Electron-impact cross sections for dipole- and spin-allowed excitations of hydrogen, helium, and lithium.Electron-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. cross sections are presented for the dipole- and spin allowed transitions from the ground states to the tip [P.sup.2] states for hydrogen hydrogen (hī`drəjən) [Gr.,=water forming], gaseous chemical element; symbol H; at. no. 1; at. wt. 1.00794; m.p. −259.14°C;; b.p. −252.87°C;; density 0.08988 grams per liter at STP; valence usually +1. 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. , and to the 1snp [P.sup.1] P states for 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. , n = 2 through 10. Two sealing formulas developed earlier by Kim Kim orphan wanders streets of India with lama. [Br. Lit.: Kim] See : Adventurousness [Phys. Rev REV Revolution REV Reverse REV Reverend REV Revision REV Review REV Revised REV Revelations (bible) REV Reversal REV Revolver (Beatles album) REV Reverendo . A 64, 032713 (2001)] for plane-wave Born cross sections are used. The scaled Born cross sections are in excellent agreement with available theoretical and experimental data. Key words: electron-impact; excitation cross section; hydrogen; helium; lithium. 1. Introduction We have scaled Plane-Wave Born (PWB (Printed Wiring Board) An alternate term for printed circuit board. See printed circuit board. ) cross sections to calculate dipole- and spin-allowed excitation cross sections from the ground state of neutral hydrogen, helium, and lithium. The scaling method was developed by one of us (1), and 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 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. being excited, the excitation energy E, and an accurate dipole 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 strength for the transition. The oscillator strength is needed only if electron correlation correlation In statistics, the degree of association between two random variables. The correlation between the graphs of two data sets is the degree to which they resemble each other. strongly affects the f value, i.e., when the wave functions used to calculate the PWB cross section are not accurate. Simplicity Simplicity is the property, condition, or quality of being simple or un-combined. It often denotes beauty, purity or clarity. Simple things are usually easier to explain and understand than complicated ones. Simplicity can mean freedom from hardship, effort or confusion. of the method to scale PWB cross sections allows us to generate a large number of cross sections reliably and quickly. In this paper, we present calculated excitation cross sections for hydrogen from the 1s [S.sup.2] ground state to the tip [P.sup.2] excited states. For helium, the cross sections are given for excitations from the [1s.sup.2] [S.sup.1] ground state to the 1snp [P.sup.1] excited states. For lithium, the results are given for excitations from the [1s.sup.2]2s [S.sup.2] ground state to the [1s.sup.2]np [P.sup.2] states. In all cases, the values of n are from n = 2 through 10. 2. Outline of Theory A PWB cross section for electron-impact excitation, [[sigma].sub.PWB], has the form [[sigma].sub.PWB] 4[pi][a.sup.2.sub.0]R/[[sigma].sup.PWB] = T [F.sub.PWB](T), (1) where T is the incident electron energy, [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 A), 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). The [F.sub.PWB](T) is the collision See CSMA/CD and collision avoidance system. Collision (physics) Any interaction between particles, aggregates of particles, or rigid bodies in which they come near enough to exert a mutual influence, generally with exchange of energy. strength (different from the standard definition by a multiplicative mul·ti·pli·ca·tive adj. 1. Tending to multiply or capable of multiplying or increasing. 