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REVIEWS, TABLES, AND PLOTS Constants, Units, Atomic and Nuclear Properties 1.Physicalconstants(rev.) ...... 137 2.Astrophysicalconstants(rev.) ...... 138 3.Internationalsystemofunits(SI) ...... 140 4. Periodic table of the elements (rev.) ...... 141 5.Electronicstructureoftheelements ...... 142 6. Atomic and nuclear properties of materials ...... 144 7. Electromagnetic relations ...... 146 8.Namingschemeforhadrons(rev.) ...... 148

1. Physical constants 137

1. Physical Constants (a major revision) Table 1.1. Revised 2019 by C.G. Wohl (LBNL). Reviewed by P.J. Mohr and D.B. Newell (NIST). Mainly from “CODATA Recommended Values of the Fundamental Physical Constants: 2018,” E. Tiesinga, D.B. Newell, P.J. Mohr, and B.N. Taylor, NIST SP961 (May 2019). The electron charge magnitude e, and the Planck, Boltzmann, and Avogadro constants h, k, and NA, now join c as having deﬁned values; the free-space permittivity and permeability constants ǫ0 and µ0 are no longer exact. These changes aﬀect practically everything else in the Table. Figures in parentheses after the values are the 1-standard-deviation uncertainties in the last digits; the fractional uncertainties in parts per 109 (ppb) are in the last column. The full 2018 CODATA Committee on Data for Science and Technology set of constants are found at https://physics.nist.gov/constants. The last set of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. See also “The International System of Units (SI),” 9th ed. (2019) of the International Bureau of Weights and Measures (BIPM), https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf.

Quantity Symbol, equation Value Uncertainty (ppb) speed of light in vacuum c 299 792 458 m s−1 exact Planck constant h 6.626 070 15 10−34 J s (or J/Hz)♯ exact Planck constant, reduced ~ h/2π 1.054 571 817×... 10−34 Js exact∗ ≡ = 6.582 119 569×... 10−22 MeVs exact∗ electron charge magnitude e 1.602 176 634 10−19×C exact conversion constant ~c 197.326 980 4...× MeVfm exact∗ conversion constant (~c)2 0.389 379 372 1... GeV2 mbarn exact∗ 2 −31 electron mass me 0.510 998 950 00(15) MeV/c = 9.109 383 7015(28) 10 kg 0.30 2 × −27 proton mass mp 938.272 088 16(29) MeV/c = 1.672 621 923 69(51) 10 kg 0.31 × = 1.007 276 466 621(53) u = 1836.152 673 43(11) me 0.053, 0.060 2 neutron mass mn 939.565 420 52(54) MeV/c = 1.008 664 915 95(49) u 0.57, 0.48 2 deuteron mass md 1875.612 942 57(57) MeV/c 0.30 unified atomic mass unit∗∗ u = (mass 12Catom)/12 931.49410242(28)MeV/c2 = 1.660 539 066 60(50) 10−27 kg 0.30 × 2 −12 −1 permittivity of free space ǫ0 =1/µ0c 8.854 187 8128(13) 10 F m 0.15 −7 × −2 permeability of free space µ0/(4π 10 ) 1.00000000055(15)NA 0.15 × 2 −3 † fine-structure constant α = e /4πǫ0~c 7.297 352 5693(11) 10 =1/137.035 999 084(21) 0.15 2 2 × −15 classical electron radius re = e /4πǫ0mec 2.817 940 3262(13) 10 m 0.45 − −1 × −13 (e Compton wavelength)/2π λe = ~/mec = reα 3.861 592 6796(12) 10 m 0.30 − 2 2 −2 × −10 Bohr radius (mnucleus = ) a∞ =4πǫ0~ /mee = reα 0.529 177 210 903(80) 10 m 0.15 wavelength of 1 eV/c particle∞ hc/(1eV) 1.239841984... 10−×6 m exact∗ 4 2 2 2 2 × −3 Rydberg energy hcR∞ = mee /2(4πǫ0) ~ = mec α /213.605693122994(26)eV 1.9 10 2 × Thomson cross section σT = 8πre /3 0.66524587321(60)barn 0.91 −11 −1 Bohr magneton µB = e~/2me 5.788 381 8060(17) 10 MeV T 0.3 × −14 −1 nuclear magneton µN = e~/2mp 3.152 451 258 44(96) 10 MeV T 0.31 e × 11 −1 −1 electron cyclotron freq./field ωcycl/B = e/me 1.758 820 010 76(53) 10 rad s T 0.30 p × 7 −1 −1 proton cyclotron freq./field ω /B = e/mp 9.578 833 1560(29) 10 rad s T 0.31 cycl × ‡ −11 3 −1 −2 4 gravitational constant GN 6.674 30(15) 10 m kg s 2.2 10 = 6.708 83(15)× 10−39 ~c (GeV/c2)−2 2.2 × 104 −2 × × standard gravitational accel. gN 9.806 65 m s exact 23 −1 Avogadro constant NA 6.022 140 76 10 mol exact Boltzmann constant k 1.380 649 10×−23 JK−1 exact = 8.617× 333 262... 10−5 eV K−1 exact∗ ×−3 3 −1 ∗ molar volume, ideal gas at STP NAk (273.15K)/(101325Pa) 22.41396954... 10 m mol exact × −3 ∗ Wien displacement law constant b = λmaxT 2.897 771 955... 10 mK exact Stefan-Boltzmann constant σ = π2k4/60~3c2 5.670 374 419... × 10−8 W m−2 K−4 exact∗ × Fermi coupling constant‡‡ G /(~c)3 1.166 378 7(6) 10−5 GeV−2 510 F × 2 †† 5 weak-mixing angle sin θ(MZ ) (MS) 0.23121(4) 1.7 10 ± b 2 × 5 W boson mass mW 80.379(12) GeV/c 1.5 10 0 2 × 4 Z boson mass mZ 91.1876(21) GeV/c 2.3 10 × 6 strong coupling constant αs(m ) 0.1179(10) 8.5 10 Z × π = 3.141 592 653 589 793 238... e = 2.718 281 828 459 045 235... γ = 0.577 215 664 901 532 860... −4 −19 1 in 0.0254 m 1 G 10 T 1 eV=1.602 176 634 10 J (exact) kT at 300 K = [38.681 740(22)]−1 eV ≡ ≡ × 1 A˚ 0.1 nm 1 dyne 10−5 N (1 kg)c2 =5.609 588 603 ... 1035 eV (exact∗) 0 ◦C 273.15 K ≡ ≡ × ≡ 1 barn 10−28 m2 1 erg 10−7 J 1C=2.997 924 58 109 esu 1 atmosphere 760 Torr 101 325 Pa ≡ ≡ × ≡ ≡ ♯ CODATA recommends that the unit be J/Hz to stress that in h = E/ν the frequency ν is in cycles/sec (Hz), not radians/sec. ∗ These are calculated from exact values and are exact to the number of places given (i.e. no rounding). ∗∗ The molar mass of 12C is 11.999 999 9958(36) g. † 2 2 2 At Q = 0. At Q mW the value is 1/128. ‡ ≈ ∼ Absolute laboratory measurements of GN have been made only on scales of about 1 cm to 1 m. ‡‡ See the discussion in Sec. 10, “Electroweak model and constraints on new physics.” †† The corresponding sin2 θ for the effective angle is 0.23153(4). 138 2. Astrophysical Constants and Parameters

2. Astrophysical Constants and Parameters Table 2.1: Revised August 2019 by D.E. Groom (LBNL) and D. Scott (U. of British Columbia). The figures in parentheses after some values give the 1-σ uncertainties in the last digit(s). Physical constants are from Ref. [1]. While every effort has been made to obtain the most accurate current values of the listed quantities, the table does not represent a critical review or adjustment of the constants, and is not intended as a primary reference. The values and uncertainties for the cosmological parameters depend on the exact data sets, priors, and basis parameters used in the fit. Many of the derived parameters reported in this table have non-Gaussian likelihoods. Parameters may be highly correlated, so care must be taken in propagating errors. Unless otherwise specified, cosmological parameters are derived from a 6-parameter ΛCDM cosmology fit to Planck cosmic microwave background 2018 temperature (TT) + polarization (TE,EE+lowE) + lensing data [2]. For more information see Ref. [3] and the original papers.

