From Nucleons to Nucleus 썸네일형 리스트형 6.1.7 Weisskopf Units and Transition Rates We can estimate the transition probability by adopting the approximation: the radial wave function is assumed to be constant inside the nucleus and zero outside. Then, by the normalization condition, \begin{eqnarray} \int g_{nl}(r) g_{nl}(r) r^2 dr \approx g_{nl}^2 \int_0^R r^2 dr = g_{nl}^2 \frac{R^3}{3} = 1 \Rightarrow g_{nl} \approx \sqrt{\frac{3}{R^3}} \ \ {\rm at} \ r \le R. \end{eqnarray} .. 더보기 6.1.5 Tables of Numerical Values of Single-Particle Matrix Elements In this posting, I will show how to obtain the numerical values of single-particle matrix elements for the electromagnetic multipole operators. In the previous section, we obtained the following reduced matrix elements for the electric operator: ( 2024.03.28 - [Nuclear Physics/From Nucleons to Nucleus] - 6.1.3 Single-Particle Matrix Elements of the Multipole Operators ) \begin{eqnarray} (a || {\.. 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 5.5.3 Isospin Representation of Two-Particle and Two-Hole Nuclei Based on the Isospin Representation, we can express the Two-Particle and Two-Hole Nuclei: $$ |a\, b; J \, M; T \, M_T \rangle = \mathcal{N}_{ab}(JT) [c_a^\dagger c_b^\dagger]_{JM}^{T M_T} | {\rm CORE} \rangle, $$ The normalization factor is given by $$ \mathcal{N}_{ab}(JT) = \frac{\sqrt{1 - \delta_{ab} (-1)^{J+T}}}{1 + \delta_{ab}}. $$ This implies that there are two possible non-zero values: $\.. 더보기 이전 1 2 3 다음
