PHY357S: Monday, 26 January 1998

Problem Set 2

due Monday, 9 February 1998

(Late penalty is 10% per day, and no problem set is accepted after February 11.)

These problems are based on Chapters 1-7 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) The magnetic moment of the L0 baryon is -0.6 mN and the quark model predicts the magnetic moment is entirely due to the strange quark. (The up and down quarks spend equal times with spin parallel and antiparallel to the L0 spin, so their contributions cancel out.) Estimate the effective mass of the strange quark inside the L0. (b) The Lb baryon has the same structure as the L0 except that the s quark is replaced by a b quark, but its magnetic moment has not yet been measured. Predict the magnetic moment of the Lb in eV/Tesla.

 

2) Most of the energy of a typical supernova comes out as about 1044 Joules of ~10MeV electron neutrinos and antineutrinos. The cross section for absorption of such neutrinos in matter is about 1043cm2 per nucleon. ("Nucleon" is the generic name for either a neutron or a proton. The cross section is independent of whatever nucleus the nucleon is part of.) A dose of 10 Gray absorbed in a short time is usually lethal. Would the neutrinos from the supernova of any of the nearest stars wipe out life on earth?

 

3) (a) What would be the differential cross section for Rutherford scattering if, instead of the 1/r Coulomb potential, the potential was

V(x) = q1q2R/r2

R is a constant. (Any integrals needed can be found in most tables of integrals or calculated by Maple or Mathematica.)
(b) Imagine you have measured a differential cross section over the range 10 GeV2 < q2 < 102 GeV2 which agrees with your answer to part (a). What further scattering data are needed to determine whether Coulomb's law is truely violated, or if the observed potential is just because instead of a point target with charge q2, the charge density is r(r)=2q2/(R2r) for r<R, and r(r)=0 for r>R, where R=10fm?
(c) Estimate the ratio for the deep inelastic cross section of electrons on helium to that on hydrogen.

 

4) Which of the following reactions can take place? If forbidden, say why not. If allowed, indicate through which interaction the reaction will proceed. You are free to choose any real momentum for the intitial particles.

(a) nmp Þ nm+ (e) ne + Ar40 atom (ground state)
         Þ K41 atom (ground state)
(b) e+e- Þ K+K- (f) nmp Þ pm-K+p+
(c) pp Þ p+p-p+p-n n (g) ne + Ar40 atom (ground state)
         Þ K40 atom (ground state)
(d) np0 Þ pK- (h) ne + K40 atom (ground state)
         Þ Ca40 atom (ground state)