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Recently, we developed a method for calculating the lifetime of a particleinside a magnetic trap with respect to spin flips, as a first step in ourefforts to understand the quantum-mechanics of magnetic traps. The 1D toy modelthat was used in this study was physically unrealistic because the magneticfield was not curl-free. Here, we study, both classically andquantum-mechanically, the problem of a neutral particle with spin S, mass m andmagnetic moment mu, moving in 3D in an inhomogeneous magnetic fieldcorresponding to traps of the Ioffe-Pritchard, `clover-leaf' and `baseball'type. Defining by omega_p, omega_z and omega_r the precessional, the axial andthe lateral vibrational frequencies, respectively, of the particle in theadiabatic potential, we find classically the region in the $(\omega_{r}%(omega_r -- omega_z) plane where the particle is trapped.  Quantum-mechanically, we study the problem of a spin-one particle in the samefield. Treating omega_r / omega_p and omega_z / omega_p as small parameters forthe perturbation from the adiabatic Hamiltonian, we derive a closed-formexpression for the transition rate 1/T_{esc} of the particle from its trappedground-state. We find that in the extreme cases, the expression for 1/T_{esc}is dominated by the largest of the two frequencies omega_r and omega_z.Comment: 25 pages + 1 EPS figur

Magnetic trapping of neutral particles: Classical and quantum-mechanical study of a Ioffe–Pritchard type trap