1. Nuclear Masses and Binding Energy Lesson 3

2. Nuclear Masses Nuclear masses and atomic masses Because B electron (Z)is so small, it is neglected in most situations.

3. Mass Changes in Beta Decay  - decay  + decay

4. Mass Changes in Beta Decay EC decay Conclusion: All calculations can be done with atomic masses

5. Nomenclature Sign convention: Q=(masses reactants -masses products )c 2 Q has the opposite sign as  H Q=+ exothermic Q=- endothermic

6. Nomenclature Total binding energy, B tot (A,Z) B tot (A,Z)=[Z(M( 1 H))+(A-Z)M(n)-M(A,Z)]c 2 Binding energy per nucleon B ave (A,Z)= B tot (A,Z)/A Mass excess (  ) M(A,Z)-A See appendix of book for mass tables

7. Nomenclature Packing fraction (M-A)/A Separation energy, S S n =[M(A-1,Z)+M(n)-M(A,Z)]c 2 S p =[M(A-1,Z-1)+M( 1 H)-M(A,Z)]c 2

8. Binding energy per nucleon

9. Separation energy systematics

10. Abundances

11. Semi-empirical mass equation Terms Volume a v A Surface -a s A 2/3 Coulomb -a c Z 2 /A 1/3

12. Asymmetry term To make A Z from Z=N=A/2, need to move q protons q  in energy, thus the work involved is q 2  =(N-Z) 2  /4. If we add that  =1/A, we are done.

13. Pairing term AZN# stable eee 201 oeo 69 ooe 61 eoo 4

14. Relative importance of terms

15. Values of coefficients

16. Modern version of semi- empirical mass equation (Myers and Swiatecki)

18. Mass parabolas and Valley of beta stability This is the equation of a parabola, a+bZ+cZ 2

22. Where is the minimum of the parabolas?

23. Valley of Beta Stability