Electron-impact cross sections for ground state to np excitations of sodium and potassium.Cross sections for electron electron, elementary particle carrying a unit charge of negative electricity. Ordinary electric current is the flow of electrons through a wire conductor (see electricity). The electron is one of the basic constituents of matter. impact excitation excitation Addition of a discrete amount of energy to a system that changes it usually from a state of lowest energy (ground state) to one of higher energy (excited state). For example, in a hydrogen atom, an excitation energy of 10. of atoms are important for modeling of low temperature plasmas and gases. While there are many experimental and theoretical results for excitation to the first excited states, little information is available for excitation to higher states. We present here calculations of excitations from the ground state to the np levels of sodium sodium, a metallic chemical element; symbol Na [Lat. natrium]; at. no. 11; at. wt. 22.98977; m.p. 97.81°C;; b.p. 892.9°C;; sp. gr. 0.971 at 20°C;; valence +1. Sodium is a soft, silver-white metal. (n = 3 through 11) and potassium potassium (pətăs`ēəm), a metallic chemical element; symbol K [Lat. kalium=alkali]; at. no. 19; at. wt. 39.0983; m.p. 63.25°C;; b.p. 760°C;; sp. gr. .862 at 20°C;; valence +1. (n = 4 through 12). We also present a calculation for a transition from the excited sodium level 3p to 3d to show the generality gen·er·al·i·ty n. pl. gen·er·al·i·ties 1. The state or quality of being general. 2. An observation or principle having general application; a generalization. 3. of the method. Scaling formulas developed earlier by Kim Kim orphan wanders streets of India with lama. [Br. Lit.: Kim] See : Adventurousness [Phys. Rev. A 64. 032713 (2001)] for plane-wave Born cross sections are used. These formulas have been shown to be remarkably accurate yet simple to use. We have used a core polarization polarization Property of certain types of electromagnetic radiation in which the direction and magnitude of the vibrating electric field are related in a specified way. potential in a Dirac-Fock wave function code to calculate target atom wave functions and a matching form of the dipole transition operator to calculate oscillator oscillator Mechanical or electronic device that produces a back-and-forth periodic motion. A pendulum is a simple mechanical oscillator that swings with a constant amplitude, requiring the addition of energy at each swing only to compensate for the energy lost because of air strengths and Born cross sections. The scaled Born results here for excitation to the first excited levels are in very good agreement with experimental and other theoretical data, and the results for excitation to the next few levels are in satisfactory agreement with the limited data available. The present results for excitation to the higher levels are believed to be the only data available. Key words: core polarization; electron-impact; excitation cross section; potassium; sodium. ********** 1. Introduction Our scaled Plane-Wave Born (PWB (Printed Wiring Board) An alternate term for printed circuit board. See printed circuit board. ) cross sections for dipole- and spin-allowed excitation from the ground state of neutral hydrogen, helium helium (hē`lēəm), gaseous chemical element; symbol He; at. no. 2; at. wt. 4.0026; m.p. below −272°C; at 26 atmospheres pressure; b.p. −268.934°C; at 1 atmosphere pressure; density 0. , and lithium lithium (lĭth`ēəm) [Gr.,=stone], metallic chemical element; symbol Li; at. no. 3; at. wt. 6.941; m.p. about 180.54°C;; b.p. about 1,342°C;; sp. gr. .534 at 20°C;; valence +1. Lithium is a soft, silver-white metal. were presented in a recent paper in this journal [1]. In this paper, we use the same scaling methods to calculate excitation cross sections for neutral sodium and potassium from their ground states (3s [.sup.2]S for sodium and 4s [.sup.2]S for potassium) to the np [.sup.2]P excited levels. The values of n are from n = 3 to 11 for sodium and n = 4 to 12 for potassium. Throughout the remainder of this paper we use the shorter notation notation: see arithmetic and musical notation. How a system of numbers, phrases, words or quantities is written or expressed. Positional notation is the location and value of digits in a numbering system, such as the decimal or binary system. of ns and np for these [.sup.2]S and [.sup.2]P levels. The scaling method, developed by one of us [2], is applicable to allowed transitions (spin-allowed and dipole-allowed) of neutral atoms. The method uses two simple scaling formulas to convert PWB excitation cross sections into reliable cross sections comparable to the most accurate theoretical or experimental data available for dipole-allowed transitions. The PWB cross sections are calculated from uncorrelated wave functions, and the scaling requires only the binding energy B of the bound electron that is excited, the excitation energy E, and an accurate dipole oscillator strength f for the transition. Simplicity of the method to scale PWB cross sections allows the user to generate a large number of cross sections reliably and quickly. This is particularly useful for modeling of low temperature plasmas and hot gases, where a large number of excitation cross sections is usually required. Polarization of the core electrons Core Electrons: the electrons in an atom that are not valence electrons and therefore do not participate in bonding. An example is carbon: Carbon has a total of 6 electrons, 4 of which are valence electrons, so the remaining 2 electrons must be core electrons. by the valence electron valence electron n. An electron in an outer shell of an atom that can participate in forming chemical bonds with other atoms. valence electron is important in alkali metal alkali metal Any of the six chemical elements in the leftmost group of the periodic table (lithium, sodium, potassium, rubidium, cesium, and francium). They form alkalies when they combine with other elements. atoms. We treat the long-range long-range adj. 1. Of, suitable for, or reaching long distances: long-range missiles. 