Magnetic-field-inhomogeneity-induced transverse-spin relaxation of gaseous Xe 129 in a cubic cell with a stem

We investigate the transverse-spin relaxations of $^{129}\\mathrm{Xe}$ due to diffusion in the presence of magnetic-field gradients in relation to the dimensions of a sub-cm sized cubiclike atomic gas cell with a stem. The transverse-spin-relaxation rate $({\\mathrm{\\ensuremath{\\Gamma}}}_{\\mathrm{\\ensuremath{\\Delta}}B})$ of $^{129}\\mathrm{Xe}$ is measured as a function of various magnetic-field gradients, $\\ensuremath{\\partial}{B}_{z}/\\ensuremath{\\partial}x$, $\\ensuremath{\\partial}{B}_{z}/\\ensuremath{\\partial}y$, $\\ensuremath{\\partial}{B}_{z}/\\ensuremath{\\partial}z$, and $\\ensuremath{\\partial}{B}_{y}/\\ensuremath{\\partial}y$. From the measured transverse-spin-relaxation rates in five atomic gas cells with different stem sizes, the quadratic coefficients of ${\\mathrm{\\ensuremath{\\Gamma}}}_{\\mathrm{\\ensuremath{\\Delta}}B}$ with respect to the magnetic-field gradients are extracted. To investigate the effect of the dimensions of the stem, we calculate the ratio between the quadratic coefficients in each atomic gas cell, which is invariant under scaling in the cell size and change in the diffusion coefficient. We compare these ratios with those obtained analytically from a rectangular parallelepiped model for the atomic gas cells and with those obtained numerically from a more precise model taking the stems directly into account. Using a scaling argument, we provide a scheme for estimating the quadratic coefficient of a cubic atomic cell with a stem. Finally, we determine the diffusion coefficient from the measured quadratic coefficient. Compared to the analytical method for a rectangular parallelepiped, numerical analysis considering the stem provides the diffusion coefficient as a value close to the value given by Fuller's equation. We estimate the diffusion coefficients of $^{129}\\mathrm{Xe}$ in the gas mixture of nitrogen, $^{129}\\mathrm{Xe}$, and $^{131}\\mathrm{Xe}$ as 0.13 ${\\mathrm{cm}}^{2}/\\mathrm{s}$ at the standard temperature and pressure condition.