Nuclear Physics/From Nucleons to Nucleus 썸네일형 리스트형 Exercise 5.16 & 5.17. Exercise 5.16: Overlap of two states in isospin representation $$ \begin{eqnarray} \langle a\, b ; J \, M ; T \, M_T | a'\, b'; J'\, M'; T' \, M_T \rangle &=& \left[ \mathcal{N}_{ab}(JT) [c_a^\dagger c_b^\dagger]_{JM}^{T M_T} |{\rm CORE} \rangle \right]^\dagger \left[ \mathcal{N}_{ab}(J'T') [ c_{a'}^\dagger c_{b'}^\dagger]_{J' M'}^{T' M_T'} | {\rm CORE} \rangle \right] \\[12pt] &=&\mathcal{N}_{a.. 더보기 5.3 (2) & 5.4 Two-Hole and Particle-Hole Nuclei In this posting, we treat the formalism of the two-hole and particle-hole nuclei. Two-Hole Nuclei FormalismAnalogous to the two-particle formalism described in (https://djlab.tistory.com/3), we can write wave functions of two-hole nuclei as follows:$$ | a^{-1} \, b^{-1} l J \, M \rangle = \mathcal{N}_{ab} [h_a^\dagger h_b^\dagger]_{JM} | {\rm HF} \rangle,$$where state ${\rm HF}$ depends on our i.. 더보기 5.5 Isospin Representation of Few-Nucleon System - (2) Tensor Operators in Isospin Representation By introducing the isospin formalism, we can describe the single particle state as follows: $$ \alpha = (a, m_\alpha, m_{t\alpha}). $$ With the new quantum number,$m_t$, the Kronecker delta is generalized to $$ \begin{eqnarray} &&\delta_{ab} = \delta_{n_a n_b} \delta_{l_a l_b} \delta_{j_aj_b}, \\[12pt] && \delta_{\alpha \beta} = \delta_{ab} \delta_{m_\alpha m_\beta} \delta_{m_{t\alpha} m_{t\beta.. 더보기 5.5 Isospin Representation of Few-Nucleon Systems - (1) General Isospin Formalism 5.5.1 General Isospin Formalism In this subsection, we introduce the isospin formalism (representation). Due to the striking similarities between neutrons and protons in the context of nuclear interactions, we can treat them as different states of a generic nuclear particle, the nucleon. This approach, known as isospin representation, allows us to describe protons and neutrons as a distinct isos.. 더보기 이전 1 ··· 4 5 6 7 8 다음
