Do angles of obliquity apply to 30 degrees scattered radiation from megavoltage beams?

The angle of obliquity is used in radiation shielding calculations to account for the longer path length x rays will see when obliquely incident on the protective barrier. According to the National Council on Radiation Protection and Measurements (NCRP), use of the angle of obliquity is explicitly assumed for primary radiation, so that an angle of obliquity for secondary radiation is never addressed. However, in the example section of the latest report, it specifically recommends against using an angle of obliquity for scattered radiation. To check this assumption, the existence or not of an angle of obliquity for scattered radiation has been investigated for bremsstrahlung x-ray beams of 4, 6, 10, 15, and 18 MV and for barriers consisting of concrete, lead, and steel using a Monte Carlo approach. The MCNP Monte Carlo code, v4.2C, has been used to generate scattered radiation at 30 degrees from a water phantom and incident on a secondary barrier at the same angle relative to the normal to the barrier. The barrier thickness was increased from zero to a thickness sufficient to reduce the fluence (f4 tally) to <10(-3). A transmission curve was created for each energy-barrier material combination by normalizing to zero thickness. The results for the first tenth-value layer (TVL) in concrete (5 energies) show an average angle of obliquity of 21.7 degrees +/- 5.6 degrees , and for the first two TVLs averaged 29.7 degrees +/- 3.9 degrees . The results for the first TVL in lead (3 energies) show an average angle of obliquity of 27.7 degrees +/- 4.0 degrees , and for the first two TVLs averaged 20.5 degrees +/- 5.8 degrees . There are no data in the NCRP reports for 30 degrees scattered radiation attenuated by steel with which to make a comparison.