What is Selection rules: Definition and 47 Discussions

In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin-forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products.
In the following, mainly atomic and molecular transitions are considered.

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  1. S

    I Selection Rules for a Diatomic Molecule?

    Hello! I have a question about selection rules and electronic transitions of a diatomic molecule: I can't find a good explanation about that, and there's so much confusion about the right rules to use. I studied that on Bransden-Joachain's "Physics of atoms and molecules", but there (to whom...
  2. nomadreid

    Selection rules in electron transitions

    Not sure if this belongs in Chemistry or Physics. Even less sure if I understand the selection rules for electron transition correctly; hence this question. So I would be grateful for someone to please correct the following: Letting n and m be energy levels An electron that absorbs a photon...
  3. ergospherical

    I Parity Selection Rules: I'm Confused

    I'm confused by the discussion in section §30 (Parity of a state), page 98 of Landau's QM. The functions ##\psi_u## and ##\psi_g## are odd an even states respectively. If ##f## is a true scalar, then it should remain unchanged by inversion of the co-ordinates. Writing ##q' = -q##, then its...
  4. S

    I Orbitals and selection rules in a synchrotron

    What orbitals are occupied in a synchrotron, and which selection rules limit charged particles in a synchrotron? A Schrödinger hydrogen atom is not actually the Bohr atom, but the Bohr theory gives correct energies (but not transition probabilities). Why? Because in a hydrogen-like atom, 2s...
  5. E

    The NMR Selection Rules: Understanding Allowed Spin State Transitions

    For simplicity I only take a system of two interacting spin-##1/2## nuclei. If the spins have quantum numbers ##m_1## and ##m_2## respectively when in a certain state, then the energy of that particular state is$$E_{m_1m_2} = m_1 v_{0,1} + m_2 v_{0,2} + m_1 m_2 J_{12}$$where ##v_{0,1}## and...
  6. dRic2

    I Understand selection rules in ##\beta##-decay/EC

    I'm not very familiar with this topic so I quickly went through some introductory books on nuclear physics and read the chpater about beta decay. What I don't understand looking at this graph is the following: Why is the direct decay to ground state absolutely forbidden ? If you take a 1st order...
  7. Diracobama2181

    Selection Rules (Time Dependent Perturbation Theory)

    I suppose my question is, since X commutes for H, does this mean that the selection rules are $$<n',l',m'|X|n,l,m>=0$$ unless $$l'=l\pm 1$$ and $$m'=m\pm 1$$, as specified in Shankar?
  8. B

    A LS vs jj couplings and their selection rules

    Two questions, where the 1st is related to previous discussion regarding thes couplings: The selection rules for LS coupling is quite clear - it's based on calculating the compatible electric dipole matrix element. However, in the case of jj coupling we end up with different selection rules...
  9. S

    A Selection rules using Group Theory: many body

    Hello, I am newish in group theory so sorry if anything in the following is not entirely correct. In general, one can anticipate if a matrix element <i|O|j> is zero or not by seeing if O|j> shares any irreducible representation with |i>. I know how to reduce to IRs the former product but I...
  10. G

    How can X-ray energy transitions be identified?

    Here is what I understand so far about x-ray energy transitions within an atom: The shells are divided up from lowest to highest as K, L, M, N, O, and so on. The X-ray associated with an electron dropping to a K shell is called K radiation. If the electron drops dropped from a shell directly...
  11. ORF

    Biology: Evolution: General selection rules?

    Hello In evolution, the archetype rule is the "natural selection" rule. Are the other selection rules? (technological selection rules, cultural rules, etc) Thank you for your time. Regards, ORF
  12. P

    I Selection rules for multiphoton vs single-photon ionization

    Question: For ionization of a homonuclear diatomic, how do the selection rules differ for a nonresonant 2-photon ionization process and a 1-photon ionization process?
  13. G

    I Could you provide me a selection rule?

    Hello. When I accessed to selection rule page in Wikipedia, I have a difficulty of how to use rules listed there. I'm now only concering electric dipole transition so column (E1) in the table there will be my only interests. Since I need to know whether transition is possible or not between...
  14. E

    A Selection rules in IXS and EELS

    Hello everybody, since I have to plan an experiment to map the energy-momentum dispersion of a bosonic excitation, I have a question related to the difference between the excitations probed by Inelastic X-ray Scattering (IXS) and Electron Energy Loss Spectroscopy (EELS). Both the techniques are...
  15. G

    Integral to show selection rules

    Homework Statement I am trying to calculate the selection rules from 2p to 1s. Above are the three results in (1152)-.(1154). And In the image one also finds the spherical harmonics factors. I can not determine which R and angular parts that give the three 2p waves. Can you show which ones...
  16. kq6up

    Trying to understand Selection Rules in Cohen-Tannoudji

    On the bottom half of page 249 Cohen-Tannoudji it talks about selection rules in terms of off diagonal elements of the matrix generated by ##\langle \phi _{ n^{ \prime },\tau ^{ \prime } } \mid \hat { B } \mid \phi _{ n,\tau } \rangle##. I thought all off diagonal matrix elements would be...
  17. C

    In an infinite quantum well, why Δn=0?