2. Having to do with multiplication. mul constant). The first scaling method, BE scaling, replaces 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 Eq. (1) by T + B + E, i.e., [[sigma].sub.BE] = [[sigma].sub.PWB] [T/(T+B+E)] (2) 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 (2), 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 (1) for excitation cross sections, T is shifted by B+E. The BE scaling not only changes the magnitude magnitude, in astronomy, measure of the brightness of a star or other celestial object. The stars cataloged by Ptolemy (2d cent. A.D.), all visible with the unaided eye, were ranked on a brightness scale such that the brightest stars were of 1st magnitude and the 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.PWsc] (3) 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 (3). The f scaling compensates for the inadequacy of the wave functions when electron correlation effect is significant. The BE and f scalings may be applied consecutively, i.e., [[sigma].sub.BEf] = ([f.sub.accu]/[f.sub.sc])[[sigma].sub.BEsc], (4) where [[sigma].sub.BEsc] is the BE-scaled PWB cross section calculated from single-configuration wave functions. Kim has shown many examples (1) 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 con·ver·gence n. 1. The act, condition, quality, or fact of converging. 2. Mathematics The property or manner of approaching a limit, such as a point, line, function, or value. 3. 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 (4) or accurate experiments. In reality, electron-impact excitation cross sections of atoms have resonances in the vicinity of the excitation thresholds caused by the formation of transient A malfunction that occurs at random intervals and lasts for a short duration such as a spike or surge in a power line or a memory cell that intermittently fails. See spike and power surge. transient - 1. compound states between the incident electron and the target atom. 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 cannot account for such compound states, and hence the present scaled cross sections do not exhibit any resonances. 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, 2, and 3 can easily 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). (5) 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 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. , the asymptotic expression becomes: [[sigma].sub.asympt](T) = 4[pi][a.sub.0.sup.2]R/T R/T rather than R/T Related To R/T Real Time R/T Room Temperature R/T Round-Trip (travel booking) R/T Response/Time R/T Running Time R/T Research & Technology R/T Race/Track R/T Rapid Transit R/T Road & Track +B+E [a ln (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]), (5) where a, b, and c are dimensionless constants. Equation (5) should be used for T> 3 keV. The values of a, b, and c are included in Tables 1, 2, and 3. 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 (5) of Eq. (5) should be used for T> 10keV. 3. Theoretical Results We present the calculated cross sections for hydrogen, helium, and lithium in Tables 1-3. 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 CCC results for these elements are from the web site of Bray (6). The experimental results by Sweeney Sweeney in poems by T. S. Eliot, symbolizes the sensual, brutal, and materialistic 20th-century man. [Br. Poetry, Benét, 978] See : Virility et al. (7) for hydrogen include all dipole-allowed and dipole-forbidden states of hydrogen for each n, and hence are higher than the cross sections for just the dipole-allowed excitations. The ionization energies B and the excitation energies E are all experimental values. Only BE scaling is needed for hydrogen as its exact wave functions are known. The accurate f values for helium have been obtained from the detailed variational calculations of Drake drake 1. male duck. 2. loliumtemulentum. (8). The f value for the 2s-2p transition in lithium is from the calculations of Yan et al. (9), while the values for the 2s-np transitions, n = 3 through 7, are from the non-relativistic multiconfiguration calculations including 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. by Qu et al. (10). For the 2s-8p, 9p, and 10p excitations of lithium, we extrapolated f[([n.sup.