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CN103197336A - A method for rapidly measuring the concentration of 222Rn and 220Rn daughters in the air by total α counting - Google Patents

A method for rapidly measuring the concentration of 222Rn and 220Rn daughters in the air by total α counting Download PDF

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CN103197336A
CN103197336A CN2013100697035A CN201310069703A CN103197336A CN 103197336 A CN103197336 A CN 103197336A CN 2013100697035 A CN2013100697035 A CN 2013100697035A CN 201310069703 A CN201310069703 A CN 201310069703A CN 103197336 A CN103197336 A CN 103197336A
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谭延亮
袁红志
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Hengyang Normal University
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Abstract

一种总α计数快速测量空气中222Rn、220Rn子体浓度的方法，是采用空气采样泵将空气中氡子体采集到滤膜上，然后测量滤膜上的α衰变总计数，从而计算得到氡子体空气浓度。测量周期有两种，分为短时间间隔测量周期和长时间间隔测量周期。以短时间间隔t为测量周期，可以利用大于等于6个测量周期的数据利用非线性拟合或最小二乘法得到开始测量时的滤膜上的222Rn、220Rn子体活度；以长时间间隔t1，t2，t3，t4，t5，t6为测量周期，测量周期为6个，也可以得到开始测量时的滤膜上的222Rn、220Rn子体活度。然后利用放射性衰变规律和采样过程中空气中222Rn、220Rn子体在滤膜上的积累规律，就可以反推得到空气中222Rn、220Rn子体浓度。

Figure 201310069703

A kind of total α counting method for fast measuring 222 Rn, 220 Rn progeny concentrations in the air is to use an air sampling pump to collect the radon progeny in the air on the filter membrane, and then measure the α decay total count on the filter membrane to calculate Obtain the radon daughter air concentration. There are two types of measurement cycle, divided into short time interval measurement cycle and long time interval measurement cycle. With a short time interval t as the measurement cycle, the data of 6 or more measurement cycles can be used to obtain the activity of 222 Rn and 220 Rn daughters on the filter membrane at the beginning of the measurement by nonlinear fitting or least square method; The intervals t 1 , t 2 , t 3 , t 4 , t 5 , and t 6 are measurement cycles, and the measurement cycle is 6. The activities of 222 Rn and 220 Rn daughters on the filter membrane at the beginning of the measurement can also be obtained. Then, using the law of radioactive decay and the law of accumulation of 222 Rn and 220 Rn progeny in the air during the sampling process on the filter membrane, the concentration of 222 Rn and 220 Rn progeny in the air can be inversely deduced.

Figure 201310069703

Description

总α计数快速测量空气中222Rn、220Rn子体浓度的方法A method for rapidly measuring the concentration of 222Rn and 220Rn daughters in the air by total α counting

技术领域 technical field

本发明涉及一种核辐射探测技术，特别是一种利用总α计数快速测量空气中222Rn、220Rn子体浓度的方法。The invention relates to a nuclear radiation detection technology, in particular to a method for quickly measuring the concentration of 222 Rn and 220 Rn daughters in the air by using the total alpha count.

背景技术 Background technique

近年来，随着人们对222Rn、220Rn及其子体研究的深入，发现在有的环境中220Rn及其子体所致剂量不可忽略且其对222Rn及其子体测量造成干扰。由于222Rn、220Rn的衰变子体的辐射剂量远远高于氡本身，加之220Rn及其子体的平衡关系随时间、地点是变化的，仅仅根据222Rn、220Rn水平的测量结果来估算222Rn、220Rn及其子体所产生的剂量是不够的。为了更加准确地评价222Rn、220Rn的危害，有必要对环境空气中222Rn、220Rn子体的水平进行同时测量。以往同时测量222Rn、220Rn子体水平的方法主要有三段法和五段法，此类测量方法属于总α方法，要么测量时间较长，要么测量误差较大。近年来α能谱法区分能量的优点在222Rn和220Rn子体水平测量中得到了运用，实现了空气中222Rn和220Rn子体水平快速、可靠测量。但是能谱仪价格昂贵，且多道能谱仪的道漂是不可避免的。In recent years, with the in-depth research on 222 Rn, 220 Rn and their progeny, it is found that in some environments the dose caused by 220 Rn and its progeny cannot be ignored and it interferes with the measurement of 222 Rn and its progeny. Since the radiation dose of the decay daughters of 222 Rn and 220 Rn is much higher than that of radon itself, and the balance relationship between 220 Rn and its daughters changes with time and place, only based on the measurement results of the levels of 222 Rn and 220 Rn Estimating the doses from 222 Rn, 220 Rn and their progeny is not sufficient. In order to evaluate the hazards of 222 Rn and 220 Rn more accurately, it is necessary to simultaneously measure the levels of 222Rn and 220 Rn daughters in the ambient air. In the past, the methods for simultaneously measuring the levels of 222 Rn and 220 Rn daughters mainly included the three-stage method and the five-stage method. This kind of measurement method belongs to the total α method, and either the measurement time is long or the measurement error is large. In recent years, the advantages of α-spectroscopy in differentiating energy have been used in the measurement of 222 Rn and 220 Rn daughter levels, and the rapid and reliable measurement of 222 Rn and 220 Rn daughter levels in the air has been realized. But the energy spectrometer is expensive, and the channel drift of the multi-channel energy spectrometer is inevitable.