Quantity Symbol, equation. Value Reference,footnote −11 3 −1 −2 Newtonian constant of gravitation GN 6.674 30(15) × 10 m kg s [1] p 19 2 −8 Planck mass MP = ~c/GN 1.220 890(14) × 10 GeV/c = 2.176 434(24) × 10 kg [1] p 3 −35 Planck length lP = ~GN /c 1.616 255(18) × 10 m [1] tropical year (equinox to equinox, 2020) yr 31 556 925.1 s = 365.242 189 days [4] sidereal year (period of Earth around Sun relative to stars) 31 558 149.8 s ≈ π × 107 s [4] mean sidereal day (Earth rotation period relative to stars) 23h 56m 04s.090 53 [4] astronomical unit au 149 597 870 700 m exact [5] parsec (1 au/1 arc sec) pc 3.085 677 581 49 × 1016 m = 3.261 56. . . ly exact [6] light year (deprecated unit) ly 0.306 601 ... pc = 0.946 073 ... × 1016 m [7] solid angle deg2 (π/180)2 sr = 3.046 17 ... × 10−4 sr [8] 2 Schwarzschild radius of the Sun 2GN M /c 2.953 250 076 100 25 km [9] 30 Solar mass M 1.988 41(4) × 10 kg [10] 8 nominal Solar equatorial radius R 6.957 × 10 m exact [11] −2 nominal Solar constant S 1361 W m exact [11, 12] nominal Solar photosphere temperature T 5772 K exact [11] 26 nominal Solar luminosity L 3.828 × 10 W exact [11, 13] 2 Schwarzschild radius of the Earth 2GN M⊕/c 8.870 055 940 mm [9] 24 Earth mass M⊕ 5.972 17(13) × 10 kg [10] 6 nominal Earth equatorial radius R⊕ 6.3781 × 10 m exact [11] −2 3 2 −2 Chandrasekhar mass MCh 3.097 972 µ MP /mH = 1.433 77(6) (µ/2) M [14, 15] 31 Eddington luminosity LEd 1.257 065 179 8(12) × 10 (M/M ) W [16, 17] 4 = 3.283 869 330 8(31) × 10 (M/M ) L jansky (flux density) Jy 10−26 W m−2 Hz−1 definition 28 −0.4 M luminosity conversion f0 3.0128 × 10 × 10 Bol W exact [18] (MBol = absolute bolometric magnitude = bolometric magnitude at 10 pc) flux conversion F 2.518 021 002 × 10−8 × 10−0.4 mBol W m−2 exact [18] (mBol = apparent bolometric magnitude) −2 −1 ABsolute monochromatic magnitude AB −2.5 log10 fν − 56.10 (for fν in W m Hz ) [19] = −2.5 log10 fν + 8.90 (for fν in Jy) −1 −1 Solar angular velocity around Galactic center Θ0/R0 27.1(5) km s kpc [20] Solar distance from Galactic center R0 8.178 ± 0.013(stat.) ± 0.022(sys.) kpc [21, 22] −1 circular velocity at R0 v0 or Θ0 240(8) km s [22, 23] −1 −1 escape velocity from the Galaxy v esc 492 km s < v esc < 587 km s (90%) [24] −24 −3 2 −3 local disk density ρ disk 6.6(9) ×10 g cm = 3.7(5) GeV/c cm [25] 2 −3 local dark matter density ρ χ canonical value 0.3 GeV/c cm within factor 2–3 [26] present-day CMB temperature T0 2.7255(6) K [27, 28] present-day CMB dipole amplitude d 3.3621(10) mK [27, 29] −1 ◦ ◦ Solar velocity with respect to CMB v 369.82(11) km s towards (l, b) = (264.021(11) , 48.253(5) ) [29] −1 ◦ ◦ Local Group velocity with respect to CMB vLG 620(15) km s towards (l, b) = (271.9(20) , 29.6(14) ) [29] 3 −3 number density of CMB photons nγ 410.7(3) (T/2.7255) cm [30] 4 −34 −3 −3 density of CMB photons ργ 4.645(4) (T/2.7255) × 10 g cm ≈ 0.260 eV cm [30] entropy density/Boltzmann constant s/k 2 891.2 (T/2.7255)3 cm−3 [30] −1 −1 −1 present-day Hubble expansion rate H0 100 h km s Mpc = h × (9.777 752 Gyr) [31] scaling factor for Hubble expansion rate h 0.674(5) [2, 32] 26 −1 26 Hubble length c/H0 0.925 0629 × 10 h m = 1.372(10) × 10 m 2 2 51 −2 2 51 2 scaling for cosmological constant c /3H0 2.85247 × 10 h m = 6.21(9) × 10 m 2 −29 2 −3 critical density of the Universe ρcrit = 3H0 /8πGN 1.878 34(4) × 10 h g cm = 1.053 672(24) × 10−5 h2 (GeV/c2) cm−3 11 2 −3 = 2.77536627 × 10 h M Mpc −10 −10 baryon-to-photon ratio (from BBN) η = nb/nγ 5.8 × 10 ≤ η ≤ 6.5 × 10 (95% CL) [33] −7 −3 number density of baryons nb 2.515(17) × 10 cm [2, 3, 34, 35] −7 −7 −3 (2.4 × 10 < nb < 2.7 × 10 ) cm (95% CL, η × nγ ) −5 4 −2 −5 CMB radiation density of the Universe Ωγ = ργ /ρcrit 2.473 × 10 (T/2.7255) h = 5.38(15) ×10 [30] --- Planck 2018 6-parameter fit to flat ΛCDM cosmology ------‡ −2 † baryon density of the Universe Ωb = ρb/ρcrit 0.02237(15) h = 0.0493(6) [2, 3, 27] ‡ −2 † cold dark matter density of the Universe Ωc = ρc/ρcrit 0.1200(12) h = 0.265(7) [2, 3, 27] ‡ 100 × approx to r∗/DA 100 × θMC 1.04092(31) [2, 3, 27] reionization optical depth τ ‡ 0.054(7) [2, 3, 27] −1 10 2 ‡ ln(power prim. curv. pert.) (k0 = 0.05 Mpc ) ln(10 ∆R) 3.044(14) [2, 3, 27] ‡ scalar spectral index ns 0.965(4) [2, 3, 27] † pressureless matter parameter Ωm = Ωc + Ωb 0.315(7) [2, 3] † dark energy density parameter ΩΛ 0.685(7) [2, 3] † −30 −3 energy density of dark energy ρΛ 5.83(16) × 10 g cm [2] cosmological constant Λ † 1.088(30) × 10−56 cm−2 [2] −1 † fluctuation amplitude at 8 h Mpc scale σ8 0.811(6) [2, 3] 2. Astrophysical Constants and Parameters 139

Quantity Symbol, equation. Value Reference,footnote † redshift of matter-radiation equality zeq 3402(26) [2, 36] † age at matter-radiation equality teq 51.1(8) kyr [2, 37] † redshift at which optical depth equals unity z∗ 1089.92(25) [2] † comoving size of sound horizon at z∗ r∗ 144.43(26) Mpc [2, 38] † age when optical depth equals unity t∗ 372.9(10) kyr [2, 37] † redshift at half reionization zi 7.7(7) [2, 39] † age at half reionization ti 690(90) Myr [2] † redshift when acceleration was zero zq 0.636(18) [2, 37] † age when acceleration was zero tq 7.70(10) Gyr [2] † age of the Universe today t0 13.797(23) Gyr [2] ] effective number of neutrinos Neff 2.99(17) [2, 40, 41] ] sum of neutrino masses Σmν < 0.12 eV (95%, CMB + BAO); ≥ 0.06 eV (mixing) [2, 41–43] −2 ] neutrino density of the Universe Ων = h Σmνj /93.14 eV < 0.003 (95%, CMB + BAO); ≥ 0.0012 (mixing) [2, 42, 43] ] curvature ΩK 0.0007(19) [2] −1 ] running spectral index, k0 = 0.05 Mpc dns/d ln k −0.004(7) [2] ] −1 tensor-to-scalar field perturbations ratio, r0.002 = T/S < 0.058 (95% CL, k0 = 0.002 Mpc , no running) [2, 44, 45] dark energy equation of state parameter w −1.028(31) [2, 46] primordial helium fraction Yp 0.245(4) [47]

