# CreateFluorescenceYield

CreateFluorescenceYield($O_1$,$O_2$,$O_3$,$\psi$) calculates $$\langle \psi | O_2^{\dagger} \frac{1}{(\omega - \mathrm{i} \Gamma/2 + E_0 - O_1^{\dagger})} O_3^{\dagger} O_3\frac{1}{(\omega + \mathrm{i} \Gamma/2 + E_0 - O_1)} O_2 | \psi \rangle,$$ with $E_0 = \langle \psi | O_1 | \psi \rangle$. The spectrum is returned as a spectrum object. Please note that fluorescence yield is the expectation value of an Hermitian operator. The returned spectrum is thus completely real. Possible options are:

## Input

• $O_1$ : Operator
• $O_2$ : Operator
• $O_3$ : Operator
• $psi$ : Wavefunction
• Possible options are
• “NTri” Positive integer specifying the number of states in the Krylov basis. (Standard value 200)
• “epsilon” Positive real defining the smallest absolute value considered different than zero. (Standard value 1.49E-8)
• “restrictions” A list of restrictions defining restrictions on configurations and occupations included. Allows one to do restricted active space calculations. Note that the action of $O_3$ is not restricted and all excitations it can make are included.
• “Emin” Real value defining the minimum energy in the spectra (Standard value determined such that the spectrum fits into the range
• “Emax” Real value defining the maximum energy in the spectra (Standard value determined such that the spectrum fits into the range
• “NE” Positive integer defining the number of points in the spectrum. (Standard value 1000)
• “Gamma” Positive real defining the full width half maximum Lorenzian broadening. (Standard value 10*(Emax-Emin)/NE)

## Output

• G : Spectra object

## Example

description text

### Input

CreateFluorescenceYield.Quanty
dofile("../definitions.Quanty")
-- define an Hamiltonian (in this case a magnetic field of 6 tesla in the z direction)
H = 6 * EnergyUnits.Tesla.value * (2*OppSz + OppLz)
-- define a transition operator (in this case a pulsed magnetic field of 20 tesla in the x direction)
T1 = 20 * EnergyUnits.Tesla.value * (2*OppSx + OppLx)
-- define a ground-state (in this case a p electron with spin and angular momentum down)
psigrd = psim1dn
-- define a feritale operator to be able to calculate FY
T2 = (2*OppSy + OppLy)

-- calculate < psigrd | T1^dag 1/(w-i*G/2+E0-H^dag) T2^dag T2 1/(w+i*G/2+E0-H) T1 | psigrd >
--   with E0 = <psigrd | H | psigrd >
spec = CreateFluorescenceYield(H, T1, T2, psigrd,{{"NE",20}})

-- the real and imaginary=0 part on a fixed energy grid
print(spec)

### Result

CreateFluorescenceYield.out
Start of LanczosTriDiagonalizeKrylovRR
#Spectra: 1
Emin______Emax       3.038900445581885E-04  7.380186796413151E-04
EminPole__EmaxPole   3.473029080665012E-04  6.946058161330025E-04
dE________Gamma      2.170643175415633E-05  2.170643175415633E-04
Energy               Re[0]                  Im[0]
3.038900445582E-04  1.445970424529857E+02  0.000000000000000E+00
3.255964763123E-04  1.522565191355002E+02  0.000000000000000E+00
3.473029080665E-04  1.492068011071571E+02  0.000000000000000E+00
3.690093398207E-04  1.352205128205129E+02  0.000000000000000E+00
3.907157715748E-04  1.147275532671071E+02  0.000000000000000E+00
4.124222033290E-04  9.357859982480973E+01  0.000000000000000E+00
4.341286350831E-04  7.573964497041422E+01  0.000000000000000E+00
4.558350668373E-04  6.273363774733638E+01  0.000000000000000E+00
4.775414985914E-04  5.465063752276871E+01  0.000000000000000E+00
4.992479303456E-04  5.113037565867757E+01  0.000000000000000E+00
5.209543620998E-04  5.189019343797783E+01  0.000000000000000E+00
5.426607938539E-04  5.693240410221549E+01  0.000000000000000E+00
5.643672256081E-04  6.658797814207658E+01  0.000000000000000E+00
5.860736573622E-04  8.143683409436844E+01  0.000000000000000E+00
6.077800891164E-04  1.020124757460593E+02  0.000000000000000E+00
6.294865208705E-04  1.280776228016981E+02  0.000000000000000E+00
6.511929526247E-04  1.573343041902881E+02  0.000000000000000E+00
6.728993843788E-04  1.842324786324788E+02  0.000000000000000E+00
6.946058161330E-04  2.010344009489918E+02  0.000000000000000E+00
7.163122478872E-04  2.024280037018893E+02  0.000000000000000E+00
7.380186796413E-04  1.895640527396284E+02  0.000000000000000E+00