This study, peak to valley method based on the ratio of counting rate between the photoelectric peak and Compton region was applied to identify the depth distribution of ¹³⁷Cs. The procedure relies on a spectrally derived coefficient Q with depth activity distribution. The extension of the forward scattering of gamma ray is related to the interaction probability associated with the photon trajectory between sources and detector providing a measurement of source burial. The gamma photon flux in soil is a function of the soil density (ρ) in additional to source depth (z) the preference may be to quantify source burial in terms of mass depth of mass per unit area, which is given by ρz.

where Q is spectrally derived coefficient, A is the area of the full energy peak, and B_T is difference between the integrals of the immediately preceding and following regions (620-650 keV and the 670-700 keV). The Q value could calculate using region integrals, and corrected the contribution of 665 keV of ²¹⁴Bi which is a number of series of the ²³⁸U. The Q value could calculate using the ration of full energy peak with the scattering region. In situ measured spectrum for calculation of the Q values shows in Figure 2.

The typical depth profiles of radioactive cesium can be fitted with an exponential function, indicating that the cesium concentration exponentially decreases with mass depth [4]. The vertical activity distribution can be described by the relaxation mass per unit area (β) given by Equation 2. The soil depth profiles collected and analyzed by conventional gamma spectrometry, we determined the initial activity concentration (A_o) and relaxation mass per unit area (g·㎝^-2), which is defined as the reciprocal of the relaxation length of the exponential distribution, by fitting expression to the activity concentrations found in each layer as a function of the mass depth. The relaxation mass per unit area approaches infinity for a source with constant activity distribution and it approaches zero for a source distribution on the soil surface. The specific activity distribution with depth A(ξ) is given in Eq. 2. The vertical activity distribution can be described by the relaxation mass per unit area (β) given by Equation 3.

where ξ is the mass depth (g·㎝^-2) and A(ξ) is the activity per unit mass (Bq·g^-1).

The observation result of relaxation mass per unit area around Fukushima area was reported main value is from 0.8 g·㎝^-2 to 1.2 g·㎝^-2 [5]. The activity depth distribution was demonstrated using the calibration pad sources. The exponential distributions from 0.5 g·㎝^-2 of surface contamination to 7.0 g·㎝^-2 of homogeneous distribution. The calibration pad source contaminated with ¹³⁷Cs was made to demonstrate the depth distribution using in situ measurement. The size of the sources was 50㎝ by 50㎝ with 1㎝ thickness and density was about 1.0 g·㎝^-3. The PE solution (PAA + PDADMAC) were applied to the contaminated soil for fixing contaminated soil. The calibration sources were made 800 ml of each solution with 2.2 kg of soil and dried at room temperature.

ISOCS system consists HPGe portable detector and a data collection with processing system. For in situ gamma spectrometry, we used ISOCS system with 40% relative efficiency, a 1.9 keV resolving power, and a peak to Compton ratio is 58:1 for the 1332.5 keV. The detector was fixed 50 ㎝ for measuring the depth distribution without shield in laboratory. The soil depth was change exponential distribution, surface contamination and homogeneous distribution from the surface to 5 cm depth with every 1 cm interval depth. To demonstrate the variety depth distribution, manufactured calibration pads was place pre-determined depth distribution. The calibration sources and experimental set up are show in Figure 3. We made an in situ gamma spectrometry of the activity and vertical profile in the contaminated area of decommissioning KRR site. In order to compare the depth distribution and contamination level the soil sample was analysis by conventional gamma spectrometry in laboratory.

In order to simulate the scattering contributions due to the depth profile, a laboratory experiment and Monte Carlo simulation was conducted with the calibration sources. The peak to valley method could be applied to establish the relation between the spectrally derived coefficients (Q) with relaxation mass per unit area (β) for various depth distribution in soil. The in situ measurement results and MCNP simulation results with correlation equation are shown in Figure 5. The simulation relationship between Q and source burial for the source layers have exponential relationship for a variety depth distributions. The statistical error on Q was calculated from measured spectrum for each depth distribution. The observation ranged from 10% to 17%. The correlation equation can be estimate the depth distribution without core samples measurement. The in situ measurement results and MCNP simulation results with correlation equation are shown in Fig. 5.

In case of recent deposition, ¹³⁷Cs will be confined in the top layer of soil and diffusion would lead to a depth profile. We applied the peak to valley method to contaminated decommissioning KRR site to determine a depth distribution and initial activity without sampling. The in situ measurement results were compared with sampling results of core boring samples. The spectrally derived coefficients (Q) with relaxation mass per unit area (β) and surface radioactivity was calculated for field measurement. It is required to calculate using Monte Carlo simulation due to the change of field of view (detected area). In this study the diameter of detected area was considered 100m with variety depth distribution. The results are given in Figures 6 and 7. For each depth distribution with different density and energy, 1×10⁸ photon histories were simulated the distributions for in situ gamma-ray measurement. The calculation result of the correction factor is shown in Figures 8 and 9. Application of peak to valley methods allows to establish a relationship the factor Q and the relaxation mass per unit area in Equation 4. The relationship factor Q and the radioactivity of the surface soil layer could express in Equation 5.

where N is the net count per second and A_o is initial activity (Bq·g^-1).

The results applied in decommissioning KRR site show in Table 1. The observed results has a good correlation, relative error between in situ measurement with sampling result is around 7% for depth distribution and 4% for initial activity.

Different environmental soil samples usually have different densities. The investigation by simulation of soil matrix with different densities in the range from 0.2 to 2.0 g·㎝^-3 was carried out to figure out the dependence of detector efficiency as a function of the density and energy with different depth distributions. The photon transport from sources in the soil to the detector was simulated for self-absorption correction various depth distributions using MCNP6 code. The composition of soil and air was taken from ICRU report 53 [6]. For each depth distribution with different density and energy, 1×10⁸ photon histories were simulated the distributions for in situ gamma-ray measurement. The calculation result of the correction factor show in Figures 8 and 9.

The homogeneous distribution have more large correction factor than exponential distribution because self-absorption increase in deeper layer. The maximum correction factor for exponential distribution has 1.80 but homogeneous distribution has 2.67 at 59.5 keV with density 2.0 g·㎝^-3.