I would expect so but the main question in this case would be how do you accelerate those neutral atoms into a beam with which you would bombard a target?

There are some methods, as railgun or coaxial gun or any other Lorentz based. The efficiency is lower but we must study if it is worthwhile

It would be interesting to have the cross section of  ions again ions

The problem I view at a first glance (but I am not a specialist) is that the atoms are not intrinsically neutral, but a conglomerate of charges. This means that at close range you will still have electrostatical forces. Ions against ions has been done several times at CERN, when they accelerate beams in oposite directions and then smash them into each other.

Think in terms of physics. A neutral atom projectile is neutral only until the electron cloud around it hits the electron clound of the target atoms. Head-on collisions causing nuclear interactions will not be affected since the Coulomb repulsion starts to act only at short distances when neutrality is upset by the disruption of the electron cloud. A small shift in energy may occur in the case of ion-ion interaction caused by the loss of speed due to Coulomb repulsion acting from infinity down to the atomic radius, but my feeling is that this is small and can be calculated analytically. Non-Nuclear scattering (i.e. the Rutherford scattering) can be described exactly analytically for ion-ion interactions. Large-angle deflections that arise in short-range interactions (less than atomic radius) will be the same. For small angles the Rutherford scattering cross section goes to infinity (valid for ion-ion interactions) but drops to zero in all other cases for angles that correspond to distances of approach greater than the atomic radius.

The effect is well known and usually refered to as "electron screening", i.e. the screening (reduction) of the repulsive Coulomb potential of the nuclei by the surrounding electron cloud leading to a small enhancement of the corresponding reaction cross section. If you search for "electron screening" you will find plenty of literature references on this topic.

The effect scales with the involved nuclear charges. However, the effect in case of nuclear reactions is only relevant for energies well below the Coulomb barrier and, thus, important for astrophysical environments, i.e. for stellar plasma (plasma screening) or laboratory measurements of the relevant cross sections for nuclear reactions taking place in stars.

Typical energies where the cross section enhancement becomes observable for instance for proton reactions on light elements are from a couple of keV to some tens of keV (as I said depending on the charge).

There are some indirect experimental techniques, e.g. the so called Trojan Horse Method, that can be used to disentangle the effect of electron screening from the reaction cross section of bare nuclei (fully stripped without electron cloud).

At present, theoretical approaches cannot explain consistently all available experimental data, but this, however, might be also partly due to the experimental difficulties in measurements at such "low" energies.

Thank you very much, it helped me a lot in the Pulsotron-3 development. It is a pity that it is not confirmed experimentally.

Perhaps in a high density matter (10xfold compression over solid) the fusion enhancement must be larger.

You might want to look into work of ions penetrating thin carbon foils and neutral atoms penetrating thin carbon foils.  I think you will find there is no difference.  My guess is that within a nanometer or two any neutral with energy greater than 1 keV is going to be ionized.

There is an exhaustive answer to your question in Charles Joachain's excellent 'Quantum Collision Theory' 

" My guess is that within a nanometer or two any neutral with energy greater than 1 keV is going to be ionized."

Kevin, you are right, using a railgun, the neutral atoms cloud would became ionized with electrons too far from ions to screen their charge at short distances (or not).

I like the idea of using thin foils to neutralize the beams, may be better than using a litle cloud of negative ionized hydrogen

Kevin, have you in Los alamos a good railgun to make the test?

Full agreement with the explanations of Frank. In the MEV range, there are attempts in progress aimed to probe electron screening by using an approach that is based on the differences between the alpha-decay half-life values of the same unstable nucleus in neutral and in bare g.s.  configurations. Few per mil differences are searched by decay curve measurements with high precision (PRC 88, 011303(R) (2013), PHYSICA SCRIPTA T150, 014028 (2012).