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

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

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

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  keV, K  keV Off-line n activation analysis: irradiate with 252 Cf neutrons, measure  -rays CHANNEL NUMBER Lab. Invest. Nucl. Sci, The Nucleus/Tennelec, 1988

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 Activity A

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)

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

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

W. Udo Schröder, 2009 Principles Meas 9 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)  -Decay of 241Am, subsequent  emission from daughter Find coincidences (E , E  ) 9  -rays, 5 

W. Udo Schröder, 2009 Principles Meas 10 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)

W. Udo Schröder, 2009 Principles Meas 11 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)

W. Udo Schröder, 2009 Principles Meas 12 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)

W. Udo Schröder, 2009 Principles Meas 13 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)

W. Udo Schröder, 2009 Principles Meas 14 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV) No  coincidences !

W. Udo Schröder, 2009 Principles Meas 15 Example Am 237 Np MeV MeV MeV MeV MeV  Energy (keV) - 5 MeV  Energy (keV)

W. Udo Schröder, 2009 Principles Meas 16 The End

Basic Counting Statistics

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

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 min).  =??

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