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Measurement of dwell times of spin polarized rubidium atoms on octadecyltrichlorosilane- and paraffin-coated surfaces
14.S. J. Seltzer, D. J. Michalak, M. H. Donaldson, M. V. Balabas, S. K. Barber, S. L. Bernasek, M. -A. Bouchiat, A. Hexemer, A. M. Hibberd, D. F. Jackson Kimball, C. Jaye, T. Karaulanov, F. A. Narducci, S. A. Rangwala, H. G. Robinson, A. K. Shmakov, D. L. Voronov, V. V. Yashchuk, A. Pines, and D. Budker, J. Chem. Phys. 133, 144703 (2010).
16.Y. W. Yi, H. G. Robinson, S. Knappe, J. E. Maclennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, J. Appl. Phys. 104, 023534 (2008).
27.Consider the diffusion path of a spin polarized Rb atom from the time it is polarized to the time it relaxes. The path can be divided into segments as depicted in Fig. 2, with each segment corresponding to the path between two consecutive wall collisions. The average Larmor frequency shift for this Rb atom before it relaxes is given by which becomes, upon dividing the numerator and denominator by , where the bar indicates the average over the segments. If is sufficiently large, as is the case for good coatings such as OTS and paraffin, the distribution of the frequency shifts for all the Rb atoms will be sufficiently narrow to allow for a well-defined ensemble average frequency shift given by Eq. (1).
28.The expression for can be derived from the well known gas kinetic formula for the total number of collisions per second of Rb atoms on the front surface of area . Thus the total number of collisions per second of Rb atoms on the front or back surface is , which can be written as , where is the total number of Rb atoms in the vapor. Thus the rate of a single Rb atom hitting the front or back surface is , the inverse of which yields the average time a Rb atom spends in the bulk between two consecutive wall collisions: . This derivation for ignores the finite relaxation time of the polarized Rb atoms. It is valid when , where is the diffusion constant of Rb atoms in , i.e. when the decay rate of the first diffusion mode is larger than the total relaxation rate of the polarized Rb atoms. Under this condition, we can concern ourselves only with the lowerst diffusion mode (constant mode), which is the reason why does not depend on . When is very small (high density) or is very large, one can no longer neglect the first diffusion mode, and the linear relationship between and breaks down. Physically, this corresponds to the fact that the Rb atoms that collide with the front surface do not reach the back surface before relaxing. Note that the Rb polarization under our experimental conditions is what Masnou-Seeuws and Bouchiat called unconfined polarization [F. Masnou-Seeuws and M. A. Bouchiat, J. Physique 28, 406 (1967)], for which the wall induced relaxation rate , being the probability of depolarization by a wall collision, is independent of buffer gas pressure.
29.The molecules in the cell could adsorb on the coating surface, the effect of which on the dwell time remains to be studied. The fact, however, that the measured dwell times depend on the type of coatings indicates that Rb atoms are interacting with atoms beneath the top layer of the surface where the molecules might reside.
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