G. Table of Nuclei
The following table lists known nuclei sorted by their mass number A. Binding
energies are taken from [2] while decay modes, lifetimes (in seconds), and
terrestrial abundances (for long-lived isotopes) are generally taken from [3].
For a given A, the binding energies shown in column 2 are the parabolic
functions of Z illustrated in Fig. 2.6. Because of the nucleon-pairing energy,
their is only one parabola for odd-A and two parabolas for even-A (one
for even-even and one for odd-odd). Nuclei on the neutron-rich side of the
parabola are generally β
−
-unstable while those on the proton-rich side are
unstable to electron-capture (Q
ec
< 2m
e
) or to both electron-capture and
β
+
decay (Q
ec
> 2m
e
). A few very weakly bound nuclei can also decay by
nucleon emission, e.g. A = 16, Z =5, 9, 10.
Because of the single or double parabolic structure, there is only one β-
stable nucleus for odd-A and two or three β-stable nuclei for even-A. For even-
A, only one nucleus is also stable against double-β decay, but the lifetime for
2β decay is generally greater than 10
20
yr so nuclei that are only 2β unstable
are still present on Earth.
Nuclei with A>150 (A>100) are also usually unstable to α-decay
(spontaneous fission). The lifetimes are generally greater than 10
20
yr for
A<208.
Decay and reaction Q’s can be calculated from the binding energies in
this table. For example
Q
β−
[(A, Z) → (A, Z + 1)] = B(Z +1) − B(Z)+(m
n
− m
p
− m
e
)c
2
= B(Z +1) − B(Z)+0.782 MeV ,
Q
β+
[(A, Z) → (A, Z − 1)] = B(Z −1) − B(Z) − (m
n
+ m
e
− m
p
)c
2
= B(Z − 1) − B(Z) − 1.804 MeV ,
Q
α
[(A, Z) → (A − 4,Z − 2)] = B(A − 4,Z−2) − B(A, Z)+B(4, 2) ,
= B(A − 4,Z −2) − B(A, Z)+28.295 .