Some further results on the Hubbell rectangular source integral

Confirmation of Accuracy of Haselgrove Method using Hubbell Radiation Rectangular Source Integral

“…However, computational accuracy for such applications has not been precisely determined. Recently the HRS integral was calculated by Timus 3) and Guseinov et al 8) with a high accuracy enough to be referred to this verification. Using these calculations, the present paper will then show the accuracy of the HM, evaluating the standard deviation and the average of relative differences between both calculations.…”

“…(4). Further comparative study of these results was quantitatively carried out by means of evaluating the standard deviation and the average relative differences (RD) with the results calculated by Timus 3) and Guseinov et al 8) These resulting values versus a skip number are shown in Fig. 1 as well as the sampling number for every HM calculation.…”

“…This has been studied thoroughly by many researchers. [2][3][4][5][6][7][8] The Haselgrove method 9,10) (HM) with quasirandom number has been proven to be effective and efficient in calculating simple gamma-ray shielding formulas. 11) Compared with the crude Monte Carlo method, execution time is significantly less.…”

Inner radiation field modeling using multipole moments

“…Both cases of disk-shaped sources (Hubbell et al, 1961;Epstein and Hubbell, 1963) and rectangular sources (Hubbell et al, 1960) have been systematically studied. Many authors, most of them relying on Hubbell's basic treatment, developed particular aspects of disk sources (Kalla and Al-Saqabi, 1991;Timus and Srivastava, 1997), ring-shaped sources (Timus and Galatanu, 1989;Timus et al, 2000) and rectangular sources (Kalla, 1993;Timus, 1993). Also, a new method for extended gamma source modeling using multipole expansions has recently been elaborated (Loussaief et al, 2006).…”

New analytical approach to calculate the detector efficiencies of NaI(Tl) using coaxial and off-axis rectangular and parallelepiped sources

“…Hubbell et al and Epstein and Hubbell [1][2][3] used the rectangular source for structure shielding problems and absorbed doses. As a result of their treatment Hubbell rectangular source integrals appeared which many authors, such as [4][5][6][7][8][9][10][11] had treated by different numerical mathematical methods. Morris et al [12] developed techniques for evaluating the detector response due to radiation from rectangular shaped surfaces.…”