https://thetechbasement.no/ 2026-05-15T12:49:11+00:00 https://thetechbasement.no/ https://thetechbasement.no/_media/wiki:logo.png text/html 2025-02-10T04:32:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-02-03-obtd?rev=1739161951&do=diff Visualising OBTDs The one-body transition density (OBTD) is used to calculate the transition probability from an initial to a final state: $$ \langle \Psi_f | \hat{O}_{\lambda \mu} | \Psi_i \rangle = \sum_{\alpha \beta} \langle \alpha | \hat{o}_{\lambda \mu} | \beta \rangle \langle \Psi_f | \hat{c}^\dagger_\alpha \hat{c}_\beta | \Psi_i \rangle \qquad(0) $$ with the OBTD defined as: $$ \rho_{fi}(\alpha, \beta) = \langle \Psi_f | \hat{c}^\dagger_\alpha \hat{c}_\beta | \Psi_i \rangle. \qquad(1)… text/html 2025-02-17T01:05:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-02-13-obtd?rev=1739754322&do=diff [SOLVED] Possible bug in the OBTD calculations So there is a possible bug that I am trying to wrap my head around. In the OBTD log files from KSHELL, the OBTDs are listed in blocks where each block represents an initial and a final state aka. one specific transition. For example$i, j$$E_\gamma = [0, 3]$$M1$ text/html 2025-03-31T12:56:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-02-17-obtd?rev=1743425808&do=diff Another possible bug in the OBTD calculations: Why are excitations stronger than decays? Making sure that initial and final states are ordered correctly Feast your eyes on the below figure: It might seem fine and dandy, but consider this: If you look at for example $0f7/2 \rightarrow 0f5/2$$0f5/2 \rightarrow 0f7/2$$0f7/2$$0f5/2$$0f5/2 \rightarrow 0f7/2$$0^-$$1^-$$j$$$ B(\sigma \lambda; \xi_i j_i \rightarrow \xi_f j_f) = \frac{1}{2 j_i + 1} \mid ( \xi_f j_f \mid \mid M_{\sigma \lambda} \mid … text/html 2025-03-07T14:13:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-03-03-lee?rev=1741356836&do=diff Orbital contributions to the LEE Let's get to the crux of the matter. We can analyse OBTDs all day, but what we're really wondering about is which orbitals are contributing to the enhancement in the low-energy region of the gamma strength function. Recall that in shell model calculations, the reduced transition strength is calculated by$$ 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)… text/html 2025-03-10T13:28:50+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-03-10-gl-gs?rev=1741613330&do=diff Which values to choose for gl and gs? The gyromagnetic ratios determine how strongly the nuclear magnetic dipole moment interacts with the electromagnetic field, which directly affects the M1 transition strength. They show up in the $M1$ operator as $$ \hat{M1} = g_l \hat{L} + g_s \hat{S}. $$ $$ \mu = \frac{q}{2m}L $$ text/html 2025-05-26T12:43:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-05-13-porter-thomas-fluctuations?rev=1748263435&do=diff Porter-Thomas fluctuations Let's talk about Porter-Thomas (PT) fluctuations! To do that, we need to start talking about: The Porter-Thomas distribution Long story short: The PT distribution is the $\chi^2$ distribution with one degree of freedom ($k = 1$). In nuclear physics we have a central concept, namely the $L = 1$$$ f_{X1}(E_{\gamma}, E_i, j_i, \pi_i) = \dfrac{16 \pi}{9 \hbar^3 c^3}\langle B(X1;\downarrow) \rangle (E_{\gamma}, E_i, j_i, \pi_i) \rho (E_i, j_i, \pi_i).\qquad (0) $$$$ \lan… text/html 2025-07-02T12:41:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://thetechbasement.no/science:phd-notes:2025-07-02-m1-operator-approximation?rev=1751460074&do=diff init