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The effects of hyperfine structure on ultracold molecular collisions inexternal fields are largely unexplored due to major computational challengesassociated with rapidly proliferating hyperfine and rotational channels coupledby highly anisotropic intermolecular interactions. We explore a new basis setfor incorporating the effects of hyperfine structure and external magneticfields in quantum scattering calculations on ultracold molecular collisions.The basis is composed of direct products of the eigenfunctions of the total{\it rotational} angular momentum (TRAM) of the collision complex $J_r$ and theelectron/nuclear spin basis functions of the collision partners. The separationof the rotational and spin degrees of freedom ensures rigorous conservation of$J_r$ even in the presence of external magnetic fields and isotropic hyperfineinteractions. The resulting block-diagonal structure of the scatteringHamiltonian enables coupled-channel calculations on highly anisotropicatom-molecule and molecule-molecule collisions to be performed independentlyfor each value of $J_r$, with an added advantage of eliminating the unphysicalstates present in the total angular momentum representation. We illustrate theefficiency of the TRAM basis by calculating state-to-state cross sections forultracold He + YbF collisions in a magnetic field. The size of the TRAM basisrequired to reach numerical convergence is 8 times smaller than that of theuncoupled basis used previously, providing a computational gain of three ordersof magnitude. The TRAM basis is therefore well suited for rigorous quantumscattering calculations on ultracold molecular collisions in the presence ofhyperfine interactions and external magnetic fields.

physical review. a/physical review, a

Ultracold molecular collisions in magnetic fields: Efficient  incorporation of hyperfine structure in the total rotational angular momentum  representation