1
Perspective and Introductory Remarks

1.1 What Do Muons Bring to Chemistry?

Like their leptonic cousins, the electron and positron, muons come in two charge states, µ+ and µ-. They were first discovered in cosmic ray showers [1] and have been actively studied in accelerator-based experiments ever since. The discovery of parity violation in muon decay [2, 3] soon led to studies of the interactions of muons in matter and the development of various experimental techniques commonly referred to as 'µSR', for muon spin rotation/relaxation/resonance, and here collectively known as 'Muon Spin Spectroscopy'.

The fundamentals and applications of µSR to solid-state physics are well covered in a variety of texts [4-8]. In contrast, the current book focuses on the importance of muons in chemistry. There has been only one previous book dedicated to this subject, but this was published in 1983 [9] and there have been major developments in the field since then.

Particle physicists view the negative muon as a heavy electron, and indeed it plays this role in muonic atom chemistry. However most chemical studies of muons make use of the antiparticle, the positive muon. The muon rest mass is 105.66?MeV, which is 206.8 times heavier than the electron, and 0.1126 (roughly 1/9th) the mass of a proton. The single-electron atom with µ+ as nucleus is known as muonium (Mu = µ+e-), and from a chemical point of view this can be viewed as the lightest isotope of hydrogen.

At the other end of the mass scale, the interaction of an energetic negative muon with helium can result in the muonic helium atom, i.e. a helium atom in which one electron has been replaced with a µ-. Given the large mass of the muon (relative to the electron) the µ- resides in a tight atomic orbital close to the nucleus, where it effectively screens half of the nuclear charge. Thus Heµ is a single-electron atom with an effective nuclear charge of +1, just like the H atom [10].

The properties of a single-electron atom of nuclear charge Ze are readily calculated by either the Bohr atomic model or standard quantum mechanics. The allowed electron energies are given by

and the Bohr radius (charge separation for the lowest energy state of the atom) is

where e is the elementary charge, ?0 is the electric constant (vacuum permittivity), ? is the Planck constant divided by 2p, and mr is the reduced mass for the two-body system:

where me and mN are the electron mass and the mass of the nucleus, respectively. As long as mN is large compared with me, the reduced mass is approximately equal to me. Thus the fundamental atomic properties given by Eqs. (1.1) and (1.2) depend only weakly on nuclear mass. This is why isotopes are considered to have the same chemistry - ionization energies and charge separation are the key chemical properties of atoms.

Isotopes are normally thought of as atoms with the same number of protons (same Z) but differing numbers of neutrons in their nuclei. However, application of Eqs. (1.1)-(1.3) shows that the series of single-electron atoms Mu, H, D, T, Heµ (Figure 1.1) should have the same chemistry. Their atomic properties are summarized in Table 1.1.

Thus muonium and Heµ can be expected to react in the same manner as the other atomic hydrogen isotopes, e.g.

Of course, the rate constants can vary with isotopic mass, and this is the basis of the kinetic isotope effect discussed in later chapters. At this stage it is sufficient to point out that muons greatly extend the range of isotope effect studies, providing a remarkable mass range of 36 from Mu to Heµ.

Another facet of isotopes that finds great utility in chemistry is their application as tracers. Reaction mechanisms are often deduced or tested by following the fate of 'labelled' molecules. The labelling may be radioactive (e.g. tritium) or spin (e.g. deuterium). Muonium qualifies in both categories: the positive muon spontaneously decays with a mean lifetime of 2.197?µs, irrespective of medium, and it has spin ½, just like a proton but with a larger magnetic moment (by a factor of 3.183). Both of these properties are utilized in muon spin spectroscopy. Furthermore, the relatively low intensity of muon beams means that each Mu atom is effectively isolated, so cross-reactions are avoided.

Figure 1.1 The series of single-electron atoms which behave as isotopes of hydrogen.

Table 1.1 Mass, reduced mass, ionization energy and atomic radius of hydrogen isotopes.

The addition of Mu to unsaturated bonds results in the formation of muonium-labelled molecules (formally referred to as 'muoniated' radicals [11]). Radicals are atoms or molecules that have one or more unpaired electrons, and are therefore typically highly reactive. They play an important role in chemistry, often as intermediates in reactions, but their transient nature makes them challenging to study with conventional spectroscopic techniques. Muoniated radicals are studied for similar reasons that Mu is studied in place of H, either to explore isotope effects, or to use Mu as a tracer. In the latter case, it could be to investigate radicals that would be difficult to produce or study with other spectroscopic techniques. Alternatively, the aim could be to label specific parts of a complex system to learn about the dynamics and local environment. Chapters 6-9 contain many examples of these varied uses.

Some Comments on Nomenclature

The common isotopes of hydrogen are named protium (H), deuterium (D) and tritium (T), and if a similar convention were followed for Mu it would be named muium. Indeed, according to the nomenclature of particle physics, the 'onium' ending implies the bound state of a particle with its antiparticle (e.g. positronium, Ps = e+e-). Nevertheless, the term muonium for µ+e- has been in use since 1957 [3] and is so well entrenched that it is endorsed by IUPAC [11].

Older literature used the term muonated radical instead of muoniated radical. This practice has been discontinued, as 'muonation' is now defined [11] to be the equivalent of protonation, i.e. the addition of Mu+ rather than neutral Mu. Even older literature refers to muonic radicals. The adjective 'muonic' is now reserved for negative muon entities.

1.2 Muon Facilities and Background to Experimental Muon Techniques

There are currently four nuclear accelerators in the world that produce intense beams of spin-polarized muons: the TRIUMF cyclotron in Vancouver, Canada; the ISIS Facility at the Rutherford Appleton Laboratory in the UK; the Paul Scherrer Institute (PSI) in Switzerland; and the Japan Proton Accelerator Research Complex (JPARC) at Tokai in Japan. These accelerators have different features, but all generate muons from the decay of charged pions, p±, which are themselves produced from the nuclear reactions of energetic protons. Pion production targets typically feed several muon beamlines, and at some accelerators there are two targets per proton beam. Nevertheless, the total number of muon beamlines suitable for muon spin spectroscopy is less than twenty worldwide.

TRIUMF and PSI produce quasi-continuous (CW) beams, while ISIS and J-PARC are pulsed sources. The CW facilities produce muons one at a time, with an even but stochastic time distribution. Such beams permit the use of...