2. Requiring or involving an extended span of time: long-range planning. effect of core polarization by including a polarization potential explicitly in our calculation of the wave functions of the target atom and we add a term to the dipole-moment operator when calculating the oscillator strength of the transition. The core polarization effect is not very noticeable for sodium but is large for potassium. 2. Outline of Theory The scaling methods for spin-allowed and dipole-allowed transitions are described in earlier papers [1,2]. The first scaling method, the BE scaling, replaces the incident electron energy T in the denominator denominator the bottom line of a fraction; the base population on which population rates such as birth and death rates are calculated. denominator of the PWB cross section by T + B + E, i.e., [[sigma].sub.BE] = [[sigma].sub.PWB][T/(T + B + E)]. (1) This scaling is similar to a scaling for ionization ionization: see ion. ionization Process by which electrically neutral atoms or molecules are converted to electrically charged atoms or molecules (ions) by the removal or addition of negatively charged electrons. cross sections used earlier by Burgess BURGESS. A magistrate of a borough; generally, the chief officer of the corporation, who performs, within the borough, the same kind of duties which a mayor does in a city. In England, the word is sometimes applied to all the inhabitants of a borough, who are called burgesses sometimes it [3], who shifted the incident energy T by B + U, where U is the kinetic energy kinetic energy: see energy. kinetic energy Form of energy that an object has by reason of its motion. The kind of motion may be translation (motion along a path from one place to another), rotation about an axis, vibration, or any combination of of the target electron. However, in the BE scaling adopted by Kim [2] for excitation cross sections, T is shifted by B + E. The BE scaling not only changes the magnitude but also the shape of the original PWB cross sections. The BE scaling corrects the deficiency A shortage or insufficiency. The amount by which federal Income Tax due exceeds the amount reported by the taxpayer on his or her return; also, the amount owed by a taxpayer who has not filed a return. in the collision theory Collision theory is a theory, proposed by Max Trautz and William Lewis in 1916 that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. ; i.e., the use of the PWB approximation approximation /ap·prox·i·ma·tion/ (ah-prok?si-ma´shun) 1. the act or process of bringing into proximity or apposition. 2. a numerical value of limited accuracy. . The second scaling formula, the f scaling, multiplies the entire cross section by the ratio of an accurate f value to the less accurate f value calculated by the actual wave functions used to generate the unscaled PWB cross sections: [[sigma].sub.f] = ([f.sub.accu] / [f.sub.sc])[[sigma].sub.PWB]. (2) where [f.sub.sc] is the single configuration (or uncorrelated) f value and [f.sub.accu] is the more accurate value obtained from correlated cor·re·late v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates v.tr. 1. To put or bring into causal, complementary, parallel, or reciprocal relation. 2. (or multiconfiguration) wave functions or from a reliable experiment. Accurate f values are frequently available [4]. The f scaling compensates for the inadequacy of the wave functions when electron correlation is significant. In principle, the f scaling should compensate for the rather large core polarization effect in the alkali metal atoms. Because the f scaling is such a large correction for potassium, however, we chose to include core polarization explicitly in calculating the PWB cross sections that are our starting values. We use only single configuration wave functions and apply f scaling. With core polarization, the calculated f values are closer to accurate experimental values but the f scaling still gives a noticeable correction. The BE and f scaling may be applied consecutively, i.e., [[sigma].sub.BEf] = ([f.sub.accu] / [f.sub.sc])[[sigma].sub.BE], (3) where [[sigma].sub.BE] is the BE-scaled PWB cross section calculated from single-configuration wave functions. Kim has shown many examples [2] in which the BE scaling alone or in combination with the f scaling transformed PWB cross sections for dipole-allowed and spin-allowed excitations into reliable cross sections comparable to the convergent close coupling (CCC CCC A very speculative grade assigned to a debt obligation by a rating agency. Such a rating indicates default or considerable doubt that interest will be paid or principal repaid. Also called Caa. ) method [5] or accurate experiments. Resonances in the electron-impact excitation cross sections of atoms in the vicinity of the excitation thresholds cannot be accounted for by first-order first-order - Not higher-order. perturbation theories perturbation theory A set of mathematical methods for obtaining approximate solutions to complex equations for which no exact solution is possible or known, generally involving an iterative algorithm in which each new term contributing to the solution has such as the PWB approximation. Hence the present scaled cross sections do not exhibit any resonances. Polarization of the core electrons by valence electrons affects the potential in which the valence electrons move. This is especially important in alkali metals alkali metals, metals found in Group 1 of the periodic table. Compared to other metals they are soft and have low melting points and densities. Alkali metals are powerful reducing agents and form univalent compounds. where the one valence electron is particularly sensitive to any core changes. The polarization can be represented by a classical model and was first used in quantum mechanical calculations by Biermann [6], although the origin of the core-polarization picture can be traced back even to the semiclassical sem·i·clas·si·cal adj. Music 1. Of, relating to, or being a work that in style or form falls between the classical and popular genres. 