Cross section

  1. What does it mean when they say s wave cross section, p wave cross section .. ?
     
  2. jcsd
  3. malawi_glenn

    malawi_glenn 4,726
    Science Advisor
    Homework Helper

    the [itex]l[/itex]-quantum number of the incoming wave. You often have a plane wave coming in to the target. The plane wave you write as a linear combination of spherical waves, and you call this "Partial Wave expansion".

    http://farside.ph.utexas.edu/teaching/qm/lectures/node70.html

    The [itex]l[/itex] that you see in eq 957 is then the "[itex]l[/itex] - QM number".
    And [itex]l[/itex] is denoted by, 0 = s, 1 = p, 2 = d, etc, same as in atomic physics notation.

    Semiclassicaly, you can see the [itex]l[/itex] as the classical angular momenta of the incoming particle with respect to the centre of the scattering potential. And also the [itex]l[/itex] is quantisized, so only some values of [itex]l[/itex] are allowed.

    Now since the sum goes to infinity in eq 957, we cut of where we expect no partial waves to contribute. And that is often assigned by [tex] l_{max} \approx R\cdot k [/tex]
    Where R is the range of the potential and k is the momenta of the incoming particle (wave number).

    Now the cross section is proportional to the scattering amplitude modulus square, i.e the modulus square of eq. 965 times a constant with alot of pi's hbar's etc.

    So the s-cross section, you only have [itex]l[/itex] = 0 in you sum, and p-cross section only [itex]l[/itex] = 1. etc.

    I hope you got the idea =)
     
  4. Hello,
    To munch the QM into an analogy:
    Another way to look at is - how does one particle look to another. If you assume the target particle to be ball-like, then in its basic form (ground state), you'll get the classic 3D cross-section - this is how it will appear to the incoming particle and such it will be scattered from the target particle. But if the particle is excited to a higher state, then it will no longer appear as a ball but something else entirely. And vice versa.
    Smoochie
     
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