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the proper - motion observations of pulsars show that the pulsars had the kick velocity in the formation stage . the young pulsars have proper velocity of @xmath4  @xcite . the physical mechanism of such kick velocity may be due to the harrison tademaru mechanism  @xcite , anisotropic emission of neutrinos , anisotropic explosion and so on ( see lorimer  @xcite for the review ) . therefore , it is also reasonable to assume the existence of the proper motion of the pulsars in the formation process of pop iii nss , although there is no direct evidence since no pop iii star or pulsar is observed . while , repetto et al . @xcite suggest that bhs also have a natal kick velocity comparable to pulsars from the galactic latitude distribution of the low mass x - ray binaries in our galaxy . but , first , this is not the direct observation of proper motion of bhs , and second , since the mass of pop iii bhs is larger than pop i and pop ii bhs , their kick velocity might be so small that it can be neglected . therefore , we take into account the natal kick for pop iii nss but not for pop iii bhs in this paper . the kick speed @xmath5 obeys a maxwellian distribution as @xmath6 \,,\ ] ] where @xmath7 is the dispersion . the details of the method how to calculate the natal kick are shown in ref . @xcite .    in this paper , we perform population synthesis monte carlo simulations of pop iii binary stars . we calculate the pop iii ns - bh and pop i and ii ns - bh for comparison . pop i and pop ii stars mean solar metal stars and metal poor stars whose metallicity is less than 10% of solar metallicity , respectively . in this paper , we consider five metallicity cases of @xmath8 ( pop iii ) , @xmath9 and @xmath10 ( pop i ) . there are important differences between pop iii and pop i and ii . pop iii stars are ( 1 ) more massive , @xmath11 , ( 2 ) smaller stellar radius compared with that of pop i and ii , and ( 3 ) no stellar wind mass loss . these properties play key roles in binary interactions .    in order to estimate the event rate of ns - bh mergers and the properties of ns - bh , we use the binary population synthesis method  @xcite which is the monte calro simulation of binary evolution . first , we choose the binary initial conditions such as the primary mass @xmath12 , the mass ratio @xmath13 , the separation @xmath14 , and the eccentricity @xmath15 when the binary is born . these binary initial conditions are chosen by the monte calro method and the initial distribution functions such as the initial mass function ( imf ) , the initial mass ratio function ( imrf ) , the initial separation function ( isf ) , and the initial eccentricity distribution function ( ief ) . we adopt these distribution functions for pop iii stars and pop i and ii stars as table  [ idf ] .    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in the population synthesis simulations of pop iii stars , many bh ( black hole)-bh binaries with merger time less than the age of the universe @xmath0 are formed , while ns ( neutron star)-bh binaries are not . 
 the reason is that pop iii stars have no metal so that no mass loss is expected . 
 then , in the final supernova explosion to ns , much mass is lost so that the semi major axis becomes too large for pop iii ns - bh binaries to merge within @xmath1 . 
 however it is almost established that the kick velocity of the order of @xmath2 exists for ns from the observation of the proper motion of the pulsar . 
 therefore , the semi major axis of the half of ns - bh binaries can be smaller than that of the previous argument for pop iii ns - bh binaries to decrease the merging time . 
 we perform population synthesis monte carlo simulations of pop iii ns - bh binaries including the kick of ns and find that the event rate of pop iii ns - bh merger rate is @xmath3 . 
 this suggests that there is a good chance of the detection of pop iii ns - bh mergers in o2 of advanced ligo and advanced virgo from this autumn .