Subatomic Physics

464 Strong Interactions
(c) The isospin.
(d) The magnetic moment.
(e) The quadrupole moment.
14.17. Show that the ground state of a two-body system with central force must be
an s state, that is, have orbital angular momentum zero.
14.18. Deuteron—Theory. Treat the deuteron as a three-dimensional square well,
with depth −V0 and range R.
(a) Write the Schrödinger equation. Justify the value of the mass used in
the Schrödinger equation.
(b) Assume the ground state to be spherically symmetric. Find the groundstate
wave function inside and outside the well. Determine the binding
energy in terms of V0 and R. Show that B fixes only the product V0R 2 .
(c) Sketch the ground-state wave function. Estimate the fraction of time
that the neutron and proton spend outside each other’s force range.
Why does the deuteron not disintegrate when the nucleons are outside
the force range?
14.19. Dineutrons and diprotons, that is, bound states consisting of two neutrons or
two protons, are not stable. Explain why not in terms of what is known about
the deuteron.
14.20. At one time evidence for a bound state consisting of an antiproton and a
neutron had been found, and the binding energy of this pn system was noted
to be 83 MeV. [L. Gray, P. Hagerty, and T. Kalogeropoulos, Phys. Rev. Lett.
26, 1491 (1971).] Describe this system by a square well with radius b =1.4fm
and depth V0. Compute V0 and compare the numerical value with that of the
deuteron.
14.21. ∗ Antideuterons have been observed. How were they identified? [D. E. Dorfan
et al., Phys. Rev. Lett. 14, 1003 (1965); T. Massam et al., Nuovo Cim. 39,
10 (1965).]
14.22. Verify that a cigar-shaped nucleus, with the nuclear symmetry axis parallel
to the z axis, has a positive quadrupole moment.
14.23. Show that the quadrupole moment of a nucleus with spin 1
2 is zero.
14.24. Show that the quadrupole moment of the deuteron is “small,” i.e., that it
corresponds to a small deformation.