‡ Parameter in 6-parameter ΛCDM fit; † Derived parameter in 6-parameter ΛCDM fit; ] Extended model parameter, Planck + BAO data [2]. References [27] D. Scott & G.F. Smoot, “Cosmic Microwave Background,” Sec. 29 in [1] CODATA recommended 2018 values of the fundamental physical con- this Review. stants: https://physics.nist.gov/cuu/Constants/index.html. [28] D. J. Fixsen, Astrophys. J. 707, 916 (2009). [2] Planck Collab. 2018 Results VI (2018), [arXiv:1807.06209]. [29] Planck Collab. 2018 Results I (2018), [arXiv:1807.06205]. 3 3 3 [3] O. Lahav & A.R. Liddle, “The Cosmological Parameters,” Sec. 25.1 in 2ζ(3) kT π2kT kT 2·43·π2 kT [30] nγ = ; ργ = ; s/k= ; this Review. π2 ~c 15 c2 ~c 11·45 ~c [4] The Astronomical Almanac for the year 2020. kT/~c = 11.90 235(T/2.7255)/cm. [5] The astronomical unit of length (au) in meters is re-defined (IAU [31] Conversion using length of sidereal year. XXVIII General Assembly 2012, Resolution B2) to be a conventional [32] Distance-ladder estimates of H0 tend to give higher values than derived unit of length in agreement with the value adopted in IAU XXVII 2009 from the CMB, e.g. Riess et al., Astrophys. J. 826, 56 (2016) give Resolution B2. It is to be used with all time scales. h = 0.732 ± 0.017; for discussion see O. Lahav & A.R. Liddle, “The [6] The distance at which 1 au subtends 1 arc sec: 1 au divided by Cosmological Parameters,” Sec. 25.1 in this Review. π/648 000. [33] B.D. Fields, P. Molaro, & S. Sarkar, “Big-Bang Nucleosynthesis,” [7] IAU XVI GA 1976, Recommendations. Sec. 24 in this Review. [34] n depends only upon the measured Ω h2, the average [8] The number of square degrees on a sphere is 3602/π = 41 259.9 ... . b b baryon mass at the present epoch [35], and G : n = 2 N b [9] Observationally determined mass parameter GN M ×2/c [1] for either (Ω h2)(h−2ρ )/(0.93711 GeV/c2 per baryon). 20 3 −2 b crit the Sun or the Earth, where GM = 1.327 124 4 × 10 m s and 14 3 −2 [35] G. Steigman, JCAP 0610, 016 (2006). GM⊕ = 3.986 004 × 10 m s [48]. [10] G M ÷ G [1]. [36] Here ‘radiation’ includes three species of light neutrinos as well as pho- N N tons. [11] IAU XXIX GA, 2015, Resolution B3, “on recommended nominal conversion constants . . . ” Calligraphic symbol indicates recommended [37] D. Scott, A. Narimani and D. N. Page, Phys. Canada 70, 258 (2014). nominal value. [38] D.H. Weinberg, M. White, “Dark Energy,” Sec. 28 in this Review. [12] See also G. Kopp & J.L. Lean, Geophys. Res. Lett. 38, L01706 (2011), [39] Planck Collab. Interm. Results XLVI, Astron. & Astrophys. 596, A108 who give (1360.8 ± 0.6) W m−2; see paper for caveats and other mea- (2016) extend the range by ∆z ≈ 1, depending on the reionization surements. model. [40] Summary Tables in this Review list N = 2.984(8) (Standard Model [13] 4π (1 au)2 × S , assuming isotropic irradiance. ν fits to LEP-SLC data). Because neutrinos are not completely decoupled [14] S. Chandrasekhar, Astrophys. J. 74, 81 (1931). at e± annihilation, the effective number of massless neutrino species [15] This value assumes an ideal Fermi gas, using a numerical constant is 3.045, rather than 3. from the Lane-Emden equation [49], and with µ the average molecular [41] J. Lesgourgues & L. Verde, “Neutrinos in Cosmology,” Sec. 26 in this weight per electron, defined relative to the mass of the single-proton Review. hydrogen atom. [42] The sum is over all neutrino mass eigenstates, the lower limit following [16] A. S. Eddington, Mon. Not. R. Astron. Soc 77, 16 (1916). from neutrino mixing results reported in this Review combined with the [17] The maximum luminosity assuming pure electron scattering for the assumptions that there are three light neutrinos and that the lightest outward force arising from radiation pressure: 4πGN Mmpc/σT . neutrino is substantially less massive than the others. [18] IAU XXIX GA, 2015, Resolution B2, “on recommended zero points for [43] Astrophysical determinations of P m , reported in the Full List- the absolute and apparent bolometric magnitude scales”. νj [19] J. Oke and J. Gunn, Astrophys. J. 266, 713 (1983). ings of this Review under “Sum of the neutrino masses,” range from < 0.17 eV to < 2.3 eV in papers published since 2003. [20] J. Bovy, Mon. Not. R. Astron. Soc 468, 1, L63 (2017). [44] P. A. R. Ade et al. (BICEP2, Keck Array), Phys. Rev. Lett. 121, 221301 [21] R. Abuter et al. (2019), [arXiv:1904.05721]. (2018). [22] IAU XIX GA (1985) suggested that “in cases where standardization [45] Planck data alone give r < 0.10; adding the BICEP/Keck data tightens on a common set of galactic parameters is desirable” that the values the constraint. R = (8.5 ± 1.0) kpc and θ = (220 ± 20) km s−1 should be used. 0 0 [46] This constraint uses BAO and SNe data, as described in Ref. [2]; see [23] M. Reid et al., Astrophys. J. 783, 2, 130 (2014). discussion in D.H. Weinberg, M. White, “Dark Energy,” Sec. 28 in this [24] T. Piffl et al., Astron. Astrophys. 562, A91 (2014), [arXiv:1309.4293]. Review. [25] C. F. McKee, A. Parravano and D. J. Hollenbach, Astrophys. J. 814, [47] E. Aver, K. A. Olive and E. D. Skillman, JCAP 1507, 07, 011 (2015). 1, 13 (2015); This is representative of other published estimates. [48] IAU XXIX GA 2015, Resolution B2. [26] J. Read, J. Phys. G41, 063101 (2014); A. M. Green, J. Phys. G44, 8, [49] G. P. Horedt, Astrophys. Space Sci. 126, 2, 357 (1986). local −3 084001 (2017); The conclusion is ρDM = 0.39 ± 0.03 GeV cm . 140 3. International system of units (SI)

3. International System of Units (SI) See “The International System of Units (SI),” NIST Special Publication 330, B.N. Taylor, ed. (USGPO, Washington, DC, 1991); and “Guide for the Use of the International System of Units (SI),” NIST Special Publication 811, 1995 edition, B.N. Taylor (USGPO, Washington, DC, 1995).

SI prefixes Physical Name 1024 yotta (Y) quantity of unit Symbol 1021 zetta (Z) Base units 18 10 exa (E) length meter m 1015 peta (P) mass kilogram kg 1012 tera (T) time second s 109 giga (G) electric current ampere A 106 mega (M) thermodynamic kelvin K temperature 103 kilo (k) amount of substance mole mol 102 hecto (h) luminous intensity candela cd 10 deca (da) Derived units with special names 10−1 deci (d) plane angle radian rad 10−2 centi (c) solid angle steradian sr 10−3 milli (m) frequency hertz Hz 10−6 micro (µ) energy joule J 10−9 nano (n) force newton N −12 pressure pascal Pa 10 pico (p) −15 power watt W 10 femto (f) electric charge coulomb C 10−18 atto (a) electric potential volt V 10−21 zepto (z) electric resistance ohm Ω 10−24 yocto (y) electric conductance siemens S electric capacitance farad F magnetic flux weber Wb inductance henry H magnetic flux density tesla T luminous flux lumen lm illuminance lux lx celsius temperature degree celsius ◦C activity (of a becquerel Bq radioactive source)∗ absorbed dose (of gray Gy ionizing radiation)∗ dose equivalent∗ sievert Sv

∗See our section 37, on “Radioactivity and radiation protection.” 4. Periodic table of the elements 141