*]).sup.3] of Qu et al. (10) from n = 5 through n = 7, where [n.sup.*] is the experimental 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. of 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. We had found that the f values by Qu et al. for the 8p and 9p transitions were inconsistent Reciprocally contradictory or repugnant. Things are said to be inconsistent when they are contrary to each other to the extent that one implies the negation of the other. with their values for n < 8. The 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 f[([n.sup.*]).sup.3] is shown in Fig. 8 through [n.sup.*] = 17 and is given by the expression: F[([n.sup.*]).sup.3] = 0.343 + 0.0283/([n.sup.*]) + 0.533/[([n.sup.*]).sup.2] - 6.289/[([n.sup.*]).sup.3] (6) Beyond [n.sup.*] [approximatly equal to] 17, the formula begins to break down but the actual curve should remain flat. At the ionization limit ([n.sup.*] [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. ]), the value of f[([n.sup.*]).sup.3] is extrapolated to be 0.345. It is apparent that for all cases where experimental data and CCC results are available, the scaled PWB cross sections give values that are in good agreement. [FIGURE 1 OMITTED] [FIGURE 2 OMITTED] [FIGURE 3 OMITTED] [FIGURE 4 OMITTED] [FIGURE 5 OMITTED] [FIGURE 6 OMITTED] [FIGURE 7 OMITTED] [FIGURE 8 OMITTED] Table 1 Hydrogen. Excitation energies E in eV, dipole f values, and BE-scaled excitation cross sections [[sigma].sub.BE] in [[Angstrom].sup.2] as functions of incident electron energy T in eV. The experimental ionization energy B = 13.5984 eV has been used in the scaling. The constants a, b, and c of Eq. (5) are included Excitation 1s-2p 1s-3p 1s-4p 1s-5p 1s-6p E 10.204 12.094 12.755 13.061 13.228 f 0.4164 0.0791 0.0290 0.0139 0.00780 Const. a 0.555512 0.089083 0.030956 0.014534 0.008031 Const. b 0.271785 0.060202 0.022984 0.011243 0.006348 Const. c 0.000112 -0.019775 -0.009279 -0.004880 -0.002853 Excitation 1s-7p 1s-8p 1s-9p 1s-10p E 13.328 13.393 13.438 13.470 f 0.004816 0.003185 0.002217 0.001606 Const. a 0.004919 0.003237 0.002246 0.001623 Const. b 0.003939 0.002550 0.001824 0.001323 Const. c -0.001806 -0.001213 -0.000854 -0.000623 T [[sigma].sub.BE] [[sigma].sub.BE] [[sigma].sub.BE] 11 0.15876 12 0.24099 13 0.30186 0.03033 0.00573 14 0.35119 0.04382 0.01274 15 0.39256 0.05372 0.01697 16 0.42786 0.06166 0.02018 17 0.45828 0.06827 0.02278 18 0.48468 0.07387 0.02496 19 0.50768 0.07867 0.02681 20 0.52779 0.08282 0.02840 21 0.54540 0.08642 0.02977 22 0.56084 0.08957 0.03096 23 0.57439 0.09231 0.03200 24 0.58627 0.09472 0.03291 26 0.60580 0.09867 0.03440 28 0.62069 0.10169 0.03554 30 0.63189 0.10398 0.03641 32 0.64013 0.10569 0.03706 34 0.64597 0.10695 0.03754 36 0.64986 0.10782 0.03788 38 0.65216 0.10840 0.03811 40 0.65315 0.10872 0.03825 45 0.65130 0.10870 0.03828 50 0.64520 0.10787 0.03801 55 0.63647 0.10654 0.03756 60 0.62615 0.10490 0.03700 65 0.61489 0.10308 0.03636 70 0.60315 0.10116 0.03569 75 0.59121 0.09919 0.03500 80 0.57929 0.09721 0.03431 85 0.56750 0.09524 0.03362 90 0.55593 0.09331 0.03294 95 0.54465 0.09142 0.03227 100 0.53369 0.08959 0.03162 110 0.51276 0.08607 0.03038 120 0.49322 0.08278 0.02922 130 0.47500 0.07972 0.02814 140 0.45805 0.07686 0.02713 150 0.44227 0.07420 0.02619 160 0.42756 0.07171 0.02531 170 0.41383 0.06940 0.02449 180 0.40100 