2. study of the helium atom by Heisenberg [7] in 1926. The most complete quantum approach to the core-polarization effect was presented by Bottcher and Dalgarno [8]. Their theory, which is based on a perturbation perturbation (pŭr'tərbā`shən), in astronomy and physics, small force or other influence that modifies the otherwise simple motion of some object. The term is also used for the effect produced by the perturbation, e.g. approach, leads to asymptotic forms of the core polarization potential [V.sub.p] and corrected dipole transition moment [d.sub.eff] which are in agreement with the classical formulas. Neither classical nor quantum mechanical approaches provide the form of the core-polarization corrections for the small or intermediate r region. Moreover, the asymptotic form for large r diverges for r [right arrow] 0. Therefore, there is a need to introduce an arbitrary Irrational; capricious. The term arbitrary describes a course of action or a decision that is not based on reason or judgment but on personal will or discretion without regard to rules or standards. cutoff function to remove this divergence divergence In mathematics, a differential operator applied to a three-dimensional vector-valued function. The result is a function that describes a rate of change. The divergence of a vector v is given by at r = 0. Migdalek and Baylis Baylis is a surname, and may refer to:
[V.sub.p] = -[[[[alpha].sub.d][r.sup.2]]/[2([r.sup.2] + [r.sub.c.sup.2])[.sup.3]]], (4) [d.sub.eff] = -r[1 - [[[alpha].sub.d]/[([r.sup.2] + [r.sub.c.sup.2])[.sup.3/2]]]], (5) where [[alpha].sub.d] is the static dipole polarizability Polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, which may be caused by the presence of a nearby ion or dipole. of the core and [r.sub.c] is the cutoff radius. Equation (5) can also be used to correct the r in the operator exp exp abbr. 1. exponent 2. exponential (iK * r) of the matrix element for the generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. oscillator strength. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke" put differently , the correction for the dipole transition operator can also be used to introduce the correction for the core polarization in plane-wave Born cross sections. The core-polarization potential [V.sub.p], Eq. (4), as well as the matching form of the dipole transition operator, Eq. (5), were introduced into a Dirac-Fock wave function code to account for the core-polarization effect in wave functions and the dipole transition operator. The polarizabilities used were [[alpha].sub.d] = 0.9457 [a.sub.0.sup.3] for Na and 5.457 [a.sub.0.sup.3] for K, where [a.sub.0] is the Bohr radius In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. (0.529 [Angstrom angstrom (ăng`strəm), abbr. Å, unit of length equal to 10−10 meter (0.0000000001 meter); it is used to measure the wavelengths of visible light and of other forms of electromagnetic radiation, such as ultraviolet ]). The cutoff radii ra·di·i n. A plural of radius. radii Noun a plural of radius were [r.sub.c] = 0.7967 [a.sub.0] and 1.433 [a.sub.0], respectively. 3. Results We present the calculated cross sections for sodium and potassium in Tables 1 and 2. Our PWB cross sections were generated from single configuration Dirac-Fock wave functions. The calculated cross sections are compared to other theories and experiments in Figs. 1-7. The numerical data Numerical data (or quantitative data) is data measured or identified on a numerical scale. Numerical data can be analysed using statistical methods, and results can be displayed using tables, charts, histograms and graphs. in Tables 1 and 2 can be extended to higher incident energies by using the well known Bethe formula The Bethe formula describes the energy loss per distance travelled of swift charged particles (protons, alpha particles, atomic ions, but not electrons) traversing matter (or, alternatively, the stopping power of the material). [10] for the plane-wave Born approximation In scattering theory and, in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. It is the perturbation method applied to scattering by an extended body. for fast (but nonrelativistic) incident electrons. In our notation, the asymptotic expression becomes: [[sigma].sub.asympt](T) = [[4[pi][a.sub.0.sup.2]R]/[T + B + E]][aln(T/R T/R Transceiver T/R Transmit/Receive T/R Transmitter/Receiver (also seen as TR) T/R Thanks and regards T/R Tail Rotor (helicopter) T/R Tip/Ring T/R Trust Receipt T/R Transmission/Reflection ) + b + cR/T]([f.sub.accu] / [f.sub.sc]), (6) where a, b, and c in the square brackets square bracket n. One of a pair of marks, [ ], used to enclose written or printed material or to indicate a mathematical expression considered in some sense a single quantity. are dimensionless constants, T is the incident electron energy, and R is the Rydberg Noun 1. rydberg - a wave number characteristic of the wave spectrum of each element rydberg constant, rydberg unit wave number - the reciprocal of the wavelength of a wave energy (13.61 eV). Equation (6) should be used for T > 3 keV. The values of a, b, and c are included in Tables 1 and 2. Note that a relativistic rel·a·tiv·is·tic adj. 1. Of or relating to relativism. 