4. Periodic Table of the Elements le 18 neon VIIIA argon radon xenon helium 39.948 83.798 krypton 20.1797 131.293 4.002602 oganesson 2 He 10 Ne 18 Ar 36 Kr 54 Xe 86 Rn 118 Og (294.21392) (222.01758) lutetium 174.9668 71 Lu 103 Lr lawrencium (262.10961) 17 VIIA 35.45 iodine 79.904 fluorine chlorine astatine bromine (294.2105) 9 F 17 Cl 35 Br 53 I 85 At 117 Ts tennessine 126.90447 (209.98715) 18.998403163 173.054 nobelium ytterbium 70 Yb 102 No ses (bottom) of stable (259.10103) 16 VIA 32.06 sulfur 15.999 78.971 127.60 oxygen selenium tellurium polonium (293.20449 8 O 16 S 34 Se 52 Te 84 Po 116 Lv livermorium (208.98243) thulium 69 Tm 101 Md 168.93422 mendelevium (258.09844) 15 VA tions. Relative isotopic abundances 14.007 arsenic bismuth 121.760 nitrogen antimony 30.973761998 208.98040 phosphorus moscovium 7 N 15 P 33 As 51 Sb 83 Bi (290.19598) 74.921595 115 Mc erbium 167.259 fermium ed November 2016. The 7th period of the 68 Er 100 Fm (257.09511) 14 tin en for the mass. Masses may be found at IVA lead 207.2 silicon carbon 72.630 28.085 12.0107 118.710 flerovium (289.19042 6 C 14 Si 32 Ge 50 Sn 82 Pb 114 Fl germanium holmium 67 Ho 99 Es 164.93033 einsteinium (252.08298) 13 IIIA C, defined to be exactly 12 unified atomic mass units 10.81 boron 69.723 204.38 indium gallium 114.818 thallium 12 nihonium aluminum 5 B 13 Al 31 Ga 49 In 81 Tl 113 Nh (286.18221) 26.9815385 162.500 66 Dy 98 Cf 12 californium dysprosium (251.07959) IIB zinc If there is no stable isotope, the atomic mass of the most stab 65.38 200.592 112.414 mercury cadmium 30 Zn 48 Cd 80 Hg 112 Cn copernicium (285.17712) terbium IB berkelium 65 Tb 97 Bk 158.92535 gold (247.07031) silver copper 63.546 roentgen. 107.8682 29 Cu 47 Ag 79 Au 111 Rg (282.16912) 196.966569 157.25 curium 10 11 64 Gd 96 Cm gadolinum nickel (247.07035) 106.42 58.6934 195.084 platinum (281.1645) palladium 28 Ni 46 Pd 78 Pt 110 Ds darmstadt. p left) is the number of protons in the nucleus. The atomic mas 9 le isotopes but do have characteristic terrestrial composi VIII 151.964 europium cobalt 63 Eu 95 Am americium iridium (243.06138) 192.217 rhodium (278.1563) 102.90550 58.933195 27 Co 45 Rh 77 Ir 109 Mt meitnerium 8 iron 150.36 55.845 190.23 101.07 samarium osmium 62 Sm 94 Pu hassium plutonium (244.06420) 26 Fe 44 Ru 76 Os 108 Hs ruthenium (269.13375) ples; this is reflected in the number of significant figures giv surface. Atomic masses are relative to the mass of 113, 115, 117, and 118 in December 2015. The names were approv c-compositions-relative-atomic-masses. 7 VIIB 186.207 rhenium bohrium 61 Pm 93 Np 25 Mn 43 Tc 75 Re 107 Bh neptunium technetium 54.938044 (270.13336) promethium manganese (144.91276) (237.04817) (97.907212) 6 VIB 95.95 183.84 51.9961 tungsten 144.242 uranium chromium 24 Cr 42 Mo 74 W 106 Sg (269.12863) seaborgium 60 Nd 92 U molybdenum 238.02891 neodymium 5 VB 50.9415 niobium dubnium tantalum 92.90637 vanadium 23 V 41 Nb 73 Ta 105 Db 180.94788 (268.12567) 231.03588 59 Pr 91 Pa 140.90766 praseodym. protactinium 4 IVB PERIODIC TABLE OF THE ELEMENTS 47.867 178.49 91.224 hafnium titanium zirconium 22 Ti 40 Zr 72 Hf 104 Rf (267.12169) cerium rutherford. thorium 140.116 232.0377 58 Ce 90 Th 3 IIIB 57–71 NIDES 89–103 yttrium 88.90584 scandium 44.955908 21 Sc 39 Y ACTINIDES LANTHA- actinium 57 La 89 Ac 138.90547 lanthanum (227.02775) 2 Revised June 2019 by D.E. Groom (LBNL). The atomic number (to IIA 1 g/mole). The exceptions are Th, Pa, and U, which have no stab 87.62 24.305 40.078 barium radium calcium 137.327 9.012182 beryllium strontium ≈ 4 Be 12 Mg 20 Ca 38 Sr 56 Ba 88 Ra magnesium (226.02541) series series Actinide 1 IA Lanthanide 6.94 1.008 isotope known as of June 2019IUPAC is announced given in verification parentheses. of the discoveries of elements periodic table is now complete. Table 4.1. elements are weighted by isotopic abundances in the Earth’s https://www.nist.gov/pml/atomic-weights-and-isotopi often vary considerably, both in natural and commercial sam (u) (1 u sodium lithium caesium 39.0983 85.4678 francium hydrogen rubidium 1 H 3 Li 11 Na 19potassium K 37 Rb 55 Cs 87 Fr (223.01974) 22.98976928 132.90545196 142 5. Electronic structure of the elements

5. Electronic Structure of the Elements

Table 5.1. Reviewed 2011 by J.E. Sansonetti (NIST). The electronic conﬁgurations and the ionization energies are from the NIST database, “Ground Levels and Ionization Energies for the Neutral Atoms,” W.C. Martin, A. Musgrove, S. Kotochigova, and J.E. Sansonetti, http://www.nist.gov/pml/data/ion energy.cfm. The electron conﬁguration for, say, iron indicates an argon electronic core (see argon) plus six 3d electrons and two 4s electrons.

Ground Ionization Electronconﬁguration state energy 5 2S+1 Element (3d = ﬁve 3d electrons, etc.) LJ (eV) 2 1 H Hydrogen 1s S1/2 13.5984 2 1 2 He Helium 1s S0 24.5874 2 3 Li Lithium (He)2s S1/2 5.3917 2 1 4 Be Beryllium (He)2s S0 9.3227 2 2 5 B Boron (He)2s 2p P1/2 8.2980 2 2 3 6 C Carbon (He)2s 2p P0 11.2603 2 3 4 7 N Nitrogen (He)2s 2p S3/2 14.5341 2 4 3 8 O Oxygen (He)2s 2p P2 13.6181 2 5 2 9 F Fluorine (He)2s 2p P3/2 17.4228 2 6 1 10 Ne Neon (He)2s 2p S0 21.5645 2 11 Na Sodium (Ne)3s S1/2 5.1391 2 1 12 Mg Magnesium (Ne)3s S0 7.6462 2 2 13 Al Aluminum (Ne)3s 3p P1/2 5.9858 2 2 3 14 Si Silicon (Ne)3s 3p P0 8.1517 2 3 4 15 P Phosphorus (Ne)3s 3p S3/2 10.4867 2 4 3 16 S Sulfur (Ne)3s 3p P2 10.3600 2 5 2 17 Cl Chlorine (Ne)3s 3p P3/2 12.9676 2 6 1 18 Ar Argon (Ne)3s 3p S0 15.7596 2 19 K Potassium (Ar) 4s S1/2 4.3407 2 1 20 Ca Calcium (Ar) 4s S0 6.1132 ------2 2 21 Sc Scandium (Ar) 3d 4s T D3/2 6.5615 2 2 r 3 22 Ti Titanium (Ar) 3d 4s e F2 6.8281 3 2a 4 23 V Vanadium (Ar) 3d 4s l F3/2 6.7462 5 n 7 24 Cr Chromium (Ar)3d 4s e S3 6.7665 5 2s 6 25 Mn Manganese (Ar) 3d 4s m S5/2 7.4340 6 2i 5 26 Fe Iron (Ar)3d 4s e D4 7.9024 t d7 s2n 4F 27 Co Cobalt (Ar)3 4 i 9/2 7.8810 8 2t 3 28 Ni Nickel (Ar) 3d 4s o F4 7.6399 10 s 2 29 Cu Copper (Ar)3d 4s n S1/2 7.7264 10 2 1 30 Zn Zinc (Ar)3d 4s S0 9.3942 ------10 2 2 31 Ga Gallium (Ar) 3d 4s 4p P1/2 5.9993 10 2 2 3 32 Ge Germanium (Ar) 3d 4s 4p P0 7.8994 10 2 3 4 33 As Arsenic (Ar) 3d 4s 4p S3/2 9.7886 10 2 4 3 34 Se Selenium (Ar) 3d 4s 4p P2 9.7524 10 2 5 2 35 Br Bromine (Ar)3d 4s 4p P3/2 11.8138 10 2 6 1 36 Kr Krypton (Ar)3d 4s 4p S0 13.9996 2 37 Rb Rubidium (Kr) 5s S1/2 4.1771 2 1 38 Sr Strontium (Kr) 5s S0 5.6949 ------2 2 39 Y Yttrium (Kr)4d 5s T D3/2 6.2173 2 2 r 3 40 Zr Zirconium (Kr)4d 5s e F2 6.6339 4 a 6 41 Nb Niobium (Kr)4d 5s l D1/2 6.7589 5 n 7 42 Mo Molybdenum (Kr)4d 5s e S3 7.0924 5 2s 6 43 Tc Technetium (Kr)4d 5s m S5/2 7.28 7 i 5 44 Ru Ruthenium (Kr)4d 5s e F5 7.3605 t d8 s n 4F 45 Rh Rhodium (Kr)4 5 i 9/2 7.4589 10 t 1 46 Pd Palladium (Kr)4d o S0 8.3369 10 s 2 47 Ag Silver (Kr)4d 5s n S1/2 7.5762 10 2 1 48 Cd Cadmium (Kr)4d 5s S0 8.9938 ------5. Electronic structure of the elements 143