0.06723 0.02372 190 0.38898 0.06520 0.02301 200 0.37771 0.06330 0.02233 250 0.33045 0.05533 0.01952 300 0.29445 0.04926 0.01737 350 0.26607 0.04447 0.01568 400 0.24309 0.04060 0.01431 450 0.22408 0.03741 0.01318 500 0.20807 0.03471 0.01223 600 0.18254 0.03042 0.01071 700 0.16303 0.02715 0.00956 800 0.14760 0.02456 0.00865 900 0.13505 0.02246 0.00790 1000 0.12463 0.02071 0.00729 1500 0.09094 0.01508 0.00530 2000 0.07236 0.01198 0.00421 3000 0.05214 0.00862 0.00303 T [[sigma].sub.BE] [[sigma].sub.BE] [[sigma].sub.BE] 11 12 13 14 0.00528 0.00267 0.00154 15 0.00752 0.00401 0.00240 16 0.00916 0.00496 0.00300 17 0.01046 0.00570 0.00346 18 0.01154 0.00632 0.00385 19 0.01245 0.00684 0.00417 20 0.01323 0.00728 0.00445 21 0.01391 0.00766 0.00468 22 0.01449 0.00799 0.00489 23 0.01500 0.00828 0.00507 24 0.01544 0.00853 0.00522 26 0.01617 0.00894 0.00548 28 0.01673 0.00925 0.00567 30 0.01715 0.00949 0.00582 32 0.01747 0.00967 0.00593 34 0.01771 0.00981 0.00602 36 0.01787 0.00990 0.00608 38 0.01799 0.00997 0.00612 40 0.01806 0.01001 0.00614 45 0.01808 0.01002 0.00615 50 0.01796 0.00996 0.00611 55 0.01775 0.00984 0.00604 60 0.01749 0.00970 0.00595 65 0.01719 0.00953 0.00585 70 0.01688 0.00936 0.00575 75 0.01655 0.00918 0.00564 80 0.01622 0.00900 0.00552 85 0.01590 0.00882 0.00541 90 0.01557 0.00864 0.00530 95 0.01526 0.00846 0.00520 100 0.01495 0.00829 0.00509 110 0.01437 0.00797 0.00489 120 0.01382 0.00766 0.00471 130 0.01331 0.00738 0.00453 140 0.01283 0.00712 0.00437 150 0.01238 0.00687 0.00422 160 0.01197 0.00664 0.00408 170 0.01158 0.00642 0.00394 180 0.01122 0.00622 0.00382 190 0.01088 0.00603 0.00370 200 0.01056 0.00586 0.00360 250 0.00923 0.00512 0.00314 300 0.00821 0.00455 0.00280 350 0.00741 0.00411 0.00252 400 0.00676 0.00375 0.00230 450 0.00623 0.00345 0.00212 500 0.00578 0.00320 0.00197 600 0.00506 0.00281 0.00172 700 0.00452 0.00250 0.00154 800 0.00408 0.00226 0.00139 900 0.00373 0.00207 0.00127 1000 0.00344 0.00191 0.00117 1500 0.00250 0.00139 0.000851 2000 0.00199 0.00110 0.000676 3000 0.00143 0.000791 0.000486 T [[sigma].sub.BE] [[sigma].sub.BE] [[sigma].sub.BE] 11 12 13 14 0.000965 0.000646 0.000455 15 0.00155 0.00106 0.000763 16 0.00195 0.00135 0.000969 17 0.00227 0.00157 0.00113 18 0.00252 0.00175 0.00126 19 0.00274 0.00190 0.00137 20 0.00292 0.00202 0.00146 21 0.00308 0.00213 0.00154 22 0.00321 0.00223 0.00161 23 0.00333 0.00231 0.00167 24 0.00344 0.00238 0.00172 26 0.00361 0.00250 0.00181 28 0.00373 0.00259 0.00187 30 0.00383 0.00266 0.00192 32 0.00391 0.00271 0.00196 34 0.00396 0.00275 0.00199 36 0.00400 0.00278 0.00201 38 0.00403 0.00280 0.00202 40 0.00405 0.00281 0.00203 45 0.00405 0.00281 0.00204 50 0.00403 0.00280 0.00202 55 0.00398 0.00277 0.00200 60 0.00392 0.00273 0.00197 65 0.00386 0.00268 0.00194 70 0.00379 0.00263 0.00190 75 0.00371 0.00258 0.00187 80 0.00364 0.00253 0.00183 85 0.00357 0.00248 0.00179 90 0.00350 0.00243 0.00176 95 0.00343 0.00238 0.00172 100 0.00336 0.00233 0.00169 110 0.00323 0.00224 0.00162 120 0.00310 0.00215 0.00156 130 0.00299 0.00207 0.00150 140 0.00288 0.00200 0.00145 150 0.00278 0.00193 0.00140 160 0.00269 0.00187 0.00135 170 0.00260 0.00181 0.00131 180 0.00252 0.00175 0.00126 190 0.00244 0.00170 0.00123 200 0.00237 0.00165 0.00119 250 0.00207 0.00144 0.00104 300 0.00184 0.00128 0.000925 350 0.00166 0.00115 0.000835 400 0.00152 0.00105 0.000762 450 0.00140 0.000970 0.000702 500 0.00130 0.000900 0.000651 600 0.00114 0.000788 0.000570 700 0.00101 0.000703 0.000508 800 0.000915 0.000636 0.000460 900 0.000837 0.000581 0.000420 1000 0.000771 0.000536 0.000387 1500 0.000561 0.000390 0.000282 2000 0.000445 0.000309 0.000224 3000 0.000320 0.000222 0.000161 Table 2 Helium. Excitation energies E in eV, dipole f values from uncorrelated wave functions ([f.sub.sc]), f values from correlated wave functions ([f.sub.accu]) by