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Register a new userFrequency shifts and relaxation rates for spin 1/2 particles moving in electromagnetic fields
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We discuss the behaviour of the Larmor frequency shift and the longitudinal relaxation rate due to non-uniform electromagnetic fields on an assembly of spin 1/2 particles, in adiabatic and nonadiabatic regimes. We also show some general relations between the various frequency shifts and between the frequency shifts and relaxation rates. The remarkable feature of all our results is that they were obtained without any specific assumptions on the explicit form of the correlation functions of the fields. Hence, we expect that our results are valid both for diffusive and ballistic regime of motion and arbitrary cell shapes and surface scattering. These results can then be applied to a wide variety of realistic systems.
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We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The Wigner function and its kinetic equations are expanded in terms of the generators of Clifford algebra and a complicated system of partial differential equations is obtained. We prove that some component equations are automattically satisfied if the rest ones are fulfilled. In this thesis two methods are proposed for calculating the Wigner function, which are proved to be equivalent. The Wigner function is analytically calculated following the standard second-quantization procedure in the following cases: free fermions with or without spin imbalance, in constant magnetic field, in constant electric field, and in constant parallel electromagnetic field. Strong-field effects, such as the Landau levels and Schwinger pair-production are reproduced using the Wigner function approach. For an arbitrary space-time dependent field configuration, a semi-classical expansion with respect to the reduced Plancks constant $hbar$ is performed. We derive general expressions for the Wigner function components at linear order in $hbar$, in which order the spin corrections start playing a role. A generalized Bargmann-Michel-Telegdi (BMT) equation and a generalized Boltzmann equation are obtained for the undetermined polarization density and net fermion number density, which can be used to construct spin-hydrodynamics in the future. We also make a comparison between analytical results and the ones from semi-classical expansion, which shows coincidence for weak electromagnetic fields and small spin imbalance.
Spin relaxation due to atom-atom collisions is measured for magnetically trapped erbium and thulium atoms at a temperature near 500 mK. The rate constants for Er-Er and Tm-Tm collisions are 3.0 times 10^-10 cm^3 s^-1 and 1.1 times 10^-10 cm^3 s^-1, respectively, 2-3 orders of magnitude larger than those observed for highly magnetic S-state atoms. This is strong evidence for an additional, dominant, spin relaxation mechanism, electrostatic anisotropy, in collisions between these submerged-shell L > 0 atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.
Isotope shifts of the 2$p_{3/2}$-2$p_{1/2}$ transition in B-like ions are evaluated for a wide range of the nuclear charge number: Z=8-92. The calculations of the relativistic nuclear recoil and nuclear size effects are performed using a large scale configuration-interaction Dirac-Fock-Sturm method. The corresponding QED corrections are also taken into account. The results of the calculations are compared with the theoretical values obtained with other methods. The accuracy of the isotope shifts of the 2$p_{3/2}$-2$p_{1/2}$ transition in B-like ions is significantly improved.
Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisions and relativistic Doppler shifts in a unified manner, and can therefore be used to accurately estimate collisional frequency shifts in trapped-atom clocks.
We present a theoretical analysis of spin relaxation, for a polarized gas of spin 1/2 particles undergoing restricted adiabatic diffusive motion within a container of arbitrary shape, due to magnetic field inhomogeneities of arbitrary form.
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