Determination of relative and absolute efficiency functions in the range of 122 keV ÷ 8.5 MeV of HPGe detector

Construction of detector is necessary. However, on large energy range the manufacturers could not also support the explicit function of relative and absolute efficiencies of detectors. One of the reasons is a restriction of energy range of gamma sources (normally < 3 MeV). This paper presents the results of construction of relative and absolute efficiency functions within a range from 122 keV to 8.5 MeV. The sources are used combining 152Eu point source and 36Cl activated isotope by thermal neutron captured reaction 35Cl of Dalat nuclear reactor (DNR) by 35Cl(n, )36Cl reaction. This result can be applied in determining quantitative analysis of samples of neutron activation and radioactivity chemistry.


INTRODUCTION
In the experimental nuclear physics and radiation applications, the determination of relative and absolute efficiencies of spectrometry is necessary and research condition exactly. However, the construction of efficiency in large energy range is a restriction of energy range of gamma sources and method.
In the previous papers, the authors used point sources of a radioisotope, so the absolute efficiency functions were < 3 MeV limited range [1,2,3]. There was also some simulated MCNP method for absolute efficiency functions in large energy range [4].
In this research, 152 Eu point source was used to select photo peaks, which are 122 keV  1408 keV range, and use neutron activation analysis method. The 35 Cl was activated on the 3 rd channel of DNR, measuring prompt gamma by 35 Cl(n, ) 36 Cl reaction. The result was used to construct relative efficiency, absolute efficiency in 122 keV  8.5 MeV range, and determine the transformation factor corresponding to E energy of detector as well.
Detector efficiency functions in large energy range are the logarithm or exponential functions. There has been a large energy range to construct efficiency function, and usage of prompt gamma from activated thermal neutron of target is necessary. When targets capture thermal neutron, some of compound nucleus of target emit prompt gamma, and do not have any delayed gamma emission.
In the compound nucleus mechanisms, particle (a) interacts target (A), then a production of nuclear compound (C) occurs. Nuclear compound (C) produces particle (b) and nucleus (B) by the following function: Compound reactions happen during a time of the order of about 10 -16 s, so the activity of target is constant when the experimental time is about some hours, and the neutron flux and geometry arrangement are unchanged.
Let's consider the case of the target and the point source are placed in the same geometry, the absolute photo peak efficiency relates the counter of detector and the number of gamma ray emitted by the the sources, by following function: The counter of detector ( ) The number of emitted gamma ray where: () abs E  is absolute efficiency value at of energy E, N is the area of the photo peak of energy E, A is the activity of the gamma source (Bq), I is branching ratio of gamma ray (%), t is the live time of the counting number (s).
The absolute efficiency error is:      Absolute efficiency depends on the geometrical conditions and on the energy. As the Fig.1 where d is distance the sourse to face detector, r is the radius of detector.
The absolute efficiency relates the relative efficiency function as follow [2]: where () E  is the transformation factor corresponding to E energy; () rel E  is the relative efficiency value at energy of E.

METERIALS AND METHODS
First, an 152 Eu point source is used. This source is covered by polymer. Its activity is 198.99 kBq. The distance between the source to the surface detector is 5.0 cm. Fig. 2 showed the geometry of 152 Eu point source. In our laboratory, the gamma spectrometer based on a high purity Ge detector, GMX35, the detector diameter is 58 mm. The time of one experiment is 1 hour.
After that, to measure the background at the 3 rd beam of DNR and to measure the activated target, the thermal neutron flux at the target local is ~ 9.25×10 4 n/cm 2 /s, neutron beam diameter is 1.3 cm, cadmi/goal ratio is 218 (measure 1 mm thickness cadmi box). The target is NH4Cl, which is 2.00 mm diameter, 1.00 mm thickness. The target is the same geometry of 152 Eu point source. The parameters of the spectrometer are unchanged completely in this research. Fig. 3 shows the experimental arrangement. The experimental time per one measurement is 5 hours. Fig. 4, Fig. 5 are 152 Eu spectrum, background spectrum and 36 Cl prompt gamma one.

RESULTS
In the experiment on point source the target is also a point source. Using the (4) and (5) formulas, the distance between detector to source is d = 5 cm, detector radius is r = 29 mm, so: Thus, following the geometrical design in this research, the experimental absolute efficiency is ~ 6.748 ‰ of intrinsic efficiency detector.
To treat 152 Eu spectrum, the photo peaks which have high branching ratio in the 122 keV to 1408 keV range are collected. Formula (2) and (3) are used to determine the absolute efficiencies. Those results are shown in Table  1. To fit experimental data of 152 Eu the nonlinear least square method is used. And this fitting method in repeated until minimizing Chi-square. The absolute efficiency function of the range from 122 keV to 1408 keV is shown in Table 2 and Fig. 6.  To treat prompt gamma of 36 Cl spectrum, a determination of area peaks and area peak errors must be carried out. After that, using the absolute efficiency function in the 122 keV to 1048 keV range to calculate the 36 Cl activity under experimental data of 788.43 keV area peak (the experimental data showed in Table 3). The activity of 36 Cl is calculated by the following function 36 Cl activity is determined. Efficiency in the 122 keV to 1408 keV assembly, we construct efficiency detector in the 122 keV to 8.5 MeV. The results are shown in Table 3, Table  4, and Fig 7, Fig. 8.