------10 2 2 49 In Indium (Kr)4d 5s 5p P1/2 5.7864 10 2 2 3 50 Sn Tin (Kr)4d 5s 5p P0 7.3439 10 2 3 4 51 Sb Antimony (Kr)4d 5s 5p S3/2 8.6084 10 2 4 3 52 Te Tellurium (Kr)4d 5s 5p P2 9.0096 10 2 5 2 53 I Iodine (Kr)4d 5s 5p P3/2 10.4513 10 2 6 1 54 Xe Xenon (Kr)4d 5s 5p S0 12.1298 2 55 Cs Cesium (Xe) 6s S1/2 3.8939 2 1 56 Ba Barium (Xe) 6s S0 5.2117 ------2 2 57 La Lanthanum (Xe) 5d 6s D3/2 5.5769 2 1 58 Ce Cerium (Xe)4f 5d 6s G4 5.5387 3 2 4 59 Pr Praseodymium (Xe)4f 6s L I9/2 5.473 4 2 5 60 Nd Neodymium (Xe)4f 6s a I4 5.5250 5 2n 6 61 Pm Promethium (Xe)4f 6s H5/2 5.582 6 2 7 62 Sm Samarium (Xe)4f 6s t F0 5.6437 7 2h 8 63 Eu Europium (Xe)4f 6s S7/2 5.6704 7 2a 9 64 Gd Gadolinium (Xe)4f 5d 6s D2 6.1498 9 2n 6 65 Tb Terbium (Xe)4f 6s H15/2 5.8638 10 2i 5 66 Dy Dysprosium (Xe)4f 6s d I8 5.9389 11 2 4 67 Ho Holmium (Xe)4f 6s e I15/2 6.0215 12 2 3 68 Er Erbium (Xe)4f 6s s H6 6.1077 13 2 2 69 Tm Thulium (Xe)4f 6s F7/2 6.1843 14 2 1 70 Yb Ytterbium (Xe)4f 6s S0 6.2542 14 2 2 71 Lu Lutetium (Xe)4f 5d 6s D3/2 5.4259 ------14 2 2 3 72 Hf Hafnium (Xe)4f 5d 6s T F2 6.8251 14 3 2 4 73 Ta Tantalum (Xe)4f 5d 6s r F3/2 7.5496 14 4 2e 5 74 W Tungsten (Xe)4f 5d 6s a l D0 7.8640 14 5 2n 6 75 Re Rhenium (Xe)4f 5d 6s e S5/2 7.8335 14 6 2s 5 76 Os Osmium (Xe)4f 5d 6s m D4 8.4382 14 7 2i 4 77 Ir Iridium (Xe)4f 5d 6s e F9/2 8.9670 14 9 t 3 78 Pt Platinum (Xe)4f 5d 6s n D3 8.9588 14 10 i t 2 79 Au Gold (Xe)4f 5d 6s o S1/2 9.2255 14 10 2s 1 80 Hg Mercury (Xe)4f 5d 6s n S0 10.4375 ------14 10 2 2 81 Tl Thallium (Xe)4f 5d 6s 6p P1/2 6.1082 14 10 2 2 3 82 Pb Lead (Xe)4f 5d 6s 6p P0 7.4167 14 10 2 3 4 83 Bi Bismuth (Xe)4f 5d 6s 6p S3/2 7.2855 14 10 2 4 3 84 Po Polonium (Xe)4f 5d 6s 6p P2 8.414 14 10 2 5 2 85 At Astatine (Xe)4f 5d 6s 6p P3/2 14 10 2 6 1 86 Rn Radon (Xe)4f 5d 6s 6p S0 10.7485 2 87 Fr Francium (Rn) 7s S1/2 4.0727 2 1 88 Ra Radium (Rn) 7s S0 5.2784 ------2 2 89 Ac Actinium (Rn) 6d 7s D3/2 5.3807 2 2 3 90 Th Thorium (Rn) 6d 7s F2 6.3067 2 2 4 ∗ 91 Pa Protactinium (Rn)5f 6d 7s A K11/2 5.89 3 2 5 92 U Uranium (Rn)5f 6d 7s c L6∗ 6.1939 4 2t 6 ∗ 93 Np Neptunium (Rn)5f 6d 7s L11/2 6.2657 6 2 7 94 Pu Plutonium (Rn)5f 7s i F0 6.0260 7 2n 8 95 Am Americium (Rn)5f 7s S7/2 5.9738 7 2i 9 96 Cm Curium (Rn)5f 6d 7s D2 5.9914 9 2d 6 97 Bk Berkelium (Rn)5f 7s H15/2 6.1979 10 2e 5 98 Cf Californium (Rn)5f 7s s I8 6.2817 11 2 4 99 Es Einsteinium (Rn)5f 7s I15/2 6.3676 12 2 3 100 Fm Fermium (Rn)5f 7s H6 6.50 13 2 2 101 Md Mendelevium (Rn)5f 7s F7/2 6.58 14 2 1 102 No Nobelium (Rn)5f 7s S0 6.65 14 2 2 103 Lr Lawrencium (Rn)5f 7s 7p? P1/2? 4.9? ------14 2 2 3 104 Rf Rutherfordium (Rn)5f 6d 7s ? F2? 6.0?

∗ The usual LS coupling scheme does not apply for these three elements. See the introductory note to the NIST table from which this table is taken. 144 6. Atomic and nuclear properties of materials