2. Physics a. Of, relating to, or resulting from speeds approaching the speed of light: relativistic increase in mass. form of the Bethe formula [11] should be used for T > 10 keV. Also, B + E can be omitted in the denominator at this high range of T. The results for excitation of the first resonance resonance, in acoustics resonance, in acoustics: see vibration. resonance, in chemistry resonance, in chemistry: see chemical bond. line of sodium is shown in Fig. 1. BEf-scaled results agree well with the accurate CCC calculations of Bray [12] and the careful experimental values of Phelps Phelps may refer to: In places in the US:
American sculptor and architect whose public works include the Vietnam Veterans Memorial in Washington, D.C. (1982). Noun 1. [13]. Phelps and Lin corrected their optical excitation data for cascading from higher levels using calculated transition probabilities that are in good agreement with experimental values. At low energies, just above the threshold for excitation, our results are in very good agreement with the optical excitation measurements of Enemark and Gallagher Gallagher may refer to: People
United States
The situation is nearly as good for excitation of the first resonance line of potassium, shown in Fig. 2. In this case, we agree with the close coupling optical (CCO (Chief or Corporate Compliance Officer) The executive person in charge of compliance issues, regulatory requirements, internal controls and managing audits within an enterprise or organization. ) calculations of Bray et al. [16] and the experimental measurements of Phelps et al. [17] above about 30 eV, but we are high in the region of the peak cross section by about 30%. The unitarized distorted wave Born calculations of Mitroy [18] above 54 eV are also shown, and agree with the other values. We are in very good agreement with the measurements of Chen and Gallagher [19] in the threshold region. The lowest excitations of Na and K have very large cross sections compared to higher excitations, reflecting the fact that the f values for the former excitations are almost unity, leaving very little for the higher excitations. Excitation to the next resonance levels of sodium and potassium are shown in Figs. 3 and 4. In these cases, our BEf-scaled results differ significantly in the peak region from the optical excitation results [13,17] and the CCC [12] and the CCO [16] calculations respectively. Our Na calculation, however, agrees well with the threshold measurements of Marinkovic, Wang (Wang Laboratories, Inc., Lowell, MA) A computer services and network integration company. Wang was one of the major early contributors to the computing industry from its founder's invention that made core memory possible, to leadership in desktop calculators and word processors. , and Gallagher [20]. Results for excitation to higher resonance levels are given in Tables 1 and 2. While not the purpose of this paper but as an additional verification of the validity of the calculational technique, we have compared the BEf-scaled calculation with experimental data for excitation from the 3p excited level of Na to the 3d level. The results are shown in Fig 5. This figure also shows the unscaled plane-wave Born (PWB) result so that the magnitude of our scaling is evident. Agreement is good with the measurements of Stumpf Stumpf may refer to: People
 rĕs`əns), luminescence in which light of a visible color is emitted from a substance under stimulation or excitation by light or other forms of electromagnetic using Born approximation results and normalized at
high energies to the Born approximation value. The Born approximation is
not valid at energies below about 300 eV but was used nevertheless for
the corrections. They used the Born-Ochkur approximation for the
polarization factor. The 3 [.sup.2][P.sub.1/2] measurements were
converted to 3p to 3d excitation by use of Born approximation results.[FIGURE 1 OMITTED] [FIGURE 2 OMITTED] [FIGURE 3 OMITTED] [FIGURE 4 OMITTED] [FIGURE 5 OMITTED] [FIGURE 6 OMITTED] [FIGURE 7 OMITTED] Figure 6 shows the effect of our scaling formulas on the Born cross section. The figure is for potassium 4s-6p excitation where core polarization is a large effect. The BE-scaling, Eq. (1), makes the largest correction to the Born cross section, decreasing it by a factor of more than 2 in the peak region. Adding the f-scaling, Eq. (2), then raises the cross section by about 10%. Figure 7 shows the effect of the core polarization on the potassium 4s-6p excitation. The cross section with polarization is larger by about a factor of 2 in the peak region. The effect of core polarization (cp) on the f values is small for sodium but large for potassium. This is evident in Figs. 8 and 9 where we have plotted f * (n*)[.sup.3] versus 1/(n*)[.sup.2], where n* is the effective principal quantum number In atomic physics, the principal quantum number symbolized as n is the first of a set of quantum numbers (which includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital. for the upper state. The change in f * (n*)[.sup.3] for potassium (Fig. 9) is much larger than for sodium (Fig. 8). Quantum defect The term quantum defect is highly ambiguous. Various meanings are discussed below. Quantum defect in laser science In laser science, therm quantum defect refers to the fact that the energy of a pump photon is generally higher than that of an signal