PHY357S: Wednesday, 25 March 1998

Problem Set 5

due Wednesday, 8 April 1998

(Late penalty is 10% per day, and no problem set is accepted after April 9.)

These problems are based on all of Frauenfelder and Henley (F&H) and the lectures.
If you have any questions about these problems, ask me.

Each problem is of equal weight, but not all problems may be marked.

 

1) (a) Write down the quark content for all possible neutral hadrons which you can make using only s, c and b quarks and antiquarks. Make your list in order of increasing mass, and clearly indicate groups of hadrons with the same mass. (Only consider the lightest hadron with a given quark content.)

(b) Explain how it is possible to make both scalar (JP=0+) and pseudoscalar (JP=0-) mesons from quarks and antiquarks.

 

2) Note: A computer will help for parts (b-d) of this question. (I used Excel.)

(a) The Bethe-Weisäcker semi-empirical mass formula (F&H Equations 16.9 or 16.10) is only approximate. Use this formula to write down an analytic expression for the proton number (Z) which gives the most strongly bound nucleus for a given (fixed) total number of nucleons (A).

(b) Plot your result for the range A=2 to A=300, but instead of ploting Z as function of A, plot Z vs neutron number (N).

(c) Use the mass formula to estimate the largest value of A for which the most strongly bound nucleus is stable. Consider alpha decays, all types of beta decays, and symmetric fission decays. (A symmetric fission decay is one in which the nucleus splits exactly in half; fission is usually asymmetric, but the symmetric assumption makes the problem easier.)

(d) Use a Chart of the Nuclides or Table of Isotopes to determine the smallest value of A which has no stable isotope. Compare with your answer to part (c). Also compare the Z vs N distribution of the stable isotopes which your answer to part (b). If there are differences, they may be do to the approximate nature of the mass formula, or because the most deeply bound nucleus may not be the most stable nucleus. (A Chart of the Nuclides can be found in the 3/4th lab hallway outside Room 245, on the web at http://datwww.dne.bnl.gov/CoN/index.html, and in some nuclear physics textbooks.)