6. Atomic and Nuclear Properties of Materials

Table 6.1 Abridged from pdg.lbl.gov/AtomicNuclearProperties by D.E. Groom (2017). See web pages for more detail about entries in this table and for several hundred others. Parentheses in the dE/dx and density columns indicate gases at 20◦ C and 1 atm. Boiling points are at 1 atm. Refractive indices n are evaluated at the sodium D line blend (589.2 nm); values 1 in brackets indicate (n 1) 106 for gases at 0◦ C and 1 atm. ≫ − × Material Z A Z/A Nucl.coll. Nucl.inter. Rad.len. dE/dx min Density Melting Boiling Refract. h i | 3 length λT length λI X0 MeV g cm− point point index 2 2 2 { 1 2 { } g cm− g cm− g cm− g− cm ( g ℓ−1 ) (K) (K) @ Na D { } { } { } } { } H2 1 1.008(7) 0.99212 42.8 52.0 63.05 (4.103) 0.071(0.084) 13.81 20.28 1.11[132.] D2 1 2.014101764(8) 0.49650 51.3 71.8 125.97 (2.053) 0.169(0.168) 18.7 23.65 1.11[138.] He 2 4.002602(2) 0.49967 51.8 71.0 94.32 (1.937) 0.125(0.166) 4.220 1.02[35.0] Li 3 6.94(2) 0.43221 52.2 71.3 82.78 1.639 0.534 453.6 1615. Be 4 9.0121831(5) 0.44384 55.3 77.8 65.19 1.595 1.848 1560. 2744. C diamond 6 12.0107(8) 0.49955 59.2 85.8 42.70 1.725 3.520 2.419 C graphite 6 12.0107(8) 0.49955 59.2 85.8 42.70 1.742 2.210 Sublimes at 4098. K N2 7 14.007(2) 0.49976 61.1 89.7 37.99 (1.825) 0.807(1.165) 63.15 77.29 1.20[298.] O2 8 15.999(3) 0.50002 61.3 90.2 34.24 (1.801) 1.141(1.332) 54.36 90.20 1.22[271.] F2 9 18.998403163(6) 0.47372 65.0 97.4 32.93 (1.676) 1.507(1.580) 53.53 85.03 [195.] Ne 10 20.1797(6) 0.49555 65.7 99.0 28.93 (1.724) 1.204(0.839) 24.56 27.07 1.09[67.1] Al 13 26.9815385(7) 0.48181 69.7 107.2 24.01 1.615 2.699 933.5 2792. Si 14 28.0855(3) 0.49848 70.2 108.4 21.82 1.664 2.329 1687. 3538. 3.95 Cl2 17 35.453(2) 0.47951 73.8 115.7 19.28 (1.630) 1.574(2.980) 171.6 239.1 [773.] Ar 18 39.948(1) 0.45059 75.7 119.7 19.55 (1.519) 1.396(1.662) 83.81 87.26 1.23[281.] Ti 22 47.867(1) 0.45961 78.8 126.2 16.16 1.477 4.540 1941. 3560. Fe 26 55.845(2) 0.46557 81.7 132.1 13.84 1.451 7.874 1811. 3134. Cu 29 63.546(3) 0.45636 84.2 137.3 12.86 1.403 8.960 1358. 2835. Ge 32 72.630(1) 0.44053 86.9 143.0 12.25 1.370 5.323 1211. 3106. Sn 50 118.710(7) 0.42119 98.2 166.7 8.82 1.263 7.310 505.1 2875. Xe 54 131.293(6) 0.41129 100.8 172.1 8.48 (1.255) 2.953(5.483) 161.4 165.1 1.39[701.] W 74 183.84(1) 0.40252 110.4 191.9 6.76 1.145 19.300 3695. 5828. Pt 78 195.084(9) 0.39983 112.2 195.7 6.54 1.128 21.450 2042. 4098. Au 79 196.966569(5) 0.40108 112.5 196.3 6.46 1.134 19.320 1337. 3129. Pb 82 207.2(1) 0.39575 114.1 199.6 6.37 1.122 11.350 600.6 2022. U 92 [238.02891(3)] 0.38651 118.6 209.0 6.00 1.081 18.950 1408. 4404. Air (dry, 1 atm) 0.49919 61.3 90.1 36.62 (1.815) (1.205) 78.80 [289] Shielding concrete 0.50274 65.1 97.5 26.57 1.711 2.300 Borosilicate glass (Pyrex) 0.49707 64.6 96.5 28.17 1.696 2.230 Lead glass 0.42101 95.9 158.0 7.87 1.255 6.220 Standard rock 0.50000 66.8 101.3 26.54 1.688 2.650 Methane (CH4) 0.62334 54.0 73.8 46.47 (2.417) (0.667) 90.68 111.7 [444.] Ethane (C2H6) 0.59861 55.0 75.9 45.66 (2.304) (1.263) 90.36 184.5 Propane (C3H8) 0.58962 55.3 76.7 45.37 (2.262) 0.493(1.868) 85.52 231.0 Butane (C4H10) 0.59497 55.5 77.1 45.23 (2.278) (2.489) 134.9 272.6 Octane (C8H18) 0.57778 55.8 77.8 45.00 2.123 0.703 214.4 398.8 Paraffin (CH3(CH2)n≈23CH3) 0.57275 56.0 78.3 44.85 2.088 0.930 Nylon (type 6, 6/6) 0.54790 57.5 81.6 41.92 1.973 1.18 Polycarbonate (Lexan) 0.52697 58.3 83.6 41.50 1.886 1.20 Polyethylene ([CH2CH2]n) 0.57034 56.1 78.5 44.77 2.079 0.89 Polyethylene terephthalate (Mylar) 0.52037 58.9 84.9 39.95 1.848 1.40 Polyimide film (Kapton) 0.51264 59.2 85.5 40.58 1.820 1.42 Polymethylmethacrylate (acrylic) 0.53937 58.1 82.8 40.55 1.929 1.19 1.49 Polypropylene 0.55998 56.1 78.5 44.77 2.041 0.90 Polystyrene ([C6H5CHCH2]n) 0.53768 57.5 81.7 43.79 1.936 1.06 1.59 Polytetrafluoroethylene (Teflon) 0.47992 63.5 94.4 34.84 1.671 2.20 Polyvinyltoluene 0.54141 57.3 81.3 43.90 1.956 1.03 1.58 Aluminum oxide (sapphire) 0.49038 65.5 98.4 27.94 1.647 3.970 2327. 3273. 1.77 Barium flouride (BaF2) 0.42207 90.8 149.0 9.91 1.303 4.893 1641. 2533. 1.47 Bismuth germanate (BGO) 0.42065 96.2 159.1 7.97 1.251 7.130 1317. 2.15 Carbon dioxide gas (CO2) 0.49989 60.7 88.9 36.20 1.819 (1.842) [449.] Solid carbon dioxide (dry ice) 0.49989 60.7 88.9 36.20 1.787 1.563 Sublimes at 194.7 K Cesium iodide (CsI) 0.41569 100.6 171.5 8.39 1.243 4.510 894.2 1553. 1.79 Lithium fluoride (LiF) 0.46262 61.0 88.7 39.26 1.614 2.635 1121. 1946. 1.39 Lithium hydride (LiH) 0.50321 50.8 68.1 79.62 1.897 0.820 965. Lead tungstate (PbWO4) 0.41315 100.6 168.3 7.39 1.229 8.300 1403. 2.20 Silicon dioxide (SiO2, fused quartz) 0.49930 65.2 97.8 27.05 1.699 2.200 1986. 3223. 1.46 Sodium chloride (NaCl) 0.47910 71.2 110.1 21.91 1.847 2.170 1075. 1738. 1.54 Sodium iodide (NaI) 0.42697 93.1 154.6 9.49 1.305 3.667 933.2 1577. 1.77 Water (H2O) 0.55509 58.5 83.3 36.08 1.992 1.000 273.1 373.1 1.33

Silica aerogel 0.50093 65.0 97.3 27.25 1.740 0.200 (0.03 H2O, 0.97 SiO2) 6. Atomic and nuclear properties of materials 145

Material Dielectric Young’s Coeﬀ. of Speciﬁc Electrical Thermal constant (κ = ǫ/ǫ0) modulus thermal heat resistivity conductivity () is (κ–1) 106 [106 psi] expansion [cal/g-◦C] [µΩcm(@◦C)] [cal/cm-◦C-sec] × for gas [10−6cm/cm-◦C]

H2 (253.9) — — — — — He (64) — — — — — Li — — 56 0.86 8.55(0◦) 0.17 Be — 37 12.4 0.436 5.885(0◦) 0.38 C — 0.7 0.6–4.3 0.165 1375(0◦) 0.057 N2 (548.5) — — — — — O2 (495) — — — — — Ne (127) — — — — — Al — 10 23.9 0.215 2.65(20◦) 0.53 Si 11.9 16 2.8–7.3 0.162 — 0.20 Ar (517) — — — — — Ti — 16.8 8.5 0.126 50(0◦) — Fe — 28.5 11.7 0.11 9.71(20◦) 0.18 Cu — 16 16.5 0.092 1.67(20◦) 0.94 Ge 16.0 — 5.75 0.073 — 0.14 Sn — 6 20 0.052 11.5(20◦) 0.16 Xe — — — — — — W — 50 4.4 0.032 5.5(20◦) 0.48 Pt — 21 8.9 0.032 9.83(0◦) 0.17 Pb — 2.6 29.3 0.038 20.65(20◦) 0.083 U — — 36.1 0.028 29(20◦) 0.064 146 7. Electromagnetic relations

7. Electromagnetic Relations Revised September 2005 by H.G. Spieler (LBNL).

Quantity Gaussian CGS SI Conversion factors: Charge: 2.997 924 58 109 esu =1C=1As × Potential: (1/299.792 458) statvolt (ergs/esu) =1V=1JC−1 Magnetic ﬁeld: 104 gauss = 104 dyne/esu =1T=1NA−1m−1 v F = q (E + B) F = q (E + v B) c × × ∇. D =4πρ ∇. D = ρ 1 ∂D 4π ∂D ∇ H = J ∇ H = J × − c ∂t c × − ∂t ∇. B =0 ∇. B =0 1 ∂B ∂B ∇ E + =0 ∇ E + =0 × c ∂t × ∂t

Constitutive relations: D = E +4πP, H = B 4πM D = ǫ0E + P, H = B/µ0 M − − Linear media: D = ǫE, H = B/µ D = ǫE, H = B/µ −12 −1 1 ǫ0 =8.854 187 ... 10 F m −7 × −2 1 µ0 =4π 10 N A × 1 ∂A ∂A E = ∇V E = ∇V − − c ∂t − − ∂t B = ∇ A B = ∇ A × × ′ ′ qi Z ρ (r ) 3 ′ 1 qi 1 Z ρ (r ) 3 ′ V = X = ′ d x V = X = ′ d x ri r r 4πǫ0 ri 4πǫ0 r r charges | − | charges | − | 1 I dℓ 1 J(r′) µ I dℓ µ J(r′) A = I = Z d3x′ A = 0 I = 0 Z d3x′ c r r′ c r r′ 4π r r′ 4π r r′ | − | | − | | − | | − | ′ ′ Ek = Ek Ek = Ek 1 E′ = γ(E + v B) E′ = γ(E + v B) ⊥ ⊥ c × ⊥ ⊥ × ′ ′ Bk = Bk Bk = Bk 1 1 B′ = γ(B v E) B′ = γ(B v E) ⊥ ⊥ − c × ⊥ ⊥ − c2 × 1 µ 1 = c2 10−7 N A−2 =8.987 55 ... 109 m F−1 ; 0 = 10−7 N A−2 ; c = =2.997 924 58 108 m s−1 4πǫ0 × × 4π √µ0ǫ0 × 7. Electromagnetic relations 147

