Physics 736. Experimental Methods in Nuclear-, Particle-, and Astrophysics. - Brief Review of Course -

Transcription

1 Physics 736 Experimental Methods in Nuclear-, Particle-, and Astrophysics - Brief Review of Course - Karsten Heeger heeger@wisc.edu

2 Final Course Presentation Date/Time for Presentations: Friday, May 11, 2-5pm

3 Physics 736 in Review... Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009

4 Physics 736 Q: What did you learn in this course?

5 Physics 736 Q: What did you learn in this course?...anything?

6 Physics 736 Topics we covered radioactivity and radioactive sources interaction of radiation with matter particle detectors statistics numerical methods analysis techniques accelerator techniques course project choose topic, write outline literature search and independent study presentation + questions

7 Radioactivity

8 Nuclear Processes and Radiation Sources basic nuclear processes alpha decay beta decay electron capture annihilation radiation internal conversion γ emission of nucleus, X-rays Auger electrons neutron sources fission nuclear reactions radiation sources source encapsulation (thick vs thin) energy of source radiation (continuous, monoenergetic, degradation) backgrounds from radiation sources (e.g. gamma)

9 Radioactive Decay Chains I T t I Relative Number of Nuclei E t I a i a 0 Na(t) (Activity) q z n.< I!.< 0 7/ '/ ^"^' tor^" (a) a) transient equilibrium b) secular equilibrium Fig: Leo

10 Interaction of Neutrons Neutron Energies

11 Interaction of Photons Example: Ge detectors

12 Stopping Power Bethe-Bloch At low β -de/dx 1/β 2 decreases rapidly as β increases. reaches a min at βγ 3 (a particle at the energy loss min is called mip). typically de/dx depends only on β (given a particle and medium)

13 Stopping Power Bragg Curve de/dx depends on kinetic energy charged particle is more ionizing towards the end of its path heavy particles pick up electrons towards the end

14 Radiation Energy Loss high-energy limit E = E 0 e x L rad exponential energy loss radiation length L rad = 716.4A Z(Z +1)ln(287/ Z) de dt E 0 radiation energy loss is independent of material type t = distance in Lrad

15 Interaction of Neutrons Neutron Moderators neutron cross-section neutron energy distribution after several elastic scatterings 6 (t,4,.9 u c, o o Hro '-"--i_-_pn'f3!_ pnotons \- \ 6 p lcrl t t0- lo-r Energy [Mev] tol original monoenergetic neutron - average lethargy change is constant - greatest delta E from early collisions

16 Energy Resolution relation between FWHM and standard deviation Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011

17 Dead Time - Extendable/Non-Extendable Paralyzable Events in detector Dead Live Nonparalyzable G-nparalvzaule Paalvraue Karsten Heeger, Univ. of Wisconsin Physics 736, Flgure Spring 4.E Variation 2011 of the observed rate rn as a function of the true rate n for two

18 Scintillation Absorption or emission intensitv Wavelength )\ + <.'..._ Photon energy hv wavelength shifting Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011 Time Time

19 Ionization Detectors Operating Regions trcoarbimtioa bdcr coircfon f.gao C linit d proportbmll'! a o t E lo' o o o, 3 to' z lonholio?roporfioncl ; chorb.r Goutl'.? : i-r-i I I -l II Nr 7 II o rorlkl I Oirbrgr rgfco I p F ttd n Vottoge, rcltr Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011

20 Time Projection Chamber TPC Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011

21 Semiconductor Detectors Energy Band Structure En =6.eV Conduction band Energy 9ap valence band electrons Valence band Insutator Semiconductor Metat Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011

22 Semiconductor Detectors pn junction without bias Karsten Heeger, Univ. of Wisconsin Physics 736, Spring 2011

23 Probability and Statistics Measurement is a random process described by a probability distribution σ=instrumental precision Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009

24 Statistical Distributions ν ν ν ν ν binomial Poisson Gaussian chisquare distribution

25 Data with Error Bars For ±1σ, 1/3 of data should be outside fit

26 Confidence Intervals: Measurements and Limits rate or flux or # of events x confidence interval (CL=68.3%) confidence interval (CL=99%) What if some measurements are in a non-physical region?

27 Frequentist vs Bayesian Approach Two philosophies Bayesian approach probability = degree of belief that something will happen or that a parameter will have a given value Frequentist approach probability = relative frequency of something happening one can define frequentist probability for observing data (which are random) but not for the true value of a parameter independent of observer

28 Acceptance/Rejection Method (von Neumann) Problem: generate a series of random numbers, xi, which follow a distribution f(x) Method: choose trial value, xtrial. accept with probability f(xtrial) choose trial x with random number λ1 x trial = x min +(x max x min )λ 1 random points are chosen inside the box and rejected if the ordinate exceeds f(x)

29 Hypothesis Testing Example - 24 tasters, 3 glasses with different beers - identify which one is different - binomial hypothesis 1 We test H0 : p = against 3 When should we reject H0? 1 Ha : p > where p = probability of a correct choice 3 Need to set critical value. At what value would we doubt the probability is 1/3? Truth about Null Hypothesis Wherever we set yc we could make an error in our conclusion. H 0 : True H 0 :False Decision Based Fail to Reject Correct Type II error on Data Reject Type I error Correct We discriminate against rejecting a true null hypothesis

30 Analysis Techniques Blind Analysis Methods - Hidden Signal Box subset of data containing signal is kept hidden open box after data selection, efficiencies, and backgrounds are estimated good for rare signals examples from rare Kaon decay experiment hidden box should be larger than signal box, can optimize S/B during analysis blind analysis does not require that events inside box are treated as signal, only that cuts may not be adjusted to reject or include events. may interpret them as new or additional background...

31 Numerical Methods Interpolation

32 Numerical Methods Interpolation - Gregory-Newton use data sets and difference tables to find values of the function between tabulated points use Taylor series expansion around tabulated points can rescale x and choose spacing h Gregory -N ewton forward fonnula : l(x1 :/(o) + x(afo) + t(tui l)6'1" * x(x - f Xx -2) ^'., - il AtoT"- Cregory -Newton backward formula : l(x1 :/10) + x(v/") * *Po'n * IGA#4v'.fn +'

33 Numerical Methods Roots of Equations - Newton s Method difficulties with certain type of functions: oscillatory functions Example 2 - procedure will converge on root B - initial guess may result in convergence to a different root - again, knowing the rough behavior of f(x) is invaluable - simple Newton technique not good for multiple roots

34 Physics 736 Q: How many of you have taken your Prelim?

35 Physics 736 Your Road to a Successful Prelim radioactivity and radioactive sources interaction of radiation with matter particle detectors statistics numerical methods analysis techniques accelerator techniques course project choose topic, write outline literature search and independent study presentation + questions

36 Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009