Towards the Formation of the Antihydrogen Molecular Ion

Sammanfattning: The ALPHA experiment at CERN is an ongoing project which tests fundamental symmetries between matter and antimatter by producing and trapping antihydrogen atoms in order to perform precision spectroscopic measurements. A logical next step is to form the antihydrogen molecular ion (consisting of one positron and two antiprotons). This system possesses net charge, and can therefore be trapped electrostatically, making repeated measurements possible. Moreover it has been suggested that the molecule has the potential to allow for higher-precision comparisons with ordinary matter than have been attained with the atom. Since both momentum and energy have to be conserved in a collision, a simple collision process between an antihydrogen atom (“Hbar”) and an antiproton (“pbar”) does not suffice in order to form the molecular ion. However it is possible, upon mixing of the two species, for a pbar colliding with an Hbar in the ground electronic state to form a metastable molecular state (i.e., a resonance) which is weakly coupled to a stable molecular state (i.e., a bound state) via spontaneous quadrupole transition. During the time a metastable ion exists, a second pbar can happen to undergo a Coulomb collision with the metastable molecular ion. The quadrupole electrostatic interaction with this secondary antiproton acts as a time-dependent perturbation on the molecular system which can strengthen the coupling between resonance and bound state. Hence a collision with a secondary pbar can induce a transition to a bound state whereby the excess energy is carried off by the secondary pbar. This work aims to determine the efficiency of the process just described. On the theoretical side, the following is done: a study is conducted on the topic of resonance scattering as it relates to the problem in consideration; building on this study a generalized time-dependent perturbation theory is constructed which is valid for transitions to and from resonant states as well as bound states. On the numerical side: the effective potential for pbar-Hbar scattering in the ground electronic state is obtained numerically within the adiabatic approximation; the energies and lifetimes of the resonant states of the molecular ion are estimated; a temperature-dependent rate coefficient is obtained for the process described which, in order to obtain a proper rate, needs to be multiplied by the square of the density of the antiproton plasma and by the number of antihydrogen atoms. It is concluded that at current capacity for trapping and storage of pbar and Hbar the process examined is not competitive with respect to other formation routes which have been proposed for the molecular ion.