The gigantic errors in theoretical half-life predictions in section 14.20.5 are disconcerting to say the least. They imply that the predicted gamma decay rates, (essentially the inverse of the half-lifes), are typically either much less than theory or much larger than theory.
To explain why some of the gamma decay rates, like the E2 and high energy E3 ones, are so much faster than ballpark is relatively straightforward. Decay much faster than ballpark is only possible if not just one proton, but a lot of nucleons participate in the transition. And since the effect is systematic in E2 and high energy E3 transitions, apparently it is normal for a lot of nucleons to participate in gamma decay. Or at least it is for these types of gamma decay. And since the theory assumes that only one proton participates, the miserable predictions of theory can be explained.
A much bigger problem is to explain why other transitions end up so
far below ballpark in a credible way. Consider in particular the
Basically, you can give two reasonable types of explanation:
This is essentially the explanation that basic nuclear textbooks that the author has seen give. Unfortunately, there are two big problems with it. First, how come that unlike the E2 and E3 transitions, suddenly only one proton participates in E1, low energy E3, M1 and most M2 transitions? If there is a very big systematic effect, there must be a reason. Worse, figure 14.65 seems to exclude the possibility of just one proton partipating in at the very least M1 transitions, and surely at least some very slow E1 transitions.
The second problem is to explain why the overlap is systematically extremely bad in some types of transitions, but apparently excellent in others. Again, this is a big systematic effect, as the figures show. So there must be a reason for this too.
Your hands are not enough to wave these problem away. If you want people to take you seriously, you should have a believable and comprehensive discussion.
But now of course, you face the apparently daunting problem of explaining why some types transitions can be so extremely slow, even now that there are many nucleons participating. In particular, you need to provide a reasonable explanation why for some types of transitions, the participation of many nucleons actually slows down the emission of electromagnetic radiation greatly, rather than increase it greatly. And apparently, this effect requires the presence of enough nucleons, as very light nuclei do not have the problem.
While standard nuclear textbooks give the first explanation above, the holes in the argument are worrisome. The magnitude of the effects pointed at by the textbooks just does not seem big enough to explain the data. And it is hard to think up reasons why not. There just is a lack of suspension of disbelieve for an engineer thinking in terms of ballparks.
Therefore, this book wants to argue that more serious consideration should be given to the second explanation. Its main liability is to explain why some transitions get slowed down greatly, rather than sped up, if a lot more nucleons participate.
Since nuclear wave functions are poorly understood, that would be difficult to explain from a quantum-mechanical viewpoint. So maybe it is again time to do what has been done before for nuclei; look for macroscopic models. And surely the macroscopic model that stands out in killing off electromagnetic effects is the cage of Faraday. (In this case the cage is assumed to shield the outside from the inside.)
Maybe then the nuclear surface acts as such a cage in some sense. In the liquid-drop idea, nucleons at the surface are in a state of increased energy. So it may not be such a crazy idea that nucleons at the surface might behave differently from nucleons in the interior.
Assume now at first, in this macroscopic model, that the nuclear surface is spherical and conducting. Then electric charge changes in the interior of the nucleus would not leak out. That would kill off the capability of transitions to emit radiation. So the model can provide a macroscopic explanation why some electromagnetic transitions can be greatly slowed down. Charges can still move around inside the nucleus, but because the surface nucleons move to compensate, that does not produce radiation outside it. So participation of many nucleons does indeed reduce, rather than increase, electromagnetic radiation greatly.
Do note that unlike normal cages of Faraday, a nucleus contains a net positive charge. And if a macroscopic cage of Faraday contains a net charge, there must always ne a nonzero electric field outside. (That is due to Maxwell's first law.) But as long as the surface remains spherical and conducting, the outside electric field will not change if charges inside the surface are moved around. So in that case, there will be an electric field, but still no electromagnetic radiation radiated away. And the reason for that is still because many nucleons are involved, rather than a single proton.
But things change when the nuclear surface changes shape. A conducting surface makes only the electric field tangential to the surface zero. Therefore there will be variations in the electric field outside the surface if it changes shape. So now we have a situation where radiation is in fact being transmitted, and again with many nucleons involved in doing that.
That opens up the possibility of explaining why some transitions can be so far from the single proton ballpark. And why it depends on the type of transition whether the transition turns out to be much slower than ballpark or much faster than ballpark.
At least for relatively light nuclei, (but still with enough nucleons
that the macroscopic picture makes sense), and small excitations,
surface tension would promote a spherical surface. And
surface roughness would not necessarily make much of a
difference. That is just like small holes in a macroscopic cage do
not make a difference. The field outside the nucleus is governed by
the so-called Laplace equation. This equation is known to kill off
short-scale perturbations quickly.
On the other hand, changes in a deformed nuclear surface shape would
definitely produce nontrivial long-range electric field perturbations.
Now nuclei are often modeled as spheroids or ellipsoids. Changes in
such a shape would produce quadrupole and hexadecapole perturbations
in the electric field outside the nuclei. So they would produce
While macroscopic cages of Faraday do not block static magnetic
fields, they do block changes in magnetic fields. So conceptually the
model could also explain why magnetic transitions of low multipole
order are often so slow. Note that there is no net magnetic
charge inside the cage. Magnetic monopoles do not
exist. So surface shape would not necessarily affect magnetic
While this model leaves many questions unanswered, at least it suggests a reasonable way to understand how it is possible at all that the one-proton model is not just extremely miserable, but systematically miserable in the observed way. For one, it seems to make figure 14.65 far less unexplainable.