Table 4.

Average percentage difference, $\Delta \frac{\overline{H}}{D}$, and maximum percentage difference, ${\left(\Delta \frac{H}{D}\right)}_{\max }$, between H/D values calculated by Monte Carlo methods and the analytical model at 40 cm OAX. E_p denotes the proton beam energy and z is the depth in the phantom.

Ep (MeV)	$\Delta \frac{\overline{H}}{D}$ (%)	${\left(\Delta \frac{H}{D}\right)}_{\max }$ (%)	z at ${\left(\Delta \frac{H}{D}\right)}_{\max }$ (cm)
100	30.0	81.7	40
120	26.0	58.9	37
140	14.8	51.7	1
160	12.3	51.8	1
180	6.6	19.7	1
200	9.0	19.3	1
225	7.4	27.6	1
250	8.4	19.0	10