photon theory predicts that f * (n*)[.sup.3] should extrapolate extrapolate - extrapolation at high n* to a constant value at the ionization threshold and connect smoothly to a value determined from the photoionization Photoionization The ejection of one or more electrons from an atom, molecule, or positive ion following the absorption of one or more photons. The process of electron ejection from matter following the absorption of electromagnetic radiation has been under cross section. Extrapolation (mathematics, algorithm) extrapolation - A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs. If the desired input is outside the range of the known values this is called extrapolation, if it is inside then of the experimental values of f * (n*)[.sup.3] to the ionization threshold (n [right arrow] [infinity infinity, in mathematics, that which is not finite. A sequence of numbers, a1, a2, a3, … , is said to "approach infinity" if the numbers eventually become arbitrarily large, i.e. ]) gives f * (n*)[.sup.3] = 0.0305 for Na and 0.00177 for K. These values agree well with independently measured values from photoionization cross sections of Marr and Creek [31] which give 0.03099 and 0.001735, respectively. The Marr and Creek values are shown in Figs. 8 and 9 as arrows on the left-hand left-hand adj. 1. Of, relating to, or located on the left. 2. Relating to, designed for, or done with the left hand. left-hand Adjective 1. axis. The f values on the NIST (National Institute of Standards & Technology, Washington, DC, www.nist.gov) The standards-defining agency of the U.S. government, formerly the National Bureau of Standards. It is one of three agencies that fall under the Technology Administration (www.technology. website [4] are not in good agreement with the latest experiments. The effect of core polarization on the f values is about 25% for sodium but a factor of 5 for potassium. We have used the accurate calculated f values of Siegel Siegel, a surname, is associated with two ethnic groups. As a Jewish surname Siegel (סג"ל) it could be an acronym of Segan Levi (סגן לוי), meaning "Assistant Levite". et al. [23] for the f scaling of Na, and values from the similar calculation of Migdalek and Kim [24] for the f scaling of K. These results differ by a negligible  This article or section is written like a personal reflection or and may require .Please [ improve this article] by rewriting this article or section in an . amount from experimental f values shown in Figs. 8 and 9. We have used these calculated values, rather than the experimental values, because they are available for the fine structure components, while the best experimental values generally do not distinguish the components. For Na, the experimental f values shown in Fig. 6 are the measurements of Filippov and Prokoviev [25] for n = 3 to n = 8, normalized to the 3s-3p measurement of Volz et al. [26]. For n = 9 to 24, the Na values are from recent measurements of Nawaz et al. [27]. For potassium, the experimental f values shown in Fig. 7 are from Shabanova and Khlyustalov [28] for n = 4 to 14, and Nawaz et al. [27] for higher n. [FIGURE 8 OMITTED] [FIGURE 9 OMITTED] The cross sections for excitation to the higher np leveis are converging con·verge v. con·verged, con·verg·ing, con·verg·es v.intr. 1. a. To tend toward or approach an intersecting point: lines that converge. b. to values that scale as (n*)[.sup.3]. A good estimate for cross sections to higher levels than presented here is to scale the cross sections for n = 11 of Tables 1 and n = 12 of Table 2 by the ratio of the n* values raised to the third power. Accurate wave functions are particularly necessary when the f values are very small, as is the case when the Cooper minimum is near (below or above) the ionization threshold. The Cooper minimum occurs at an energy where the dipole matrix element goes to zero because positive and negative contributions arising from overlap o·ver·lap n. 1. A part or portion of a structure that extends or projects over another. 2. The suturing of one layer of tissue above or under another layer to provide additional strength, often used in dental surgery. v. of the lower and upper state wave functions cancel (character) Cancel - (CAN, Control-X) ASCII character 24. each other. The Cooper minimum is particularly evident for alkali alkali (ăl`kəlī) [Arab., al-gili=ashes of saltwort], hydroxide of an alkali metal. Alkalies are readily soluble in water and form strongly basic solutions with a characteristic acrid taste. atoms because of core polarization. The minimum appears closer to the ionization limit in K than in Na because of the latter's larger core polarization. Table 1. Excitation cross sections for dipole- and spin-allowed excitations from the ground state of Na. Excitation energies E in eV, dipole f values from uncorrelated wave functions ([f.sub.sc]), accurate f values ([f.sub.accu]) by Siegel et al. [23], and BEf-scaled excitation cross sections [[sigma].sub.BEf] in [[Angstrom].sup.2] as functions of incident electron energy T in eV. The initial state is 3s [.sup.2]S. The experimental ionization energy B = 5.139077 eV has been used in the scaling. The constants a, b, and c of Eq. (6) are included Final state 3p 4p 5p E 2.104E+00 3.753E+00 4.345E+00 [f.sub.sc] 9.650E-01 1.180E-02 1.591E-03 [f.sub.accu] 9.720E-01 1.331E-02 1.980E-03 Const. a 6.241E+00 4.276E-02 4.981E-03 Const. b 1.611E+01 5.477E-01 1.396E-01 Const. c -2.062E-01 -4.093E-02 -8.539E-03 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2.102298 0 2.5 1.774E+01 3.0 2.508E+01 3.5 2.954E+01 4.0 3.257E+01 6.921E-01 4.5 3.471E+01 1.050E+00 5.0 3.624E+01 1.209E+00 2.882E-01 5.5 3.733E+01 1.294E+00 3.370E-01 6.0 3.811E+01 