发明内容 Contents of the invention

本发明的目的是克服现有技术的上述不足而提供一种根据222Rn、220Rn子体放射性衰变特性，对采样后222Rn、220Rn子体样品的放射性衰变产生的高能α粒子总计数随时间变化的规律进行测量，应用两种不同的测量方法得到222Rn、220Rn子体浓度。The purpose of the present invention is to overcome the above-mentioned deficiency of prior art and provide a kind of according to 222 Rn, 220 Rn daughter body radioactive decay characteristic, the high-energy α particle total count that the radioactive decay of 222 Rn, 220 Rn daughter body sample after sampling produces Time-varying laws were measured, and the concentrations of 222 Rn and 220 Rn progeny were obtained by using two different measurement methods.

本发明的技术方案是：一种利用α粒子总计数测量空气中222Rn、220Rn子体的方法，最简便且实用有效的空气中氡子体采样和测量过程，是采用空气采样泵将空气中氡子体采集到滤膜上，然后测量滤膜上的α衰变总计数，从而计算得到氡子体空气浓度。The technical scheme of the present invention is: a kind of method that utilizes the total count of alpha particles to measure 222 Rn, 220 Rn daughters in the air, the easiest and most practical and effective radon daughter sampling and measurement process in the air is to adopt air sampling pump to extract the air The radon progeny is collected on the filter membrane, and then the total count of α decay on the filter membrane is measured, so as to calculate the air concentration of the radon progeny.

在222Rn子体衰变链中，有剂量学意义的是RaA(218Po)、RaB(214Pb)、RaC(214Bi)，由于RaC’(214Po)的半衰期很短，只有164μs，因此将RaC’的放射性归结为RaC的放射性；在220Rn子体衰变链中，有剂量学意义的是ThB(212Pb)、ThC(212Bi)，将ThC’(212Po)、ThC’’(208Tl)的放射性归结为ThC(212Bi)的放射性。In the decay chain of 222 Rn progeny, the dosimetrically significant ones are RaA ( 218 Po), RaB ( 214 Pb), RaC ( 214 Bi). Since the half-life of RaC' ( 214 Po) is very short, only 164 μs, it will The radioactivity of RaC' is attributed to the radioactivity of RaC; in the decay chain of 220 Rn progeny, ThB ( 212 Pb) and ThC ( 212 Bi) are dosimetrically significant, and ThC' ( 212 Po), ThC'' ( 208 The radioactivity of Tl) is attributed to the radioactivity of ThC ( 212 Bi).

本测量方法基于以下条件：This measurement method is based on the following conditions:

1) 采样过程中222Rn、220Rn子体浓度和空气采样泵采样流率恒定不变；1) The concentration of 222 Rn, 220 Rn daughters and the sampling flow rate of the air sampling pump are constant during the sampling process;

2) 滤膜的过滤效率和自吸收因子均为恒定常数，且不依气溶胶粒径改变，在使用微孔滤膜时，没有自吸收；2) The filtration efficiency and self-absorption factor of the filter membrane are constant and do not change according to the particle size of the aerosol. When using a microporous filter membrane, there is no self-absorption;

3) 探测器的探测效率为恒定常数，且不依α粒子能量改变，依赖于滤膜具有较小的自吸收和滤膜到探测器距离较小。3) The detection efficiency of the detector is a constant constant, and does not change according to the energy of the α particle, depending on the small self-absorption of the filter membrane and the small distance from the filter membrane to the detector.

在222Rn、220Rn子体采样过程中，滤膜上的氡子体数量随着采样而不断增长，其数量还会由于从母体核素衰变而增加和自身衰变而减少，用下述微分方程组表述：During the sampling process of 222 Rn and 220 Rn daughters, the number of radon daughters on the filter membrane will continue to increase with the sampling, and its number will also increase due to the decay of the parent nuclide and decrease due to its own decay, using the following differential equation Group representation:

dNdN RaARaA // dtdt == QGCQGC RaARaA // λλ RaARaA -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == QGCQGC RaBRaB // λλ RaBRaB ++ NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == QGCQGC RaCR // λλ RaCR ++ NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == QGCQGC ThBThB // λλ ThBThB -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == QGCQGC ThCTHC // λλ ThCTHC ++ NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 11 ))

式中G为过滤效率，Q为采样流率，CRaA、CRaB CRaC、CThB、CThC分别为RaA、RaB、RaC、ThB、ThC活度浓度，λ、λRaB λRaC、λThB、λThC分别为RaA、RaB、RaC、ThB、ThC的半衰期，NRaA、NRaB NRaC、NThB、NThC分别为采样过程中滤膜上积累的RaA、RaB、RaC、ThB、ThC的原子数。In the formula, G is the filtration efficiency, Q is the sampling flow rate, C RaA , C RaB C RaC , C ThB , C ThC are the activity concentrations of RaA, RaB, RaC, ThB, ThC respectively, λ, λ RaB λ RaC , λ ThB , λ ThC are the half-lives of RaA, RaB, RaC, ThB, ThC respectively, N RaA , N RaB N RaC , N ThB , N ThC are the time intervals of RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane during the sampling process atomic number.

对式（1）求解能得到：采样时间T1结束时滤膜上积累的RaA、RaB、RaC、ThB、ThC的原子数与空气中RaA、RaB、RaC、ThB、ThC活度浓度的关系。Solving formula (1) can get: the relationship between the number of atoms of RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane at the end of sampling time T1 and the activity concentration of RaA, RaB, RaC, ThB, ThC in the air.

