I have an answer to establish expectations from first principles. I have not looked up real values, nor am I hopeful of finding such values. All I'm doing here is setting a general expectation for the difference in cross sections of ion-ion fusion and ion-atom or atom-atom fusion. I should note that the one glaring piece of information missing from the question is the energy of the reaction. As such, my answer will be somewhat non-specific on that point, but my position is that it doesn't affect my overall conclusion that no major reaction rate benefit could be obtained in fusion machines by this proposed mechanism.
I used a number of simplifications to craft a simple algebraic form for the difference in cross sections. I should first specify though, I used a "radius" for the cross section defined as $a=\sqrt{\sigma / \pi}$. Yes, it is true that cross-sections aren't really areas, but for the relative scales here they can be treated as such. Now, here are the assumptions I used:
- Fusion cross section << Atomic radius
- Physics are identical to ion-ion interaction after atomic radii meet
- Only the impact of cross section broadening considered, the increase in energy due to atom charge interaction not considered
- Target nucleus doesn't move. You could try to eliminate this with reduced mass or an adjustment to reaction energy, I'll leave that for someone else to try. This assumption isn't really necessary but I just didn't see a quick way around it.
The basic proposition we have is that the ion-ion cross sections of the reactions are already known. This, naturally, depends on the energy.
My proposition is that, whatever the ion-ion reaction trajectory is, it will be different from the ion-atom interaction by the electrostatic force operating at distances greater than the atomic radius. I hope my method is already starting to seem clear, but I'll use an illustration. The proposition is that
- We know $a_{++}$
- We know the profile of the $y-y_{++}$ with simple electrostatic physics.
Using the assumption that the atomic radius is small compared to the fusion cross section radius, I can claim $\sin{ \theta} = a/s$. The electrostatic force from the net charges on the atom/ion will operate along the line between the moving atom/ion and the target atom/ion. The distance between these can be approximated to be equal to $s$. If we don't bother with the speedup from this force, then we'll just consider the component inward.
$$F_{in} = \sin{\theta} \frac{ k q_1 q_2 }{ s^2 } = \frac{ k e^2 z_1 z_2 a }{ s^3 } $$
The speed of the incoming atom/ion is roughly constant, so I can give this approximate expression to get the above math in terms of time. This applies from $-\infty$ to $-r/v$. The $v$ follows from the energy of the reaction.
$$s(t) = - v t$$
Then the basic kinematics follow logically.
$$v_{in}(t) = \int_{-\infty}^{t} \frac{F_{in}(t')}{m} dt' = \frac{ k e^2 z_1 z_2 a }{2 v^3 m t^3}$$
$$ y(r) - y_{++} (r) = \int_{-\infty}^{-r/v} v_{in}(t) dt $$
$$ a - a_{++} = v_{in}(r) \frac{r}{v} + ( y(r) - y_{++} (r) ) = \frac{ k e^2 z_1 z_2 /r }{m v^2} a$$
This gives the difference in cross section radius due to atom-ion or atom-atom interaction beyond that atomic radius. This is a particularly useful form if we introduce $E_c=k e^2 / r$ and the kinetic energy of the incoming atom/ion. The difference in cross sections will be about twice this difference in radii.
$$\sigma - \sigma_{++} = \pi ( a^2 - a_{++}^2 ) \approx - 2 \pi a^2 z_1 z_2 \frac{E_c}{E_k}$$
$$\frac{ \sigma - \sigma_{++} }{ \sigma_{++} } \approx 2 z_1 z_2 \frac{E_c}{E_k}$$
$$E_c = 0.027 keV$$
This makes intuitive sense. The cross section will be affected by an amount proportional to the electrostatic energy of the two touching atoms and inversely proportional to the kinetic energy of the interaction.
The interaction energy in ITER will be about $8 keV$, and the optimal energy for DT fusion is $80 keV$ (previous graph). If you had two neutral atoms interacting, the cross sections will be greater than the ion-ion interaction by 0.6 % at ITER energies. It would be an improvement of 0.06 % at optimal DT energies.
The best you could ever hope for would be the pB interaction with the B fully ionized (+5) and the Hydrogen with (-1). Even this is likely unattainable as some comments have pointed out. If we look at this at ITER energies (impossible but this is best-case), that would increase the cross section by about 5%. Pretty much all other scenarios would have less of an improvement than this.
The bottom line is that the Coulomb attraction at distances beyond the atomic radius is very very small compared with the Coulomb repulsion that the nuclei have to overcome as they get closer than that. Any adjustments to the cross section from this atom-ion or atom-atom interaction will really be <1% for most conceivable fusion reactions.
Fusion happens between light nuclei. It cannot happen in room temperatures and pressures, it needs very high energies in order to strip the electrons from the nucleus and to overcome the electromagnetic repulsion of the positive charges .
The fusion reaction rate increases rapidly with temperature until it maximizes and then gradually drops off. The DT rate peaks at a lower temperature (about 70 keV, or 800 million kelvin) and at a higher value than other reactions commonly considered for fusion energy.
Fusion experimentally, apart from the Hbomb, has been sustained at JET, an experimental facility, by confining a plasma at the high temperatures necessary, in a tokamak, a specially designed magnetic field. This design is extended into ITER which is a prototype fusion energy reactor, i.e, will give out more energy than spent in creating the magnetic field and the plasma. If you look at the links these are huge constructs not suitable for bombs.
A second direction in creating the plasma temperatures necessary for sustained fusion is with very strong lasers. If you look at the photo of the system needed to reach fusion energies again you will realize that it cannot become the central part of a bomb.
That is where present day technology is. Hopefully by the time nanotechnology catches up with fusion humanity will have matured enough to use fusion only for getting unlimited energy.
Best Answer
the ratio of energy to mass would arguably be lower than H-H or D-T fusion, so it would hardly be a preferred fusion reaction for space travel applications
For production purposes (be them energy, manufacture, etc.) we humans usually prefer more result (i.e: more energy output) as a result of less investment (i.e: less energy expenditure) to improve the efficiency of the conversion. As such, any fusion reaction for heavier elements will undoubtly be less energetic per dollar spent having it working, regardless if the purpose is weaponry, energy production or propulsion