Drake (8), 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 [1s.sup.2] [S.sup.1]. The experimental ionization energy B = 24.5874 eV has been used in the scaling. The constants a, b, and c of Eq. (5) are included Final state 1s2p [P.sup.1] 1s3p [P.sup.1] 1s4p [P.sup.1] E 21.218 23.087 23.742 [f.sub.sc] 0.2583 0.07061 0.02899 [f.sub.accu] 0.2762 0.07343 0.02986 Const. a 0.165601 0.041611 0.016111 Const. b -0.076942 -0.018087 -0.007040 Const. c 0.033306 0.002104 -0.000045 Final state 1s5p [P.sup.1] 1s6p [P.sup.1] 1s7p [P.sup.1] E 24.046 24.211 24.311 [f.sub.sc] 0.01466 0.00844 0.00529 [f.sub.accu] 0.01504 0.00863 0.00541 Const. a 0.008298 0.004740 0.002963 Const. b -0.003475 -0.001972 -0.001227 Const. c -0.000228 -0.000194 -0.000146 Final state 1s8p [P.sup.1] 1s9p [P.sup.1] 1s10p [P.sup.1] E 24.375 24.420 24.452 [f.sub.sc] 0.00354 0.00248 0.00181 [f.sub.accu] 0.00361 0.00253 0.00184 Const. a 0.001975 0.001383 0.001006 Const. b -0.000816 -0.000570 -0.000414 Const. c -0.000108 -0.000080 -0.000061 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 23 0.01939 24 0.02474 0.00337 25 0.02933 0.00498 0.00159 26 0.03343 0.00625 0.00216 27 0.03716 0.00735 0.00264 28 0.04058 0.00832 0.00305 29 0.04375 0.00921 0.00342 30 0.04669 0.01002 0.00376 35 0.05875 0.01329 0.00510 40 0.06757 0.01565 0.00607 45 0.07413 0.01740 0.00678 50 0.07903 0.01871 0.00731 60 0.08542 0.02043 0.00802 70 0.08883 0.02138 0.00841 80 0.09043 0.02185 0.00861 90 0.09088 0.02202 0.00868 100 0.09060 0.02199 0.00868 110 0.08983 0.02184 0.00862 120 0.08876 0.02161 0.00853 130 0.08748 0.02132 0.00842 140 0.08609 0.02100 0.00830 150 0.08462 0.02066 0.00817 160 0.08313 0.02030 0.00803 170 0.08162 0.01995 0.00789 180 0.08012 0.01959 0.00775 190 0.07864 0.01923 0.00761 200 0.07718 0.01888 0.00747 225 0.07370 0.01805 0.00714 250 0.07046 0.01726 0.00683 275 0.06747 0.01654 0.00655 300 0.06471 0.01587 0.00628 350 0.05982 0.01468 0.00581 400 0.05564 0.01365 0.00541 450 0.05203 0.01277 0.00506 500 0.04890 0.01201 0.00476 600 0.04372 0.01074 0.00425 700 0.03962 0.00973 0.00386 800 0.03628 0.00891 0.00353 900 0.03350 0.00823 0.00326 1000 0.03116 0.00766 0.00303 1500 0.02333 0.00573 0.00227 2000 0.01885 0.00463 0.00183 3000 0.01383 0.00340 0.00135 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 23 24 25 0.000684 0.000354 0.000206 26 0.000997 0.000543 0.000329 27 0.00125 0.000688 0.000421 28 0.00146 0.000812 0.000500 29 0.00165 0.000922 0.000569 30 0.00182 0.00102 0.000631 35 0.00250 0.00141 0.000878 40 0.00299 0.00169 0.00105 45 0.00335 0.00190 0.00118 50 0.00362 0.00206 0.00128 60 0.00397 0.00226 0.00141 70 0.00417 0.00237 0.00148 80 0.00427 0.00243 0.00152 90 0.00431 0.00245 0.00153 100 0.00431 0.00245 0.00153 110 0.00428 0.00244 0.00152 120 0.00424 0.00242 0.00151 130 0.00419 0.00239 0.00149 140 0.00413 0.00235 0.00147 150 0.00406 0.00231 0.00144 160 0.00399 0.00227 0.00142 170 0.00392 0.00224 0.00139 180 0.00385 0.00220 0.00137 190 0.00378 0.00216 0.00135 200 0.00372 0.00212 0.00132 225 0.00355 0.00202 0.00126 250 0.00340 0.00194 0.00121 275 0.00326 0.00186 0.00116 300 0.00313 0.00178 0.00111 350 0.00289 0.00165 0.00103 400 0.00269 0.00153 0.000957 450 0.00252 0.00144 0.000896 500 0.00237 0.00135 0.000842 600 0.00212 0.00121 0.000753 700 0.00192 0.00109 0.000683 800 0.00176 0.00100 0.000625 900 0.00162 0.000925 0.000578 1000 0.00151 0.000861 0.000537 1500 0.00113 0.000645 0.000402 2000 0.000913 0.000521 0.000325 3000 0.000670 0.000382 0.000238 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 23 24 25 0.000130 0.0000879 0.0000621 26 0.000214 0.000148 0.000106 27 0.000277 0.000192 0.000139 28 0.000330 0.000229 0.000166 29 0.000376 0.000262 0.000190 30 0.000418 0.000291 0.000211 35 0.000583 0.000407 0.000295 40 0.000700 0.000489 0.000355 45 0.000787 0.000550 0.000399 50 0.000851 0.000595 0.000432 60 