Introductory Nuclear Physics

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PHY431 Homework Set 5 Reading: Lecture Notes Homework: See below: Due date: Wednesday March 1 Hints and Solutions Problem V.1 Show that the Angular Momentum Barrier "potential" L ² / 2 I = l ( l +1) h ² / 2 mr ² for the radioactive decay: 209 83 Bi(J P = 9 / 2 - ) 205 81 Tl(J P = 1 / 2 + ) + 4 2 He(J P =0 + ) is small compared to the Coulomb potential for the region r > R , where R is the sum of the radii of the daughter nucleus and the alpha particle. Hints: First, show that angular momentum and parity conservation dictates that l =5 Solution: orbital angular momentum l = | 9 / 2 ± 1 / 2 | = 4 or 5. Parity changes from -ve to +ve, so the angular momentum in the final state must be odd: -1 = (-) l ; thus l = 5. V L = l ( l +1)/(2 mR ²) = 5×6×(197 MeV·fm)²/(2×3730 MeV ×(9.0 fm)²) = 1.9 MeV; we took R = 1.2 fm × (205 1/3 +4 1/3 ) = 9.0 fm. V C = [ e ²/4 πε 0 ] zZ / R = 197 MeV/137 × 2×81/9.0 fm = 26 MeV; i.e. 13× larger than V L . Problem V.2
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solutions 05 - phy431_s99_hw05 PHY431 Homework Set 5...

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