uncertainty. However, in the case of fundamental constants or tests of physical theory, the uncertainty naturally entered directly.

Responding to a generally accepted need to improve this reference transition, NBS mounted an effort to extend the optically based measurement chain into the y-ray region. Results for both the 411 keV and the 675 keV transitions in a strong 198Au source activated in the NBS reactor were reported in 1978 along with new measurements of nine transitions in 192Ir covering the range from 205 keV to 612 keV. In the case of the 411 keV line from 198 Au the result was 25 × 10 higher than the previous value and claimed a forty-fold improvement in accuracy [11].

The combined effects of this initial work and subsequent efforts toward improved linkages among the several wavelength regions have effectively unified the entire electromagnetic scale. The efforts arising from the subject paper may be thought of as beginning the process of extending the reach of frequency synthesis from the visible wavelength region into the domain of x rays and y rays. The improved visible-to-x-ray and visible-to-y-ray connections yielded new values for certain elementary particle masses, more critical tests of quantum electrodynamics (QED) (in the spectroscopy of one-electron heavy ions), a new, SI-based, all-Z tabulation of x-ray transitions, and improved estimates of nuclear binding energies with sufficient accuracy to impact nuclear mass values. Aside from these developments, which were anticipated, the NIST y-ray instrumentation has had significant unanticipated usefulness in the determination of lifetimes of nuclear excited states in the sub-picosecond range and determination of interatomic potentials in the 10 eV to 100 eV range.

Several of the national metrology institutes (NMIS) have formed an international Avogadro group focusing on a possible atomic replacement for the artifact kilogram. Major programs are currently underway in Germany, Japan, Italy, and Australia. The needed isotopic abundance ratios are being determined at the Institute for Reference Materials and Measurements (IRMM) in Belgium, sponsored by the European Union. Most of the procedures in this worldwide effort are direct descendants of the initial NBS effort of the 1970's. NIST no longer has significant activity in this area with the exception of relative lattice parameter measurements and ad hoc contributions to the understanding of the troublesome molar volume anomaly in the period from 1994 to 2000. Overall, the initial Avogadro work at NBS led to improved methods of measurement in the areas of density, displacement, and molar mass as well as to the viable possibility of an atomically based replacement for the artifact kilogram.

The first generation of y-ray measurements at NBS used radioactive sources activated in the NBS reactor. Extension of this work to higher energies required access to short-lived excited nuclei only accessible through targets internal to a high flux reactor. Only the research reactor at the Institut Laue-Langevin (ILL) in Grenoble is configured to allow access to such sources. A new y-ray instrument specifically matched to this application was installed at the ILL in the mid-eighties and is now included in the ILL facilities inventory as GAMS4.

GAMS4 extends the optically based y-ray wavelength scale to energies far higher than were accessible with activated sources from the NBS reactor. It has allowed determination of specific y-ray transition energies leading to new values for the neutron mass [17] and to the possibility of a y-ray/atomic mass determination of the molar Planck constant [18]. The neutron mass was addressed at an early stage and recently revisited with further improved results [19]. Because of the evolution in other parts of the fundamental physical constants, the molar Planck constant is now accurately established indirectly. The associated y-ray measurements now are verifiers of high accuracy trap-based mass spectrometry results.

In addition to its use in high accuracy measurements, GAMS4 delivers higher spectroscopic resolving power than had been available previously. This exceptional resolution revealed (initially unexpected) broadening and fine-scale structural detail within individual y-ray profiles. The basic understanding of these line shapes as recoil-induced Doppler profiles, modulated by collisional deceleration, emerged from a brief but very fruitful period in 1987 [20]. Our principal ILL collaborators, Hans Börner and his associates, have further developed the understanding of this complex process [21]. GAMS4 is now seen as an effective means for determination of nuclear excited state lifetimes in the sub-picosecond domain [22] and a fertile test bed for models of interatomic potentials in the 10 eV to 100 eV range [23]. This work has been widely recognized in Europe. It was identified as one of the two most significant nuclear physics results for 1992 [24]. Börner received the 1990 Roentgen prize of the German Physical Society, and a student who used GAMS4 for his thesis research received the F. Schlafli Prize of the Swiss Academy of Natural Sciences [25].

Two international workshops on applications of high precision y-ray spectroscopy have now taken place. The first was in Grenoble in 1992, and the second, in South Bend, Indiana, in 1998, is summarized in a special issue of the NIST Journal of Research, January-February 2000. Most contributions to these meetings were based

on experimental work carried out using GAMS4 or on theoretical developments in molecular dynamic simulations attuned to past or future experimental results from GAMS4. As an ILL user facility, GAMS4 applications are part of the normal proposal stream. Up to 2000, when this commentary is being prepared, requests for access to GAMS4 have exceeded available time by a factor of two. In response to this proposal pressure, and to increase the very low efficiency of GAMS4, the ILL has undertaken new instrument development. This new facility, GAMS5, is operational but still under development.

