### Introduction

### Materials and Methods

### 1. Measurement Location

^{th}floor of the five-story concrete building of FMU built in 1988. The two measurement spots are at the center of the room and by the window. The former one is located about 5 m away from the window and is a place where FMU staff typically carry out their activities (Fig. 2). The latter one faces the window and is 7 cm away from it (Fig. 3).

### 2. Exp 1: Measurement at the Center of the Room

^{137}Cs; Teledyne Brown Engineering Environmental Services) observed gamma radiation in air from September 2010 to April 2020 (Fig. 2). Every 4-hour period, data were stored in a personal computer. The present report discusses only the gross counting rate expressed as a unit of counts per second (cps).

### 3. Exp 2: Measurement by the Window

^{137}Cs; EMF Japan Co. Ltd.) and digital processor (GAMMA-RAD5; Amptek Inc.) observed gamma radiation in the air from July 2012 to March 2023 (Fig. 3). Every hour, counting data was stored in a personal computer. Average values were calculated every 24 hours. The present report discusses mainly dose rate, expressed as a unit of nSv/hr. This series of measurements was interrupted due to equipment failure from July 9, 2015, to November 4, 2015.

### Results and Discussion

### 1. Exp 1: Measurement at the Center of the Room

^{th}floor of the five-story concrete building of FMU for the period from March 1 to April 30, 2011. There was no change in counts at the time of the earthquake on March 11 at 2:46 PM, but a sudden increase in counts was observed around 6:00 PM on March 15 and the radiation dose reading reached the maximum value of 9.3 times the usual values. Afterward, the counts appeared to decrease exponentially, and the half-life was roughly estimated to be about 3 days. After 1 month had passed, the semi-log plot of the counting rate versus time did not fit to a single line. It was considered that this was due to the addition of counts from the long-term half-life. A detailed discussion of the measurements up to August 2011, including the information mentioned above, is presented in reference [3]. Afterward, the measurements were continued until April 2020, when the equipment’s aging required an interruption, for the first 3 years by Kobayashi, and for the following 8 years by the present author.

^{th}day. The counting rate during the first 5 days is mainly dominated by radiation from radioactive isotopes with a short half-life, while after the 5

^{th}day, radiation from radioactive isotopes with longer half-lives is considered to be dominant.

^{th}day. Let the half-life of this exponential function be

*T*

_{all}. Assuming that the total counting rate is exponentially decreasing, the counting rate

*C*is calculated based on the following formula:

*t*is days from the day when the counting rate reached its maximum, and the constant

*c*represents the value of the counting rate at the day when the counting rate reached its maximum.

*T*

_{all}was obtained by fitting Equation (1) to the counting rate after subtracting the pre-accident average value of 212.558±0.027 cps using the least squares method.

*C′*is represented by the following Equation (2):

*t*is days from the day when the counting rate reached its maximum,

*T*

*and*

_{a}*T*

*are the short half-live and long half-live, respectively. Constants*

_{b}*a*and

*b*represent the intensities of the counting rates from radioactive isotopes with short and long half-lives, respectively. Nonlinear least squares regression, using a command of S-PLUS [4], obtained values of

*T*

*,*

_{a}*T*

*,*

_{b}*a*, and

*b*for several time periods (period A–E indicated in Fig. 6). Table 1 shows

*T*

*,*

_{a}*T*

*,*

_{b}*a*,

*b*, and

*T*

_{all}of each time period. Since these are results from simplified model calculations, it is difficult to ascertain the radioactive isotopes from which these half-lives originate. However, a discussion regarding the derivation of the prolonged half-life from Cs will be engaged in the subsequent chapter. It would be possible to make rough discussions and predict whether similar decreases will occur in the future based on these data. As time periods, which is the number of days from the day with the maximum counting rate, increased, it was found that both the short half-lives

*T*

*and long half-lives*

_{a}*T*

*, as well as the overall half-lives*

_{b}*T*

_{all}, increased. The values of the short half-lives

*T*

*were obtained to be in the range of 3.63 to 4.36 days. These values are close to the 8-day half-life of*

_{a}^{131}I, which is considered to be one of the radioactive isotopes leaked from the nuclear plant. The physical half-life of

^{131}I is 8 days, but it is consistent to assume that the environmental half-life has been shortened by factors such as rain. The values of the long half-lives

*T*

*were obtained to be in the range of 181 to 683 days. Among the radioactive isotopes that are considered to have leaked out from the nuclear plant,*

_{b}^{134}Cs with a half-life of 2.1 years and

^{137}Cs with a half-life of 30 years are likely to have values similar to

*T*

*.*

_{b}*T*

_{all}also tended to increase as the measurement period increased and was larger than

