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- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/13%3A_Atomic_Structure/13.03%3A_Electron_SpinJust like an electron, a proton is spin 1/2 and has a magnetic moment. (According to nuclear theory, this moment is due to the orbital motion of quarks within the proton.) The hyperfine structure of t...Just like an electron, a proton is spin 1/2 and has a magnetic moment. (According to nuclear theory, this moment is due to the orbital motion of quarks within the proton.) The hyperfine structure of the hydrogen spectrum is explained by the interaction between the magnetic moment of the proton and the magnetic moment of the electron, an interaction known as spin-spin coupling.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/08%3A_Atomic_Structure/8.04%3A_Electron_SpinThe spin angular momentum quantum of an electron is = +½. The spin angular momentum projection quantum number is ms =+½or−½ (spin up or spin down). The energy of the electron-proton system is differen...The spin angular momentum quantum of an electron is = +½. The spin angular momentum projection quantum number is ms =+½or−½ (spin up or spin down). The energy of the electron-proton system is different depending on whether or not the moments are aligned. Transitions between these states (spin-flip transitions) result in the emission of a photon.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/11%3A_Time-Independent_Perturbation_Theory/11.10%3A_Hyperfine_StructureThus, the perturbing Hamiltonian is written \[H_1=\frac{\mu_0\,g_p\,e^{\,2}}{8\pi\,m_p\,m_e}\, \frac{3\,({\bf S}_p\cdot{\bf e}_r)\,({\bf S}_e\cdot{\bf e}_r) - {\bf S}_p\cdot{\bf S}_e}{r^3} + \frac{\mu...Thus, the perturbing Hamiltonian is written \[H_1=\frac{\mu_0\,g_p\,e^{\,2}}{8\pi\,m_p\,m_e}\, \frac{3\,({\bf S}_p\cdot{\bf e}_r)\,({\bf S}_e\cdot{\bf e}_r) - {\bf S}_p\cdot{\bf S}_e}{r^3} + \frac{\mu_0\,g_p\,e^{\,2}}{3\,m_p\,m_e}\,{\bf S}_p\cdot{\bf S}_e\,\delta^{\,3}({\bf r}).\] Note that, because we have neglected coupling between the proton spin and the magnetic field generated by the electron’s orbital motion, the previous expression is only valid for \(l=0\) states.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Stellar_Atmospheres_(Tatum)/07%3A_Atomic_Spectroscopy/7.18%3A_Hyperfine_StructureThe levels and lines of many atoms have a hyperfine structure that is detectable only with high resolution, which may require not only interferometry but also a low temperature and low pressure source...The levels and lines of many atoms have a hyperfine structure that is detectable only with high resolution, which may require not only interferometry but also a low temperature and low pressure source so that the intrinsic line width is small.