1.342E+00 3.613E-01 7 3.898E+01 1.379E+00 3.802E-01 8 3.925E+01 1.376E+00 3.821E-01 9 3.916E+01 1.356E+00 3.768E-01 10 3.883E+01 1.326E+00 3.682E-01 15 3.581E+01 1.150E+00 3.162E-01 20 3.251E+01 9.967E-01 2.717E-01 25 2.960E+01 8.758E-01 2.371E-01 30 2.712E+01 7.801E-01 2.100E-01 35 2.503E+01 7.032E-01 1.884E-01 40 2.324E+01 6.400E-01 1.708E-01 45 2.170E+01 5.875E-01 1.562E-01 50 2.037E+01 5.430E-01 1.439E-01 60 1.816E+01 4.719E-01 1.243E-01 70 1.641E+01 4.176E-01 1.095E-01 80 1.500E+01 3.747E-01 9.787E-02 90 1.382E+01 3.400E-01 8.849E-02 100 1.283E+01 3.114E-01 8.077E-02 110 1.198E+01 2.873E-01 7.431E-02 120 1.125E+01 2.667E-01 6.882E-02 130 1.060E+01 2.490E-01 6.409E-02 140 1.004E+01 2.336E-01 5.998E-02 150 9.531E+00 2.200E-01 5.637E-02 160 9.078E+00 2.079E-01 5.318E-02 170 8.669E+00 1.971E-01 5.033E-02 180 8.299E+00 1.875E-01 4.778E-02 190 7.961E+00 1.787E-01 4.547E-02 200 7.652E+00 1.708E-01 4.339E-02 225 6.981E+00 1.538E-01 3.893E-02 250 6.427E+00 1.399E-01 3.531E-02 275 5.960E+00 1.284E-01 3.232E-02 300 5.561E+00 1.187E-01 2.980E-02 350 4.913E+00 1.032E-01 2.580E-02 400 4.409E+00 9.140E-02 2.276E-02 450 4.005E+00 8.206E-02 2.036E-02 500 3.674E+00 7.450E-02 1.843E-02 600 3.160E+00 6.299E-02 1.550E-02 700 2.780E+00 5.464E-02 1.339E-02 800 2.486E+00 4.828E-02 1.179E-02 900 2.252E+00 4.329E-02 1.054E-02 1000 2.060E+00 3.925E-02 9.527E-02 2000 1.141E+00 2.058E-02 4.904E-03 3000 8.045E-01 1.409E-02 3.325E-03 Final state 6p 7p 8p E 4.624E+00 4.778E+00 4.872E+00 [f.sub.sc] 4.480E-04 1.810E-04 9.100E-05 [f.sub.accu] 6.020E-04 2.580E-04 1.340E-04 Const. a 1.319E-03 5.160E-04 2.530E-04 Const. b 5.822E-02 3.037E-02 1.802E-02 Const. c -3.035E-03 -1.417E-03 -7.780E-04 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2.102298 2.5 3.0 3.5 4.0 4.5 5.0 1.072E-01 4.788E-02 2.325E-02 5.5 1.418E-01 7.414E-02 4.395E-02 6.0 1.573E-01 8.479E-02 5.154E-02 7 1.691E-01 9.261E-02 5.699E-02 8 1.709E-01 9.399E-02 5.801E-02 9 1.688E-01 9.297E-02 5.744E-02 10 1.650E-01 9.093E-02 5.619E-02 15 1.414E-01 7.781E-02 4.806E-02 20 1.211E-01 6.658E-02 4.109E-02 25 1.054E-01 5.790E-02 3.572E-02 30 9.321E-02 5.114E-02 3.154E-02 35 8.348E-02 4.577E-02 2.821E-02 40 7.557E-02 4.141E-02 2.552E-02 45 6.903E-02 3.780E-02 2.329E-02 50 6.352E-02 3.477E-02 2.142E-02 60 5.479E-02 2.997E-02 1.845E-02 70 4.818E-02 2.634E-02 1.621E-02 80 4.300E-02 2.349E-02 1.445E-02 90 3.884E-02 2.120E-02 1.304E-02 100 3.541E-02 1.932E-02 1.188E-02 110 3.254E-02 1.775E-02 1.091E-02 120 3.011E-02 1.642E-02 1.009E-02 130 2.802E-02 1.527E-02 9.383E-03 140 2.620E-02 1.428E-02 8.769E-03 150 2.461E-02 1.340E-02 8.232E-03 160 2.320E-02 1.263E-02 7.757E-03 170 2.194E-02 1.194E-02 7.334E-03 180 2.082E-02 1.133E-02 6.955E-03 190 1.980E-02 1.077E-02 6.613E-03 200 1.888E-02 1.027E-02 6.304E-03 225 1.692E-02 9.199E-03 5.645E-03 250 1.533E-02 8.332E-03 5.111E-03 275 1.402E-02 7.615E-03 4.670E-03 300 1.292E-02 7.012E-03 4.299E-03 350 1.116E-02 6.056E-03 3.712E-03 400 9.833E-03 5.331E-03 3.266E-03 450 8.788E-03 4.762E-03 2.917E-03 500 7.946E-03 4.303E-03 2.635E-03 600 6.672E-03 3.610E-03 2.209E-03 700 5.753E-03 3.110E-03 1.903E-03 800 5.058E-03 2.733E-03 1.672E-03 900 4.515E-03 2.438E-03 1.491E-03 1000 4.078E-03 2.201E-03 1.346E-03 2000 2.085E-03 1.122E-03 6.850E-04 3000 1.408E-03 7.560E-04 4.610E-04 Final state 9p 10p 11p E 4.934E+00 4.976E+00 5.007E+00 [f.sub.sc] 5.200E-05 3.300E-05 2.200E-05 [f.sub.accu] 7.900E-05 5.100E-05 3.500E-05 Const. a 1.430E-04 8.900E-05 5.900E-05 Const. b 1.163E-02 7.972E-03 5.714E-03 Const. c -4.750E-04 -3.130E-04 -2.180E-04 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2.102298 2.5 3.0 3.5 4.0 4.5 5.0 5.5 2.832E-02 1.936E-02 1.384E-02 6.0 3.389E-02 2.355E-02 1.706E-02 7 3.781E-02 2.646E-02 1.927E-02 8 3.857E-02 2.703E-02 1.971E-02 9 3.822E-02 2.680E-02 1.955E-02 10 3.740E-02 2.623E-02 1.913E-02 15 3.198E-02 2.243E-02 1.636E-02 20 2.733E-02 1.916E-02 1.397E-02 25 2.375E-02 1.665E-02 1.214E-02 30 2.096E-02 1.469E-02 1.071E-02 35 1.875E-02 1.314E-02 9.577E-03 40 1.695E-02 1.188E-02 8.658E-03 45 1.547E-02 1.084E-02 7.899E-03 50 1.422E-02 9.963E-03 7.262E-03 60 1.225E-02 8.580E-03 6.253E-03 70 1.076E-02 7.534E-03 5.490E-03 80 9.591E-03 6.715E-03 4.893E-03 90 8.653E-03 6.058E-03 4.414E-03 100 7.883E-03 5.518E-03 4.020E-03 110 7.239E-03 5.067E-03 3.691E-03 120 6.693E-03 4.684E-03 3.412E-03 130 6.224E-03 4.355E-03 3.173E-03 140 5.816E-03 4.070E-03 2.965E-03 150 5.459E-03 3.820E-03 2.782E-03 160 5.143E-03 3.599E-03 2.621E-03 170 4.863E-03 3.402E-03 2.478E-03 180 4.611E-03 3.226E-03 2.349E-03 190 4.384E-03 3.067E-03 2.234E-03 200 4.179E-03 2.923E-03 2.129E-03 225 3.741E-03 2.617E-03 1.905E-03 250 3.387E-03 2.369E-03 1.725E-03 275 3.094E-03 2.164E-03 1.575E-03 300 2.848E-03 1.992E-03 1.450E-03 350 2.458E-03 1.719E-03 1.251E-03 400 2.163E-03 1.512E-03 1.100E-03 450 1.931E-03 1.350E-03 9.820E-04 500 1.744E-03 1.219E-03 8.870E-04 600 1.462E-03 1.022E-03 7.430E-04 700 1.259E-03 8.800E-04 6.400E-04 800 1.106E-03 7.720E-04 5.620E-04 900 9.860E-04 6.890E-04 5.010E-04 1000 8.900E-04 6.210E-04 4.520E-04 2000 4.520E-04 3.160E-04 2.290E-04 3000 3.040E-04 2.120E-04 1.540E-04 Table 2. Excitation cross sections for dipole- and spin-allowed excitations from the ground state of K. Excitation energies E in eV, dipole f values from uncorrelated wave functions ([f.sub.sc]), accurate f values ([f.sub.accu]) by Migdalek and Kim [24], and BEf-scaled excitation cross sections [[sigma].sub.BEf] in [[Angstrom].sup.2] as functions of incident electron energy T in eV. The initial state is 4s [.sup.2]S. The experimental ionization energy B = 4,340665 eV has been used in the scaling. The constants a, b, and c of Eq. (6) are included Final state 4p 5p 6p E 1.615E+00 3.064E+00 3.596E+00 [f.sub.sc] 1.047E+00 