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1.1 Useful constants

electron charge=3D4.8x10-10 esu=3D1.6x10-19C

electron mass=3D 9.1 x10-28gm

1.05 x10-27 ergs-s=3D6.58 x10-16 <= /sup> eV

 Avogardro number=3D 6.022x1023 /mol

 Boltzman= n's constant  k =3D 1.380658 x 10<= sup>-23 J/K=3D8.617 x 10-5 eV/K

 

1.2.  Energy conversion factors

 

        =         1 eV  =3D  8065.54   cm-1

        =             &nb= sp;   1 a.u =3D   27.211396 eV   =3D  219 474.63 05 cm<= sup>-1 =3D2 Ry
            =     1 Ry =3D   13.6057      eV

        =         1 degree kelvin  =3D   0.0862          meV  (energy units for = cold atoms)
     &nb= sp;            =                   =         =3D 0.695             cm= -1

         1 Kcal/mol=3D 0.0434 eV =3D 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.) <= span style=3D'mso-spacerun:yes'>     k=3D 2.7 x10-4 E (eV)<= /span>

 de Broglie wavelength  for electron:     (in   ;  

        =             &nb= sp;            =             &nb= sp;            =  

 

1.3. Atomic units  (au)  e=3D=3Dm=3D1

 

 Unit of =  length=3D  a0=3DBohr radius= =3D    0.529  (  

 Unit of velocity=3D =3D v0 =3D electron velocity in the first Bohr orbit= al=3D αc

        =             &nb= sp;            (: fine structure const)

 Unit of = time =3D a0/αc  =3D 24.2 asec          =  (1 fs=3D41 au)  asec=3D10-18= sec  (attosecond)

 Unit of = frequency=3D  v0 /a0  =3D 4.13 x1016 se= c-1

 Unit of = Electric field=3D 5.14x109 V/cm =3De/a02=

 Unit of = Magnetic field=3D 2.35 x105 tesla

 Unit of = magnetic dipole moment=3DBohr magneton=3DµB=3De/2m=3D5.79x10-5 eV/Telsa

 Unit of = electric dipole moment=3Dea0

 

1.4.    Short hand notations

109=3Dgig= a, 1012  =3Dtera;   1015=3D peta ;    1018 =3Dexa= ; 1021=3Dzetta ;     1024= =3Dyocto 

  10-9=3Dnano 10-12 =3Dpico;=     10-15=3Dfem= to; 10-18=3Datto;   10-21=3Dzepto;   10-24=3Dyotta

 

 

1.4. Lasers

For 1 oA, photon energy=3D 455.71 au   for 800 nm ->

laser peak intensity (line= ar polarized) =3D3.5 x1016 W/cm2

UP=3DE2/4=3D9.33 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 wi= th   is 1.83 eV

1.5. Oscillator strength and transition rates
  A=3D 2*(E2/c3) f   (4.= 13 x1016)    1/sec
   where E is in a.u. , c=3D137.03604 and f  is the oscillat= or strength for emission

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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