The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallelsided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.

A femtosecond optical frequency comb and continuous-wave pulse-amplified laser were used to measure 12 transition frequencies of antiprotonic helium to fractional precisions of 9-16 10 ÿ9 . One of these is between two states having microsecond-scale lifetimes hitherto unaccessible to our precision laser spectroscopy method. Comparisons with three-body QED calculations yielded an antiproton-to-electron mass ratio of M p =m e 1836:152 6745. DOI: 10.1103/PhysRevLett.96.243401 PACS numbers: 36.10.ÿk, 06.20.Dk, 14.20.Dh, 32.70.Jz We report here new measurements on the transition frequencies of antiprotonic helium atoms ( pHe e ÿ ÿ p ÿ 4 He 2 ) [1] using a femtosecond optical frequency comb [2,3] in conjunction with a continuous-wave (cw) pulse-amplified laser (Fig. 1). Their experimental precision is a factor 6 -20 better than our previous best ones [4], and now approaches those of, e.g., the 1 1 s-2 1 s [5] and 1 1 s-2 1 p [6] transitions in ordinary helium. From the frequencies of 12 transitions measured to the Doppler-broadened limit at a cryogenic temperature of 10 K, we have deduced the mass and charge of the antiproton relative to both the proton and the electron with a precision of the order of the known proton-to-electron mass ratio [7].Reference [4] describes how a radio-frequency quadrupole decelerator was used to slow down the antiprotons emerging from the CERN Antiproton Decelerator to 100-keV energies. They were then stopped in a helium target of low atomic density 10 18 cm ÿ3 to produce pHe atoms which filled a volume V 100 cm 3 . Antiprotons in pHe states with high principal (n 38) and angular momentum (') quantum numbers reach the helium nucleus over a period of several microseconds. The resulting delayed annihilation time spectra (DATS), i.e., the annihilation rate versus time elapsed since pHe formation, was measured by Cherenkov counters [ Fig. 2(a)]. In all but one of the present experiments, linearly polarized laser pulses of energy density " 0:04-1 mJ=cm 2 (e.g., applied here at t 1 s) stimulated transitions with dipole moments 0.02 -0.3 D from these pHe states, to states with nanosecond-scale lifetimes against Auger emission [1] and annihilation. The resulting peak in the DATS signaled the resonant frequency.Only pulsed lasers can provide the megawatt-scale intensities needed here to induce the pHe transitions. However, fluctuations in their frequency and linewidth and the difficulty of calibrating the wide range of pHe wavelengths 264:7-726:1 nm have so far limited our experimental precision [4]. We have now circumvented these problems by basing our experiments on a cw laser whose frequency cw could be stabilized with a precision <4 10 ÿ10 against an optical comb. Its intensity was then amplified [6,8,9] by a factor 10 6 to produce a pulsed laser beam of frequency pl cw with an accuracy and resolution 1-2 orders of magnitude higher than before [4].This was done as follows: First, a Nd:YVO 4 laser (Coherent Verdi, B in Fig. 1

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Six laser-resonant transitions have been detected in metastable antiprotonic helium atoms produced at the CERN Antiproton Decelerator. They include UV transitions from the last metastable states in the y n 2 ᐉ 2 1 0 and 1 cascades. Zero-density frequencies were obtained from measured pressure shifts with fractional precisions between 1.3 3 10 27 and 1.6 3 10 26 . By comparing these with QED calculations and the antiproton cyclotron frequency, we deduce that the antiproton and proton charges and masses agree to within 6 3 10 28 with a confidence level of 90%. Two transitions were in the previously unstudied UV region; two others were to final states with large Auger widths which provide particularly stringent tests of such calculations. These studies were done using the Antiproton Decelerator (AD) recently built at CERN.A variety of antiprotonic atoms exists for every element, but only p He 1 atoms have microsecond-scale lifetimes against annihilation. This extreme longevity (typically t 3 4 ms) arises because antiprotons in states with large principal ͑n ϳ 38͒ and angular momentum ͑ᐉ ϳ n͒ quantum numbers (see Fig. 1) cannot easily deexcite by Auger emission of the electron. With this electron in place, the atom is protected against collisional Stark mixing with low-ᐉ states, which overlap with the nucleus. It deexcites by radiating a series of optical-frequency photons, as the antiproton traverses a constant y n 2 ᐉ 2 1 cascade of these metastable states.Recent variational calculations [3-5] claim a precision of ,1 3 10 27 , for radiative transition frequencies involving states with small natural widths (G # 50 MHz). Relativistic [4] and one-loop QED corrections [5] are taken into account, as well as nuclear size and order-a 4 effects. Another calculation using the nonadiabatic coupledrearrangement-channel method [6] has also been made. The two calculations agree within #2 3 10 27 for transitions with natural widths of G , 50 MHz, while a larger difference is seen ͑.2 3 10 26 ͒ for states having large Auger widths (G $ 15 GHz).As in previous experiments [7,8], we measured the delayed annihilation time spectrum (the distribution of the number of annihilations, as a function of the time elapsed since p He 1 formation). We tuned pulsed laser beams to stimulate antiproton transitions from metastable states to levels that are not protected in the way described above, thereby revealing the resonance condition between the laser beam and the atom as a sharp peak in the annihilation rate (see Fig. 2). We have already measured one such transition frequency of ͑n, ᐉ͒ ͑39, 35͒ ! ͑38, 34͒ to an accuracy of 5 3 10 27 , which agreed with theoretical calculations at a level of 2 3 10 26 [9].The present experiments were done during the first months of operation at the AD, which provided a pulsed beam containing 2 3 10 7 antiprotons, with an energy of 5.3 MeV, a pulse length of 250 ns, and a repetition rate of 1 pulse per 2 min. Metastable p He 1 atoms were produced by stopping the antiproton pulses in a cryogenic helium

