  AIMS: For six neutron-star atoll sources (4U 1608-52, 4U 1636-53, 4U 0614+09,
4U 1728-34, 4U 1820-30 and 4U 1735-44) we investigate the relationship between
the observed fractional rms amplitudes of the twin kHz QPOs. We discuss whether
this displays features that could have a physical meaning in terms of the
proposed QPO models. METHOD: We consider the difference in rms amplitude
between the upper and lower kHz QPOs, as a function of the frequency ratio R.
We compare two data sets. Set I is a collection taken from published data. Set
II has rms amplitude values obtained by automatic fitting of continuous
segments of RXTE-PCA observations. RESULTS: For each of the six sources, we
find that there is a point in the R domain around which the amplitudes of the
two twin kHz QPOs are the same. We find such a point located inside a narrow
interval R=1.5 +-3%. Further investigation is needed in the case of two sources
to explore this finding, since we have not determined this point in Set II.
There is evidence of a similar point close to R = 1.33 or R = 1.25 in the four
sources. We suggest that some of these points may correspond to the documented
clustering of the twin kHz QPO frequency ratios. CONCLUSIONS: For the sources
studied, the rms amplitudes of the two kHz peaks become equal when the
frequencies of the oscillations pass through a certain ratio R, which is
roughly the same for each of the sources. In terms of the orbital QPO models,
with some assumptions concerning the QPO modulation, this finding implies the
existence of a specific orbit at a common value of the dimensionless radius, at
which the oscillations corresponding to the two peaks come into balance. In a
more general context, the amplitude difference behaviour suggests the possible
existence of an energy interchange between the upper and lower QPO modes.
