Electromagnetic transition 썸네일형 리스트형 6.2 Electromagnetic Transitions in One-Particle and One-Hole Nuclei - 6.2.1 Reduced Transition Probabilities In this blog posting, for the simple case of one-particle and one-hole nucleus, I will introduce how to obtain reduced transition probabilities: \begin{eqnarray} (\xi_f \, J_f || {\pmb {\cal M}}_{\sigma \lambda} || \xi_i \, J_i ) = \hat{\lambda}^{-1} \sum_{ab} (a || {\pmb {\cal M}}_{\sigma \lambda} || b) (\xi_f \, J_f || [c_a^\dagger \tilde{c}_b ]_\lambda || \xi_i \, J_i). \tag{1}\label{1}\end{e.. 더보기 6.1.4 Properties of the Radial Integrals (+Python code) In this section, our purpose is to evaluate the radial integrals in the single-particle matrix elements of the multipole operators: 2024.03.28 - [Nuclear Physics/From Nucleons to Nucleus] - 6.1.3 Single-Particle Matrix Elements of the Multipole Operators 6.1.3 Single-Particle Matrix Elements of the Multipole Operators In this posting, I derive the single-particle matrix elements of the multipole.. 더보기 6.1.3 Single-Particle Matrix Elements of the Multipole Operators In this posting, I derive the single-particle matrix elements of the multipole operators. 1. Single particle matrix elements for electric tensor operator ($\sigma = E$) The electric tensor operator is given as \begin{eqnarray} Q_{\lambda \mu} = \zeta^{\rm E \lambda} \sum_{j=1}^A e(j) r^\lambda_j Y_{\lambda \mu } (\Omega_j), \end{eqnarray} so we can simply rewrite it as follows: \begin{eqnarray} .. 더보기 6.1.2 Selection Rules for Electromagnetic Transitions The selection rules for electromagnetic transitions are summarized in this blog posting. 1. The first selection rule: There are no E0 and M0 gamma transitions. We have derived the electromagnetic tensor operator in the previous posting: https://djlab.tistory.com/20. According to the given form, for $\lambda = 0$, \begin{eqnarray} Q_{00} \propto Y_{0 0} (\Omega_j) = const., \ \ M_{00} \propto \na.. 더보기 이전 1 2 다음
