Spin statistic terms in absorption cross section

FunkyDwarf
Messages
481
Reaction score
0
'Ello,

I have a question regarding the results in this paper (and another which I will mention later)

http://arxiv.org/abs/hep-ph/0212199

Now, I'm not so concerned about the 'braney' bit, but more their definition of the cross section in Eqn. (46). They have included the usual (2j+1) term (which is present even in non-relativistic physics) but it seems to me it should be the full g(j) = (2j+1)/((2a+1)(2b+1)) where a and b are the spins of the incident particle and the target (in this case one of them can be zero as they consider a black hole target which is modeled as a classical potential, in some sense).

A similar definition seems to be used in this paper by R. Fabbri:
http://prd.aps.org/abstract/PRD/v12/i4/p933_1

in this case in Eqn. (34)

In both cases they consider spin 1 and so one would expect a factor of (2j+1)/3, or no?

Any help would be appreciated :\

Cheers!
-Z
 
Physics news on Phys.org
Isn't the rule "average over initial, sum over final." Meaning that if the reaction probability is independent of the initial spin orientations, they don't contribute any weight. But the final spins are summed over, and do contribute a factor.
 
Well the transmission probability will certainly be spin dependent, but I'm talking about the spin term in the general cross section definition. I'm simply trying to work out why they include (2j+1) instead of the 'full' general term, given they are not considering a scalar incident particle.
 
Ok, slightly different question :)

The absorption cross section for spin 0 is defined as

<br /> \sigma =\frac{\pi}{\epsilon^2} \Sigma (2l+1) T_l<br />
for transmission coefficient $T_l$.

I understand the (2l+1) factor comes from the expansion of the plane wave to look at scattering. I don't suppose someone could point me to a similar expansion in the spin half case where the cross section is

<br /> \sigma =\frac{\pi}{\epsilon^2} \Sigma|\kappa| T_l<br />

Clearly the direct transformation between kappa and l doesn't allow you to go between these two equations (at least without a factor of 2).

Thanks,
-Z
 
Ok so apparently I'm a spazz and can't find the edit button, solved the above problems so thread can be closed/removed if needed :) Thanks guys!
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...
Back
Top