采样结束后，取下滤膜送入α计数测量仪进行测量，该时间间隔为T2，滤膜上的222Rn、220Rn子体以采样结束时刻的数量为初始值开始衰变，同时子体核素还由于母体核素的衰变而增加，用下述微分方程组表述：After the sampling is over, remove the filter membrane and send it to the α counting instrument for measurement. The time interval is T 2 . The 222 Rn and 220 Rn daughters on the filter membrane begin to decay with the number at the end of sampling as the initial value, and at the same time the daughters The nuclide also increases due to the decay of the parent nuclide, expressed by the following differential equations:

dNdN RaARaA // dtdt == -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 22 ))

对式（2）求解得到采样结束后经过T2时间衰变，滤膜上的RaA、RaB、RaC、ThB、ThC的原子数与采样结束时刻的RaA、RaB、RaC、ThB、ThC的原子数的关系。Solve the formula (2) to get T2 time decay after the end of sampling. relation.

利用α计数测量仪开始对滤膜测量瞬间，滤膜上的RaA、RaB、RaC、ThB、ThC的原子数分别为NRaA1、NRaB1 NRaC1、NThB1、NThC1，根据式（1）、（2）倒推得到空气中的RaA、RaB、RaC、ThB、ThC活度浓度。At the moment when the α counting instrument starts to measure the filter membrane, the atomic numbers of RaA, RaB, RaC, ThB, and ThC on the filter membrane are respectively N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , according to formula (1), (2) The activity concentrations of RaA, RaB, RaC, ThB, and ThC in the air can be obtained by backward calculation.

采样后，将滤膜送入α计数测量仪，开始测量总α计数。222Rn子体的α衰变包括：RaA(218Po)6.0MeV、RaC`(214Po)7.69MeV；220Rn子体的α衰变包括：ThC (212Bi) 6.05MeV、ThC`(212Po) 8.78MeV。After sampling, the filter is fed into an alpha count meter to begin measuring total alpha counts. The alpha decay of 222 Rn daughters includes: RaA( 218 Po) 6.0MeV, RaC`( 214 Po) 7.69MeV; the alpha decay of 220 Rn daughters includes: ThC ( 212 Bi) 6.05MeV, ThC`( 212 Po) 8.78 MeV.

α计数测量仪开始测量后，滤膜上的222Rn、220Rn子体仍然按式（2）衰变，对式（2）求解，解得测量过程中滤膜上任意时刻的RaA、RaB、RaC、ThB、ThC的原子数为：After the α counting measuring instrument starts to measure, the 222 Rn and 220 Rn daughters on the filter membrane still decay according to the formula (2). Solve the formula (2), and solve the RaA, RaB, RaC on the filter membrane at any time during the measurement process. , ThB, ThC atomic numbers are:

NN RaARaA (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 33 ))

NN RaBRaB (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ RaARaA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt -- -- -- (( 44 ))

NN RaCR (( tt )) == -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt -- -- -- (( 55 ))

NN ThBThB (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 66 ))

NN ThCTHC (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt -- -- -- (( 77 ))

将式（3）、（4）、（5）、（6）、（7）转换为活度形式：Convert formulas (3), (4), (5), (6), and (7) into activity forms:

AA RaARaA (( tt )) == λλ RaARaA NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 88 ))

AA RaBRaB (( tt )) == λλ RaBRaB [[ NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ ThATHA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt ]] -- -- -- (( 99 ))

AA RaCR (( tt )) == λλ RaCR {{ -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt }} -- -- -- (( 1010 ))

AA ThBThB (( tt )) == λλ ThBThB NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 1111 ))

AA ThCTHC (( tt )) == λλ ThCTHC [[ NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt ]] -- -- -- (( 1212 ))

滤膜上的RaA、RaB、RaC、ThB、ThC的活度分别为ARaA、ARaB ARaC、AThB、AThC。The activities of RaA, RaB, RaC, ThB, ThC on the filter membrane are A RaA , A RaB A RaC , A ThB , A ThC , respectively.

根据222Rn、220Rn放射性衰变规律知道，滤膜上任意时刻的总的α衰变活度Aα(t)为：According to the law of radioactive decay of 222 Rn and 220 Rn, the total α decay activity A α (t) at any time on the filter membrane is:

Aα(t)=ARaA(t)+ARaC(t)+AThC(t)+A0              （13）A α (t)=A RaA (t)+A RaC (t)+A ThC (t)+A 0 (13)

式中A0为α计数测量仪的本底计数率。In the formula, A 0 is the background count rate of the α counting instrument.

α计数测量仪测量周期有两种，分为短时间间隔测量周期和长时间间隔测量周期：There are two types of measurement cycles for α counting measuring instruments, which are divided into short time interval measurement cycles and long time interval measurement cycles:

一、以短时间间隔t为测量周期，时间t为1-10分钟，周期数量大于或等于6个。1. Take the short time interval t as the measurement cycle, the time t is 1-10 minutes, and the number of cycles is greater than or equal to 6.

其计算方法有两种：There are two calculation methods:

A、根据第i个测量周期的总α计数n(i)，求得第i个测量周期的单位时间的平均计数，由于测量周期较短，这些平均计数与Aα(t)在该测量周期中点的值近似相等，有：A. According to the total α count n(i) of the i-th measurement cycle, the average count per unit time of the i-th measurement cycle is obtained. Since the measurement cycle is short, these average counts are related to A α (t) in the measurement cycle The values at the midpoints are approximately equal, with:

nno (( ii )) // tt == EAEA αα (( itit -- 11 22 tt )) -- -- -- (( 1414 ))

E为α计数测量仪对α粒子的探测效率。E is the detection efficiency of the α counting instrument for α particles.