0.000937 0.000655 0.000476 70 0.000985 0.000689 0.000501 80 0.00101 0.000706 0.000513 90 0.00102 0.000713 0.000518 100 0.00102 0.000713 0.000518 110 0.00101 0.000709 0.000515 120 0.00100 0.000702 0.000510 130 0.000991 0.000693 0.000504 140 0.000976 0.000683 0.000497 150 0.000961 0.000672 0.000489 160 0.000945 0.000661 0.000481 170 0.000929 0.000650 0.000472 180 0.000912 0.000638 0.000464 190 0.000896 0.000627 0.000456 200 0.000880 0.000616 0.000448 225 0.000841 0.000589 0.000428 250 0.000805 0.000563 0.000410 275 0.000772 0.000540 0.000393 300 0.000740 0.000518 0.000377 350 0.000685 0.000479 0.000349 400 0.000638 0.000446 0.000324 450 0.000597 0.000417 0.000304 500 0.000561 0.000392 0.000285 600 0.000502 0.000351 0.000255 700 0.000455 0.000318 0.000231 800 0.000416 0.000291 0.000212 900 0.000385 0.000269 0.000196 1000 0.000358 0.000250 0.000182 1500 0.000268 0.000187 0.000136 2000 0.000216 0.000151 0.000110 3000 0.000159 0.000111 0.0000807 Table 3 Lithium. Excitation energies E in eV, dipole f values calculated from uncorrelated wave functions ([f.sub.sc]), f values calculated from correlated wave functions ([f.sub.accu]) as explained in the text, and BEf-scaled excitation cross sections [[sigma].sub.BEf] in [[Angstrom].sup.2] as functions of incident electron energy T in eV. The experimental ionization energy B = 5.3917 eV has been used in the scaling. The constants a, b, and c of Eq. (5) are included Excitation 2s-2p 2s-3p 2s-4p 2s-5p 2s-6p E 1.848 3.834 4.522 4.837 5.008 [f.sub.sc] 0.7685 0.00340 0.00353 0.00217 0.00135 [f.sub.accu] 0.7468 0.00483 0.00428 0.00260 0.00158 Const. a 5.658148 0.012056 0.010631 0.006113 0.003666 Const. b 17.288057 0.219978 0.047005 0.018340 0.009244 Const. c -0.226058 0.0.22768 0.011300 0.005517 0.003062 Excitation 2s-7p 2s-8p 2s-9p 2s-10 E 5.110 5.177 5.222 5.254 [f.sub.sc] 0.000880 0.000601 0.000427 0.000314 [f.sub.accu] 0.00101 0.000683 0.000482 0.000353 Const. a 0.002342 0.001580 0.001113 0.000813 Const. b 0.005372 0.003419 0.002319 0.001650 Const. c 0.001872 0.001229 0.000850 0.000613 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2 14.59367 2.5 27.24288 3 33.14707 3.5 36.69134 4 38.97838 0.53291 4.5 40.48711 0.87436 5 41.47440 0.97533 0.15740 5.5 42.09531 1.00527 0.18668 6 42.45067 1.00592 0.19520 8 42.33337 0.92889 0.18523 10 41.07186 0.83871 0.16733 15 36.87740 0.66670 0.13449 20 32.98349 0.55296 0.11354 25 29.73768 0.47298 0.09886 30 27.06106 0.41366 0.08789 35 24.83566 0.36787 0.07932 40 22.96265 0.33143 0.07241 45 21.36655 0.30171 0.06671 50 19.99071 0.27700 0.06190 60 17.73927 0.23823 0.05425 70 15.97298 0.20918 0.04839 80 14.54840 0.18657 0.04375 90 13.37361 0.16847 0.03998 100 12.38704 0.15364 0.03684 110 11.54596 0.14126 0.03420 120 10.81975 0.13076 0.03193 130 10.18588 0.12175 0.02996 140 9.62741 0.11393 0.02823 150 9.13135 0.10707 0.02671 160 8.68756 0.10101 0.02535 170 8.28799 0.09561 0.02413 180 7.92620 0.09077 0.02303 190 7.59694 0.08641 0.02203 200 7.29592 0.08246 0.02112 225 6.64488 0.07403 0.01917 250 6.10761 0.06719 0.01756 275 5.65611 0.06153 0.01621 300 5.27096 0.05677 0.01507 350 4.64769 0.04920 0.01323 400 3.77721 0.03892 0.01068 450 3.77721 0.03892 0.01068 500 3.46013 0.03526 0.00976 600 2.97030 0.02972 0.00834 700 2.60850 0.02570 0.00730 800 2.32962 0.02267 0.00650 900 2.10765 0.02028 0.00587 1000 1.92652 0.01836 0.00535 1500 1.36023 0.01251 0.00375 2000 1.06067 0.00953 0.00291 3000 0.74561 0.00649 0.00203 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2 2.5 3 3.5 4 4.5 5 0.04132 5.5 0.06775 0.03110 0.01653 6 0.07506 0.03657 0.02057 8 0.07364 0.03691 0.02123 10 0.06671 0.03351 0.01930 15 0.05414 0.02736 0.01582 20 0.04625 0.02354 0.01367 25 0.04071 0.02085 0.01215 30 0.03654 0.01881 0.01099 35 0.03324 0.10719 0.01007 40 0.03056 0.01586 0.00932 45 0.02832 0.01475 0.00868 50 0.02643 