sigma_y - p_y \sigma_x\right)$$
I am asked to find the energy eigenvalues and...
Hello all.
I was wondering if there was any generalized (simplified) formulation of spin-orbit coupling equation like the ones we see for energy transfer between two species (molecules or ions). Foerster and Dexter's equation are famous simplified formulation of energy transfer. Multipole...
Hi, guys.
I'm beginning to fit XPS peaks from a environmental measurement but, as I'm unfamiliar with the exact process I have a lot of doubts. I have solved some of them using the info in http://xpssimplified.com/periodictable.php [Broken] and in the XPS manual from Moulder and Stickle but I'm...
Hello.
I have studied about DWBA (distorted wave born approximation).
But, I do not know the physical meaning of "DWBA without spin-orbit interaction".
I think, I can not understand about meaning of spin-orbit.
How can I understand "without spin-orbit intertaction".
Thanks.
I was looking at grotrian diagrams for helium and I see that there is no splitting of energy levels due to spin-orbit coupling. In my book it is said that spin-orbit coupling in helium is small and can be neglected but no further explanation is given. At the same time we do spin-spin coupling...
Kepler problem explains closed elliptic trajectories for planetary systems or in Bohr's classical atomic model - let say two approximately point objects, the central one has practically fixed position, they attract through 1/r^2 Newton's or Coulomb force.
Kind of the best motivated expansion we...
Hi,
I have read that Hund's rules are valid for Atoms with low z.
Because the third Hund's rule is build of Russell-Saunders coupling.
Can I still use the first and second Hund's rule for heavy atoms and jj-coupling( for the third rule)?
Or how can I know the groundstate for an atom with large...
Dear all,
The Hamiltonian for a spin-orbit coupling is given by:
\mathcal{H}_1 = -\frac{\hbar^2\nabla^2}{2m}+\frac{\alpha}{2i}(\boldsymbol \sigma \cdot \nabla + \nabla \cdot \boldsymbol \sigma)
Where
\boldsymbol \sigma = (\sigma_x, \sigma_y, \sigma_z)
are the Pauli-matrices.
I have to...
Good day everyone,
The question is as following:
Consider an electron gas with Hamiltonian:
\mathcal{H} = -\frac{\hbar^2 \nabla^2}{2m} + \alpha (\boldsymbol{\sigma} \cdot \nabla)
where α parameterizes a model spin-orbit interaction. Compute the eigenvalues and eigenvectors of wave vector k...
Electric and magnetic parts of Maxwell's equations are kind of similar, so physical effects relating these properties have many 'dual' analogues - with exchanged places.
For example in Aharonov-Bohm effect, the phase of charged particle depends on side of magnetic flux tube it comes through...
In all the places where Spin-Orbit interaction is discussed, the equations are derived by going to electron's rest frame and considering the interaction of nucleus' magnetic field with electrons spin magnetic moment. But from SR, we know that there as to be an explantion from the nucleus's rest...
Hello! This is my first time posting, so please correct me if I have done anything incorrectly.
There's something that I don't understand about the spin-orbit interaction.
First of all I know that
[\hat{S} \cdot \hat{L}, \hat{L_z}] \ne 0
[\hat{S} \cdot \hat{L}, \hat{S_z}] \ne 0
so this means...
I have some XPS spectrums that I am trying to fit (my first time doing so), using XPSpeak.
I understand that for spin-orbit splitting the FWHM, line shape (i.e.% gaussian/lorentzian) must be equal (more or less), peak area ratios set (i.e. 2:3 for 3d3/2 and 3d5/2), and the peak separation...
Can anyone explain why the energy levels separate as a result of spin-orbit coupling?
Also, what determines the *new* number of "sub-levels" which are obtain after the original energy levels are separated as a result of spin-orbit coupling?
Please give examples, if you want, using the...
Hi,
In many quantum physics books I see questions such as "what is the spin-orbit interaction in this case?" Sorry if this seems like a dumb question, but what do they mean by this? Do they mean the ENERGY of the spin-orbit interaction or something else?
Also, could anyone give (or write a...
Hello,
I see a Hamiltonian of spin-orbit coupling, it is like this
H=\frac{1}{2m} \sum_{\alpha} \left( \left( -\partial_{\alpha}^2 - 2i\kappa_{\alpha} \sigma_{\alpha} \partial_{\alpha} \right) + \kappa_{\alpha}^2\right)
Here \hbar = 1. \kappa_{\alpha} is the strength of spin-orbit...
Fron wiki:
spin–orbit interaction causes shifts in an electron's atomic energy levels due to electromagnetic interaction between the electron's spin and the magnetic field generated by the electron's orbit around the nucleus. This is detectable as a splitting of spectral lines.
The...
In most introductory discussions on spin-orbit coupling in the hydrogen atom that I've come across, the analysis is often performed on a Bohr-orbital model. The electron is treated as orbiting the nucleus in a circular orbit. They then transform to the frame of the electron, and then assert that...
I was reading Griffiths's book on quantum mechanics.
In chapter 6, he tried to derive the spin-orbit coupling using a classical approach.
H=-\vec{\mu}\cdot \vec{B}
1. Finding the relation between \vec{μ} and \vec{S}
He consider a spinning charged ring with mass m, radius r, total charge...
