1.1 Useful constants

electron charge=4.8x10-10 esu=1.6x10-19C

electron mass= 9.1 x10-28gm

1.05 x10-27 ergs-s=6.58 x10-16 eV

Avogardro number= 6.022x1023 /mol

Boltzmann's constant k = 1.380658 x 10-23 J/K=8.617 x 10-5 eV/K

 

1.2. Energy conversion factors

 

1 eV  =  8065.54   cm-1

1 a.u =   27.211396 eV   =  219 474.63 05 cm-1 =2 Ry
     1 Ry =   13.6057      eV

1 degree kelvin = 0.0862          meV (energy units for cold atoms)
                             = 0.695             cm-1

1 Kcal/mol= 0.0434 eV = 43.4 meV (energy units used by chemists)

1 GHz in photon 4.13x10-6 eV (energy units by laser physicists)

photon momentum (a.u.) k= 2.7 x10-4 E (eV)

de Broglie wavelength for electron: (in ; ( at 100 eV is 1.22

 

1.3. Atomic units (au) e==m=1

Unit of length= a0=Bohr radius= 0.529 (

Unit of velocity= = v0 = electron velocity in the first Bohr orbital= αc

(: fine structure const)

Unit of time = a0/αc = 24.2 asec (1 fs=41 au) asec=10-18 sec (attosecond)

Unit of frequency= v0 /a0 = 4.13 x1016 sec-1

Unit of Electric field= 5.14x109 V/cm =e/a02

Unit of Magnetic field= 2.35 x105 tesla

Unit of magnetic dipole moment=Bohr magneton=B=e/2m=5.79x10-5 eV/Telsa

Unit of electric dipole moment=ea0

 

1.4. Short hand notations

109=giga, 1012 =tera; 1015= peta ; 1018 =exa ; 1021=zetta ; 1024=yocto

10-9=nano 10-12 =pico; 10-15=femto; 10-18=atto; 10-21=zepto; 10-24=yotta

 

 

1.4. Lasers

For 1 oA, photon energy= 455.71 au for 800 nm ->

laser peak intensity (linear polarized) =3.54 x1016 W/cm2

UP=E2/4=9.33 I(1014 W/cm2)(inm)

( 6eV for 800 nm at 1014 W/cm2)

Keldysh parameter

time-frequency width relation:

Gaussian pulse

(is FWHM in time domain)

width in eV for a Gaussian pulse with is 1.83 eV

 

1.5. Oscillator strength and transition rates


  A= 2*(E2/c3)   (4.13 x1016)    1/sec
   where E is in a.u. , c=137.03604 and f  is the oscillator strength for emission

 

1.6 pressure

1 atm=1.01x105 Pa= 760 Torr =1.013 bar

1 mbar= 0.75 Torr

1 psi= 51.7 torr = 0.068 atom

 

1.7. Binding energies and equilibrium distance

 

Kr: 14.0 eV, Xe: 12.3 eV

 

N2: 15.6 eV, 17.2 eV, 18.7 eV RO=1.10 A, N2+: 1.12A

O2: 12.3 eV, 16.7 eV, 18.2 eV R0= 1.21 A, O2+: 1.12A

CO2: 13.8 eV, 17.6 eV, 18.1 eV