0.01380 0.00813 60 0.02337 0.01226 0.00725 70 0.02100 0.01106 0.00655 80 0.01911 0.01009 0.00599 90 0.01755 0.00930 0.00553 100 0.01625 0.00863 0.00513 110 0.01515 0.00806 0.00480 120 0.01419 0.00756 0.00451 130 0.01336 0.00713 0.00426 140 0.01263 0.00675 0.00403 150 0.01198 0.00641 0.00383 160 0.01140 0.00611 0.00365 170 0.01087 0.00583 0.00349 180 0.01040 0.00558 0.00334 190 0.00997 0.00536 0.00321 200 0.00958 0.00515 0.00309 225 0.00872 0.00470 0.00282 250 0.00802 0.00433 0.00260 275 0.00743 0.00402 0.00241 300 0.00693 0.00375 0.00225 350 0.00611 0.00331 0.00200 400 0.00497 0.00270 0.00163 450 0.00497 0.00270 0.00163 500 0.00455 0.00248 0.00150 600 0.00391 0.00213 0.00129 700 0.00344 0.00188 0.00114 800 0.00307 0.00168 0.00102 900 0.00278 0.00152 0.000923 1000 0.00254 0.00139 0.000845 1500 0.00179 0.000988 0.000600 2000 0.00140 0.000773 0.000470 3000 0.000984 0.000545 0.000332 T [[sigma].sub.BEf] [[sigma].sub.BEf] [[sigma].sub.BEf] 2 2.5 3 3.5 4 4.5 5 5.5 0.00976 0.00622 0.00421 6 0.01277 0.00851 0.00598 8 0.01341 0.00905 0.00643 10 0.01221 0.00825 0.00586 15 0.01003 0.00679 0.00483 20 0.00869 0.00589 0.00420 25 0.00775 0.00526 0.00375 30 0.00702 0.00478 0.00341 35 0.00645 0.00439 0.00314 40 0.00597 0.00407 0.00291 45 0.00557 0.00380 0.00272 50 0.00522 0.00357 0.00255 60 0.00466 0.00319 0.00228 70 0.00422 0.00289 0.00207 80 0.00386 0.00264 0.00190 90 0.00357 0.00244 0.00175 100 0.00332 0.00227 0.00163 110 0.00310 0.00213 0.00153 120 0.00292 0.00200 0.00144 130 0.00276 0.00189 0.00136 140 0.00261 0.00179 0.00129 150 0.00248 0.00170 0.00123 160 0.00237 0.00163 0.00117 170 0.00226 0.00155 0.00112 180 0.00217 0.00149 0.00107 190 0.00208 0.00143 0.00103 200 0.00200 0.00138 0.000991 225 0.00183 0.00126 0.000907 250 0.00169 0.00116 0.000837 275 0.00157 0.00108 0.000778 300 0.00147 0.00101 0.000727 350 0.00130 0.00894 0.000644 400 0.00106 0.000732 0.000580 450 0.00106 0.000732 0.000528 500 0.000976 0.000673 0.000485 600 0.000842 0.000580 0.000419 700 0.000742 0.000512 0.000369 800 0.000664 0.000458 0.000331 900 0.000603 0.000416 0.000300 1000 0.000522 0.000381 0.000275 1500 0.000393 0.000271 0.000196 2000 0.000308 0.000213 0.000154 3000 0.000218 0.000151 0.000109 Acknowledgements We gratefully acknowledge partial financial support by the Office of Fusion Energy Sciences of the U.S. Department of Energy. Accepted: June June: see month. 3, 2002 Available online: http://www.nist.gov/jres 4. References (1.) Y.-K. Kim, Phys. Rev. A 64, 032713 (2001). (2.) 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. 1, 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. (3.) See, for example, NIST's public web site http://physics.nist.gov See .gov and GovNet. (networking) gov - The top-level domain for US government bodies. (2002). (4.) I. Bray and A. T. Stelbovics, Adv. At. Mol. Opt OPT Options (File Name Extension) OPT Optional OPT Optimization OPT Optical OPT Optimum OPT Occupied Palestinian Territory OPT Optional Practical Training OPT Outpatient Physical Therapy OPT Overprint . Phys. 35, 209 (1995). (5.) See for example, M. Inokuti, Rev. Mod. Phys. 43, 297 (1971). (6.) I. Bray and Y. Ralchenko, http://atom.murdoch.edu See .edu. (networking) edu - ("education") The top-level domain for educational establishments in the USA (and some other countries). E.g. "mit.edu". The UK equivalent is "ac.uk". .aulCCCWWW/index.html (2002). (7.) C. J. Sweeney, A. Grafe, and T. W. Shyn, Phys. Rev. A 64, 032704 (2001). (8.) G. W. F. Drake Chap. 11 in Atomic, Molecular, and Optical Physics Atomic, molecular, and optical physics is the study of matter-matter and light-matter interactions on the scale of single atoms or structures containing a few atoms. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the Handbook
This article is about reference works. For the subnotebook computer, see .
