We investigate the correlation between the frequencies of the twin kilohertz quasi-periodic oscillations ( kHz QPOs ) and the neutron star ( NS ) spins in low mass X-ray binaries ( LMXBs ) , based on the data sets of 12 sources with simultaneously detected twin kHz QPOs and NS spins , and find that the histogram of the ratio between the frequency difference of twin kHz QPOs ( \Delta \nu \equiv \nu _ { 2 } - \nu _ { 1 } ) and NS spin \nu _ { s } shows a non-uniform distribution with a gap at \Delta \nu / \nu _ { s } \sim 0.65 .
We try to classify the 12 sources into two categories according to this gap : ( I ) The slow rotators with \langle \nu _ { s } \rangle \sim 311 Hz , XTE J1807.4-294 , 4U 1915-05 , IGR J17191-2821 , 4U 1702-43 , 4U 1728-34 and 4U 0614+09 follow a relation \Delta \nu / \nu _ { s } > 0.65 ; ( II ) The fast rotators with \langle \nu _ { s } \rangle \sim 546 Hz , SAX J1808.4-3658 , KS 1731-260 , Aql X-1 , 4U 1636-53 , SAX J1750.8-2900 and 4U 1608-52 satisfy the relation \Delta \nu / \nu _ { s } < 0.65 .
However , the linear fittings of \Delta \nu versus \nu _ { s } relations of group ( I ) and ( II ) are unsatisfactory to ensure any certain correlations .
We suggest that this phenomenon may arise from the fact that most measured kHz QPOs and spins satisfy the conditions of 1.1 \nu _ { s } \leq \nu _ { 2 } < 1300 Hz and \Delta \nu decreasing with \nu _ { 2 } .
Apparently , the diversified distribution of \Delta \nu / \nu _ { s } refutes the simple beat-frequency model , and the statistical correlations between the twin kHz QPOs and NS spins may arise from the magnetosphere-disk boundary environments , e.g. , co-rotation radius and NS radius , that modulate the occurrences of X-ray signals .
Furthermore , we also find that the distribution of the ratio of \nu _ { 2 } to \nu _ { 1 } clusters around the value of \langle \nu _ { 2 } / \nu _ { 1 } \rangle \sim 3 : 2 , which shows no obvious correlation with NS spins .