Lecture4MassformulaBetaDecayandAccelerators_001

Lecture4MassformulaBetaDecayandAccelerators_001 - 1 Lecture...

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1 Lecture 4 : Beta stability, the LD Mass Formula, and Accelerators Simplest form of LD Mass Formula TBE = C 1 A C 2 A 2/3 C 3 Z 2 /A 1/3 C 4 (N-Z) 2 /A 2 + C 6 /A 1/2 <BE> = C 1 C 2 A 1/3 C 3 Z 2 /A 4/3 C 4 (N-Z) 2 /A 3 + C 6 /A 3/2 E. 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 2. Example: A = 75 chain 30 75 Zn 31 75 Ga 32 75 Ge 33 75 As 34 75 Se 35 75 Br 36 75 Kr   3. Isobaric Mass Formula Since in 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) Z A X = Z H + N n TBE plug in LD Mass Equation Z A X = d 1 Z 2 + d 2 Z d 3 + d + d 4 , where d i = f (Ci, A) This is equation for a parabola; minimum defines most stable nuclide for a given A. These values define the "valley of stability". Atomic number of this nucleus is Z A . Beta- Stable Nucleus n p n p N/Z= 1.08 N/Z= 1.5
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2 Two Cases a. Case I: odd-A nuclei ( = 0) Single parabola: Z A X = d 1 Z 2 + d 2 Z + d 3 ; one Parabola Most probable charge: ( Z A X Z ) = 2d 1 Z A + d 2 A=125 mass parabola RESULT: ONE STABLE ISOTOPE PER MASS NUMBER M(Z)-M(Z A ) in MeV Z
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3 Consider the two mass parabolas of A=75 and A=157. What do you notice?
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4 b. Case II: even A nuclei ( = 1) ( 2 A X ) = d 1 Z 2 + d 2 Z + d 3 d 4 RESULT: Two parabolae ; even-Z always lower CAN HAVE 1, 2 OR 3 STABLE NUCLEI PER A A=128 Upper parabola is odd-odd; Lower parabola is even-even.
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Lecture4MassformulaBetaDecayandAccelerators_001 - 1 Lecture...

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