Context : The kHz quasiperiodic oscillations ( QPOs ) observed in low-mass X-ray neutron star binaries are most likely connected to the orbital motion in the accretion disc .
The ratio between frequencies of the upper and lower observed QPOs mode cluster close to ratios of small natural numbers , most often close to the 3 / 2 value , but the other rational ratios occur in some sources as well .
The class of QPOs models considers a resonance between Keplerian and epicyclic frequencies of the geodesic motion .
It was suggested that a multipeaked ratio distribution may follow from different resonances .
The atoll source 4UÂ 1636-53 shows datapoints clustering around two distinct values ( 3 / 2 and 5 / 4 ) of the frequency ratio .
The same frequency ratios correspond to the change in the sign of the twin peak QPOs amplitude difference , suggesting existence of a resonant energy overflow .

Aims : We explore the idea that the two clusters of datapoints in 4U 1636-53 result from two different instances of the same orbital resonance corresponding to the two resonant points .

Methods : Assuming the neutron star external spacetime to be described by the Hartle-Thorne metric , we search for a frequency relation , matching the two observed datapoints clusters , which may correspond to a resonance .
We consider orbital and associated epicyclic frequencies with accuracy up to the second order terms in the neutron star angular momentum j and first order terms in its quadrupole moment q .

Results : We have identified a suitable class of frequency relations well fitting the observed data .
These models imply for central compact object in 4UÂ 1636-53 the mass M = 1.6 – 2.5 M _ { \sun } , dimensionless angular momentum j = 0 – 0.4 , and quadrupole momentum q = 0 – 0.25 , with most preferred values M \doteq 1.77 M _ { \sun } , j \doteq 0.05 , and q \doteq 0.003 .

Conclusions : The relationship implied for a particular case of so called total precession resonance between the Keplerian and the total precession frequency introduced in this paper resembles the twin peak QPOs observed in 4U 1636-53 with a \chi ^ { 2 } \sim 3 { d . o . f . } which is about one order lower than \chi ^ { 2 } reached by other theoretical relationships which we examine .
Moreover , the position of 3/2 and 5/4 resonant points implied by the total precession relationship well coincides with frequencies given by the change of the rms-amplitude difference sign .
Notice that if a resonance ( in our opinion most likely present ) is not considered , the total precession relation has a similar kinematic meaning as the periastron precession relation involved in the model of Stella and Vietri , but gives substantially better fit and lower neutron star mass .