u0192 l s u03c3 u03c1 on formation bulk density u03c1 may be a second order effect therefore it may be desirable to treat the dependence on the formation bulk density u03c1 as a separate term that is the function u0192 l s u03c3 u03c1 may be separated into two terms m u03c1 and h l s u03c3 as shown below ratio u0192 l s u03c3 u03c1 m u03c1 u00d7 h l s u03c3 therefore one can consider the dependence of countrate ratios on the formation sigma u03c3 and formation bulk density u03c1 separately the dependence i e h l s u03c3 of countrate ratios on the formation sigma u03c3 is illustrated in fig6 the data points shown in fig6 are derived from modeling the countrate ratios are computed using a neutron monte carlo modeling code while the corresponding slowing down lengths and formation densities are computed using snupar u00ae for the same formations fig6 shows the results obtained for limestone and sandstone at several slowing down lengths and sigma for both lithologies the cnl u00ae ratios rapidly increase as the slowing down lengths decrease from less than 1 at l s 24 0 cm to more than 5 at l s 7 2 cm in all curves the cnl u00ae ratios increase slowly as sigma u03c3 increases.