Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 1 If t 1/2 is too long, How can we measure N? If t 1/2 is too short, multiscaling or coincidences or Doppler or..! Multiscaling Multiscaling, dwell time, accept logic pulses, register number of logic pulses during dwell time in successive channels  decay curve. If t 1/2 is less than 1 ms, need high activity, detector and electronics maximum count rate!! say 10 5 /s, dwell time 1 ms, maximum counts per channel = 100  bad statistics!! Coincidences….. Doppler……. Doppler……. Radioactivity HW 4 Specific activity. Project 1

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 2 RadioactivityTAC TAC

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 3 Radioactivity If parent nucleus decays by two modes: Derive.

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 4 Radioactivity two 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.

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 5 Radioactivity If radioactive species 1 is produced in a reactor or accelerator with rate R. R = N 0  I Flux (~10 14 s -1 cm -2 ) Xsection (~b) Almost constant! ProductionDecay Show that and thus secular equilibrium almost linear “or current!!” HW 5

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 6 Radioactivity How long should we irradiate? Activity per cost?

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 7 Radioactivity If species 2 is radioactive. Possible also that species 3 is radioactive. 1  2  3  4 ….. until we reach a stable isotope. But for now let us consider species 3 to be stable. For the parent nucleus assume that N 1 (t=0)=N 0. For the daughters assume that N 2 (t=0) = N 3 (t=0) = 0. Verify the following: What if 2 = 0? What if 1 is very small? N 1 ( t ) = ? HW 6

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 8 Secular equilibrium 1 is very small ( 1 << 2 ) ► For large time t, A 2  N 0 1 which is the limiting value for secular equilibrium. Constant activity ► production = decay. Radioactivity ▼ What if t ½ for 132 Te were 78d?

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 9 Radioactivity Transient equilibrium If 1 is smaller than 2 ( 1 < 2 ), show that and correspondingly reproduce reproduce the following graphs (compare to Fig. 6.7 in Krane). Project 2a

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 10 Radioactivity As t increases, but the activities themselves are not constant. 230 Th decays, in effect, with the decay constant of 234 U. Parallel !?

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 11 Radioactivity Discuss the case when 1 is larger than 2 ( 1 > 2 ). Project 2b

Radiation Detection and Measurement, JU, 1st Semester, (Saed Dababneh). 12 Radioactivity In general, 1  2  3  4 ….. until we reach a stable isotope. If N 0 of type 1 and N 2 (t=0) = N 3 (t=0) = … = 0 ► Bateman equations. Exclude the term ( k - k ). Project 3 Write an appropriate code.