    I've been reading up a bit on semiconductor quantum wells, and came across a selection rule for an infinite quantum well that says that "Δn = n' - n = 0", where n' is the quantum well index of an excited electron state in the conduction band, and n is the index of the valence band state where...
  18. A

    Confusion about selection rules

    While I am reviewing my undergrad physics for qualifying exam, I became confused about the numerous selection rules. (1) We have the selection rules for spontaneous emission in a hydrogen atom: Δl=±1 ,Δml=0,±1. This rule is the easiest to understand by evaluating <n'l'm'|z|nlm> (2) We have the...
  19. temp050505

    Are \(\Delta n = 0\) Transitions Allowed in Hydrogen Atom Selection Rules?

    Good afternoon, Does the selection rules have a condition on \Delta n ? I have not found a website or a book that show transitions between 2S_{1/2} and 2P_{3/2}, that's why I was wondering if \Delta n = 0, with respect to the other selection rules, are allowed transitions. Thank you for your...
  20. uselesslemma

    Collisional excitation: selection rules for rotations?

    To be specific, I am referring to CO molecules undergoing collisions with H2, resulting in CO transitioning to an excited vibrational state. I can't seem to find any rotational selection rules for collisions, meaning ΔJ could be essentially anything, as long as energy and angular/linear momentum...
  21. blue_leaf77

    Selection rules in electric dipole appoximation

    Some literatures say that the selection rule in electric dipole approx. for angular momentum ##\Delta j = 0,-1,1## some other say ##\Delta l = -1,1##. I follow the notation used in my references, despite the difference I think since j and l are both angular momenta which fulfill angular momentum...
  22. Z

    Selection Rules and Light with Orbital Angular Momentum

    When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum. However, photons can have arbitrarily high integer quantities of orbital...
  23. T

    Nuclear Spin and Selection Rules

    Suppose we define the total angular momentum as F = I+J where I is the nuclear spin angular momentum and J is the total electronic angular momentum. mF and mJ are the respective magnetic quantum numbers. The relevant F selection rules are delta_mF = 0, 1 and -1, delta_F = 0, 1 and -1. And...
  24. R

    Transition Moments and Selection Rules

    My instructor was talking about allowed transitions for IR spectroscopy and how you can predict them relatively well using PIB wavefunctions. It was stated that you could solve for the probability of a transition moment to determine if a transition is forbidden or not. <μ>=∫ΨfμΨidτ...
  25. T

    Photon angular momentum and magnetic quantum number selection rules

    For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1. As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the...
  26. U

    What Transitions Create Calcium's Emission Lines at These Wavelengths?

    Homework Statement Strong emission lines from calcium were observed at ##422.7nm##, ##610.3nm##, ##612.3nm##, ##616.3nm##, ##1034.9nm##, from transitions between ##4s^2##, ##4s5s## and ##4s4p##. The transition of ##422.7nm## was also observed at absorption. The singlet-triplet splitting of...
  27. L

    Qualitative explanation of radiative transitions and selection rules.

    Hi, I'm looking get a deeper conceptual grip on A&M spectroscopy, particularly what actually goes on between atoms/molecules and photons during an emission/absorption event. In general I just want to understand the "why's and how's" of the selection rules for dipole/quadrupole transitions, but...
  28. D

    Exploring Selection Rules for Hydrogen Atom

    I have a couple of questions about selection rules for the hydrogen atom. When we talk about these rules in an undergraduate context we are usually assuming LS coupling where we ignore spin orbit coupling so orbital and spin angular momentum are essentially independent. Is that correct...
  29. M

    Understanding Hydrogen Selection Rules: Emission vs. Absorption and the p-Series

    Please see attachment. What are the arrow heads supposed to mean? Only emission is allowed and no absorption? I mean, selection rules allow Δl=±1. But the figure is saying otherwise. I also read in another book, that the only series observed in absorption is that to the ground state, where...
  30. C

    Selection rules for atomic transitions

    Hi, I'm a little confused by the selection rules for atomic transitions. In pretty much any standard QM text, they derive the fact that an electron can't transition in an atom unless \Delta\ell=\pm1, i.e. unless the orbital angular momentum changes by one unit. Then the books go on to say that...
  31. G

    Excited states and selection rules

    If you have a meson in the states ## ^3S_1## and ## ^1S_0 ## this means that ##J^P = 1^+ ## and ## 0^+## doesn't it? But if you have excited states ## ^1P_1 ## this is ##J^P=1^- ## but isn't ## ^3P_1 ## supposed to be ##J^P = 1^- ##? Does this matter? ##^3P_0##, ##^3P_1## and ##^3P_2## for...
  32. P

    Selection rules electrostatic field

    Hi all , I need some help with this problem, Homework Statement A hydrogen atom, which is in its ground state |1 0 0 > , is put into a weak time-dependent external electric field, which points into the z direction: \boldsymbol{E}(t,\boldsymbol{r}) =...
  33. N

    Can the Selection Rule Δl = ±1 Be Applied to Helium Transitions?