Publication of the first comprehensive (all-Z) theoretical study of x-ray transition energies [26] came just after the first few of the new NBS experimental measurements. The extraordinary clarity of the initial comparisons and the unexpected linear Z-dependence of the discrepancy invited extension and refinement on the part of both theory and experiment. This first comprehensive calculation was in the Dirac-HartreeSlater framework, and the puzzling Z-dependence shown in Fig. 3 was found to be due to use of incorrect values for nuclear radii. Subsequent refinements included some relativistic corrections and inclusion of a properly diffuse nuclear boundary [27].

Following this early period, a collaboration with Paul Indelicato (Paris) was initiated, aimed at progressively more refined, more rigorous and more detailed calculations. These initial efforts involved theoretical work at the level of multi-configuration Dirac-Fock with approximate allowance for QED effects. As this work progressed through stages of increasing refinement and understanding, it became clear that hole-state dynamics would have to be considered. NIST was fortunate in this respect to engage the collaboration of Eva Lindroth, who brought the techniques of many-body perturbation theory to bear on estimation of level shifts due to coupling of inner vacancy states to their associated decay continua [28].

All of these theoretical developments have now been linked with an expanded and improved experimental framework to produce a new and unprecedented view of principal x-ray transitions for all elements from neon to fermium. Previous attempts at such a synoptic overview have been for the most part entirely empirical, while there have been a few attempts to produce a comprehensive theoretical database. The NIST effort has combined these two approaches with certain important changes. First, the experimental database is skeletal rather than comprehensive. Items included in the experimental

database were either measured directly in accordance with the best of modern practice, or were referenced to other transitions that had been directly measured according to best practice. Second, the theoretical component was constructed with a high level of rigor that included not only a multi-configuration basis set with relativistic and QED corrections, but also the modification of these levels due to their coupling to associated decay continua.

Richard Deslattes began work in the Crystal Chemistry Section of the Analytical Chemistry Division in 1962. He subsequently headed a newly named. Quantum Metrology Section in the Physics Division of the Center for Absolute Physical Quantities. This Section became for a brief time the Quantum Metrology Division in the Physics Laboratory. Its remnants remain as the Quantum Metrology Group of the Atomic Physics Division of the NIST Physics Laboratory. In 1981-2 he served as Director of the Physics Division of the

National Science Foundation. In 1983 he was designated as a Senior NBS Fellow. In 1984-5 he was a U.S. Senior Awardee of the Alexander von Humboldt Stiftung, visiting the University of Heidelberg and working at the Max Planck Institute for Nuclear Physics, the Gesellschaft für Schwerionenforschung and the Institut Laue-Langevin. His awards include the Gold and Silver Medals of the Commerce Department.

Albert Henins came to NBS in 1970 as a Physicist. He continued to serve in that capacity until his retirement in 1998.

Prepared by Richard D. Deslattes.

Bibliography

[1] Richard D. Deslattes and A. Henins, X-Ray to Visible Wavelength Ratios, Phys. Rev. Lett. 31, 972-975 (1973).

[2] U. Bonse and M. Hart, An X-ray interferometer, Appl. Phys. Lett. 6, 155-156 (1965).

[3] M. Hart, An Ångström Ruler, Br. J. Appl. Phys., Ser. 2 1, 1405-1408 (1968).

[4] U. Bonse and E. te Kaat, A Two-Crystal X-Ray Interferometer, Z. Phys. 214, 16-21 (1968).

[5] Richard D. Deslattes, Optical and X-Ray Interferometry of a Silicon Lattice Spacing, Appl. Phys. Lett. 15, 386-388 (1969). [6] J. Martin, U. Kuetgens, J. Stümpel, and P. Becker, The silicon lattice parameter—an invariant quantity of nature?, Metrologia 35, 811-817 (1998).

[7] Peter Becker, Klaus Dorenwendt, Gerhard Ebeling, Rolf Lauer, Wolfgang Lucas, Reinhard Probst, Hans-Joachim Rademacher, Gerhard Reim, Peter Seyfried, and Helmut Siegert, Absolute Measurement of the (220) Lattice Plane Spacing in a Silicon Crystal, Phys. Rev. Lett. 46, 1540-1543 (1981).

[8] Richard D. Deslattes, Mitsuru Tanaka, Geoffrey L. Greene, Albert Henins, and Ernest G. Kessler, Jr., Remeasurement of a Silicon Lattice Period, IEEE Trans. Instrum. Meas. IM-36, 166169 (1987).

