1. W. Udo Schröder, 2009 Principles Meas 1 Principles of Measurement

2. Basic Counting System Detector Pulse Height Analysis/Digitization unipolar bipolar 0 Amplifier/Shaper: differentiates (1x or 2x) Final amplitude 2-10V Binary data to computer Pre Amp Amp Shaper Radiation Source

3. W. Udo Schröder, 2009 Principles Meas 3 Slow Fast Produce logical signal  Fast-Slow Signal Processing CFTD PreAmp Amp Gate Gener ator Data Acquisition System Energy Gate 0 0 t t CFTD Output CFTD Internal t CFTD Input Principle of a Constant-Fraction Timing Discriminator:  t independent of E here f = 0.5 Source Produce analog signal  Binary data to computer

4. W. Udo Schröder, 2009 Principles Meas 4 Trace Element Analysis: X-Ray Fluorescence Irradiate sample, measure characteristic fluorescence CFTD PreAmp Amp Gate Gener ator Data Acquisition System Energy Gate Slow Fast Binary data to computer Ring- Source/ Aperture Sample Si detector Water sample from treatment plant Source: 25 mCi 55 Fe (2.60 a) Mn-X rays K  5.898 keV, K  6.490 keV Off-line n activation analysis: irradiate with 252 Cf neutrons, measure  -rays CHANNEL NUMBER Lab. Invest. Nucl. Sci, The Nucleus/Tennelec, 1988

5. W. Udo Schröder, 2009 Principles Meas 5 Coincidences: Absolute Emission Rate (Activity) N1N1 N2N2 N 12 Activity A [disintegrations/time], radiation types i =1,2 detection probabilities P i =  i  i No angular correlations between rad’s 1,2. CFTD Gate Gener ator Pre Amp CFTD Gate Gener ator Coincidence Counter Coinc. Counter 1 Counter 2 1 2 Activity A

6. W. Udo Schröder, 2009 Principles Meas 6 Time Measurement CFTD Gate Gener ator PreAmp Amp Energy 1 Time PreAmp CFTD Gate Gener ator Amp Time to Amplitude Converter Energy 2 Start Stop Data Acquisition System prompt coincident events t counts time spectrum Delay var. delayed events calibrate time axis with variable known delays (cables)

7. W. Udo Schröder, 2009 Principles Meas 7 Pulse Shape Analysis Time DAQ Different signal decay times for 2 radiation types are translated into different amplitudes Slow Amp Energy DAQ Neutrons Gammas CFTD Fast Amp DD Amp Time-to- Amplitude Converter Zer- Cross Disc. Integr Amp Delay T d Start Stop

8. W. Udo Schröder, 2009 Principles Meas 8 2-Dimensional Measurement coincident signals CFTD Gate Gener ator PreAmp Amp Energy 1 Gate PreAmp CFTD Gate Gener ator Amp Gate Gener ator Energy 2 Coincidence Data Acquisition System

9. W. Udo Schröder, 2009 Principles Meas 9 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)  -Decay of 241Am, subsequent  emission from daughter Find coincidences (E , E  ) 9  -rays, 5 

10. W. Udo Schröder, 2009 Principles Meas 10 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

11. W. Udo Schröder, 2009 Principles Meas 11 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

12. W. Udo Schröder, 2009 Principles Meas 12 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

13. W. Udo Schröder, 2009 Principles Meas 13 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

14. W. Udo Schröder, 2009 Principles Meas 14 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV) No  coincidences !

15. W. Udo Schröder, 2009 Principles Meas 15 Example 159 103 76 60 33 0 241 Am 237 Np 5.378 MeV 5.433 MeV 5.476 MeV 5.503 MeV 5.546 MeV 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 30 40 50 60 70 80 90 100 110 120  Energy (keV) - 5 MeV  Energy (keV)

16. W. Udo Schröder, 2009 Principles Meas 16 The End

17. Basic Counting Statistics

18. Uncertainty and Statistics Nucleus is a quantal system described by a wave function  (x,…;t) (x,…;t) are the degrees of freedom of the system and time. Probability density (e.g., for x, integrate over others) 1 2 Probability rate for disappearance (decay of 1) can vary over many orders of magnitude  no certainty

19. W. Udo Schröder, 2009 Principles Meas 19 Experimental Mean and Variance What can be measured: ensemble (sampling) averages (expectation values) and uncertainties 236 U (0.25mg) sample counted  particles emitted during N = 10 time intervals (@1 min).  =??

20. W. Udo Schröder, 2009 Principles Meas 20 Moments of Transition Probabilities Small probability for process, but many trials (n 0 = 6.38·10 17 )    n 0 · < ∞ Statistical process follows a Poisson distribution: n=“random” Different statistical distributions: Binomial, Poisson, Gaussian