Quantized motion of atoms in a quadrupole magnetostatic trap

We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all quantum levels have a nonzero decay rate. The Schrodinger equation associated with the potential gAB S (S is the total atomic spin) takes the form of coupled equations in r when the spinor components are expanded in spherical harmonics. We integrate the multichannel problem numerically to obtain asymptotic phase shifts, resonance energies, and widths. For S = 1/2, the lowest levels have widths somewhat less than their spacing. Thus the trap quantum-level structure might possibly be observable if the atoms are sufficiently cold, namely, in the 0.1-, uK regime for most atoms and attainable trap field gradients. The width decreases rapidly with increasing Mj, the angular momentum about the symmetry axis. Spectroscopic linewidths of a few hertz are possible if there is enough population in the lowest levels with a few Mj quanta. The decay rate of the lowest levels, however, is probably too rapid for studying Bose-Einstein condensation in such a trap.