Reaction cross section calculations for deformed nuclei

directly from cross section data using a spherical density OL reaction calculation. Equation ~1! was then used to subtract the effects of the projectile deformation through a chain of isotopes to yield a spherical part of the nuclear radius ^r 2 &b50 .I n @10# the onset of deformation, going from spherical to deformed Hartree-Fock calculations, was shown to lead to an increased rms size for the projectile, consistent with Eq. ~1!. This increased rms size then enhanced the cross section obtained using a spherical density OL calculation. Within the reaction cross section calculation, the deformed density function enters the nuclear transparency ~see below! in the argument of an exponential function. It is not clear therefore to what extent the cross section computed using a spherical angle average of the deformed density in this exponent will yield an accurate deduced matter radius. In this Brief Report we therefore calculate the reaction cross section, taking explicit account of the effects of the projectile ~or target! deformation in the collision. We show that Eq. ~1!, interpreted appropriately, can be used to provide an accurate estimate of these effects. The projectile nucleus, denoted ~1!, will be assumed to be quadrupole deformed with deformation b[b 2. The orientation of the symmetry axis is denoted V ˆ. The target nucleus, denoted ~2!, will be assumed to be spherical. We consider, for simplicity only, a zero-range underlying NN interaction. Figure 1 shows the coordinates used in our model calculations where R, the projectile-target separation, has cylindrical coordinates, R[(b,Z), with respect to the beam direction as the Z axis. The optical limit reaction cross section for a fixedorientation of the incident projectile is then @9#