^{4}He

^{++}atoms in

^{4}He superfluid. The research article by ASACUSA researchers Anna Soter et al is published in Nature (this).

The formation of anti-proton-^{4}He^{++} hybrid atoms containing also an electron in ^{4}He was studied both above and below the critical temperature for the transition to Helium superfluid. The temperatures considered are in Kelvin range corresponding to a thermal energy of order 10^{-4} eV.

Liquid Helium is much denser than Helium gas. As the temperature is reduced, a transition to liquid phase takes place and the Helium liquid gets denser with the decreasing temperature. One would expect that the perturbations of nearby atoms to the state should increase the width of both electron and antiproton spectral lines in the dense liquid phase.

This widening indeed occurs for the lines of electrons but something totally different occurs for the spectral lines of the antiproton. The width decreases and when the superfluidity sets on, an abrupt further narrowing of He^{++} spectral lines takes place. The antiproton does not seem to interact with the neighboring ^{4}He atoms.

Researchers think that the fact that the surprising behavior is linked to the radius of the hybrid atom's electronic orbital. In contrast to the situation for many ordinary atoms, the electronic orbital radius of the hybrid atom changes very little when laser light is shone on the atom and thus does not affect the spectral lines even when the atom is immersed in superfluid helium.

Consider now the TGD inspired model.

- It seems that either antiprotons or the atoms of
^{4}He superfluid effectively behave like dark matter. For the electrons, the widening however takes place so that it seems that the antiproton seems to be dark. In the TGD framework, where dark particles corresponds h_{eff}=nh_{0}>h, h=n_{0}h_{0}phases of ordinary matter, the first guess is that the antiprotons are dark and reside at the magnetic flux tube like structures.The dark proton would be similar to a valence electron of some rare earth atoms, which mysteriously disappear when heated (an effect known for decades, see this). Dark protons would indeed behave like a dark matter particle is expected to behave and would have no direct quantum interactions with ordinary matter. The electron of the hybrid atom would be ordinary.

- Darkness might also relate to the formation mechanism of the hybrid atoms. Antiproton appears as a Rydberg orbital with a large principal quantum number N and large size proportional to N
^{2}. N>41 implies that the antiproton orbital is outside the electron orbital but this leaves the interactions with other Helium atoms. For a smaller value of N the dark proton overlaps the electronic orbital. Note that for N=1, the radius of the orbital is 10^{-3}/8a_{0}, a_{0}∼ .53 × 10^{-10}m, in the Bohr model. - The orbital radii are proportional to h
_{eff}^{2}∝ (n/n_{0})^{2}so that dark orbitals with the same energy and radius as for ordinary orbitals but effective principal quantum number (n/n_{0})N_{d}=N_{eff}, are possible. (n/n_{0})N_{d}=N_{eff}condition would give the same radius and energy for the dark orbital characterized by N_{d}and ordinary orbital characterized by N.

- The minimal change of the effective principal quantum number N
_{eff}in dark-to-dark transitions would be n/n_{0}and be larger than one for n>n_{0}. There is evidence for n=n_{0}/6 found by Randel Mills (seethis) discussed from the TGD view here. In this case one would have effectively fractional values of N _{eff}. One can also consider a stronger condition, h_{eff}/h=m , one has mN_{d}=N. The transitions would be effectively between ordinary orbitals for which Δ N_{eff}is a multiple of m. This could be tested if the observation of dark-to-dark transition is possible. The transformation of dark photons to ordinary photons would be needed. - Energy conserving dark-to-ordinary transitions producing an ordinary photon cannot be distinguished from ordinary transitions if the condition (n/n
_{0})N_{d}=N_{eff}is satisfied.The transitions (37,35)→ (38,34) and (39,35)→ (38,34) at the visible wavelengths λ =726 nm and 597 nm survive in the Helium environment. The interpretation could be that the transitions occur between dark and ordinary states such that the dark state satisfies the condition that (n/n

_{0})N_{d}=N_{eff}is integer, and that an ordinary photon with λ = h/Δ E is produced. This does not pose conditions on the value of h_{eff}/h.If the condition that (n/n

_{0})N_{d}=N_{eff}is an integer is dropped, effective principal quantum numbers N_{eff}coming as multiples of n/n_{0}are possible and the photon energy has fractional spectrum.

See the article TGD and condensed matter or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.