A: We discuss a technique for measuring a charged particle's momentum by means of multiple Coulomb scattering (MCS) in the MicroBooNE liquid argon time projection chamber (LArTPC). This method does not require the full particle ionization track to be contained inside of the detector volume as other track momentum reconstruction methods do (range-based momentum reconstruction and calorimetric momentum reconstruction). We motivate use of this technique, describe a tuning of the underlying phenomenological formula, quantify its performance on fully contained beam-neutrino-induced muon tracks both in simulation and in data, and quantify its performance on exiting muon tracks in simulation. Using simulation, we have shown that the standard Highland formula should be re-tuned specifically for scattering in liquid argon, which significantly improves the bias and resolution of the momentum measurement. With the tuned formula, we find agreement between data and simulation for contained tracks, with a small bias in the momentum reconstruction and with resolutions that vary as a function of track length, improving from about 10% for the shortest (one meter long) tracks to 5% for longer (several meter) tracks. For simulated exiting muons with at least one meter of track contained, we find a similarly small bias, and a resolution which is less than 15% for muons with momentum below 2 GeV/c. Above 2 GeV/c, results are given as a first estimate of the MCS momentum measurement capabilities of MicroBooNE for high momentum exiting tracks.

The all-electron spin-polarized generalized gradient approximation to the density-functional theory is used to determine the binding energies, ground-state structures, electronic structures, and magnetic properties of the Y n clusters ͑n ഛ 17͒. The structural evolution of yttrium clusters, which favors a compact and icosahedral structural growth pattern, is elucidated and compared with the other group-III elemental clusters. The results show that clusters with n =7,13 are more stable than their respective neighbors. Furthermore, the maxima of magnetism at n = 8 and n = 13 observed experimentally are well described and the magnetic moments for most yttrium clusters are quite small except for Y 6 , Y 8 , and Y 12 -Y 14 . Particularly, the regular icosahedron structure with a giant moment of 19 B is favored for the Y 13 cluster. The similar magnetic features of the scandium and yttrium clusters shown in experiments can be attributed to a common structural motif for these two series of clusters. A change of magnetic ordering from ferromagnetic to antiferromagnetic is observed at n = 7, the exception being the systems Y n with n =8,13,14 which are found to be ferromagnetic. In addition, the calculated ionization potentials are in good agreement with the experimental results, which imply that the predictions of the ground-state geometries of those clusters are accurate.

The structural evolutions and electronic properties of bimetallic Aun–xPtx (n = 2–14; x ⩽ n) clusters are investigated by using the density functional theory (DFT) with the generalized gradient approximation (GGA). The monatomic doping Aun–1Pt clusters are emphasized and compared with the corresponding pristine Aun clusters. The results reveal that the planar configurations are favored for both Aun–1Pt and Aun clusters with size up to n = 13, and the former often employ the substitution patterns based on the structures of the latter. The most stable clusters are Au6 and Au6Pt, which adopt regular planar triangle (D3h) and hexagon-ring (D6h) structures and can be regarded as the preferential building units in designing large clusters. For Pt-rich bimetallic clusters, their structures can be obtained from the substitution of Pt atoms by Au atoms from the Ptn structures, where Pt atoms assemble together and occupy the center yet Au atoms prefer the apex positions showing a segregation effect. With respect to pristine Au clusters, AunPt clusters exhibit somewhat weaker and less pronounced odd-even oscillations in the highest occupied and lowest unoccupied molecular-orbital gaps (HOMO-LUMO gap), electron affinity (EA), and ionization potential (IP) due to the partially released electron pairing effect. The analyses of electronic structure indicate that Pt atoms in AuPt clusters would delocalize their one 6s and one 5d electrons to contribute the electronic shell closure. The sp-d hybridizations as well as the d-d interactions between the host Au and dopant Pt atoms result in the enhanced stabilities of AuPt clusters.

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The spin-polarized generalized gradient approximation to the density-functional theory has been used to determine the lowest energy structure, electronic structure, and magnetic property of Gd(13) cluster. Our results show that the ionic bonding is combined with the covalent characteristics in stabilizing the Gd cluster. The ferrimagnetic icosahedron is found to be the lowest energy configuration, in which the centered Gd atom couples antiferromagnetically with the rest Gd atoms surrounding it. No spin non-collinear evidence has been detected in our calculations. It is identified that the local magnetic moments of Gd atom are about 8 μ(B) regardless of geometrical structure. Finally, the comprehensive electronic structure analyses show that the indirect long-range magnetic coupling between the polarized 4f is mediated by the polarization of 5d, 6s, and 6p conduction electrons, which is the typical Ruderman-Kittel-Kasuya-Yosida interactions.