The well known neutron-induced fission of a uranium-235 nucleus, commonly written as

n+ ^ vn+ P, + /*2 (12.1)

is known to proceed at room temperature because one of the reactants is a neutral particle and a uranium-235 nucleus possesses a substantial fission cross-section for thermal neutrons. The absence of Coulomb forces of repulsion and the presence of nuclear forces of attraction at short distances of separation (< R0) suggests a potential energy diagram as depicted in Fig. 12.la.

In contrast to the above, fusion of a deuterium ion with a tritium ion is represented by

d +1 —^ ті + ос (12.2)

but requires a high reactant temperature to allow a sufficient number of ions to overcome the Coulomb barrier, or to penetrate it by tunnelling. This will lead to substantial reaction rates and the consequent energy yield. The corresponding ion-ion fusion potential energy diagram is shown in Fig. 12.lb.

These two potential energy diagrams, Fig. 12.la and 12.1b, represent two conceivable extremes. A case between these extremes can be conceived of by the following conceptualization for deuteron-triton fusion. Consider a deuterium atom and a catalytic tritium nearby with both particles at low kinetic energy of relative motion, that is in a medium of low temperature. The catalytic tritium is taken to consist of the usual nucleus-а proton and two neutrons-but rather than its normal electron in a Bohr orbit, it contains a catalyst x in an orbit very close to the nucleus. This particle x is expected to possess an electric charge so as to

render the catalytic particle neutral. We add that this particle x may or may not be stable against radioactive decay and may or may not be in a stable tight orbit around the nucleus. As for any two approaching hydrogen atoms, here the deuterium atom and the catalytic tritium will tend to combine by hydrogen molecule formation, which accounts for the range of attraction outside R0 in Fig. 12.1c. To the neighbouring deuteron, the catalytic tritium will, during the lifetime of the catalytic state, appear like an oversize neutron; the two may thus form a compound ionic state where the deuteron and triton are close enough for nuclear forces of attraction to dominate and therefore render fusion at low temperature. In Fig. 12.1c, a "Coulomb sliver" occurs at the distance of the catalyst’s orbit and is expected to be thin enough to be penetrated on account of the nuclei’s available energy in the molecularly bound state.

b) ion-ion fusion at high temperature

C) neutral-neutral low temperature catalytic fusion

Fig. 12.1: Graphical depiction of low temperature fission, high temperature ion-ion fusion,
and low temperature catalytic fusion.

The sequence of events for this low temperature catalytic fusion event consist of three distinct stages:

1. catalytic atom formation:

x + t^xt (12.3a)

2. unstable intermediate formation:

xt + d^xtd (12.3b)

3. decay into fusion reaction products:

xtd^n + a + x. (12.3c)

These three stages may also be written in sequential form

x + t + d —^ xt + d —> xtd —У n + cc + x (12.3d)

and evidently possess some similarity to a fission process which, with a more detailed accounting of the process of reaction (12.1), may be written as

n+^U^U*<^36U + y (12.4)

^vn+ Px + P2 .

Indeed, we will show that branching reaction channels, each with their own probability, shown here in fission also apply to the catalytic reaction chain of Eq.(12.3d).

Low temperature fusion for which the catalyst x is a muon-recall our discussion of Sec. 7.7-has been experimentally demonstrated in liquid media at elevated pressures and in the temperature range 300 К to 900 K, formidable to muonic molecular formation. Evidently, if the process can be sustained as energetically and technologically favourable, then this novel approach might become a contender for a fusion device.

Some elementary aspects of muon physics can be described by the following. We begin with muon production. It is known that many high energy nuclear reactions yield the negative pi meson, 7t", as a reaction product,

(High Energy Reaction) -» n +■■■ — (12.5a)

This pion possesses a mean life of ~ 10’8 s and decays via

7г"-»р"+у^ (12.5b)

where Уц is the muon antineutrino. The negative muon p" decays with a mean life of 2.2 x 10"6 s according to

p —> e + Ve + (12.6)

where e" is an electron, v<? is an electron antineutrino, and vu is the muon

neutrino. It is common to dispense with the adjective "negative" for the muon and simply represent this particle by p rather than p’.

The initial kinetic energy of a produced muon depends upon the details of the initiating reaction but is typically about 200 MeV. In a dense liquid hydrogenous medium, this high energy subatomic particle slows down to about 2 keV in ~ 10’8 s and in another ~ 10"” s cascades down into a K-orbit around a deuteron or triton to form a muonic atom, pd or pt.

The details of the subsequent muon-nucleus, muon-atom and muon-molecule interactions are complex; for example, resonance phenomena involving muonic atoms and associated molecule formations have been identified suggesting the appearance of a variety of nuclear and atomic states. However, for present purposes, and in order to illustrate low temperature fusion, we incorporate these various processes in a collective dynamic characterization using macroscopic reaction parameters.