In standard QM textbooks, when calculating the spin-orbit interaction term as a relativistic perturbation for hydrogenic atoms, it is said that the term gives 0 contribution for the s-orbitals (l = 0). This is apparently because the term has the form of S*L and L=0 for the s-orbitals.
However...
the proton is stationary, and we're assuming there is no magnetic field in the rest frame of the proton. I know if we move to the rest frame of the electron there will be a magnetic field.
but shouldn't we be able to analyze it in the rest frame of the proton?
Can someone explain to me how to get the states for an electron in a given orbital (lets say... d orbital l=2) and how to calculate the Clebsch-Gordan Coefficients for this system? I tried reading my book but I'd like someone to explain in simpler language.
Hi,
It never occurred to me before, but when you derive the spin-orbit Hamiltonian as a perturbation to the hydrogen Hamiltonian, you imagine your electron orbiting around the nucleus, and of course that's not the correct picture because of the electromagnetic radiation that leaks out. So I...
Hi.
please help me. i really need a quick reply.
I study the bandStructure of SrS with and without Spin-orbit but I have no enough information to explanation it.
the Sr has([kr] 4s2 4p6 5s2) and S has([Ne] 3s2 3p4) Structure. I attache the bandStructure of this compound calculated using...
Hello,
I've seen spin orbit coupling being explained by going to the rest frame of the electron and noting that the proton is then a moving charge and hence has a magnetic field, which interacts with the spin of the electron, effectively coupling the spin and angular momentum of the electron...
Hey everyone,
I've been reading about the Spin-Orbit coupling effect in the Hydrogen atom.
However, there's something I don't quite understand.
The effect is being explained and calculated like this: we move to the rest frame of the electron, in which the electron has no orbital angular...
Can anyone recommend books/reviews that derives the spin-orbit coupling in second quantization. I am working on a tightbinding model and I should be able to convert the spin-orbit hamiltonian from k-space to atomic representation using Warnier states, but I can't figure out some of the aspects...
Homework Statement
The spin-orbit interaction splits the hydrogen 4f state into many (a) Identify these states and rank them in order of increasing energy. (b) If a weak external magnetic field were now introduced (weak enough that it does not disturb the spin-orbit coupling), into how many...
Homework Statement
List all of the elements through calcium that you would expect not to have a spin-orbit interaction that splits the ground state energy. Explain.
Homework Equations
Not quite sure, but I'll list a few.
If there are two electrons:
L=|l1-l2| to |l1+l2|
S=|s1-s2| to...
For a particular energy level in hydrogen, with quantum numbers n and l, one will find when considering the spin-orbit interaction, the level is split into two fine structure levels with energy separation:
\Delta E_{s.o.}=\beta_{nl}(l+1/2)
I was trying to prove this result. The spin of an...
Hi,
In the usual tight-binding Hamiltonian for semiconductor materials, say GaAs, the basis in which the Hamiltonian matrix elements are specified are the atomic wavefunctions for each atom in the basis. So for GaAs, including just the valence wavefunctions 2s,2px,2py,2pz, we have 8 basis...
I was trying to explain the origin of spin-orbit coupling to a beginning student and I used the following naive analogy:
An electron orbiting around the nucleus "sees" the nucleus rotating about itself (the electron) in its own (electron's) reference frame, thus this is like a current loop...
Homework Statement
Hi all.
I wish to evaluate the following dipole moment
<1| x |2>,
where |1> and |2> are stationary states of the hydrogen atom when one accounts for spin-orbit coupling. I am a little unsure of if I am allowed to use the "normal" unperturbed wavefunctions for...
i am now reading the book by woodgate: elementary atomic strucure, 2nd edition.
on page 62, he discusses the spin-orbit coupling in hydrogen atom, and calculates the first order shift of the energy due to this effect.
I have some doubt about his procedure from eq.4.25 to eq.4.27
the...
When considering a simple hydrogen atom, which essentially is an electron moving in a spherical electric field, you don't need to take spin-orbit coupling into account. For larger atoms you do. I don't understand my books' very brief explanation of this. I am thinking that the electron has as...
Homework Statement
The problem is to determine which has a more dominant effect on the energy of a given state in mercury, spin-orbit interaction or the Zeeman effect, when the applied magnetic field B is about 2T.
Homework Equations
As long as the spin-orbit interaction is the dominant...
Homework Statement
An electron in a hydrogen atom is in the n = 2, l = 1 state. It experiences a spin-orbit interaction H' = \alpha \mathbf{L} \cdot \mathbf{S}. Calculate the energy level shifts due to the spin-orbit interaction.Homework Equations
Degenerate perturbation theory.
The Attempt...
Hi,
I'm having a little problem understanding why splitting occurs in an atom. For example when you look at the line spectra for Sodium-D, then two lines appear very close together.
I understand that there is a magnetic interaction where the magnetic field has been generated by the orbital...
Spin-orbit effects splits !?
Hi AllL
the spin-orbit effect splits the 3P-->3S transition in sodium(which gives rise to the yellow light of sodium vapor highway lamps) into two lines 589.0 nm corresponding to 3P sub 3/2-->3S sub 1/2 and 589.6nm corresponding to 3P sub 1/2 --> 3S sub 1/2.
How...