The Tech Basement

Let's get to the crux of the matter. We can analyse OBTDs all day, but what we're really wondering about is which orbitals are contributing to the enhancement in the low-energy region of the gamma strength function. Recall that in shell model calculations, the reduced transition strength is calculated by

$$ B(\sigma \lambda; \xi_i j_i \rightarrow \xi_f j_f) = \frac{1}{2 j_i + 1} \mid ( \xi_f j_f \mid \mid M_{\sigma \lambda} \mid \mid \xi_i j_i ) \mid^2, \qquad(0) $$

$$ \langle \Psi_f | \hat{O}_{\lambda \mu} | \Psi_i \rangle = \sum_{\alpha \beta} \langle \alpha | \hat{o}_{\lambda \mu} | \beta \rangle \langle \Psi_f | \hat{c}^\dagger_\alpha \hat{c}_\beta | \Psi_i \rangle. \qquad(1) $$

I so happen to be in possession of all the OBTDs and reduced matrix elements needed to re-calculate any transition of my desire. Now, what if I were to simply skip certain orbitals ($\alpha$ and $\beta$) in eq. (1)? I could for example decide to skip any mention of $0f7/2 \rightarrow 0f7/2$, or any other single-particle transitions for that matter. Re-calculating all of the transition strengths with the modified OBTD files consequently gives me the possibility to re-calculate the $M1$ GSF with the modified values. We can then directly see how the LEE is affected by the modification! That's what I call a home-run! schmack

During my OBTD quest I have become increasingly confused about how values are structured in the KSHELL log files; which value is B decay and which is excite? I think I'll circumvent these shenanigans and simply use the reduced matrix element and its relation to the initial and final state as seen in eq. (0). In that equation, $i$ and $f$ says nothing about whether it is a decay or an excitation. To decide that, we have to make sure that what we call initial in eq. (0) is the state with the higher energy of the two. If that is the case, then $i \rightarrow f$ certainly means a decay probability. I have now made sure of this!

To change the different orbital contributions in eq. (1) means that we skip both OBTDs and reduced M matrix elements (M red). But first, to be sure that my re-calculations of the B values work as expected, I will try to re-calculate the $M1$ strength function without modifying anything.

I was expecting to perfectly re-calculate the $M1$ strength function, and it is almost perfect, but there are some tiny differences… Don't know what is the cause and I don't think I'll spend any time figuring it out as it looks good enough for me.