Download Chapter 3 Nuclear Force and Two

58
Chap. 3 Nuclear Force and Two-Nucleon Systems
-~
difference between
M" :
kfd
and the sum of those for a neutron, M,,, and a hydrogen atom,
+
Mnc2= 939.5656 MeV
MHc2= 938.7833 MeV
=1878.3489 MeV
- Mdcz=1876.1244 MeV
E,=
(3-1)
2.2245 MeV
A more precise value, Es =2.22457312(22) MeV, is obtained from radiative capture
of a neutron by hydrogen. In this reaction, represented as p(n,'y)d, a slow neutron is
captured by a hydrogen atom followed by the emission of a y-ray (see Ref. (781 for
details). If the energy of the incident neutron is negligible, the energy of the y-ray
emitted gives the deuteron binding energy. Since itl is usually far easier to determine
y-ray energies accurately than measurements of atomic masses, binding energies are
often better known than absolute masses.
Partly because of the small binding energy, the deuteron has no excited state;
all observations on the deuteron are made on the ground state. The results of the
more important measured quantities are listed in Table 3-1. In spite of the small
number of independent pieces of data available, we stand to learn a great deal about
the two-nucleon system from the deuteron. Furthermore, because of their fundamental
importance, many carefiil and sophisticated measiirernents have been carried out and
the available values represent some of the best that can be obtained for the type of
measurement. In this section we shall make use only of spin, parity, and isospin,
leaving the study of the magnetic dipole moment and electric quadrupole moment to
the next two sections.
Table 3-1: Ground state properties of deuteron.
Ground State Property
Value
2.22457312(22) MeV
Binding energy, EB
1+
Spin and parity, J"
Isospin, T
0
Magnetic dipole moment, &
0.857438230(24) p N
Electric quadrupole moment, Qd 0.28590(30) efm'
Radius. r A
1.963(4) fm
Note: Uncertainties in last digits of the measured values are
given in parentheses.
I
Spin and parity. The parity of a state describes the behavior of its wave function
under a reflection of the coordinate system through the origin, &s shown in §A-1. For
the deuteron, it is known that the parity is positive. Let us see what we can learn from
this piece of experimental information. For this purpose, it is useful to separate the
wave function into a product of three parts: the intrinsic wave function of the proton,