What did you learn in the last lecture?

Transcription

1 What did you learn in the last lecture?

2 What did you learn in the last lecture?

3 Beta stability, the LD Mass Formula, and Accelerators Simplest form of LD Mass Formula TBE = C 1 A C A /3 C 3 Z /A 1/3 C 4 (N-Z) /A + C 6 δ/a 1/ <BE> = C 1 C A 1/3 C 3 Z /A 4/3 C 4 (N-Z) /A 3 + C 6 δ/a 3/ Line of Beta Stability Isobars 1. Beta Decay Form of Radioactive Decay n p conversion inside nucleus A doesn't change; just N/Z ratio ISO BARS Most probable N/Z ratio Line of Beta Stability. Example: A = 75 chain N/Z= 1.5 N/Z= Zn 75 Ga Ge 75 As Se 75 Br Kr n p Beta- Stable Nucleus n p

4 3. Isobaric Mass Formula Since in β decay the mass number remains constant, it is useful to develop an isobaric mass formula ( iso means same in Greek). A is constant in Binding Energy Equation ( & <BE> form) ( A Z X ) = Z H + N n TBE plug in LD Mass Equation ( A Z X ) = d 1 Z + d Z d 3 + d + d 4 δ, where d i = f (Ci, A) What is the functional form of this equation? minimum defines most stable nuclide for a given A. These values define the "valley of stability". Atomic number of this nucleus is Z A.

5 Valley (line) of Beta stability

6 Two Cases a. Case I: odd-a nuclei (δ = 0) Single parabola: A X Z = d 1 Z + d Z + d 3 ; one Parabola Most probable charge: ( A X Z ) = d1 Z A + d Z RESULT: ONE STABLE ISOTOPE PER MASS NUMBER A=15 mass parabola M(Z)-M(Z A ) in MeV Z

7 Consider the two mass parabolas of A=75 and A=157. What do you notice?

8 b. Case II: even A nuclei (δ = ± 1) ( A X ) = d1 Z + d Z + d 3 ± δ d 4 RESULT: Two parabolae ; even-z always lower CAN HAVE 1,, OR 3 STABLE NUCLEI PER A. A=18 Upper parabola is odd-odd Lower parabola is even-even.

9

10 INTRODUCTION: Uses of Accelerators Accelerators World wide inventory of accelerators, in total 15,000. The data have been collected by W. Scarf and W. Wiesczycka (See U. Amaldi Europhysics News, June 31, 000) Category Number Ion implanters and surface modifications 7,000 Accelerators in industry 1,500 Accelerators in non-nuclear research 1,000 Radiotherapy 5,000 Medical isotopes production 00 Hadron therapy 0 Synchrotron radiation sources 70 Nuclear and particle physics research 110 Good Overview of accelerators (no equations) :

11 I. Electrostatic Devices (constant E field) Van de Graaf/Cockroft-Walton Accelerators High Voltage Devices A. Principle of Operation: One or Two Big Kicks 1. E = qe V E q e V Change in KE of particle Atomic charge state (ion charge) Electric charge in units of ev Potential difference in volts

12 . Limitations on V Electric discharge: V Volts (Oak Ridge) E = (qe) 5 MeV; SF 6 as insulator

13 Schematic of a Van de Graaf. Typically a voltage of 00 kv can be reached. Problems: belt moves at ~ 60 km/hr; Belt dust sparking; Need for an insulating gas (SF 6 );

14 3. Tandem Van de Graaf: Two-step Acceleration negative X q X +Z ion source V V Beam Stripper foil Ground E = q e V 1 E = Ze V a. Total Energy Gain: E = E 1 + E = ( q + Z) e V b. Example: S ion ; terminal voltage = 5 MV E = { + 16} 5 emv = 450 MeV c. Large V leads to higher charge state in second stage. Tandem accelerator at Brookhaven National Lab. (BNL)

15 B. Properties 1. Ions: most of periodic table. V 5 MV ; high precision, simple operation I 3. I ~ 10µA 4. Time structure: Continuous 5. Uses Largely applications today; e.g., ion implantation; chargedparticle activation analysis ; 14 C dating. t

16 II. Electrodynamic (Time varying E and B fields) A. Cyclotron (Lawrence, 199, Nobel Prize) Idea: Confine the motion of the particle with a magnetic field while you accelerate it.

17 1. Equations of Motion for a Charged Particle in a Magnetic Field Particle mass: M Charge state: qe Magnetic field: H H radius: r M, q a. Trajectory is Circular path of radius r F centripetal = Mv r F magnetic = Hvqe c The two forces are balanced so equate them! r = Mv c Hvqe = Mc Hqe v i.e. r = f(v) (classically) b. Orbit time: v << c t πr π Mcv πmc = = v v Hqe HqE = CONSTANT! CYCLOTRON PRINCIPLE: orbit time is independent of particle energy for classical motion ion-cyclotron resonance

18 c. Frequency-ω Hqe He q ω = π for q/m ~ 0.5 (e.g., 4 He +, 1 C +6 ), = = ω ~ MHz for H ~ 1.5 tesla. t Mc c M (lower end of FM frequency.) Notice that for a fixed magnetic field H, the cyclotron frequency is proportional to q/m of the particle.. Acceleration a. Supply radiofrequency energy for each revolution i.e., E = qe V, where V ~ kv b. Result: velocity increases and particle spirals outward c. Energy is limited by magnetic field H and radius r ($) d. Total energy: defined by number of orbits required to reach maximum radius, r max = n: E = n (qe) V e.g. for n = 500, V = 00 kv (q = ), E = 00 MeV

19 3. Classical Kinetic Energy: E K = = = A q c e H r c M e q H r M Mv E K ion cyclotron K A q K E K = For v < c; limited by relativity K is the figure of merit for the cyclotron If we insert values for the constants we get: E K = H r (q /A) MeV/tesla -cm

20 B. Properties 1. Ions: Most of periodic table (electron cyclotron resonance (ECR) sources yield high q) ion sources permit up to U ions. Higher energy, less precision than Van de Graafs 3. Energy limits: H and He: K = 15 (IU); K=500 (TRIUMF/CANADA) Heavy ions: K = 100 (MSU) 4. Intensity: I 10µA 5. Time structure of beam: Pulses I t More historical information: Original paper on cyclotrons: Facts about the IU cyclotron (IUCF) :