# Questions tagged [fermis-golden-rule]

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### Can inelastic scattering still give rise to diffraction?

I am having a conceptual difficulty reconciling inelastic events and diffraction, particularly whether or not you can have inelastic diffraction. Here is my thought experiment that I am working ...
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### Electric quadrupole allowed transitions mathematical proof

Consider the electric quadruple moment operators as follows: $Q_{20} = \frac{e}{2}(x^2+y^2-2z^2)$ $Q_{2 \pm1} = \frac{e\sqrt{6}}{2}z(x\pm iy)$ $Q_{2 \pm2} = - \frac{e\sqrt{6}}{4}(x\pm iy)^2$ I ...
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### Is there any simple way to predict beta decay half lives?

Question For nuclides that decay by alpha emission, the Geiger-Nuttall law gives a simple and reasonably accurate estimate of the half-life. Essentially, one can model the alpha particle as a ...
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### How does dirac's delta function appear in transition rate in fermi's golden rule?

In the context of time dependent perturbation theory as in 8.06, video's code L 11.2 from mit ocw, I can't see any Dirac delta function appear anywhere. When I read about "Fermi's Golden Rule&...
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### Two-body decay: Heavier particles live longer than light particles

From Fermi's Golden Rule one can derive that the decay rate for a two-particle decay ($A\to B+C$) is given by $$\Gamma = \frac{p^*}{32\pi^2m_A^2} \int |{\cal M}|^2 d\Omega,$$ where the absolute value ...
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### Fermi's golden rule, Hamiltonian

I have 1 question about the Fermi's golden rule. The question is: In the introduction of this theory, for explaining the $\beta$ decay, we suppose that the Hamiltonian is of the form: $H=H_0+H_I$ ...
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### Does a photon interact with the spin of an electron?

In optical transitions which involve collisions between photons (from light) and electrons present in a solid, say, the transition rate is typically given by Fermi's golden rule. But the equation ...
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### What is the difference between the joint density of states and the density of state?

I think I understood the density of states, but I didn't understand the joint DOS. What is the main difference? What is the exact definition of the joint DOS? When do we use the joint DOS and when do ...
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### Delta function in Fermi's Golden rule [duplicate]

I am currently trying to understand the Fermi's golden rule. We consider a system with Hamiltonian: $$\hat H = \hat H_0 + \hat Ue^{i \omega t},$$ where the expectation value of $\hat U$ i much ...
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### Fourier transform of a scatering potential

The Fermi golden rules states $$\Gamma(\vec{k},\vec{k}') = \frac{2\pi}{\hbar} \left| \left \langle \vec{k}|V|\vec{k}' \right \rangle \right|^2 \delta(E(\vec{k})-E(\vec{k}')) \, .$$ Many places (for ...
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### Why is the Fermi Golden rule called so?

I was studying time dependent perturbation theory and this rule came under the case of constant (weak) perturbations. I understood the rule and the derivation but what I cannot understand is that is ...
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### How to prove that the spectral line-width is given by the imaginary part the self energy?

I am trying to understand the computational methods to calculate the spectral line-width as done in this paper, http://www.nature.com/articles/ncomms11755 Here, they say that the line-width is ...
As I understand, Fermi's golden rule is a result from first order perturbation, which says that the transition rate of an initial state $|i\rangle$ to a final state $|f\rangle$ is  \Gamma_{i\...