G.F.Knoll – Radiation Detection and Measurements – Wiley 2000 (only the part of organic scintillators and photomultipliers: Chap 8.I e Chap. 9 (I-V)
Concepts of Theory of Probability and Statistics, with applications to data analysis in the field of modern experimental Physics
Basic concepts on electrical noise and semiconductor diodes.
Basic concepts about muon and muon decay. Muon production by cosmic rays. Mean life. Delayed coincidences method for mean life estimation. Transmission lines. Some knowledge of dedicated electronics for nuclear physics measurements. Liquid (organic) scintillator detectors and PMT. Calibration of a system for time measurements in nuclear physics. Fit of particle lifetime distribution for mean life estimation.
the student is expected to become familiar with statistical analysis of experimental data, relevant to Physics and other basic sciences.
Skills acquired (at the end of the course):
the student should be able to interpret and analyse data, using fitting techniques and advanced error a
The student should be able to derive the electric noise in a network.
Courses required: Physics laboratory II
Courses recommended: all the courses of the first and second year
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 140
There will be an initial part of theoretical lessons for the presentation of the subjects reported in the program of the course. After that, students will have to realize experiments in the laboratory organizing, typically, in groups of three.
There is the compulsory attendance, accomplished with the presence in the laboratory during the shifts assigned.
After the classes or by appointment by e-mail.
After the classes or by appointment.
Type of Assessment
oral exam, including a discussion of the code used to fit data and of the relevant results
Basic concepts of the Theory of Probability. Komogorov's axioms. Mutually exclusive events. Conditional probability. Bayes Theorem. Independence of events. Cumulative distribution function. Probability density function (pdf). Mean value and variance. Expectation value of a random variable. Moments and central moments. Reduced (or standardized) random variables. Distribution of n random variables. Joint probability density. Marginal and conditional probability density. Independence of random variables. Covariance, correlation coefficient and covariance matrix. Transformation of 1 and n- dimension random variables. Linear transformation of random variables. Law of error propagation, i.e. law of covariance matrix transformation (CO98, Ch.1).
Characteristic function. Characteristic function of two independent random variables. The normal (gaussian) distribution as the limit of binomial and poissonian distribution. The characteristic function of a gaussian. Moments of a gaussian. Pdf of a linear combination of independent random variables: examples of use of the characteristic function. Convolution. The Central Limit Theorem. (CO98 Ch. 10.1, 10.2 and 10.3).
Distribution of continuous and discrete random variables: binomial, poissonian, gaussian, exponential, uniform, Cauchy's, chi-square distributions. Uniform distribution of any Cumulative distribution function and basic concepts of Monte Carlo techniques (CO98 Ch..2.1, 2.2, 2.3, 2.4, 2.5, 2.7, 2.8).
Multivariate distribution. Covariance ellipse (mainly notes of the teacher). Basic Statistics. Statistical tests. Pearson's Chi-square test (CO98 Ch.4.1, 4.5 (outline), 4.7).
Random sampling. Unbiased, biased, consistent and non-consistent estimators. The arithmetic mean as an unbiased estimator of the mean value. Estimators of the variance and the empiric variance. Empiric variance of an n-dimension random sample and its distribution like a chi-square of n-1 degrees of freedom (notes given by the teacher). Counting statistics and relevant errors (CO98 Ch.5.1, 5.2 (first part)).
Basic concepts of the Maximum Likelihood Criterion for determining the parameters (estimation of parameters) of a distribution, starting from a random sample of data (CO98 Ch.6.1, 6.2-first part) .
Principle of Least Squares (LS) and its close relationship with the Maximum Likelihood. LS and direct estimation of parameters (weighted mean). LS for indirect determination of parameters, for the linear and non-linear case ( CO98 Ch.7.1, 7.2, 7.4-first part, 7.6 and notes prepared by the teacher).
Outline of the iterative procedure for the non-linear model case.. Errors of the parameters for the LS case. Confidence interval for the parameters. Confidence interval for a measurement and the concept of Coverage (CO98 Ch. 9.1, 9.2 basic ideas).
Poissonian distribution: example of the determination of the lower limit for the lifetime a particle supposed to be unstable (CO98 Ch. 9.4).
Statistical and systematic errors.
Noise in the frequency domain.
Noise spectral density. Noise sources.
Noise in a semiconductor diode.
CCD readout noise.
Mean and half life
Delayed coincidences method
Muons. Muon decay. Muon production by cosmic rays
Scintillation detector (liquid organic scintillator)
Photo multiplier tube
A system for muon mean life measurement (trigger system, time calibrator, energy measurements)
Transmission lines. Coaxial cables.
Acquisition system and analysis program
Fit of spectra for mean life estimation.