[9] R. D. Deslattes, A. Henins, H. A. Bowman, R. M. Schoonover, C. L. Carroll, I. L. Barnes, L. A. Machlan, L. J. Moore, and W. R. Shields, Determination of the Avogadro Constant, Phys. Rev. Lett. 33, 463-466 (1974).

[10] R. D. Deslattes, A. Henins, R. M. Schoonover, C. L. Carroll, and H. A. Bowman, Avogadro Constant-Corrections to an Earlier Report, Phys. Rev. Lett. 36, 898-900 (1976).

198

[11] E. G. Kessler, Jr., R. D. Deslattes, A. Henins, and W. C. Sauder, Redetermination of Au and 192Ir y-Ray Standards between 0.1 and 1.0 MeV, Phys. Rev. Lett. 40, 171-174 (1978). [12] E. G. Kessler, Jr., R. D. Deslattes, and A. Henins, Wavelength of the W Ka, x-ray line, Phys. Rev. A 19, 215-218 (1979). [13] E. G. Kessler, Jr., R. D. Deslattes, D. Girard, W. Schwitz, L. Jacobs, and O. Renner, Mid-to-high-Z precision x-ray measurements, Phys. Rev. A 26, 2696-2706 (1982).

[14] Ivars Henins and J. A. Bearden, Silicon-Crystal Determination of the Absolute Scale of X-Ray Wavelengths, Phys. Rev. 135A, A890-A898 (1964).

[15] H. A. Bowman, R. M. Schoonover, and C. L. Carroll, The Utilization of Solid Objects as Reference Standards in Density Measurements, Metrologia 10, 117-121 (1974).

[16] I. L. Barnes, L. J. Moore, L. A. Machlan, T. J. Murphy, and W. R. Shields, Absolute Isotopic Abundance Ratios and the Atomic Weight of a Reference Sample of Silicon, J. Res. Natl. Bur. Stand. 79A, 727-735 (1975).

[17] G. L. Greene, E. G. Kessler, Jr., R. D. Deslattes, and H. Börner, New Determination of the Deuteron Binding Energy and the Neutron Mass, Phys. Rev. Lett. 56, 819-822 (1986).

[18] E. G. Kessler, G. L. Greene, M. S. Dewey, R. D. Deslattes, H. Börner, and F. Hoyler, High accuracy, absolute wavelength determination of capture gamma-ray energies for E≤5 MeV and the direct determination of binding energies in light nuclei, J. Phys. G: Nucl. Phys. 14 Suppl., S167-S174 (1988).

[19] E. G. Kessler, Jr., M. S. Dewey, R. D. Deslattes, A. Henins, H. G. Börner, M. Jentschel, C. Doll, and H. Lehmann, The deuteron binding energy and the neutron mass, Phys. Lett. A 255, 221-229 (1999).

[20] H. G. Börner, J. Jolie, F. Hoyler, S. Robinson, M. S. Dewey, G. Greene, E. Kessler, and R. D. Deslattes, Determination of Short Lifetimes with Ultra High Resolution (n,y) Spectroscopy, Phys. Lett. B 215, 45-49 (1988).

[21] H. G. Börner, J. Jolie, S. J. Robinson, R. L. Gill, and R. F. Casten, New Reactor Based Methods to Measure Short Lifetimes of Nuclear Excited States, Neutron News 2 (4), 20-24 (1991).

[22] H. G. Börner and J. Jolie, Sub-picosecond Lifetime Measurements by Gamma Ray Induced Doppler Broadening, J. Phys. G: Nucl. Phys. 19, 217-248 (1993).

[23] M. Jentschel, K. H. Heinig, H. G. Börner, J. Jolie, and E. G. Kessler, Atomic collision cascades studied with the CrystalGRID method, Nucl. Instrum. Methods Phys. Res., Sect. B 115, 446-451 (1996).

[24] Encyclopedia Britannica, in Yearbook of Science and the Future (1992) pp. 395-396.

[25] N. Stritt, J. Jolie, M. Jentschel, H. G. Börner, and C. Doll, Investigation of the interatomic potential using the crystal gamma-ray-induced Doppler-broadening method on oriented Ni single crystals, Phys. Rev. B: Condens. Matter 59, 6762-6773 (1999).

[26] Keh-Ning Huang, Michio Aoyagi, Mau Hsiung Chen, Bernd Crasemann, and Hans Mark, Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations, 2≤ Z≤ 106, At. Data Nucl. Data Tables 18, 243291 (1976).

[27] Mau Hsiung Chen, Bernd Crasemann, Michio Aoyagi, Keh-Ning Huang, and Hans Mark, Theoretical Atomic InnerShell Energy Levels, 70≤ Z≤ 106, At. Data Nucl. Data Tables 26, 561-574 (1981).

