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Unformatted text preview: Physics 135c
H. W. Assignment 6
1.) The semi-empirical mass formula (with coeﬃcients in MeV) is
(A − 2Z ) 2
Z (Z − 1)
A 1 /3
with ∆ = +25 MeV for even-even nuclei, ∆ = 0 MeV for odd-even nuclei and ∆ = −25
MeV for odd-odd nuclei. Use this formula to calculate the binding energy per nucleon vs.
A for stable nuclei for A = 1 − 200. Sketch the resulting curve and determine THE most
stable nucleus. [Hint: use the above formula to ﬁnd stable nuclei by identifying for a given
A what value of Z gives the largest binding energy].
Eb (M eV ) = 16A − 18A2/3 − .71 2.) Use the Fermi Gas Model to determine the fourth term in the semi-empirical mass
formula (Prob. 1). You should be able to determine both the dependence on A and Z as
well as the coeﬃcient.
3.) Use the semi-empirical mass formula (in Prob. 1) to investigate the stability of 235 U
against emission of (a) a proton, (b) a neutron, (c) an α particle (the α particle is a 4 He
nucleus; Note - don’t use the semi-empirical formula to calculate the mass of the α!). For
any of these cases where the decay is possible calculate the kinetic energy of the emitted
4.) The single particle shell model can be used to calculate the magnetic moments of
odd-even nuclei (by assuming that the magnetic moment is due to the odd nucleon only).
Using the formula for magnetic moment we derived for the deuteron, we can write the
magnetic moment operator for a heavy nucleus A as
µn = 2µn s3 ; for an odd neutron
µp = 2µp s3 + µN L3 ; for an odd proton
Use these operators and the Clebsch-Gordan coeﬃcients appended to the Ph135c web page
(at bottom) to derive the shell model predictions:
µn = µn ; for j = l +
µp = µp + µN (j − ) ; for j = l +
−µp + µN j +
; for j = l −
µn = −µn
ˆA µp =
2 5.) Bertulani Probs. 8.3 & 8.4 & 8.5 j
j+1 ; for j = l − ...
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