recently, i am working on 3 things, both are calculation.
the 1st thing is a concrete foundation of microwave inducted optical nuclear polarization theory, which is the theory that my experiment is current using. i found some papers talk on the theoretical treatment on this subject. however, they are all start from some un-stated assumptions, for example, they are started with the Hamiltonian of hyperfine interaction, without state clear where the term comes from. i guess it is very elementary. nevertheless, different papers may use different Hamiltonians. moreover, some of the mathematics techniques or steps were skipped and directly jump to result. Thus. that is my motivation on building a concrete theory, based on dipole -magnetic field interaction.
when i finished the hyperfine interaction, i have to apply a magnetic field and it cause a Zeemen splitting of energy level. and the Zeeman effect depends on the strength of the magnetic field. they are called strong field, intermedia field and weak field. in different field strength, the origina Hamiltonian may or may not be treated as a perturbation. Thus, i have to know the magnitude of the hyperfine structure. at the point, i come up with in-consistance value that cannot smoothy translate from weak field to intermedia field and strong field.
So, i restudy the atomic theory on Hydrogen atom. Start from Bohr model, fine structure to hyperfine structure and calculated the energy level numerically, so that i can get a full and complete picture on this matter. then i can now compare the magnetic field strength. it turns out that it is not that clear when is weak or strong, because it is depends on the total vale of the Hamiltonian, not the coefficient. Thus, for higher orbital angular momentum, a very small magnetic field can be treated as strong field, coz it already large enough to break the coupling. i am still working on the hyperfine Zeeman effect.
Meanwhile, my professor asked me to calculate the filling factor of the sample and NMR coil. the NMR signal strength depends on the geometry of the coil and sample. and this geometric factor is called filling factor. it is a good name, i thing, since the maximum value is that the sample completely filled the coil. In order to calculated this, i parallel calculated the magnetic field generated by a cylindrical uniformly magnetized rod and the magnetic induction due to multiple from a single coil. the far field of the rod is done and basically, it is dipole, but the near field is complicated, the multiple terms appear and they are convergence slowly.
that’s why i don’t have post for 2 weeks.