利用式（14）对n(i)/t的数据进行非线性拟合，能得到NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值；然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度。Using formula (14) to carry out nonlinear fitting on n(i)/t data, the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , A 0 can be obtained; then according to formula (1), (2 ) to obtain the activity concentrations of RaA, RaB, RaC, ThB, and ThC in the air.

B、求Aα(t)在第i个测量周期的积分：B. Find the integral of A α (t) in the i-th measurement period:

AA αα (( ii )) == ∫∫ (( ii -- 11 )) tt itit AA αα (( tt )) dtdt -- -- -- (( 1515 ))

应用最小二乘法求解222Rn,220Rn子体浓度，引入残差R：Apply the least square method to solve the 222 Rn, 220 Rn daughter concentration, and introduce the residual R:

RR == ΣΣ ii == 11 nno ww ii (( nno (( ii )) -- EAEA αα (( ii )) )) 22 -- -- -- (( 1616 ))

式中wi是i计数段的权重因子，权重因子的引入是考虑每个计数段的计数统计误差不同对拟合结果的误差影响。In the formula, w i is the weight factor of the i counting segment, and the introduction of the weighting factor is to consider the influence of the error of the counting statistics of each counting segment on the fitting result.

根据最小二乘法原理，使得残差R取最小值，能得到NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值，然后根据式（1）、（2）倒推得到空气RaA、RaB、RaC、ThB、ThC活度浓度。According to the principle of the least square method, the residual R takes the minimum value, and the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , and A 0 can be obtained, and then the air RaA can be obtained according to formulas (1) and (2). , RaB, RaC, ThB, ThC activity concentration.

二、以长的时间间隔t1，t2，t3，t4，t5，t6为测量周期，时间t1，t2，t3，t4，t5，t6分别为10-120分钟，测量周期为6个。2. Take the long time interval t 1 , t 2 , t 3 , t 4 , t 5 , t 6 as the measurement cycle, and the time t 1 , t 2 , t 3 , t 4 , t 5 , t 6 are 10- 120 minutes, 6 measurement cycles.

其计算方法为：Its calculation method is:

6个测量周期的计数分别为n(1)，n(2)，n(3)，n(4)，n(5)，n(6)。The counts of the 6 measurement cycles are n(1), n(2), n(3), n(4), n(5), n(6) respectively.

nno (( 11 )) == EE. ∫∫ 00 tt 11 AA αα (( tt )) dtdt -- -- -- (( 1717 ))

nno (( 22 )) == EE. ∫∫ tt 11 tt 11 ++ tt 22 AA αα (( tt )) dtdt -- -- -- (( 1818 ))

nno (( 33 )) == EE. ∫∫ tt 11 ++ tt 22 tt 11 ++ tt 22 ++ tt 33 AA αα (( tt )) dtdt -- -- -- (( 1919 ))

nno (( 44 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 AA αα (( tt )) dtdt -- -- -- (( 2020 ))

nno (( 55 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 ++ tt 44 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 AA αα (( tt )) dtdt -- -- -- (( 21twenty one ))

nno (( 66 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 ++ tt 66 AA αα (( tt )) dtdt -- -- -- (( 22twenty two ))

将n(1)，n(2)，n(3)，n(4)，n(5)，n(6)值带入式（17）、（18）、（19）、（20）、（21）、（22），解得NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值的值，然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度。Put the values of n(1), n(2), n(3), n(4), n(5), and n(6) into formulas (17), (18), (19), (20), (21) and (22), get the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , and A 0 , and then get RaA, RaB, RaC, ThB, ThC activity concentration.

本方法采用的222Rn、220Rn子体采集系统由带有滤膜的采样头、采样杆、流量计、连接管和空气采样泵组成，采样头和采样杆连接，采样杆和流量计连接，流量计通过连接管和空气采样泵连接。The 222 Rn, 220 Rn progeny collection system that this method adopts is made up of sampling head with filter membrane, sampling rod, flowmeter, connecting pipe and air sampling pump, and sampling head is connected with sampling rod, and sampling rod is connected with flowmeter, The flow meter is connected to the air sampling pump through the connecting pipe.

本发明与现有技术相比具有如下特点：Compared with the prior art, the present invention has the following characteristics:

不用先测量本底计数率，从而减少了测量时间，提高了测量精度，减少了测量成本。It is not necessary to measure the background count rate first, thereby reducing the measurement time, improving the measurement accuracy and reducing the measurement cost.

以下结合附图和具体实施方式对本发明的详细结构作进一步描述。The detailed structure of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

附图说明 Description of drawings

附图为222Rn、220Rn子体采集系统示意图。The accompanying drawing is a schematic diagram of the collection system for 222 Rn and 220 Rn daughters.

具体实施方式 Detailed ways

实施例一、一种利用α粒子总计数测量空气中222Rn、220Rn子体的方法，本实施例采用的222Rn、220Rn子体采集系统由带有滤膜6的采样头1、采样杆2、流量计3、连接管4和空气采样泵5组成，采样头1和采样杆2连接，采样杆2和流量计3连接，流量计3通过连接管4和空气采样泵5连接。Embodiment one, a kind of method utilizing α particle total count to measure 222 Rn, 220 Rn daughter body in the air, the 222 Rn that present embodiment adopts, 220 Rn daughter body collecting system is by the sampling head 1 that has filter membrane 6, sampling Composed of rod 2, flow meter 3, connecting pipe 4 and air sampling pump 5, sampling head 1 is connected to sampling rod 2, sampling rod 2 is connected to flow meter 3, flow meter 3 is connected to air sampling pump 5 through connecting pipe 4.

