Atomic units

In this book we have used the atomic units, that is the unit system in which the numerical values of the basic units in tab:au are unity.

 

 

Table: Basic quantities for the atomic unit system

Constant	Symbol
rest mass of the electron	me
elementary charge	e
Planck's constant divided by $2\pi$	$\hbar=h/2\pi$
$4\pi$ times the permittivity of free space	$4\pi \epsilon_0$

Other units in the system are obtained by combining these four basic quantities and are shown in tab:au1

 

 

Table: Quantities for the atomic unit system

Constant	Symbol	Recommended value
length, Bohr	$a_0= 4\pi \epsilon_0 \hbar^2 /m_e e^2$	5.291 772 49(24) $\times 10^{-11}$ m
velocity,	$v_B = \alpha c$	2.187 691 42(10) $\times 10^{6}$ ms-1
energy, Hartree	$E_h=\hbar^2 / m_e a_0^2$	4.359 748 2(26) $\times 10^{-18}$ J
time	$\tau_0 = \hbar / E_h$	2.418 884 326 555(53) $\times 10^{-17}$ s
magnetic dipole moment	$\mu_B= e\hbar /2m_e$	9.274 015 4(31) $\times 10^{-24}$ JT-1
electric dipole moment	d0= ea0	8.478 357 9(26) $\times 10^{-30}$ Cm

From the expression for the velocity it is seen that the velocity of light has the value ${\alpha}^{-1}=137.035~989~5(611)$ in atomic units.