A calculation method of frequency distributions for the microdosimetric quantity J (number of effective primary events produced in a target), h
J, is presented. This method is briefly compared with other approaches developed by Kellerer and Chmelevsky, and Wilson and Paretzke for numerical calculations of microdosimetric quantities. The hj distributions are calculated for nanometer-size targets in water irradiated with
60Co γ rays as a practical application. It was found that the h
J distribution remarkably depends on two parameters, Dσ
0 and 1/W'', where D is the absorbed dose, σ
0 is the mean geometrical cross section of the target, 1 is the mean target thickness, and W'' is the mean energy to produce an effective primary event in the target. Our h
J distributions are compared with those in the conventional target theory. Finally, the quantity z'' and the frequency distribution for z'', h
z'', which correspond to the specific energy z and the probability density f(z) defined in ICRU Report 36, are derived from J and the h
J distribution, respectively. The h
z'' distribution depends on the values of Dσ
0 and 1/W'' and the frequency mean of z'', z'', is equal to the absorbed dose D.
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