Experimental Techniques in

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1 Experimental Techniques in uclear Physics Course web or

2 Grading Mid-term Exam 30% HW s 0% Projects 0% Final Exam 50% Homeworks (small projects) are due after one week (two weeks) unless otherwise announced. Remarks or questions marked in red without being announced as homeworks should be also seriously considered! Some tasks can (or should) be sent by bau@dababneh.com 2

3 Projects Please do your own thorough research on relevant topics you may find appropriate. Provide your suggestion next week. Final decision on the subject of your project should be taken before mid March. Due date for written version is Tuesday, May 8 th. Presentation date will be decided later. 3

4 HW How can the element 06 (seaborgium) in general be produced? What makes 4 C famous? What is the medical importance of 8 F? Comment on 52 Dy. How can its gamma decay be measured? 4

5 d dt d = λ dt ( t ) = 0 e λt λ decay constant. It does not change with time, and does not depend (to a good approximation) on any environmental factors. (It does in extreme cosmic conditions. How?). HW HW 2 5

6 t = 2 ln 2 λ τ = Show that the mean lifetime. is difficult to measure. λ Instead, measure number of decays between t and t + t: = 0 e λt 0 e λ ( t+ t ) = 0 e λt ( e λ t ) Slope=?!!!!!!!!!! Be careful. If t << τ (i.e. << /2 t ) then show that λ = λ t 0e t, and thus defining the activity A(t): d dt = λ 0 e λt = λ( t) = A( t) = A0e λt ( A = λ 0) = A t? 0. 6

7 HW 3 Krane Problem 6. 7

8 Activity measured in units of becquerel (Bq) = decay/s. curie (Ci) = 3.7 x 0 0 Bq. Activity is not dose!!!!! Isotope (initial number 0 ) decays into stable isotope 2: 2 λt 0e + 2 = λ t = ( ) 0 e 2 (0) = 0 = In order to measure λ using the exponential decay curve: The half-life lif should be not too long; we need to see the sample decaying!!! Actually we can use λ = A provided this information is available. The half-life should be not too short; we need to do a series of measurements!! But there are other alternatives!! should not be produced, 2 should not be radioactive. Krane

9 Exponential decay of species and exponential growth of species 2. 9

10 0

11 In order to measure /2 t when it is not too long and not too short compared to practical experimental time, use the exponential decay curve. 56 Mn 847 kev 8 kev Which line to measure?

12 d dt Radioactivity Specific activity. = λ = A. HW 4 If /2 t is too long, How can we measure? If /2 t is too short, multiscaling or coincidences or Doppler or..! Multiscaling, dwell time, accept logic pulses, register number of logic pulses during dwell time in successive channels decay curve. If /2 t is less than ms, need high activity, detector and electronics maximum count rate!! say 0 5 /s, dwell time ms, maximum counts per channel = 00 bad statistics!! Coincidences.. Doppler. Project 2

13 TAC TAC 3

14 + a + = If parent nucleus decays by two modes: 2, 2, b 0 d dt d dt a b ( t ) 2, a 2, b = = = λ a = λ b ( 0 λ λ = 0 e a ttl total λ λ b total λ d dt total t 0( e ( 0 e λ λ total total t t total ) Derive. ) = d dt a d + dt b = ( λ + λ ) a b = λ total 4

15 If we measure gross activity for a sample containing two isotopes. Better, and if possible, measure each isotope separately using its signatures with suitable spectroscopic techniques. We will encounter such techniques later in this course. 5

16 If radioactive species is produced in a reactor or accelerator with rate R. R d Almost constant! dt R λ R = 0 σi X-section (~b) Flux (~0 4 s - cm -2 ) or current!! = R Show that λ t ( t ) = ( e ) HW 5 λ Production Decay and thus λt A ( t) = λ ( t) = R( e ) A ( t) R R Rλλ t t t << >> t 2 t 2 almost linear secular equilibrium 6

17 How long should we irradiate? Activity per cost? 7

18 If species 2 is radioactive. Possible also that species 3 is radioactive until we reach a stable isotope. But for now let us consider species 3 to be stable. For the parent nucleus assume that (t=0)= 0. For the daughters assume that 2 (t=0) = 3 (t=0) = 0. Verify the following: HW 6 d d 2 = λ = λ λ2 2 dt dt λ λ t λt ( t) = 0e 2 t) = 0 ( e e λ 2 λ λt λλ2 A ( t) = λ ( t) = λ 0e A2 t) = λ2 2( t) = 0 ( e λ 2 λ What if λ is very small? (t) =? λ2 ( λt λ2 ( e t ) t ) 8

19 Secular equilibrium A λt ( t) = A e A 0 λ2 λ t is very small (λ << λ 2 ) A2 ( t) = λ2 2( t) = 0λ( e ) For large time t, A 2 0 λ which is the limiting value for secular equilibrium. Total activity = 2 A 0. Constant activity production = decay. d 2 dt 2 = = λ2 2 Turner 0 λ 0 λ = λ 2 2 t 9

20 λ << λ 2 A 20 = 0 7t / 2 of daughter 20

21 early Secular Equilibrium Project 2a What if t ½ for 32 Te were 78d? 2

22 Transient equilibrium If λ is smaller than λ 2 (λ < λ 2 ), show that A A = λ = λ2 ( e λ λ ( λ2 λ ) t λ 2 and correspondingly gy reproduce the following graphs (compare to Fig. 6.7 in Krane). Project 2b ) 22

23 As t increases, A A 2 λ2 λ λ 2 but the activities themselves are not constant. 230 Th decays, in Parallel!? effect, with the decay constant of 234 U. 23

24 HW 7 λ < λ 2 At what time does the daughter activity take its maximum value? At what time does the total activity it take its maximum value? 24

25 Discuss the case when λ is larger than λ 2 (λ > λ 2 ). Study the examples in Turner. Project 2c 25

26 In general, until we reach a stable isotope. d dt i = i i λ λ If 0 of type and 2 (t=0) = 3 (t=0) = = 0 Bateman equations. c m = A ( t ) = n 0 λ λ ( λ λ )( λ m 2 2 λ 3 n i=... λ c e i λ )...( i λ t i m n m n λ i Project 3 Write an appropriate code. λ ) Exclude the term (λ k - λ k ). 26

27 atural Radioactivity Radon also breaks secular equilibrium between 238 U and daughters. Why? Read Section 4.6 in Turner. 27

28 atural Radioactivity Draw the = Z line. What do you conclude? 28

29 atural Radioactivity atural decay series 4n+3 4n 29

30 atural Radioactivity Look for radon. What is thoron? 4n+2 4n+ What is actinon? 30

31 atural Radioactivity 3

32 atural Radioactivity 40 K (β and γ source) => internal and external dose. What is the isotopic i abundance of 40 K? 32

33 atural Radioactivity 33