A radio frequency quadrupole decelerator and achromatic momentum analyzer were used to decelerate antiprotons and produce p 4 He and p 3 He atoms in ultra-low-density targets, where collision-induced shifts of the atomic transition frequencies were negligible. The frequencies at near-vacuo conditions were measured by laser spectroscopy to fractional precisions of 6-19 10 ÿ8 . By comparing these with QED calculations and the antiproton cyclotron frequency, we set a new limit of 1 10 ÿ8 on possible differences between the antiproton and proton charges and masses. DOI: 10.1103/PhysRevLett.91.123401 PACS numbers: 36.10.-k, 14.20.Dh, 32.70.Jz Recently, we measured some transition frequencies in antiprotonic 4 He atoms [1] (p 4 He e ÿ ÿ p ÿ 4 He 2 ) to sub-ppm precision [2] at the Antiproton Decelerator (AD) of CERN. By comparing these with three-body QED calculations and using the measured value of the antiproton cyclotron frequency [3], a 60-ppb limit was obtained for the possible differences p between the antiproton and proton charges and masses. Any such difference, however small, would imply CPT violation, i.e., that physical laws are not perfectly invariant under a combined transformation of charge conjugation, parity, and time reversal [4]. The precision of the experiment [2] was limited by the high density of the cryogenic helium targets (atomic density 10 21 cm ÿ3 , corresponding to pressures p 10-200 bars at room temperature) used to stop the 5.3-MeV antiproton beam and produce these atoms. The p 4 He underwent many collisions with helium atoms, resulting in large shifts [1,2,5] in the transition frequencies. We here report on new laser spectroscopy measurements at ultralow target densities of 10 17 cm ÿ3 , some 10 4 times lower than those previously used. These experiments were made possible by a radio frequency quadrupole decelerator (RFQD, Fig. 1) [6], which decelerated the 5.3-MeV antiprotons used previously [2] to energies E 10-120 keV. The collisional shifts thus became negligible (jj 1 MHz) compared to the natural widths of the transitions, so that the observed frequencies were effectively in vacuo. We also extended our high-precision studies to the isotope p 3 He , and to transitions which could not be observed at high densities, thus increasing the number of measured frequencies with small natural widths (ÿ < 50 MHz) from 4 [2] to 13.In these experiments, laser pulses induced antiproton transitions from metastable pHe states ( Fig. 2) with large principal (n 38) and angular momentum (' n) quantum numbers, to states with short Auger lifetimes [1]. The two-body pHe 2 ions formed after Auger emission suffered collisional Stark effects, which caused the rapid annihilation of the antiproton in the helium nucleus. The resulting spike in the rate of annihilations signaled the transition frequency. In previous experiments made at higher densities, collisions produced large frequency shifts (jj 0:5-5:0 GHz) which were of the order of 10 ÿ6 -10 ÿ5 of the measured transition frequencies . The frequencies 0...

We have performed laser spectroscopy of metastable antiprotonic helium atoms (p He ϩ ) formed in helium media of 0.2-8.0 bars at 5.8-6.3 K and have observed a density dependence of the resonance vacuum wavelengths for the known transitions (n,l)ϭ(39,35)→(38,34) and (37,34)→(36,33). They showed linear redshifts of 0.61Ϯ0.01 GHz and 0.22Ϯ0.02 GHz per 1 g/l, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding 0 ϭ597.2570Ϯ0.0003 nm and 0 ϭ470.7220Ϯ0.0006 nm, respectively. These values, with a 0.5-ppm precision, were compared with the result of recent theoretical calculations on the energy of the Coulombic three-body system, including relativistic corrections and the Lamb shift. The agreement between our experimental values and the calculations has become as good as 2ϫ10 Ϫ6 . This excellent agreement in turn provides a precise value of the antiproton Rydberg constant that surpasses the currently known precision and sets a severe constraint on the antiproton charge (ϪQ p ) and the mass (M p ) that both ͉Q p ϪQ p ͉/e and ͉M p ϪM p ͉/M p be less than 5ϫ10 Ϫ7 , when a more precisely known constraint on the charge-to-mass ratio is combined. Thus we have opened a possibility of determining fundamental constants of the antiproton.

In the scanning electron microscope (SEM), using electron backscattered diffraction (EBSD), it is possible to measure the spacing of the layers in the reciprocal lattice. These values are of great use in confirming the identification of phases. The technique derives the layer spacing from the HOLZ rings which appear in patterns from many materials. The method adapts results from convergent-beam electron diffraction (CBED) in the transmission electron microscope (TEM). For many materials the measured layer spacing compares well with the calculated layer spacing. A noted exception is for higher atomic number materials. In these cases an extrapolation procedure is described that requires layer spacing measurements at a range of accelerating voltages. This procedure is shown to improves the accuracy of the technique significantly. The application of layer spacing measurements in EBSD is shown to be of use for the analysis of two polytypes of Sic.

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