7.620E-03 7.240E-04 [f.sub.accu] 1.002E+00 8.220E-03 8.200E-04 Const. a 8.820E+00 3.383E-02 2.740E-03 Const. b 2.437E+01 6.465E-01 1.602E-01 Const. c -2.041E-01 -3.857E-02 -6.663E-03 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 1.614726 0 2.0 3.029E+01 2.5 4.308E+01 3.0 5.062E+01 3.5 5.552E+01 1.251E+00 4.0 5.880E+01 1.590E+00 3.239E-01 4.5 6.099E+01 1.747E+00 4.153E-01 5.0 6.243E+01 1.826E+00 4.552E-01 5.5 6.332E+01 1.863E+00 4.740E-01 6 6.381E+01 1.874E+00 4.818E-01 7 6.397E+01 1.855E+00 4.807E-01 8 6.345E+01 1.809E+00 4.694E-01 9 6.252E+01 1.751E+00 4.540E-01 10 6.137E+01 1.689E+00 4.373E-01 15 5.477E+01 1.403E+00 3.596E-01 20 4.879E+01 1.187E+00 3.018E-01 25 4.387E+01 1.027E+00 2.593E-01 30 3.984E+01 9.036E-01 2.270E-01 35 3.651E+01 8.069E-01 2.019E-01 40 3.373E+01 7.291E-01 1.817E-01 45 3.136E+01 6.651E-01 1.652E-01 50 2.932E+01 6.115E-01 1.514E-01 60 2.600E+01 5.270E-01 1.298E-01 70 2.340E+01 4.633E-01 1.137E-01 80 2.131E+01 4.136E-01 1.011E-01 90 1.959E+01 3.736E-01 9.101E-02 100 1.814E+01 3.409E-01 8.278E-02 110 1.691E+01 3.135E-01 7.593E-02 120 1.585E+01 2.903E-01 7.013E-02 130 1.492E+01 2.703E-01 6.515E-02 140 1.411E+01 2.529E-01 6.085E-02 150 1.338E+01 2.377E-01 5.708E-02 160 1.273E+01 2.243E-01 5.375E-02 170 1.215E+01 2.123E-01 5.079E-02 180 1.162E+01 2.016E-01 4.814E-02 190 1.114E+01 1.919E-01 4.576E-02 200 1.070E+01 1.831E-01 4.361E-02 225 9.750E+00 1.644E-01 3.902E-02 250 8.965E+00 1.492E-01 3.531E-02 275 8.305E+00 1.366E-01 3.225E-02 300 7.742E+00 1.260E-01 2.968E-02 350 6.831E+00 1.092E-01 2.561E-02 400 6.123E+00 9.641E-02 2.252E-02 450 5.557E+00 8.635E-02 2.011E-02 500 5.093E+00 7.823E-02 1.817E-02 600 4.376E+00 6.591E-02 1.523E-02 700 3.845E+00 5.700E-02 1.312E-02 800 3.436E+00 5.025E-02 1.152E-02 900 3.110E+00 4.495E-02 1.028E-02 1000 2.844E+00 4.069E-02 9.274E-03 2000 1.571E+00 2.109E-02 4.722E-03 3000 1.106E+00 1.436E-02 3.182E-03 Final state 7p 8p 9p E 3.853E+00 3.996E+00 4.084E+00 [f.sub.sc] 1.480E-04 4.500E-05 1.800E-05 [f.sub.accu] 1.750E-04 5.500E-05 2.200E-05 Const. a 5.240E-04 1.540E-04 5.900E-05 Const. b 6.641E-02 3.461E-02 2.055E-02 Const. c -2.013E-03 -8.140E-04 -3.950E-04 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 1.614726 2.0 2.5 3.0 3.5 4.0 6.216E-02 4.5 1.643E-01 8.185E-02 4.718E-02 5.0 1.895E-01 9.918E-02 5.972E-02 5.5 2.011E-01 1.068E-01 6.506E-02 6 2.061E-01 1.102E-01 6.746E-02 7 2.072E-01 1.113E-01 6.840E-02 8 2.027E-01 1.091E-01 6.713E-02 9 1.962E-01 1.057E-01 6.503E-02 10 1.889E-01 1.018E-01 6.263E-02 15 1.550E-01 8.339E-02 5.130E-02 20 1.297E-01 6.974E-02 4.288E-02 25 1.112E-01 5.975E-02 3.673E-02 30 9.726E-02 5.221E-02 3.208E-02 35 8.637E-02 4.634E-02 2.847E-02 40 7.766E-02 4.165E-02 2.558E-02 45 7.054E-02 3.782E-02 2.323E-02 50 6.461E-02 3.463E-02 2.126E-02 60 5.532E-02 2.963E-02 1.819E-02 70 4.836E-02 2.590E-02 1.589E-02 80 4.296E-02 2.300E-02 1.411E-02 90 3.865E-02 2.068E-02 1.269E-02 100 3.513E-02 1.879E-02 1.153E-02 110 3.219E-02 1.721E-02 1.056E-02 120 2.971E-02 1.588E-02 9.741E-03 130 2.759E-02 1.475E-02 9.041E-03 140 2.575E-02 1.376E-02 8.436E-03 150 2.414E-02 1.290E-02 7.906E-03 160 2.272E-02 1.214E-02 7.439E-03 170 2.146E-02 1.146E-02 7.024E-03 180 2.033E-02 1.086E-02 6.654E-03 190 1.932E-02 1.031E-02 6.320E-03 200 1.840E-02 9.821E-03 6.018E-03 225 1.645E-02 8.775E-03 5.377E-03 250 1.487E-02 7.932E-03 4.859E-03 275 1.357E-02 7.236E-03 4.432E-03 300 1.248E-02 6.653E-03 4.075E-03 350 1.076E-02 5.730E-03 3.509E-03 400 9.450E-03 5.033E-03 3.081E-03 450 8.429E-03 4.487E-03 2.747E-03 500 7.608E-03 4.049E-03 2.478E-03 600 6.368E-03 3.387E-03 2.072E-03 700 5.478E-03 2.912E-03 1.781E-03 800 4.807E-03 2.554E-03 1.562E-03 900 4.283E-03 2.275E-03 1.391E-03 1000 3.862E-03 2.051E-03 1.254E-03 2000 1.955E-03 1.036E-03 6.330E-04 3000 1.313E-03 6.950E-04 4.240E-04 Final state 10p 11p 12p E 4.142E+00 4.183E+00 4.212E+00 [f.sub.sc] 8.000E-06 4.000E-06 2.000E-06 [f.sub.accu] 1.100E-05 6.000E-06 3.000E-06 Const. a 2.700E-05 1.400E-05 8.000E-06 Const. b 1.329E-02 9.119E-03 6.547E-03 Const. c -2.170E-04 -1.300E-04 -8.400E-05 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 1.614726 2.0 2.5 3.0 3.5 4.0 4.5 2.989E-02 2.022E-02 1.439E-02 5.0 3.931E-02 2.747E-02 2.009E-02 5.5 4.320E-02 3.040E-02 2.236E-02 6 4.495E-02 3.172E-02 2.338E-02 7 4.571E-02 3.232E-02 2.385E-02 8 4.490E-02 3.177E-02 2.346E-02 9 4.350E-02 3.079E-02 2.274E-02 10 4.191E-02 2.966E-02 2.190E-02 15 3.431E-02 2.428E-02 1.793E-02 20 2.867E-02 2.029E-02 1.498E-02 25 2.455E-02 1.737E-02 1.282E-02 30 2.145E-02 1.517E-02 1.120E-02 35 1.903E-02 1.346E-02 9.935E-03 40 1.710E-02 1.209E-02 8.926E-03 45 1.552E-02 1.098E-02 8.102E-03 50 1.421E-02 1.005E-02 7.416E-03 60 1.215E-02 8.593E-03 6.343E-03 70 1.062E-02 7.506E-03 5.540E-03 80 9.424E-03 6.663E-03 4.918E-03 90 8.473E-03 5.990E-03 4.421E-03 100 7.697E-03 5.441E-03 4.016E-03 110 7.050E-03 4.984E-03 3.678E-03 120 6.504E-03 4.598E-03 3.393E-03 130 6.037E-03 4.267E-03 3.149E-03 140 5.632E-03 3.981E-03 2.938E-03 150 5.278E-03 3.731E-03 2.753E-03 160 4.966E-03 3.510E-03 2.590E-03 170 4.689E-03 3.314E-03 2.446E-03 180 4.442E-03 3.139E-03 2.316E-03 190 4.219E-03 2.982E-03 2.200E-03 200 4.017E-03 2.839E-03 2.095E-03 225 3.589E-03 2.536E-03 1.871E-03 250 3.243E-03 2.292E-03 1.691E-03 275 2.958E-03 2.090E-03 1.542E-03 300 2.719E-03 1.921E-03 1.418E-03 350 2.341E-03 1.654E-03 1.220E-03 400 2.056E-03 1.452E-03 1.071E-03 450 1.832E-03 1.294E-03 9.550E-04 500 1.653E-03 1.168E-03 8.610E-04 600 1.382E-03 9.760E-04 7.200E-04 700 1.188E-03 8.390E-04 6.190E-04 800 1.042E-03 7.360E-04 5.430E-04 900 9.270E-04 6.550E-04 4.830E-04 1000 8.360E-04 5.900E-04 4.350E-04 2000 4.220E-04 2.980E-04 2.190E-04 3000 2.820E-04 1.990E-04 1.470E-04 Acknowledgments See About this product. We are pleased to acknowledge J. P. Desclaux and P. Indelicato for use of their computer program for calculation of the Dirac-Fock wave functions and plane-wave Born cross sections. We also gratefully acknowledge partial financial support by the Office of Fusion Energy Sciences of the U.S. Department of Energy. Accepted: October October: see month. 