Globular clusters ( GCs ) are the ideal environment for the formation of neutron stars ( NSs ) and millisecond pulsars ( MSPs ) .
NSs origin and evolution provide a useful information on stellar dynamics and evolution in star clusters .
NSs are among the most interesting astrophysical objects , being precursors of several high-energy phenomena such as gravitational waves and gamma-ray bursts .
Due to a large velocity kick that they receive at birth , most of the NSs escape the local field , affecting the evolution and dynamics of their parent cluster .
In this paper , we study the origin and dynamical evolution of NSs within GCs with different initial masses , metallicities and primordial binary fractions .
We find that the radial profile of NSs is shaped by the BH content of the cluster , which partially quenches the NS segregation until most of the BHs are ejected from the system .
Independently on the cluster mass and initial configuration , the NSs map the average stellar population , as their average radial distance is \approx 60 - 80 \% of the cluster half-mass radius .
Finally , by assuming a recycling fraction of f _ { \mathrm { rec } } = 0.1 and an average MSP gamma-ray emission of L _ { \gamma } = 2 \times 10 ^ { 33 } erg s ^ { -1 } , we show that the typical gamma-ray emission from our GCs agrees with observations and supports the MSP origin of the gamma-ray excess signal observed by the Fermi-LAT telescope in the Galactic Centre .