Sunday, 20 January 2013

The size of lead

Overlap of the different quantum orbits of
the extra neutrons in lead isotopes with the
proton orbits
Sorry to have been a bit silent since the new year.  The day after my last post, I went for a week-long holiday, and since I've been back blogging has not quite made the top of the list of things to do.  Still, following mention of a paper I recently wrote with my student and his co-supervisor, I've been meaning to write a bit more about the physics of what the paper contains.  I think the concepts involved are mostly quite simple, and so I hope I can do a reasonable job of explaining what it's about.

Nuclear physics is the study of the really tiny nuclei that are at the centre of every atom, and atoms are what make up all material.  Atoms are small enough that the conclusive evidence that they exist only came around 100 years thanks to advances in physics.  Nuclei, though, are far smaller.  The usual analogy is that if the atom is the size of a cathedral, then a nucleus is sized like a fly buzzing round inside.  Despite the tiny size, though, we can measure the size of a nucleus and see that some nuclei are different sizes to some others.

A nucleus can be charaterised by the number of protons and neutrons it contains, as these two more basic objects are the sole constituents of nuclei.  The number of protons tells you what chemical element the nucleus corresponds to and the number of neutrons tells you what isotope of that chemical element you have (see Elizabeth Williams' excellent recent explanation for more of the basics).

It turns out that if you keep adding neutrons or protons to a nucleus, you expect it to grow in a steady way (quite unlike the way atoms grow when you add electrons), so that a nucleus with more protons and neutrons will be larger than one with fewer with a very regular kind of pattern.  By and large, this is true.  In fact, I've just presented a rather circular argument - it's expected more because it has been observed to be generally true, rather than us having guessed in before-hand.

One particular anomaly in nuclear sizes comes in isotopes of lead nuclei.  All lead nuclei have 82 protons, but can exist with a number of neutrons ranging from around 100 to at least a little over 130.  At least, this range has been seen in experiments, though many of the combinations are short-lived an radioactive.  If you keep adding neutrons to lighter lead isotopes, and measure the size of the proton distribution, which is much easier than measuring the size of the neutron distribution, then you observe that the protons get pulled out a bit by the extra neutrons, and the radius of the proton matter distribution increases, and it does it in a steady way, all the way up to 126 neutrons.  As soon as you go over 126 neutrons the size starts increasing much more rapidly.

Various reasons have been given for why this is so.  Some are in terms of particular nuclear models which either do or don't correctly reproduce this "anomalous kink effect," as it has been termed.  Other reasons use a description based on the fact that quantum mechanics dictates that neutrons and protons have to exist in certain shells or orbits (roughly analogous to planetary orbits) and that different models predict different radii for different shells.  What we have suggested, in our new paper, is that although their might be some truth in the previous explanations, the key factor seems to be not the size of the orbits themselves, but how much the orbits make the extra neutrons interact with the existing protons.  It turns out that tighter orbits, with smaller radii, can generate more of a pull on the protons and make their density distribution larger, than larger orbits that don't interact so much with the protons.

On the level of some of the advanced and complex ways now available to theoretical nuclear physics, it is on the basic side.  Sometimes the simple explanations turn out to be correct.  We at least hope that this sheds some light on the puzzle.


Goddard, P., Stevenson, P., & Rios, A. (2013). Charge Radius Isotope Shift Across the N=126 Shell Gap Physical Review Letters, 110 (3) DOI: 10.1103/PhysRevLett.110.032503