[28] P. Indelicato and E. Lindroth, Current status of the relativistic theory of inner hole states in heavy atoms, Comments At. Mol. Phys. 32, 197-208 (1996).

The concept of radiation-pressure cooling of atoms was independently suggested in 1975 for the case of a gas of neutral atoms by Hänsch and Schawlow, and for atomic ions bound in an electromagnetic trap by Wineland and Dehmelt. While the notion that momentum exchange from a photon moving in the opposite direction could slow an individual atom was well understood, until this time no one had come up with a means for producing an aggregate cooling of a larger ensemble of atoms (a gas). If all atoms in a hot gas absorb photons, then some will be heated and some cooled, and the ensuing equilibrium temperature is not lowered. The general feature of the cooling concepts is that a gas of atoms or ions can be cooled by ensuring that photon absorption takes place preferentially when the atoms or ions are moving against the flow of photons from a laser.

In 1978, following these ideas, Wineland, Drullinger, and Walls performed their seminal experiment [1] in which they demonstrated the very first radiationpressure cooling below ambient temperature of any atomic species. The key to the experiment was the variation in photon absorption associated with the Doppler frequency shift. They used a collection of positive magnesium ions contained in an electromagnetic trap subjected to laser radiation near the ~280 nm resonance of the magnesium ion. When this laser radiation was tuned slightly below resonance, cooling to below 40 K was observed. For this particular tuning, those ions with motions opposing the laser radiation are Doppler shifted toward resonance and are more likely to absorb photons, thus slowing their motions. Ions moving away from the source are Doppler shifted further from resonance and are thus less likely to absorb photons. Since the re-radiation from this excited state is symmetric, the net effect averaged over the ensemble of atoms is a cooling of the gas of ions. The very next year, Wineland and Itano [2] published a paper providing the first detailed theoretical analysis of laser cooling, which served as the foundation for the rapid development of this field. In ensuing years, they improved their methods and soon cooled ions to millikelvin temperatures.

This experimental demonstration stimulated the development of a large number of ion-cooling groups around the world and encouraged others to attempt to

Fig. 1. A schematic diagram of a linear ion trap using alternating and static electric fields to confine linear arrays or "strings" of ions. The expanded ultraviolet image at the bottom shows the fluorescence image of an array of positive mercury ions.

cool neutral atoms. In fact, it was only a few years later (in 1982) that a beam of neutral atoms was cooled by Bill Phillips and his collaborators at NIST (as described elsewhere in this volume). These ideas have contributed significantly to atomic-clock technology. Clocks using both trapped ions [3] and cooled neutral atoms [4] have now demonstrated frequency uncertainties of a few parts in 1015, an improvement of an order of magnitude over conventional atomic-clock technology. Further improvements will certainly be demonstrated over the next few years. The potential of the cooled-ion standards can be appreciated by recognizing that, for a small group of ions, the systematic frequency shifts are now understood at an uncertainty level of 1 part in 1018.

Based on this early work, NBS established an Ion Storage Group in Boulder; the Group now includes five full-time staff members and a number of postdoctoral associates, guests, and students. After the initial cooling experiments, the methods were improved, but particularly striking results were obtained by cooling at the sideband frequency created by the periodic motion of the trapped ions. Using this method, the Group achieved, for the first time, cooling to the zero-point energy of motion [5,6], the fundamental limit for any cooling technique.

A unique aspect of the ion-cooling work has been the ability to do experiments with individual atoms. The NBS Group developed remarkable techniques that allowed them to observe and control both the motional and internal quantum states of individual ions, and thereby to confirm experimentally some of the fundamental concepts upon which quantum mechanics is based. For example, they observed individual quantum transitions of a single ion with 100 % probability [7], performed Young's classical light interference experiment with radiation scattered by two ions [8], performed absorption spectroscopy on a single ion [9], observed fundamental quantum-projection noise [10], and demonstrated a "Schrödinger-cat" entangled superposition state of an atom [11]. The ability to control completely the states of ions has led them to show that properly coupled ions can perform simple quantum

logic operations [12]. While the realization of a useful quantum computer faces severe obstacles, the projected performance of such a computer is so great that many groups worldwide have now begun to pursue this objective. The NIST Ion-Storage Group continues to work at the forefront of this field.

Another important line of work that grew out of this program has been the study of the behavior of larger groups of ions that form what are called nonneutral plasmas [13]. The NIST Group has cooled these plasmas to the point where they exhibit liquid and even crystalline behavior [14]. The surprising thing is that these cooled plasmas exhibit behavior analogous to that of very dense, hot neutron stars. In addition, they can be controlled well enough to allow precision studies of fundamental equilibria and dynamical behavior.