通过空气采样泵5将空气中氡子体采集到滤膜6上，然后测量滤膜6上的α衰变总计数，从而计算得到氡子体空气浓度。The radon progeny in the air is collected on the filter membrane 6 by the air sampling pump 5, and then the total count of α decay on the filter membrane 6 is measured, so as to calculate the air concentration of the radon progeny.

本测量方法基于以下条件：This measurement method is based on the following conditions:

1) 采样过程中222Rn、220Rn子体浓度和空气采样泵5采样流率恒定不变；1) 222 Rn, 220 Rn progeny concentrations and air sampling pump 5 sampling flow rates are constant during the sampling process;

2) 滤膜6的过滤效率和自吸收因子均为恒定常数，且不依气溶胶粒径改变，在使用微孔滤膜时，没有自吸收；2) The filtration efficiency and self-absorption factor of the filter membrane 6 are constant, and do not change according to the particle size of the aerosol. When using a microporous filter membrane, there is no self-absorption;

3) 探测器的探测效率为恒定常数，且不依α粒子能量改变，依赖于滤膜6具有较小的自吸收和滤膜6到探测器距离较小。3) The detection efficiency of the detector is a constant constant, and does not change according to the energy of the α particle, and depends on the smaller self-absorption of the filter membrane 6 and the smaller distance from the filter membrane 6 to the detector.

在222Rn、220Rn子体采样过程中，滤膜6上的氡子体数量随着采样而不断增长，其数量还会由于从母体核素衰变而增加和自身衰变而减少，用下述微分方程组表述：During the sampling process of 222 Rn and 220 Rn daughters, the number of radon daughters on the filter membrane 6 will continue to increase along with the sampling, and its number will also increase due to the decay of the parent nuclide and decrease by its own decay, using the following differential Expression of equations:

dNdN RaARaA // dtdt == QGCQGC RaARaA // λλ RaARaA -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == QGCQGC RaBRaB // λλ RaBRaB ++ NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == QGCQGC RaCR // λλ RaCR ++ NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == QGCQGC ThBThB // λλ ThBThB -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == QGCQGC ThCTHC // λλ ThCTHC ++ NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 11 ))

式中G为过滤效率，Q为采样流率，CRaA、CRaB CRaC、C、CThC分别为RaA、RaB、RaC、ThB、ThC活度浓度，λRaA、λRaB λRaC、λThB、λThC分别为RaA、RaB、RaC、ThB、ThC的半衰期，NRaA、NRaB NRaC、NThB、NThC分别为采样过程中滤膜6上积累的RaA、RaB、RaC、ThB、ThC的原子数。In the formula, G is the filtration efficiency, Q is the sampling flow rate, C RaA , C RaB C RaC , C, and C ThC are the activity concentrations of RaA, RaB, RaC, ThB, and ThC respectively, λ RaA , λ RaB λ RaC , λ ThB , λ ThC are the half-lives of RaA, RaB, RaC, ThB, ThC respectively, N RaA , N RaB N RaC , N ThB , N ThC are RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane 6 during the sampling process respectively number of atoms.

对式（1）求解能得到：采样时间T1结束时滤膜6上积累的RaA、RaB、RaC、ThB、ThC的原子数与空气中RaA、RaB、RaC、ThB、ThC活度浓度的关系。Solving equation (1), we can get: the relationship between the atomic number of RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane 6 at the end of sampling time T1 and the activity concentration of RaA, RaB, RaC, ThB, ThC in the air .

采样结束后，取下滤膜6送入α计数测量仪进行测量，该时间间隔为T2，滤膜6上的222Rn、220Rn子体以采样结束时刻的数量为初始值开始衰变，同时子体核素还由于母体核素的衰变而增加，用下述微分方程组表述：After the sampling is finished, remove the filter membrane 6 and send it to the α counting instrument for measurement. The time interval is T 2 . The 222 Rn and 220 Rn daughters on the filter membrane 6 start to decay with the number at the end of sampling as the initial value, and at the same time The daughter nuclide also increases due to the decay of the parent nuclide, which is expressed by the following differential equations:

dNdN RaARaA // dtdt == -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 22 ))

对式（2）求解得到采样结束后经过T2时间衰变，滤膜6上的RaA、RaB、RaC、ThB、ThC的原子数与采样结束时刻的RaA、RaB、RaC、ThB、ThC的原子数的关系。Solve formula (2) to obtain the time decay of T2 after the end of sampling, the number of atoms of RaA, RaB, RaC, ThB, ThC on the filter membrane 6 and the number of atoms of RaA, RaB, RaC, ThB, ThC at the end of sampling Relationship.

利用α计数测量仪开始对滤膜6测量瞬间，滤膜6上的RaA、RaB、RaC、ThB、ThC的原子数分别为NRaA1、NRaB1 NRaC1、NThB1、NThC1，根据式（1）、（2）倒推得到空气中的RaA、RaB、RaC、ThB、ThC活度浓度。Utilize the α counting instrument to start measuring the filter membrane 6 at the moment, the atomic numbers of RaA, RaB, RaC, ThB, ThC on the filter membrane 6 are respectively N RaA1 , N RaB1, N RaC1 , N ThB1 , N ThC1 , according to the formula (1 ), (2) Reversely get the activity concentration of RaA, RaB, RaC, ThB, ThC in the air.