AIP Acute intermittent porphyria , Woodbury Woodbury. 1 Residential city (1990 pop. 10,904), seat of Gloucester co., SW N.J., in the Philadelphia–Camden metropolitan area; settled 1683, inc. as a city 1871. It is a trade and service center, and petrochemical companies are nearby. , NY (1996). (9.) Z. C. Yan, M. Tambasco, and G. W. F. Drake, Phys. Rev. A 57, 1652 (1998). (10.) L. Qu, Z. 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 B. Li, Eur. Phys. J. D 5, 173 (1999). (11.) A. Grafe, C. J. Sweeney, and T. W. Shyn, Phys. Rev. A 63, 052715 (2001). (12.) H. Merabet, M. Bailey Bailey may refer to:
In the United Kingdom:
Max Bruch , J. Hanni Hanni may refer to: People with the given name Hanni:
tang: see butterfly fish. and C. D. Lin Lin , Maya Ying Born 1959. American sculptor and architect whose public works include the Vietnam Veterans Memorial in Washington, D.C. (1982). Noun 1. , Phys. Rev. A 64, 012712 (2001). (13.) F. J. de Heer n. 1. A yarn measure of six hundred yards or NDS - Netware Directory Services )-385, Vienna Vienna, city and province, Austria Vienna (vēĕn`ə), Ger. Wien, city and province (1991 pop. 1,539,848), 160 sq mi (414 sq km), capital and largest city of Austria and administrative seat of Lower Austria, NE Austria, on , Austria Austria (ô`strēə), Ger. Österreich [eastern march], officially Republic of Austria, federal republic (2005 est. pop. 8,185,000), 32,374 sq mi (83,849 sq km), central Europe. (1998). Unpublished--Recommended values. (14.) W. B. Westerveld Westerveld ( (helpinfo)) is a municipality in the northeastern Netherlands. The municipality Westerveld was established in 1998 out of de municipalities of Diever, Dwingeloo, Havelte en Vledder. , H. G. M. Heideman, and J. van Eck Eck , Johann 1486-1543. German Roman Catholic theologian who opposed the reforms of Martin Luther and procured from Rome the papal bull that declared Luther a heretic (1520). Noun 1. , J. Phys. B 12, 115 (1979). (15.) D. E. Shemansky, J. M. Ajello, D. T. Hall, and B. Franklin Franklin, cities, United States Franklin. 1 City (1990 pop. 12,907), seat of Johnson co., S central Ind., inc. 1823. It is a farm trade center. Manufactures include auto parts, aluminum doors and windows, and copper panels. , Astrophy. J. 296, 774 (1985). (16.) S. Trajmar, J.M. Ratliff Ratliff is a surname of English origin. Variations include Ratcliff, Radcliff, Ratcliffe, Radcliffe, and others. In the United States, the surname can be found in all parts of the country but it is not common. , G. Csanak, and D. C. Cartwright, Z. Phys. D 22, 457 (1992). (17.) D. C. Cartwright, G. Csanak, S. Trajmar, and D. F. Register, Phys. Rev. A 45, 1602 (1992). (18.) D. Leep and A. Gallagher Gallagher may refer to: People
(19.) W. Williams, S. Trajmar, and D. Bozinis, J. Phys. B 9, 1529 (1976). (20.) L. Vuskovic, S. Trajmar, and D. F. Register, J. Phys. B 15, 2517 (1982). (21.) I. Bray, D. 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, 1101 (1993). (22.) J. Schweinzer, R. Brandenburg Brandenburg, city, Germany Brandenburg, city (1994 pop. 89,200), Brandenburg, E Germany, a port on the Havel River. It is an industrial center and rail junction. Manufactures include steel, machinery, and textiles. , I. Bray, R. Hoekstra, F. Aumayer, R. K. Janev, and H. P. Winter, At. Data Nucl, Data Tables 72, 239 (1999). About the authors: 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. Stone is a guest researcher and Yong-Ki Kim is a physicist, both in the Atomic Physics Division of the NIST Physics Laboratory. Jean-Paul Desclaux has recently retired from the French Atomic Energy Commission Atomic Energy Commission (AEC), former U.S. government commission created by the Atomic Energy Act of 1946 and charged with the development and control of the U.S. atomic energy program following World War II. . The 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. is an agency of the Technology Administration, U.S. Department of Commerce. |
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