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We have observed a linear pressure dependence of longitudinal relaxation time ($T_1$) at 4.2 K and 295 K in gaseous $^3$He cells made of either bare pyrex glass or Cs/Rb-coated pyrex due to paramagnetic sites in the cell wall. The paramagnetic wall relaxation is previously thought to be independent of $^3$He pressure. We develop a model to interpret the observed wall relaxation by taking into account the diffusion process, and our model gives a good description of the data.doi:10.1103/physreva.83.061401 fatcat:6twwbsxlyjg55m4efflfr5s6pu