We study density cusps in the center of clusters of galaxies to reconcile X-ray mass estimates with gravitational lensing masses .
For various mass density models with cusps we compute X-ray surface brightness distribution , and fit them to observations to measure the range of parameters in the density models .
The Einstein radii estimated from these density models are compared with Einstein radii derived from the observed arcs for Abell 2163 , Abell 2218 , and RX J1347.5-1145 .
The X-ray masses and lensing masses corresponding to these Einstein radii are also compared .
While steeper cusps give smaller ratios of lensing mass to X-ray mass , the X-ray surface brightnesses estimated from flatter cusps are better fits to the observations .
For Abell 2163 and Abell 2218 , although the isothermal sphere with a finite core can not produce giant arc images , a density model with a central cusp can produce a finite Einstein radius , which is smaller than the observed radii .
We find that a total mass density profile which declines as \sim r ^ { -1.4 } produces the largest radius in models which are consistent with the X-ray surface brightness profile .
As the result , the extremely large ratio of the lensing mass to the X-ray mass is improved from 2.2 to 1.4 for Abell 2163 , and from 3 to 2.4 for Abell 2218 .
For RX J1347.5-1145 , which is a cooling flow cluster , we can not reduce the mass discrepancy .