Validation of Radiative Calculation G4SUWS_2009_Sudhakar_TransitionProbabilities

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Validation of RadiativeValidation of Radiative

Transition Probability CalculationsTransition Probability Calculations

Manju Sudhakar, M. G. Pia, P. Saracco

INFN Sezione di Genova and INFN Laboratori Nazionali di Frascati, Italy


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Theme Message (List 3 strengths ?)

Manju Sudharka: Validation of Radiative Transition Probability CalculationsValidation of Radiative Transition Probability CalculationsMay 25, 2009

Why relevant? One out of many examples:Why relevant? One out of many examples:

PIXE = Particle Induced X-ray Emission

Used for e.g. material diagnostics

But also important for astronomy: protons induce X-ray

background of X-ray telescopes


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Radiative transition probabilitiesRadiative transition probabilities

Two theoretical methods of calculation Hartree-Slater

Hartree-Fock

Hartree-Slater Used in EADL (Evaluated Atomic Data Library)

Indirectly used by all the Monte Carlo codes that use EADL

(EGSnrc, Geant4, MCNP etc.)

Hartree-Fock Used by GUPIX

Experimental database: Elam et al. Based on fits to experimental data collected by Salem et al.


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This projectThis project

Validation of Hartree-Slater and Hartree-Fock calculationsagainst experimental data

Experimental source S. I. Salem, S. I. Panossian and R. A. Krause, ``Experimental K

and L Relative X-ray Emission Rates'',Atom. Data Nucl. Data

Tables, vol. 14, pp. 91-109, 1974. Still the most complete collection of experimental transition

probabilities data Cross-check: compared to more recent measurements Original raw data used in the validation (not Salems fits)

Theoretical sources Hartree-Slater calculations by Scofield Hartree-Fock calculations by Scofield EADL (in principle the same as Hartree-Slater calculations by

Scofield)


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KL2 transitionKL2 transition

KL2

.0 25

.0 26

.0 27

.0 28

.0 29

.0 3

.0 31

.0 32

.0 33

.0 34

19 29 39 49 59 69 79 89 99

Z

Probability

Hartree-Slater Hartree-Fock Elam Experimental


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KM2KM2

KM2

0.040

0.045

0.050

0.055

0.060

0.065

0.070

45 55 65 75 85 95

Z

Probability

Elam Hartree-Slater Hart ree-Fock Experimental


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KM3KM3

KM3

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

60 65 70 75 80 85 90 95 100

Z

Probability

Elam Hartree-Slater Hartree-Fock Experimental


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KM45KM45

KM45

0.001

0.002

0.003

0.004

0.005

0.006

60 70 80 90 100

Z

Probability

Elam Hart ree-Slater Hartree-Fock experimental


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KN23KN23

KN23 transition

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

35 40 45 50 55 60 65 70 75 80 85 90 95 100

Z

Probability

Hart ree-Slater Hart ree-Fock Experimental Experimental - series 2 EADL


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KN45KN45

KN45

0

0.0005

0.001

0.0015

0.002

0.0025

60 65 70 75 80 85 90 95 100

Z

Probability

Elam Hartree-Fock Hartree-Slater Experimental


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L1 M2L1 M2

L M1 2

.0 20

.0 25

.0 30

.0 35

.0 40

.0 45

.0 50

40 50 60 70 80 90 100

Z

Probability

Elam Hartree-Slater Hartree-Fock Experimental Exp. series r 2


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Statistical analysisStatistical analysis

Look at all transitions and compare measurements withtheory

Perform 2 test

The results of the 2 test hint that Hartree-Fock is more

accurate than Hartree-Slater How significant is the difference in accuracy between

Hartree-Fock and Hartree-Slater?

Evaluated through contingency tables + Fisher test

Input of contingency tables: count pass and fail of2test at 95% CL

Result of Fisher test: p-value = 0.007

i.e. the difference between the two is highly significant


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Validation of Radiative Calculation G4SUWS_2009_Sudhakar_TransitionProbabilities