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 à 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=µB=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) f   (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