1, 2004 Available online: http://www.nist.gov/jres 4. References [1] P. M. Stone, Y.-K. Kim, and J. P. Desclaux, J. Res Natl. Inst. Stand. Technol. 107, 327 (2002). [2] Y.-K. Kim, Phys. Rev. A 64, 032713 (2001). [3] See L. Vriens, in Case Studies in Atomic Physics atomic physics Scientific study of the structure of the atom, its energy states, and its interaction with other particles and fields. The modern understanding of the atom is that it consists of a heavy nucleus of positive charge surrounded by a cloud of light, negatively , Vol. I, E. W. McDaniel McDaniel may refer to: People:
American surgeon who performed (1809) the first recorded ovariotomy. , eds., North Holland, Amsterdam Amsterdam, city, Netherlands Amsterdam (ăm`stərdăm', Dutch ämstərdäm`), city (1994 pop. 724,096), constitutional capital and largest city of the Kingdom of the Netherlands, North Holland prov. (1969) p. 335. [4] See, for example, NIST's public web site http://physics.nist.gov/cgi-bin/AtData/main_asd (2004). [5] I. Bray and A. T. Stelbovics, Adv. At. Mol. Opt. Phys. 35, 209 (1995). [6] L. Biermann, Z. Astrophys. 22, 157 (1943). [7] W. Heisenberg, Z. Phys. 39, 499 (1926). [8] C. Bottcher and A. Dalgarno, Proc. Roy Roy, city (1990 pop. 24,603), Weber co., N Utah, near Great Salt Lake; settled by Mormons 1877, inc. 1937. Computer equipment is manufactured, and many residents work at nearby Hill Air Force Base. . Soc. A 340, 187 (1974). [9] J. Migdalek and W. E. Baylis, J. Phys. B 11, L497 (1978). [10] M. Inokuti, Rev. Mod. Phys. 43, 297 (1971). [11] See for example, Y.-K. Kim, J. P. Santos Santos (sän`t  s), city (1996 pop. 412,288), São Paulo state, SE Brazil, on the island of São Vicente in the Atlantic just off the mainland. , and F. Parente.
Phys. Rev. A 62, 052710 (2000).[12] I. Bray, Phys. Rev. A 49, 1066 (1994). [13] J. O. Phelps and C. C. Lin, Phys. Rev. A 24, 1299 (1981). [14] E. A. Enemark and A. Gallagher, Phys. Rev. A 6, 192 (1972). [15] D. L. Moores and D. W. Norcross, J. Phys. B 5, 1482 (1972). [16] I. Bray, D. V. Fursa, and I. E. McCarthy Mc·Car·thy , Joseph Raymond 1908-1957. American politician. A U.S. senator from Wisconsin (1947-1957), he presided over the permanent subcommittee on investigations and held public hearings in which he accused army officials, members of the media, , Phys. Rev. A 47, 3951 (1993). [17] J. O. Phelps, J. E. Solomon Solomon, d. c.930 B.C., king of the ancient Hebrews (c.970–c.930 B.C.), son and successor of David. His mother was Bath-sheba. His accession has been dated to c.970 B.C. According to the Bible. , D. F. Korff, and C. C. Lin, Phys. Rev. A 20, 1418 (1979). [18] J. Mitroy, J. Phys. B 26, 2201 (1993). [19] S. T. Chen and A. C. Gallagher, Phys. Rev. A 17, 551 (1978). [20] B. Marinkovic, P. Wang, and A. Gallagher, Phys. Rev A 46, 2553 (1992). [21] B. Stumpf and A. Gallagher, Phys. Rev. A 32, 3344 (1985). [22] D. L. Moores, D. W. Norcross and V. B. Sheorey, J. Phys. B 7, 371 (1974). [23] W. Siegel, J. Migdalek, and Y.-K. Kim, Atomic Indivisible. An atomic operation, or atomicity, implies an operation that must be performed entirely or not at all. For example, if machine failure prevents a transaction to be processed to completion, the system will be rolled back to the start of the transaction. Data and Nuclear Data Tables 68, 303 (1998). [24] J. Migdalek and Y.-K. Kim, J. Phys. B 31, 1947 (1998). [25] A. Filippov and V. K. Prokofiev Pro·kof·iev , Sergei Sergeyevich 1891-1953. Russian composer whose works include ballets, operas, and the symphonic fairy tale Peter and the Wolf (1936). Noun 1. , Z. Phys. 56, 458 (1929) normalized to Volz et al. [26] U. Volz, M. Majerus, H. Liebel, A. Schmitt Schmitt is a common family name in German. See Smith variations. Schmitt is a very common name in southern Indiana. Schmitt may refer to:
n. A member of a Baltic people constituting the main population of Latvia. [German Lette, from Latvian Latvi.] . 76, 2862 (1996). [27] M. Nawaz, W. A. Faroq, and J-P Connerade, J. Phys. B 25, 5327 (1992). [28] L. N. Shabanova and A. N. Khlyustalov Opt. Spektrosk. (USSR USSR: see Union of Soviet Socialist Republics. ) 59, 123 (1984). [29] B. Marinkovic, V. Pejcev, D. Filipovic, I. Cadez, and L. Vuskovic, J. Phys. B 25, 5179 (1992). [30] Cheng Zhu, Jian-Guo Wang, Yi-Zhi Qu, and Jia-Ming Li, Phys. Rev A 57, 1747 (1998). [31] G. V. Marr and D. M. Creek, Proc. Roy. Soc. A 304, 233 (1968). Philip Philip, tetrarch of Ituraea Philip, d. A.D. 34, tetrarch of Ituraea, son of Herod the Great. He was perhaps the ablest of the Herod dynasty. He is mentioned in the Gospel of St. Luke. M. Stone and Yong-Ki Kim National Institute of Standards and Technology National Institute of Standards and Technology, governmental agency within the U.S. Dept. of Commerce with the mission of "working with industry to develop and apply technology, measurements, and standards" in the national interest. , Gaithersburg, MD 20899-8421 philip.stone@nist.gov See .gov and GovNet. (networking) gov - The top-level domain for US government bodies. yong-ki.kim@nist.gov About the authors: Philip Stone is a Guest Researcher and Yong-Ki Kim is a physicist (retired), both in the Atomic Physics Division of the NIST Physics Laboratory. The National Institute of Standards and Technology is an agency of the Technology Administration, U. S. Department of Commerce. |
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