采样后，将滤膜6送入α计数测量仪，开始测量总α计数。222Rn子体的α衰变包括：RaA(218Po)6.0MeV、RaC`(214Po)7.69MeV；220Rn子体的α衰变包括：ThC (212Bi) 6.05MeV、ThC`(212Po) 8.78MeV。After sampling, the filter membrane 6 is sent to the alpha count meter to start measuring the total alpha count. The alpha decay of 222 Rn daughters includes: RaA( 218 Po) 6.0MeV, RaC`( 214 Po) 7.69MeV; the alpha decay of 220 Rn daughters includes: ThC ( 212 Bi) 6.05MeV, ThC`( 212 Po) 8.78 MeV.

α计数测量仪开始测量后，滤膜6上的222Rn、220Rn子体仍然按式（2）衰变，对式（2）求解，解得测量过程中滤膜6上任意时刻的RaA、RaB、RaC、ThB、ThC的原子数为：After the α counting measuring instrument starts to measure, the 222 Rn and 220 Rn daughters on the filter membrane 6 still decay according to the formula (2), solve the formula (2), and solve the RaA and RaB at any time on the filter membrane 6 during the measurement process , RaC, ThB, ThC atomic numbers are:

NN RaARaA (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 33 ))

NN RaBRaB (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ RaARaA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt -- -- -- (( 44 ))

NN RaCR (( tt )) == -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt -- -- -- (( 55 ))

NN ThBThB (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 66 ))

NN ThCTHC (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt -- -- -- (( 77 ))

将式（3）、（4）、（5）、（6）、（7）转换为活度形式：Convert formulas (3), (4), (5), (6), and (7) into activity forms:

AA RaARaA (( tt )) == λλ RaARaA NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 88 ))

AA RaBRaB (( tt )) == λλ RaBRaB [[ NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ ThATHA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt ]] -- -- -- (( 99 ))

AA RaCR (( tt )) == λλ RaCR {{ -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt }} -- -- -- (( 1010 ))

AA ThBThB (( tt )) == λλ ThBThB NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 1111 ))

AA ThCTHC (( tt )) == λλ ThCTHC [[ NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt ]] -- -- -- (( 1212 ))

滤膜6上的RaA、RaB、RaC、ThB、ThC的活度分别为ARaA、ARaB ARaC、AThB、AThC。The activities of RaA, RaB, RaC, ThB and ThC on the filter membrane 6 are A RaA , A RaB A RaC , A ThB and A ThC , respectively.

根据222Rn、220Rn放射性衰变规律知道，滤膜6上任意时刻的总的α衰变活度Aα(t)为：Know according to 222 Rn, 220 Rn radioactive decay rule, the total α decay activity A α (t) of any moment on filter membrane 6 is:

Aα(t)=ARaA(t)+ARaC(t)+AThC(t)+A0              （13）A α (t)=A RaA (t)+A RaC (t)+A ThC (t)+A 0 (13)

式中A0为α计数测量仪的本底计数率。In the formula, A 0 is the background count rate of the α counting instrument.

以短时间间隔t为测量周期，时间t为1-10分钟，周期数量大于或等于6个。Take the short time interval t as the measurement cycle, the time t is 1-10 minutes, and the number of cycles is greater than or equal to 6.

其计算方法有两种：There are two calculation methods:

A、根据第i个测量周期的总α计数n(i)，求得第i个测量周期的单位时间的平均计数，由于测量周期较短，这些平均计数与Aα(t)在该测量周期中点的值近似相等，有：A. According to the total α count n(i) of the i-th measurement cycle, the average count per unit time of the i-th measurement cycle is obtained. Since the measurement cycle is short, these average counts are related to A α (t) in the measurement cycle The values at the midpoints are approximately equal, with:

nno (( ii )) // tt == EAEA αα (( itit -- 11 22 tt )) -- -- -- (( 1414 ))

E为α计数测量仪对α粒子的探测效率。E is the detection efficiency of the α counting instrument for α particles.

利用式（14）对n(i)/t的数据进行非线性拟合，能得到NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值；然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度。Using formula (14) to carry out nonlinear fitting on n(i)/t data, the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , A 0 can be obtained; then according to formula (1), (2 ) to obtain the activity concentrations of RaA, RaB, RaC, ThB, and ThC in the air.

B、求Aα(t)在第i个测量周期的积分：B. Find the integral of A α (t) in the i-th measurement period:

AA αα (( ii )) == ∫∫ (( ii -- 11 )) tt itit AA αα (( tt )) dtdt -- -- -- (( 1515 ))

应用最小二乘法求解222Rn,220Rn子体浓度，引入残差R：Apply the least square method to solve the 222 Rn, 220 Rn daughter concentration, and introduce the residual R:

RR == ΣΣ ii == 11 nno ww ii (( nno (( ii )) -- EAEA αα (( ii )) )) 22 -- -- -- (( 1616 ))

式中wi是i计数段的权重因子，权重因子的引入是考虑每个计数段的计数统计误差不同对拟合结果的误差影响。In the formula, w i is the weight factor of the i counting segment, and the introduction of the weighting factor is to consider the influence of the error of the counting statistics of each counting segment on the fitting result.

根据最小二乘法原理，使得残差R取最小值，能得到NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值，然后根据式（1）、（2）倒推得到空气RaA、RaB、RaC、ThB、ThC活度浓度。According to the principle of the least square method, the residual R takes the minimum value, and the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , and A 0 can be obtained, and then the air RaA can be obtained according to formulas (1) and (2). , RaB, RaC, ThB, ThC activity concentration.