7.1. Impedances (SI units) 7.3. Synchrotron radiation (CGS units) For a particle of charge e, velocity v = βc, and energy E = γmc2, traveling in a circular orbit of radius R, the classical energy loss per ρ = resistivity at room temperature in 10−8 Ω m: revolution δE is 2 1.7 for Cu 5.5 for W 4π e δE = β3 γ4 . (7.10) ∼ 2.4 for Au ∼ 73 for SS 304 3 R ∼ ∼ 2.8 for Al 100 for Nichrome For high-energy electrons or positrons (β 1), this becomes ∼(Al alloys may have∼ double the Al value.) ≈ δE (in MeV) 0.0885 [E(in GeV)]4/R(in m) . (7.11) ≈ For alternating currents, instantaneous current I, voltage V , For γ 1, the energy radiated per revolution into the photon energy angular frequency ω: interval≫d(~ω) is V = V ejωt = ZI. (7.1) 8π 0 dI = α γ F (ω/ω ) d(~ω) , (7.12) 9 c Impedance of self-inductance L: Z = jωL . where α = e2/~c is the fine-structure constant and Impedance of capacitance C: Z =1/jωC . 3γ3c ωc = (7.13) 2R Impedance of free space: Z = pµ0/ǫ0 = 376.7 Ω . is the critical frequency. The normalized function F (y) is High-frequency surface impedance of a good conductor: 9 ∞ F (y)= √3 y Z K (x) dx , (7.14) (1 + j) ρ 8π 5/3 Z = , where δ = skin depth ; (7.2) y δ where K5/3 (x) is a modified Bessel function of the third kind. For ρ 6.6 cm electrons or positrons, δ = r for Cu . (7.3) 3 πνµ ≈ pν (Hz) ~ωc (in keV) 2.22 [E(in GeV)] /R(in m) . (7.15) ≈ Fig. 7.1 shows F (y) over the important range of y. 7.2. Capacitors, inductors, and transmission Lines The capacitance between two parallel plates of area A spaced by the 0.6 distance d and enclosing a medium with the dielectric constant ε is C = KεA/d , (7.4) 0.5 where the correction factor K depends on the extent of the fringing field. If the dielectric fills the capacitor volume without extending 0.4 beyond the electrodes. the correction factor K 0.8 for capacitors of ≈ typical geometry. ) y The inductance at high frequencies of a straight wire whose length ( 0.3

ℓ F is much greater than the wire diameter d is File [deg.pdg]synch.top nH 4ℓ 0.2 L 2.0 ℓ ln 1 . (7.5) ≈ cm · d − For very short wires, representative of vias in a printed circuit board, 0.1 the inductance is L(in nH) ℓ/d . (7.6) ≈ 0.0 0.01 0.1 1.0 10 A transmission line is a pair of conductors with inductance L and y capacitance C. The characteristic impedance Z = L/C and the p Figure 7.1: The normalized synchrotron radiation spectrum F (y). phase velocity vp = 1/√LC = 1/√µε, which decreases with the inverse square root of the dielectric constant of the medium. Typical For γ 1 and ω ωc , coaxial and ribbon cables have a propagation delay of about 5 ns/cm. ≫ ≪ dI The impedance of a coaxial cable with outer diameter D and inner 3 3 ( )1/3 (7 16) ~ . α ωR/c , . diameter d is d( ω) ≈ 1 D Z = 60Ω ln , (7.7) whereas for · √εr d γ 1 and ω & 3ωc , ≫ where the relative dielectric constant εr = ε/ε0. A pair of parallel 1/2 dI r3π ω −ω/ω 55 ωc wires of diameter d and spacing a> 2.5 d has the impedance αγ e c 1+ + ... . (7.17) d(~ω) ≈ 2 ωc 72 ω 1 2a Z = 120Ω ln . (7.8) The radiation is confined to angles . 1/γ relative to the instantaneous · √εr d direction of motion. For γ 1, where Eq. (7.12) applies, the mean ≫ This yields the impedance of a wire at a spacing h above a ground number of photons emitted per revolution is plane, 5π = (7 18) 1 4h Nγ αγ , . Z = 60Ω ln . (7.9) √3 · √εr d and the mean energy per photon is A common configuration utilizes a thin rectangular conductor above 8 ~ω = ~ωc . (7.19) a ground plane with an intermediate dielectric (microstrip). Detailed h i 15√3 calculations for this and other transmission line configurations are When ~ω & O(E), quantum corrections are important. given by Gunston.* h i

See J.D. Jackson, Classical Electrodynamics, 3rd edition (John Wiley * M.A.R. Gunston. Microwave Transmission Line Data, Noble Pub- & Sons, New York, 1998) for more formulae and details. (Note that lishing Corp., Atlanta (1997) ISBN 1-884932-57-6, TK6565.T73G85. earlier editions had ωc twice as large as Eq. (7.13). 148 8. Naming Scheme for Hadrons

8. Naming Scheme for Hadrons

Revised August 2019 by V. Burkert (Jefferson Lab), S. Eidelman mine its symbol. Conversely, these properties may be inferred (Budker Inst., Novosibirsk; Novosibirsk U.), C. Hanhart (Jülich), unambiguously from the symbol. The name X is used for states E. Klempt (Bonn U.), R.E. Mitchell (Indiana U.), U. Thoma with still unknown quantum numbers. (Bonn U.), L. Tiator (KPH, JGU Mainz) and R.L. Workman The mass label used in particle names is chosen using the best (George Washington U.). information available when a name is assigned. A more accurate value of a particle mass may become available at a later time. In the 1986 edition [1], the Particle Data Group extended and PDG will decide on a case-by-case basis whether to revise the systematized the naming scheme for mesons and baryons. The mass label, taking into account the updated information. extensions were necessary in order to name the new particles con- With u, d, and s quarks, there are two isospin-0 mesons. A taining c or b quarks that were rapidly being discovered. With the prime is used to distinguish one from the other (e.g. η and η0). discoveries of particles that are candidates for states with more complicated structures than just qq or qqq, it is necessary to ex- Vector mesons decoupling to uu + dd and ss (ideal mixing) are la- tend the naming scheme again. beled ω and φ, respectively. As usual, we assign the spectroscopic name (e.g. Υ (1S)) as the primary name to most of those ψ, Υ , 8.1 “Neutral-flavor” mesons and χ states whose spectroscopic identity is known. We use the The naming of mesons is based on their quantum numbers. Al- form Υ (9460) as an alternative, and as the primary name when though we use names established within the naive quark model, the spectroscopic identity is not known. the name does not necessarily designate a (predominantly) qq Since the top quark is so heavy that it decays too rapidly to state. In other words, the name provides information on the quan- form bound states, no name is assigned to structures like tt. tum numbers of a given state and not about its dominant compo- Mesons with quantum numbers JPC = nent, which might well be qq (if allowed) or tetraquark, molecule, 0−−, 0+−, 1−+, 2+−, 3−+, etc. cannot be qq. For such a etc. In many cases, exotic states will be difficult to distinguish “manifestly exotic" meson, we use the same symbol as for a qq from qq states and will likely mix with them, and we make no at- meson; the exotic nature of the meson can be inferred from the tempt to, e.g., distinguish those that are “mostly gluonium” from values of the P and C quantum numbers (given by the symbol), those that are “mostly qq.” and the spin J (given by the subscript). For example, an isospin-0 1−+ meson containing only u, d, and s quarks and antiquarks −− Table 8.1: Symbols for mesons with strangeness would be denoted η1 and an isospin-1 0 meson containing and heavy-flavor quantum numbers equal to zero. only u, d, and s quarks and antiquarks would be denoted ρ0. States that do not yet appear in the RPP are The last two lines of Table 8.1 list isospin-1 states that also listed in parentheses. contain hidden heavy flavor, i.e. whose minimal quark content includes cc or bb. We have assigned new names to these states, in n 0−+ 1+− 1−− 0++ keeping with the practice in the light-quark sector, where the I = JPC = 2−+ 3+− 2−− 1++ 0 and I = 1 states have distinct names. The currently established . . . . I = 1 states in the heavy-quark sector have quantum numbers . . . . JPC = 1+− and the proposed scheme keeps their original names Minimal quark content Z. ¯ ¯ ud, uu¯ − dd, du¯ (I = 1) π b ρ a 8.2 Remarks on “neutral-flavor” mesons with dd¯+ uu¯ and/or ss¯ (I = 0) η,η0 h,h0 ω,φ f,f 0 ∗ hidden charm or bottom not classified as qq cc¯ ηc hc ψ χc ¯ In the heavy-quark sector, there are several states with prop- bb ηb hb Υ χb erties – such as masses, decay patterns, and widths – that are I = 1 with cc¯ (Πc) Zc Rc (Wc) ¯ in disagreement with predictions from the naive quark model. I = 1 with bb (Πb) Zb (Rb)(Wb) For example, the vector state at 4260 MeV does not decay into DD, although within the naive quark model its quantum numbers ∗ The J/ψ remains the J/ψ. would call for this decay channel to be dominant. In recent literature, these states have been called X, Y , or Z, with their masses Table 8.1 shows the names for mesons having strangeness and added in parentheses. This nomenclature conflicts with the rules all heavy-flavor quantum numbers equal to zero. The rows of Ta- outlined in the previous section, since the meson names are not ble 8.1 give the minimal qq content. The columns give the possible related to their quantum numbers. However, these states have parity/charge-conjugation states, properties in conflict with the naive quark model and therefore deserve some special labeling. PC = −+, +−, −−, and ++ . Therefore in the Review of Particle Physics we will keep two Within the naive quark model, these combinations correspond names, one that carries the quantum number information and the 2S+1 other the original name. However, the former name will be given one-to-one to the angular-momentum state LJ of the qq system being priority. In particular, it will be used when the particle appears as a decay product. Thus, in the Listings as well as Summary Tables 1 1 3 3 (L even)J , (L odd)J , (L even)J , or (L odd)J , from the 2018 edition onwards (listed are only some examples of the particles that appear in the Summary Tables), respectively. Here S, L, and J are the spin, orbital, and total angular momenta of the qq system. Within the naive quark • X(3872) will appear as ‘χc1(3872) also known as X(3872)’; L+1 model, the quantum numbers are related by P = (−1) , • X(3900)± will appear as ‘Z (3900)±’; C = (−1)L+S , and G parity = (−1)L+S+I , where the quantum c number C is only relevant to neutral mesons with neutral-flavor • X(4260) will appear as ‘ψ(4260) also known as Y (4260)’; quantum numbers and G extends to isovector mesons; see the re- In addition, states with quantum numbers allowed by the naive view on the quark model. These expressions impose restrictions quark model but showing some peculiarities, such as an unusual on the quantum numbers that are allowed for qq states. How- decay pattern, will have the following information in the header: ever, they do not apply to more complicated structures such as tetraquarks. This state shows properties different from a conventional The spin J is added as a subscript in the name except for pseu- qq state. A candidate for an exotic structure. See the doscalar and vector mesons, and the mass is added in parentheses minireview on non-qq states. for mesons that decay strongly. However, for some of the familiar mesons (e.g. η0, φ, ω), we omit the mass. The states that cannot be classified as qq states (such as charged Measurements of the mass, quark content (where relevant), and states with strong decays to heavy quarkonia) will have in the quantum numbers I, J, P , and C (or G) of a meson thus deter- header: 8. Naming Scheme for Hadrons 149

