physics. Symbol a.u. Any one of the coherent set of units based on the Bohr radius plus other natural sub-atomic units introduced by Hartree in 1927.
[Hartree D. R. Proc. Camb. Phil. Soc. Vol. 24, 89 (1927)] (Compare natural unit.) Named generically atomic unit of action, etc. (and earlier sometimes the Hartree unit of action, etc., though that personal name is used now to mean the atomic unit of energy), the members and their current values (with 108 times the relative standard uncertainty appended to each)
[Mohr P. J., Taylor B. N. CODATA Recommended Values of the Fundamental Physical Constants: 2002 (to be published)]
[Mohr P. J., Taylor B. N. Rev. Mod. Phys. Vol. 72:351-495 (2000)]
[Mohr P. Phys. Today Vol. 53:7, 11-16 (2000)]
[For latest recommended values, see http://physics.nist.gov/cuu/Constants/index.html] of the derived units are shown in Table 4.
Table 4| Base units: atomic unit of | | | |
| action | ℏ | the Planck constant over 2 π | |
| charge | e | the elementary charge | |
| length | a0 | Bohr radius | |
| mass | me | electron mass | |
| Derived units: atomic unit of | | | |
| charge density | e/a03 | 1.081 202 317(93) × 1012 C·m-3 | 8.6 |
| current | e·Eh/ℏ | 6.623 617 82(57) × 10-3 A | 8.5 |
| electric dipole moment | e·a0 | 8.478 353 09(73) × 10-30 C·m | 8.6 |
| electric field | Eh/e·a0 | 5.142 206 42(44) × 1011 V·m-1 | 8.6 |
| electric field gradient | Eh/e·a02 | 9.717 361 82(83) × 1021 V·m-2 | 8.6 |
| electric polarizability | e2·a02/Eh | 1.648 777 274(16) × 10-41 C2·m2·J-1 | 1.0 |
| electric potential | Eh/e | 27.211 384 5(23) × 101 V | 8.5 |
| electr. quadrupole moment | e·a02 | 4.486 551 24(39) × 10-40 C·m2 | 8.6 |
| energy (Hartree) | Eh = me·e4/ℏ2 | 4.359 744 17(75) × 10-18 J | 17 |
| force | Eh/a0 | 8.238 722 5(14) × 10-8 N | 17 |
| magnetic dipole moment | e·ℏ/me | 1.854 801 90(16) × 10-23 J·T-1 | 8.6 |
| magnetic flux density | ℏ/e·a02 | 2.350 517 42(20) × 105 T | 8.6 |
| magnetizability | e2·a02/me | 7.891 036 60(13) × 10-29 J·T-2 | 1.7 |
| momentum | ℏ/a0 | 1.992 851 66(34) × 10-24 kg·m·s-1 | 17 |
| permittivity | e2/a0·Eh | 1.112 650 056~ × 10-10 F·m-1 | (exact) |
| time | ℏ/Eh | 2.418 884 326 505(16) × 10-17 s | 0.0* |
| velocity (or speed) | a0·Eh/ℏ | 2.187 691 263 3(73) × 106 m·s-1 | 0.33 |
| The asterisked figure is 0.000 66. |