实施例二、一种利用α粒子总计数测量空气中222Rn、220Rn子体的方法，本实施例采用的222Rn、220Rn子体采集系统由带有滤膜6的采样头1、采样杆2、流量计3、连接管4和空气采样泵5组成，采样头1和采样杆2连接，采样杆2和流量计3连接，流量计3通过连接管4和空气采样泵5连接。Embodiment two, a kind of method utilizing α particle total count to measure 222 Rn, 220 Rn daughter body in the air, the 222Rn, 220Rn daughter body collection system that the present embodiment adopts is by the sampling head 1 that has filter membrane 6, sampling rod 2 , a flow meter 3, a connecting pipe 4 and an air sampling pump 5, the sampling head 1 is connected to the sampling rod 2, the sampling rod 2 is connected to the flow meter 3, and the flow meter 3 is connected to the air sampling pump 5 through the connecting pipe 4.

通过空气采样泵5将空气中氡子体采集到滤膜6上，然后测量滤膜6上的α衰变总计数，从而计算得到氡子体空气浓度。The radon progeny in the air is collected on the filter membrane 6 by the air sampling pump 5, and then the total count of α decay on the filter membrane 6 is measured, so as to calculate the air concentration of the radon progeny.

本测量方法基于以下条件：This measurement method is based on the following conditions:

1) 采样过程中222Rn、220Rn子体浓度和空气采样泵5采样流率恒定不变；1) 222 Rn, 220 Rn progeny concentrations and air sampling pump 5 sampling flow rates are constant during the sampling process;

2) 滤膜6的过滤效率和自吸收因子均为恒定常数，且不依气溶胶粒径改变，在使用微孔滤膜时，没有自吸收；2) The filtration efficiency and self-absorption factor of the filter membrane 6 are constant, and do not change according to the particle size of the aerosol. When using a microporous filter membrane, there is no self-absorption;

3) 探测器的探测效率为恒定常数，且不依α粒子能量改变，依赖于滤膜6具有较小的自吸收和滤膜6到探测器距离较小。3) The detection efficiency of the detector is a constant constant, and does not change according to the energy of the α particle, and depends on the smaller self-absorption of the filter membrane 6 and the smaller distance from the filter membrane 6 to the detector.

在222Rn、220Rn子体采样过程中，滤膜6上的氡子体数量随着采样而不断增长，其数量还会由于从母体核素衰变而增加和自身衰变而减少，用下述微分方程组表述：During the sampling process of 222 Rn and 220 Rn daughters, the number of radon daughters on the filter membrane 6 will continue to increase along with the sampling, and its number will also increase due to the decay of the parent nuclide and decrease by its own decay, using the following differential Expression of equations:

dNdN RaARaA // dtdt == QGCQGC RaARaA // λλ RaARaA -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == QGCQGC RaBRaB // λλ RaBRaB ++ NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == QGCQGC RaCR // λλ RaCR ++ NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == QGCQGC ThBThB // λλ ThBThB -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == QGCQGC ThCTHC // λλ ThCTHC ++ NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 11 ))

式中G为过滤效率，Q为采样流率，CRaA、CRaB CRaC、CThB、CThC分别为RaA、RaB、RaC、ThB、ThC活度浓度，λRaA、λRaB λRaC、λThB、λThC分别为RaA、RaB、RaC、ThB、ThC的半衰期，NRaA、NRaB NRaC、NThB、NThC分别为采样过程中滤膜6上积累的RaA、RaB、RaC、ThB、ThC的原子数。In the formula, G is the filtration efficiency, Q is the sampling flow rate, C RaA , C RaB C RaC , C ThB , C ThC are the activity concentrations of RaA, RaB, RaC, ThB, ThC respectively, λ RaA , λ RaB λ RaC , λ ThB and λ ThC are the half-lives of RaA, RaB, RaC, ThB and ThC, respectively; N RaA , N RaB N RaC , N ThB and N ThC are the RaA, RaB, RaC, ThB, ThB and Atomic number of ThC.

对式（1）求解能得到：采样时间T1结束时滤膜6上积累的RaA、RaB、RaC、ThB、ThC的原子数与空气中RaA、RaB、RaC、ThB、ThC活度浓度的关系。Solving equation (1), we can get: the relationship between the atomic number of RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane 6 at the end of sampling time T1 and the activity concentration of RaA, RaB, RaC, ThB, ThC in the air .

采样结束后，取下滤膜6送入α计数测量仪进行测量，该时间间隔为T2，滤膜6上的222Rn、220Rn子体以采样结束时刻的数量为初始值开始衰变，同时子体核素还由于母体核素的衰变而增加，用下述微分方程组表述：After the sampling is finished, remove the filter membrane 6 and send it to the α counting instrument for measurement. The time interval is T 2 . The 222 Rn and 220 Rn daughters on the filter membrane 6 start to decay with the number at the end of sampling as the initial value, and at the same time The daughter nuclide also increases due to the decay of the parent nuclide, which is expressed by the following differential equations:

dNdN RaARaA // dtdt == -- NN RaARaA λλ RaARaA dNdN RaBRaB // dtdt == NN RaARaA λλ RaARaA -- NN RaBRaB λλ RaBRaB dNdN RaCR // dtdt == NN RaBRaB λλ RaBRaB -- NN RaCR λλ RaCR dNdN ThBThB // dtdt == -- NN ThBThB λλ ThBThB dNdN ThCTHC // dtdt == NN ThBThB λλ ThBThB -- NN ThCTHC λλ ThCTHC -- -- -- (( 22 ))

对式（2）求解得到采样结束后经过T2时间衰变，滤膜6上的RaA、RaB、RaC、ThB、ThC的原子数与采样结束时刻的RaA、RaB、RaC、ThB、ThC的原子数的关系。Solve formula (2) to obtain the time decay of T2 after the end of sampling, the number of atoms of RaA, RaB, RaC, ThB, ThC on the filter membrane 6 and the number of atoms of RaA, RaB, RaC, ThB, ThC at the end of sampling Relationship.