*T*

*for each period. As the measurement period gets longer, the influence of radioactive isotopes with longer half-lives becomes more significant. The proportions of constants*

_{b}*a*and

*b*, which represent the intensities of counting rates from radioactive isotopes with short and long half-lives, were calculated (Table 1). The initial values were 87% for

*a*and 13% for

*b*, but they gradually saturated to 91% for

*a*and 9% for

*b*as the period got longer. These results suggest that

^{131}I is more easily removed in the natural environment compared to

^{134}Cs and

^{137}Cs. As shown in Fig. 6, while the counting rate and the fitting line seem to be in good agreement from around 330 to 2,500 days, the counting rate shows a different trend during the initial period of about 300 days, and after the 2,500

^{th}day. It may be considered that radioactive isotopes with a half-life of

*T*

*dominate in the region of time period A or B, and radioactive isotopes with a half-life of*

_{a}*T*

*dominate in the region from time period C to D. The former is considered likely to be*

_{b}^{131}I with a half-life of 8 days and the latter

^{134}Cs with a half-life of 2.1 years. It is possible that the influence of

^{137}Cs with a half-life of 30 years is dominant in the region after time period D. Comparing, for example, the value of

*T*

*during period A (3.63 days) with the half-life of*

_{a}^{131}I, and the value of

*T*

*during period E (647 days) with the half-life of*

_{b}^{134}Cs, it can be said that this inference is consistent.

*T*

_{all}increases as the time period lengthens, and its value as of time period E is 884 days. If

*T*

_{all}remains constant for the time period E, then the counting rate is expected to be 1.021 times the pre-accident level after 4,000 days from March 16, 2011, and 1.0097 times after 5,000 days. Fig. 7 presents the dependency of the overall half-live

*T*

_{all}on the time periods. The results of the least squares fitting using a logarithmic function revealed that

*T*

_{all}behaves logarithmically with respect to the time periods. The fitted equation is shown below:

*p*is the time periods in unit of day. Assuming that the Equation (3) continues to hold in the future,

*T*

_{all}would be 1,065.8 days 20 years after March 16, 2011, and 1,171.6 days 30 years after that date. Therefore, the predicted decrease in radiation based on the assumption that

*T*

_{all}remains constant is expected to be revised upward.

### 2. Exp 2: Measurement by the Window

^{137}Cs) that could measure radiation dose rate accurately as a unit of Sv/hr in July 2012. The Teledyne S-1211-T was measured in the center of the room where staff were usually active, so the new equipment was set to measure facing outdoors near the window. Fig. 8 presents serial gamma radiation dose rate measurements in air with EMF211 and GAMMA-RAD5 for the period from July 7, 2012, to July 8, 2015. The equipment is facing the window and is 7 cm away from it in a room on the 4

^{th}floor of the five-story concrete building at FMU. The radiation dose rate exhibited exponential behavior, decreasing from 127.0 to 47.9 nSv/hr over a period of 3 years. Fig. 9A presents serial gamma radiation dose rate measurements for the period from November 5, 2015, to March 31, 2023. The equipment malfunctioned in July 2015, and repairs and calibration were conducted. Measurements resumed in November 2015. Therefore, the continuity of the dose rate between the two periods is not guaranteed. Fig. 9B presents serial gamma radiation dose rate measurements on a logarithmic scale for the same period. For reference, the result of fitting an exponential function is shown as a black solid line. This fitting was conducted for the dose rate, including the natural background radiation, and the apparent half-life is 6.5 years. Assuming that the decreasing pace of this approximation curve continues, the dose rate is predicted to be 21.11 nSv/hr on March 11, 2024, 18.98 nSv/hr on March 11, 2025, and 17.06 nSv/hr on March 11, 2026. Since 2021, there seems to be a tendency for the dose rate to show values greater than the approximation curve, so the rate of decrease may be slower than this prediction. At least, calculating the annual dose simply from the predicted dose rate of 21.11 nSv/hr on March 11, 2024, yields 185 μSv, which is sufficiently low to maintain a normal lifestyle.

^{134}Cs (i.e., 605 keV and 796 keV) were observed in the center of the room, these peaks were distinctly observed by the window. The

^{137}Cs (662 keV) peak was scarcely observed in the center of the room, whereas it was prominently observed by the window. The

^{131}I peak (i.e., 364 keV) was not clearly observed in either location. These results appear to reinforce the argument made in the previous chapter that the radioactive element with a longer half-life is likely to be Cs.