All Questions
Tagged with scattering-cross-section quantum-mechanics
74
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Incident flux in a plane wave
As mentioned in Nuclear Structure by Bohr and Mottelson
Flux of incident particles associated with waves normalized per unit energy is
$$(\rho v)_\text{incident channel} = p^2/(2\pi\hbar)^3$$
How does ...
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Reciprocity theorem of reaction cross section
The reciprocity equation for reaction cross section reads
$$ka^{2}\sigma_{ab}=kb^{2}\sigma_{ba}$$
or
$$pa^{2}\sigma_{ab}=pb^{2}\sigma_{ba}$$
Here
$\sigma_{ab}$ is the total reaction cross section for ...
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Extending Quantum Treatment of Attentuation Coefficient
I was reading this document to understand the links between the attenuation coefficient and quantum scattering. Consider a beam of number density $\rho$ and velocity $v$ in the z direction. $I = \rho ...
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How to interpret the scattering cross section in quantum mechanics? [closed]
I am following Sakurai's Modern Quantum Mechanics, 3ed.
Define the scattering, or S-matrix elements as
$$S_{ni} \equiv \delta_{ni} - 2\pi i\delta(E_n - E_i)T_{ni}.$$
We can then derive the ...
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How does the cross section of bound state look like in scattering process?
I am studying the non-relativistic scattering theory. I know when the incident particle is in the bound state the scattering amplitude diverges. Then does it mean the cross section also diverge? If so,...
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Phase shift in hard sphere scattering
Consider scattering towards a hard sphere with radius a and potential (Assume ka=1):
$$ V(r) =\begin{cases}
\infty , &r<a\\
0 , &r>a \\
\end{cases} $$
So first I ...
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Maximum number of partial waves and matching point
I have read that a large number of partial waves, around 200, are required in a situation such as ${}^{16}$O incident on ${}^{152}$Sm at c.m. 65 MeV in Coulomb excitation
Anybody familiar with ...
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2
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What is a cross section, really? [closed]
Upon looking at different resources, there is a common definition of a cross section (in the context of QFT) to be the probability that some scattering process occurs. For example, here is a ...
user310742
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Physical mechanism of $s$-wave neutron resonances in nuclear physics
In this answer by Arturo don Juan, and also, in section $7.8$ of Sakurai's Modern Quantum Mechanics, it is argued that resonances in the scattering cross-section at certain energies are due to the ...
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Scattering cross section for distinguishable particles
I am reading Quantum Mechanics book by N. Zettili (2nd ed.) and encountered something confusing in the chapter of scattering theory, section 11.5: scattering of identical particles.
This is the ...
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Proving that the interference current integrated over a small cone does not depend on the angle of the cone
I'm studying quantum mechanical scattering and I have gotten to $$\psi=\psi_{in}+\psi_{scattering}=e^{ikrcos\theta}+f(\theta,\phi)\frac{e^{ikr}}{r}$$ and when calculating the current, i get three ...
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How to get Absorption cross section of Gaseous Ions for photons?
How or where can I find the Absorption cross-section of Gaseous Ions? I have looked over the internet and can only find it for neutral atoms. Does it increase or decrease for ions?
I have found ...
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Is it a coincidence to calculate Rutherford scattering using the first order Born approximation?
It is well-known that we can use Born first approximation to calculate the differential cross section. To be precise, firstly we modify the potential as Yukawa potential
$$V(r)=\dfrac{\alpha e^{-r/a}}{...
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Conservation of angular momentum affects the amplitude of the wave
In Griffiths Quantum mechanics book (Scattering theory-phase shifts):
Because the angular momentum is conserved (by a spherically symmetric potential), each partial wave(labelled by a particular l) ...
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Doubt regarding the calculation of first Born approximation of Yukawa potential
The expression for the scattering amplitude upto first Born approximation for Yukawa potential is
$$f^{1}(\mathbf{k},\mathbf{k'})=\int_0^\infty r^2 dr \int_0^{2\pi} d\phi \int_0^{\pi}\sin{\theta}\frac{...
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