    Hi I am reading about transition in Helium, and I have come across a question. It is clear that triplet-singlet transition are not allowed, i.e. ΔS=0. But in my book (Foot's Atomic Physics) it says that Δl = ±1. This is what I don't understand. The selection rule Δl = ±1 we derived for...
  34. N

    Selection rules and quantum numbers

    Homework Statement From past paper: State the selection rules for (electric) quantum numbers n,l,m,s and j. Homework Equations The Attempt at a Solution My problem is that looking online, there seems to be an m(s) and m(l). Is the question assuming that I state the selectrion...
  35. Z

    Selection rules beyond the central field approximation

    Hi I'm trying to figure out how to get the electric dipole selection rules for an atom with many electrons. In all textbooks that I've seen it's shown for Hydrogen, or in the central field approximation (which is, in some sense, equivalent to Hydrogen). Obviously the central field...
  36. B

    Allowed Transition from 2s^2 to 2p^2 in Hydrogen: Why is it Missing?

    Why is there no allowed transition from the 2s^2 S_{\frac{1}{2}} state to the 2p^2 P_{\frac{3}{2}} state in the attached image? It seems to fulfill the selection rules \Delta l = \pm 1 and \Delta j = 0, \pm 1. This is for electric dipole transitions by the way.
  37. D

    Selection Rules for EM Dipole Radiation

    hey, I was asking myself a few questions about the selection rules for EM dipole radiation which occurs if electrons "jump" into lower bound states according to the selection rules. now I know that the full explanation about matrix elements of the dipole operator comes from fermi's golden...
  38. S

    Why Do These Quantum Mechanical Selection Rules Result in Zero?

    I am having trouble showing: <4 3 0 | p_z^2 | 4 0 0 > = 0 and <4 2 1 | x p_y | 3 1 0 > = 0 I know the usual selection rules for parity, spherical tensors (Wigner-Eckart for x,y,z) but I can't convert these two to anything I know. You could also help by telling me how to convert these to...
  39. C

    Why is the transition from 3P1 to 3S1 in Helium forbidden?

    The transition in the n=2 state of Helium from 3P1 (m=0) to 3S1 (m=0) is forbidden. I know this, because I went to a lecture where a group measured the fine structure constant very precisely using this fact. However, as far as I can see, according to atomic selection rules (available here...
  40. K

    Understanding Zeeman Effect Selection Rules | Exploring Spin Physics

    I am reading some online article on Zeeman effect http://math.ucr.edu/home/baez/spin/node10.html In the article, the author mentions 4 selection rules, I wonder the corresponding transition is allowed by satisfying one of these selection rules or the corresponding line will be allowed only...
  41. A

    Can Spins Flip in an EPR Experiment?

    hello I got al little bit confused about spins flipping in an EPR experiment. As far as I know, the idea of EPR is to measure the absorption of an electromagnetic wave induced by spin flips if the energy is conserved by \hbar \omega = g_{spin} \mu_B B_0. But now I heard several times that a...
  42. C

    Electric Dipole Selection Rules

    Homework Statement For \Deltal = 0 the transition rate can be obtained by evaluating the electric dipole matrix elements given by \vec{I} = \int \Psi^{*}_{1,0,0} (e \vec{r}) \Psi_{2,0,0} d\tau Homework Equations The Attempt at a Solution I've got the two wave functions...
  43. W

    Selection rules and related stuffs

    I'm quite confuse with some concepts here. The selection rules are derived from the requirements that quantum numbers must be conserved. It's OK. Then I see they give rules for so-called electric dipole transitions. I just wonder why dipole comes in here. How do you classify these kinds of...
  44. J

    Wigner-Eckart theorem and selection rules

    If you have an operator which in spherical tensor language T^k_q are V=T^2_2 + T^2_{-2} + T^2_0 you get a selection rule for j' abs(j-k)=< j' <= j+k in my case i start with angular momentum j=1 and k=2 from above so the possible new states are 1=< j' <= 3...
  45. Y

    Electric dipole selection rules

    Hi, I am confused about the electric dipole selection rules. Delta l = +/- 1 Delta m_l = 0, +/- 1 but are there rules for Delta j and Delta m_s and Delta n? Is there a (semi-rigorous) way to conceptually understand selection rules? Thanks.
  46. Y

    Selection Rules (Electric Dipole)

    Hi, I have a question on selection rules for electric dipole transitions. It has to do with a GRE Physics exam question that's confusing a number of students at grephysics.net ... if any of the quantum guru's here would like to help, please check it out at...
  47. C

    A Question About Selection Rules

    A hydrogen atom is in the 4p state. To what state or states can it go by radiating a photon in an allowed transition? Anyone have any ideas?