We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to ten ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.PACS numbers: 32.80.Pj, 03.67. Lx, 52.25.Wz, Ions confined in linear radio-frequency traps, and cooled by laser radiation, will condense into a crystalline state. Such crystals are the most rarefied form of condensed matter known [1]. Besides being of inherent scientific interest for this reason, cold trapped ions have a growing number of applications, notably spectroscopy [2-4], frequency standards [3,5], and quantum computing [6,7]. The existence of different kinds of phase transitions of these crystals has been known for some time [8,9] and has been the subject of various theoretical and numeric studies [1,10,11]. Previous experimental work identified different crystal phases/configurations in a quadrupole ring trap [9]. Here we explicitly investigate the transition between two of these phases: the linear and the zigzag configurations. We report the first experimental confirmation of one of the key theoretical/numeric predictions for the linear-to-zigzag transition, namely, the existence of a power law relating the critical anisotropy parameter to the number of ions in the crystal. Further, we discuss the usefulness of this power-law expression in determining the ultimate size of a quantum logic register realizable using a single ion trap.The potential energy of a crystal of N identical ions of mass M and charge e confined in an effective threedimensional harmonic potential is U͑r 1 , r 2 , . . . , r N ͒ M͑2p͒ 2 2 N

Cross sections for (223,)(225)Ra, (225)Ac and (227)Th production by the proton bombardment of natural thorium targets were measured at proton energies below 200 MeV. Our measurements are in good agreement with previously published data and offer a complete excitation function for (223,)(225)Ra in the energy range above 90 MeV. Comparison of theoretical predictions with the experimental data shows reasonable-to-good agreement. Results indicate that accelerator-based production of (225)Ac and (223)Ra below 200 MeV is a viable production method.

The development and theory of an experiment to investigate quantum computation with trapped calcium ions is described. The ion trap, laser and ion requirements are determined, and the parameters required for quantum logic operations as well as simple quantum factoring are described.

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Accelerator production of 225 Ac addresses the global supply deficiency currently inhibiting clinical trials from establishing 225 Ac's therapeutic utility, provided that the accelerator product is of sufficient radionuclidic purity for patient use. Two proton activation experiments utilizing the stacked foil technique between 40 and 200 MeV were employed to study the likely co-formation of radionuclides expected to be especially challenging to separate from 225 Ac. Foils were assayed by nondestructive -spectroscopy and by -spectroscopy of chemically processed target material. Nuclear formation cross sections for the radionuclides 226 Ac and 227 Ac as well as lower lanthanide radioisotopes 139 Ce, 141 Ce, 143 Ce, and 140 La whose elemental ionic radii closely match that of actinium were measured and are reported. The predictions of the latest MCNP6 event generators are compared with measured data, as they permit estimation of the formation rates of other radionuclides whose decay emissions are not clearly discerned in the complex spectra collected from 232 Th(p,x) fission product mixtures.