ABSTRACT
For an interaction potential V3(r) = –C3r3; EA,S are characteristic energies of the atom and surface; g = 1 for a free-electron metal and g = (ε∞ – 1)/(ε∞ + 1) for an ionic crystal
Relationship between α(ν) and oscillator strengths α π
v e
( ) = − ( )
e h m
f E hv
2 2 24 Σ Here, fk is the oscillator strength from the ground state to an
excited state k, with excitation energy Ek . This formula is often used to estimate static polarizabilities (ν = 0)
Dynamic polarizability α α
ν v r
r ( ) =
− ( ) E
E h 2
Approximate variation of the frequency-dependent polarizability α(ν) from ν = 0 up to the first dipole-allowed electronic transition, of energy Er; the static dipole polarizability is α(0); infrared contributions ignored
Rayleigh scattering cross section α
π πν
α ν γ ν
v( ) = ( )
× ( ) + ( )[ ]
8 9 2
3 2 3
c
/
The photon frequency is ν; the polarizability anisotropy (the difference between polarizabilities parallel and perpendicular to the molecular axis) is γ(ν)
Verdet constant V nm cν
ν α ν ν( ) = ( )
2 2e
d d
Defined from θ = V(ν)B, where θ is the angle of rotation of linearly polarized light through a medium of number density n, per unit length, for a longitudinal magnetic field strength B (Faraday effect)
Atomic number Atom
Polarizability
Estimated accuracy
(%) Method Ref. 1 H 0 .666793 “exact” calc MB77 2 He 0 .2050522 “exact” calc LJS04
0 .2050519 0 .0009 diel SGMM07 3 Li 24 .33 0 .16 beam MJBTV06 4 Be 5 .60 2 calc MB77 5 B 3 .03 2 calc MB77 6 C 1 .67 2 calc TASSS08 7 N 1 .10 2 calc/
index MB77
8 O 0 .802 2 calc/ index
MB77
9 F 0 .557 2 calc MB77 10 Ne 0 .39432 0 .003 diel GF10 11 Na 24 .11 0 .12 inter-
ferom ESCHP94
12 Mg 10 .6 2 calc MB77 11 .1 5 calc S71 10 .6 5 calc BM02
13 Al 6 .8 4 .4 beam MMD90 14 Si 5 .53 2 calc TASSS08 15 P 3 .63 2 calc MB77 16 S 2 .90 2 calc MB77 17 Cl 2 .18 2 calc MB77 18 Ar 1 .6411 0 .05 index/
diel NB65/OC67
19 K 43 .4 2 beam MB77 20 Ca 22 .8 2 calc MB77
Atomic number Atom
Polarizability
Estimated accuracy
(%) Method Ref. 25 .0 8 beam MB77
21 Sc 17 .8 25 calc D84 22 Ti 14 .6 25 calc D84 23 V 12 .4 25 calc D84 24 Cr 11 .6 25 calc D84 25 Mn 9 .4 25 calc D84 26 Fe 8 .4 25 calc D84 27 Co 7 .5 25 calc D84 28 Ni 6 .8 25 calc D84 29 Cu 6 .2 6 calc BM02
6 .1 25 calc D84 30 Zn 5 .75 2 index GHM96
6 .1 6 calc BM02 5 .6 25 calc D84
31 Ga 8 .12 2 calc MB77 32 Ge 5 .84 2 calc TASSS08 33 As 4 .31 2 calc MB77 34 Se 3 .77 2 calc MB77 35 Br 3 .05 2 calc MB77 36 Kr 2 .4844 0 .05 diel OC67 37 Rb 47 .3 2 beam MB77 38 Sr 27 .6 8 beam MB77
23 .5 6 calc BM02 39 Y 22 .7 25 calc D84 40 Zr 17 .9 25 calc D84 41 Nb 15 .7 25 calc D84 42 Mo 12 .8 25 calc D84