Properties incompatible with a qq structure (exotic 8.5 Exotic baryons state). See the minireview on non-qq states. In 2003, several experiments reported finding a strangeness S = +1, charge Q = +1 baryon, and one experiment reported finding The names Zc and Zb used in the literature for isovector states an S = −2, Q = −2 baryon. Baryons with such quantum numbers in the cc and bb sector, respectively, will now also be the official cannot be made from three quarks, and thus they are exotic with PDG names. No heavy isovector PC = −+, −−, or ++ states respect to the naive quark model. However, these “discoveries” have yet been confirmed, but provisional names for such states – were then ruled out by many experiments with far larger statistics: Π, R, and W , respectively – are listed in Table 8.1. Note that See our 2008 Review [3]. the heavy isovector PC = ++ states were predicted to exist as More recently, the LHCb collaboration found a series of can- spin partners of the Z states in [2], where the name W was also didates for pentaquark states in the J/ψp system extracted from introduced. 0 − ∗∗ data on Λb → J/ψK p [4,5]. These have the quantum numbers By analogy to the light-quark sector, states with quantum num- of excited nucleons, but have a minimal quark content of ccuud¯ . bers that are in conflict with the naive quark model are labeled Following the name established by the LHCb collaboration, we + P according to their I, P , C, and spin J. The exotic nature can be label these Pc (mass)J , with the mass given in parentheses. inferred from the quantum numbers. 8.6 Change of meson names 8.3 Mesons with nonzero S, C and/or B For the recently discovered particles above open-flavor thresh- Mesons with nonzero strangeness S or heavy flavor C and/or B old in the charmonium and bottomonium systems (previously the are not eigenstates of charge conjugation, and in each of them one “XYZ” mesons), there are a number of differences between the of the quarks is heavier than the other (as above, states containing names newly adopted by the PDG and those that have commonly top quarks are not considered). The rules have been and remain: appeared in the literature. Table 8.2 maps the names now used in the PDG to former commonly used names.

1. The main symbol is an upper-case italic letter indicating the Footnotes and References: heavier quark as follows: ∗ See the “Note on Charmed Baryons” in the Charmed Baryon Listings. s → K c → D b → B, ∗∗ See our review “Pentaquarks” in the 2016 Edition. We use the convention that the flavor quantum number and the charge of a quark have the same sign. Thus the Table 8.2: A comparison of current PDG names strangeness of the s quark is negative, the charm of the c to former names commonly used in the literature. quark is positive, and the bottomness of the b quark is negative. The effect of this convention is as follows: any flavor Mesons with complete IGJPC assignment carried by a charged meson has the same sign as its charge. PDG Name Former Common Name(s) + + + ∗ Thus the K , D , and B have positive strangeness, charm, ψ2(3823) X(3823) and bottomness, respectively, and all have positive I3. The χ (3872) X(3872) + c1 Ds has positive charm and strangeness. Furthermore, the Zc(3900) Zc(3900) ∆(flavor) = ∆Q rule, best known for the strange kaons, ap- † χc2(3930) χc2(2P ), Z(3930) plies to every flavor. χc1(4140) Y (4140) 2. If the lighter quark is not a u or a d quark, its identity is Zc(4200) Zc(4200) + given by a subscript. The Ds is an example. ψ(4230) Y (4230) 3. When the spin-parity is in the natural series, JP = Rc0(4240) Zc(4240) 0+, 1−, 2+, ··· , a superscript “∗” is added. ψ(4260) Y (4260) 4. The spin is added as a subscript except for pseudoscalar or χc1(4274) Y (4274) vector mesons. ψ(4360) Y (4360) Zc(4430) Zc(4430) 8.4 Ordinary (3-quark) baryons χc0(4500) X(4500) All baryons having quantum numbers consistent with a minimal ψ(4660) X(4630), Y (4660) quark content of three quarks are denoted by the symbols N, ∆, Λ, χc0(4700) X(4700) Σ, Ξ, and Ω introduced more than 50 years ago. These symbols Zb(10610) Zb(10610) P (0) are followed by J signifying their spin J and parity P . For those Zb(10650) Zb (10650) where the minimal content involves one or more heavier quarks Mesons with incomplete IGJPC assignment than the light (u, d, and s) quarks, subscripts are added to their PDG Name Former Common Name(s) symbols, (c and b) as appropriate. The rules are: ‡ X(3915) χc0(3915), X(3915), Y (3940) X(3940) X(3940) 1. Baryons with miminal content of three u and/or d quarks are (0) X(4020) Zc (4020) N’s (isospin 1/2) or ∆’s (isospin 3/2). ± X(4050) Z1(4050) ± 2. Baryons with two u and/or d quarks are Λ’s (isospin 0) or Σ’s X(4055) Zc(4055) (isospin 1). If the third quark is a c or b quark, its identity X(4160) X(4160) ± is given by a subscript. X(4250) Z2(4250) 3. Baryons with one u or d quark are Ξ’s (isospin 1/2). One X(4350) X(4350) or two subscripts are used if one or both of the remaining ∗ quarks are heavy: thus Ξc, Ξcc, Ξb, etc. ∗The 2016 edition used ψ(3823). † 4. Baryons with no u or d quarks are Ω’s (isospin 0), and sub- The 2016 edition used χc2(2P ). The mass is now used in the name scripts indicate any heavy-quark content. following the current prescription. ‡ PC The 2016 edition used χc0(3915). The J have since been ques- 5. A baryon that decays strongly has its mass in parentheses. tioned. Examples are the ∆(1232) 3/2+, Σ(1385) 3/2+, N(1440) + + 1/2 , Ξc(2645) 3/2 . References In short, the minimal number of u plus d quarks together with the [1] M. Aguilar-Benitez et al. (Particle Data Group), Phys. Lett. isospin determine the main symbol, and subscripts indicate any 170B, 1 (1986). content of heavy quarks. A Σ always has isospin 1, an Ω always [2] M. B. Voloshin, Phys. Rev. D84, 031502 (2011), has isospin 0, etc. [arXiv:1105.5829]. 150 8. Naming Scheme for Hadrons

[3] C. Amsler et al. (Particle Data Group), Phys. Lett. B667, 1 [arXiv:1507.03414]. (2008). [5] R. Aaij et al. (LHCb), Phys. Rev. Lett. 122, 22, 222001 (2019), [arXiv:1904.03947]. [4] R. Aaij et al. (LHCb), Phys. Rev. Lett. 115, 072001 (2015),