Difference between revisions of "Levelpop.m"

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Equilibrium populations of the energy levels of a user-specified spin at
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{{DISPLAYTITLE:levelpop.m}} __NOTOC__
the user-specified temperature. Energies are reported as fractions of kT
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Equilibrium populations of the energy levels of a user-specified spin at the user-specified temperature. Energies are reported as fractions of kT at the temperature specified.
at the temperature supplied. Note that the function is sensitive to the
 
sign of the magnetogyric ratio (negative for electrons, positive for pro-
 
tons, etc.). Syntax:
 
  
                [E,P,dP]=levelpop(isotope,field,temperature)
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==Syntax==
  
Parameters:
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    [E,P,dP]=levelpop(isotope,field,temperature)
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==Parameters==
  
 
       isotope      - character string specifying the isotope.
 
       isotope      - character string specifying the isotope.
 
                       e.g. '1H', '13C', 'E', etc.
 
                       e.g. '1H', '13C', 'E', etc.
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      field        - primary magnet field in Tesla
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      temperature  - spin temperature, Kelvin
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==Outputs==
  
       field       - primary magnet field in Tesla
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       E            - vector of level energies, frac-
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                      tions of kT at the temperature
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                      specified
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      P            - vector of level populations
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       dP          - vector of population differences
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                      for adjacent levels
  
      temperature  - spin temperature, Kelvin
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==Examples==
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Free electron energy level populations at 4.0 Kelvin:
  
Outputs:
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    >> [~,P]=levelpop('E',14.1,4.0)
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    P =
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        (1,1)      0.0087
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        (2,1)      0.9913
  
      E            - vector of level energies
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==Notes==
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The function is sensitive to the sign of the magnetogyric ratio - negative for electrons, positive for protons, ''etc.''
  
      P            - vector of level populations
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==See also==
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[[spin.m]], [[equilibrium.m]], [[pauli.m]], [[carrier.m]], [[hamiltonian.m]], [[brokensymm.m]], [[quad_shift.m]], [[r1csa2tauc.m]], [[r1n_dnp.m]], [[r2csa2tauc.m]], [[rlx_csa.m]], [[rlx_dd_csa.m]], [[rlx_dip.m]], [[rlx_hfc.m]], [[rlx_nqi.m]], [[trosy_eff.m]], [[Textbook_module]]
  
      dP          - vector of level population differences
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''Version 2.4, authors: [[Ilya Kuprov]]''

Latest revision as of 19:38, 6 June 2026

Equilibrium populations of the energy levels of a user-specified spin at the user-specified temperature. Energies are reported as fractions of kT at the temperature specified.

Syntax

    [E,P,dP]=levelpop(isotope,field,temperature)

Parameters

      isotope      - character string specifying the isotope.
                     e.g. '1H', '13C', 'E', etc.

      field        - primary magnet field in Tesla

      temperature  - spin temperature, Kelvin

Outputs

      E            - vector of level energies, frac-
                     tions of kT at the temperature
                     specified

      P            - vector of level populations

      dP           - vector of population differences
                     for adjacent levels

Examples

Free electron energy level populations at 4.0 Kelvin:

    >> [~,P]=levelpop('E',14.1,4.0)

    P =

       (1,1)       0.0087
       (2,1)       0.9913

Notes

The function is sensitive to the sign of the magnetogyric ratio - negative for electrons, positive for protons, etc.

See also

spin.m, equilibrium.m, pauli.m, carrier.m, hamiltonian.m, brokensymm.m, quad_shift.m, r1csa2tauc.m, r1n_dnp.m, r2csa2tauc.m, rlx_csa.m, rlx_dd_csa.m, rlx_dip.m, rlx_hfc.m, rlx_nqi.m, trosy_eff.m, Textbook_module

Version 2.4, authors: Ilya Kuprov