Atomic number Atom
Polarizability
accuracy
(%) Method Ref. 43 Tc 11 .4 25 calc D84 44 Ru 9 .6 25 calc D84 45 Rh 8 .6 25 calc D84 46 Pd 4 .8 25 calc D84 47 Ag 7 .2 25 calc D84 48 Cd 7 .36 3 index GH95
7 .4 6 calc BM02 7 .2 25 calc D84
49 In 10 .2 12 beam GMBSJ84 9 .1 25 calc D84
50 Sn 6 .28 26 beam TASSS08 7 .84 2 calc TASSS08
51 Sb 6 .6 25 calc D84 52 Te 5 .5 25 calc D84 53 I 5 .35 25 index A56
4 .7 25 calc D84 54 Xe 4 .044 0 .5 diel MB77 55 Cs 59 .42 0 .13 beam AG03 56 Ba 39 .7 8 beam MB77 57 La 31 .1 25 calc D84 58 Ce 29 .6 25 calc D84 59 Pr 28 .2 25 calc D84 60 Nd 31 .4 25 calc D84 61 Pm 30 .1 25 calc D84 62 Sm 28 .8 25 calc D84 63 Eu 27 .7 25 calc D84 64 Gd 23 .5 25 calc D84 65 Tb 25 .5 25 calc D84 66 Dy 24 .5 25 calc D84 67 Ho 23 .6 25 calc D84 68 Er 22 .7 25 calc D84 69 Tm 21 .8 25 calc D84 70 Yb 20 .9 2 calc TS09 71 Lu 21 .9 25 calc D84 72 Hf 16 .2 25 calc D84 73 Ta 13 .1 25 calc D84 74 W 11 .1 25 calc D84
Atomic number Atom
Polarizability
accuracy
(%) Method Ref. 75 Re 9 .7 25 calc D84 76 Os 8 .5 25 calc D84 77 Ir 7 .6 25 calc D84 78 Pt 6 .5 25 calc D84 79 Au 5 .8 25 calc D84 80 Hg 5 .02 1 index GH96
5 .7 25 calc D84 81 Tl 7 .6 15 beam NYU84
7 .5 25 calc D84 82 Pb 6 .98 15 beam TASSS08
7 .01 2 calc TASSS08 83 Bi 7 .4 25 calc D84 84 Po 6 .8 25 calc D84 85 At 6 .0 25 calc D84 86 Rn 5 .3 25 calc D84 87 Fr 48 .60 2 calc LSMS05
47 .1 5 calc DJSB99 88 Ra 38 .3 25 calc D84 89 Ac 32 .1 25 calc D84 90 Th 32 .1 25 calc D84 91 Pa 25 .4 25 calc D84 92 U 24 .9 6 beam KB94 93 Np 24 .8 25 calc D84 94 Pu 24 .5 25 calc D84 95 Am 23 .3 25 calc D84 96 Cm 23 .0 25 calc D84 97 Bk 22 .7 25 calc D84 98 Cf 20 .5 25 calc D84 99 Es 19 .7 25 calc D84 100 Fm 23 .8 25 calc D84 101 Md 18 .2 25 calc D84 102 No 16 .4 1 calc TS09 112 E112 4 .06 2 calc PBEK08 114 E114 4 .59 2 calc TASSS08
4 .37 2 calc PBEK08 119 ekafrancium 24 .26 2 cal LSMS05
References A56 . Atoji, M ., J. Chem. Phys . 25, 174, 1956 . Semiempirical method based
on molecular polarizabilities and atomic radii . AG03 . Amini, J . M ., and Gould, H ., Phys. Rev. Lett. 91, 153001, 2003 . BM02 . Bromley, M . W . J ., and Mitroy, J ., Phys. Rev. A 65, 062505, 2002;
062506, 2002 . D84 . Doolen, G . D ., Los Alamos National Laboratory, unpublished . A
relativistic linear response method was used . The method is that described by Zangwill, A ., and Soven, P ., Phys. Rev. A 21, 1561, 1980 . Adjustments of less than 10% across the periodic table have been made to these results to bring them into agreement with accurate experimental values where available, for the purpose of presenting “recommended” polarizabilities in Table 2 .