利用α计数测量仪开始对滤膜6测量瞬间，滤膜6上的RaA、RaB、RaC、ThB、ThC的原子数分别为NRaA1、NRaB1 NRaC1、NThB1、NThC1，根据式（1）、（2）倒推得到空气中的RaA、RaB、RaC、ThB、ThC活度浓度。Utilize the α counting instrument to start measuring the filter membrane 6 at the moment, the atomic numbers of RaA, RaB, RaC, ThB, ThC on the filter membrane 6 are respectively N RaA1 , N RaB1, N RaC1 , N ThB1 , N ThC1 , according to the formula (1 ), (2) Reversely get the activity concentration of RaA, RaB, RaC, ThB, ThC in the air.

采样后，将滤膜6送入α计数测量仪，开始测量总α计数。222Rn子体的α衰变包括：RaA(218Po)6.0MeV、RaC`(214Po)7.69MeV；220Rn子体的α衰变包括：ThC (212Bi) 6.05MeV、ThC`(212Po) 8.78MeV。After sampling, the filter membrane 6 is sent to the alpha count meter to start measuring the total alpha count. The alpha decay of 222 Rn daughters includes: RaA( 218 Po) 6.0MeV, RaC`( 214 Po) 7.69MeV; the alpha decay of 220 Rn daughters includes: ThC ( 212 Bi) 6.05MeV, ThC`( 212 Po) 8.78 MeV.

α计数测量仪开始测量后，滤膜6上的222Rn、220Rn子体仍然按式（2）衰变，对式（2）求解，解得测量过程中滤膜6上任意时刻的RaA、RaB、RaC、ThB、ThC的原子数为：After the α counting measuring instrument starts to measure, the 222 Rn and 220 Rn daughters on the filter membrane 6 still decay according to the formula (2), solve the formula (2), and solve the RaA and RaB at any time on the filter membrane 6 during the measurement process , RaC, ThB, ThC atomic numbers are:

NN RaARaA (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 33 ))

NN RaBRaB (( tt )) == NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ RaARaA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt -- -- -- (( 44 ))

NN RaCR (( tt )) == -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt -- -- -- (( 55 ))

NN ThBThB (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 66 ))

NN ThCTHC (( tt )) == NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt -- -- -- (( 77 ))

将式（3）、（4）、（5）、（6）、（7）转换为活度形式：Convert formulas (3), (4), (5), (6), and (7) into activity forms:

AA RaARaA (( tt )) == λλ RaARaA NN RaARaA 11 ee -- λλ RaARaA tt -- -- -- (( 88 ))

AA RaBRaB (( tt )) == λλ RaBRaB [[ NN RaARaA 11 ee -- λλ RaARaA tt λλ RaBRaB -- λλ ThATHA -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) ee -- λλ RaBRaB tt ]] -- -- -- (( 99 ))

AA RaCR (( tt )) == λλ RaCR {{ -- (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB ee -- λλ RaBRaB tt λλ RaCR -- λλ RaBRaB ++ NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB ee -- λλ RaARaA tt λλ RaCR -- λλ RaARaA ++ [[ NN RaCR 11 ++ (( NN RaARaA 11 λλ RaBRaB -- λλ RaARaA -- NN RaBRaB 11 )) λλ RaBRaB λλ RaCR -- λλ RaBRaB -- NN RaARaA 11 λλ RaBRaB -- λλ RaARaA λλ RaBRaB λλ RaCR -- λλ RaARaA ]] ee -- λλ RaCR tt }} -- -- -- (( 1010 ))

AA ThBThB (( tt )) == λλ ThBThB NN ThBThB 11 ee -- λλ ThBThB tt -- -- -- (( 1111 ))

AA ThCTHC (( tt )) == λλ ThCTHC [[ NN ThBThB 11 ee -- λλ ThBThB tt λλ ThCTHC -- λλ ThBThB -- (( NN ThBThB 11 λλ ThCTHC -- λλ ThBThB -- NN ThCTHC 11 )) ee -- λλ ThCTHC tt ]] -- -- -- (( 1212 ))

滤膜6上的RaA、RaB、RaC、ThB、ThC的活度分别为ARaA、ARaB ARaC、AThB、AThC。The activities of RaA, RaB, RaC, ThB and ThC on the filter membrane 6 are A RaA , A RaB A RaC , A ThB and A ThC , respectively.

根据222Rn、220Rn放射性衰变规律知道，滤膜6上任意时刻的总的α衰变活度Aα(t)为：Know according to 222 Rn, 220 Rn radioactive decay rule, the total α decay activity A α (t) of any moment on filter membrane 6 is:

Aα(t)=ARaA(t)+ARaC(t)+AThC(t)+A0              （13）A α (t)=A RaA (t)+A RaC (t)+A ThC (t)+A 0 (13)

式中A0为α计数测量仪的本底计数率。In the formula, A 0 is the background count rate of the α counting instrument.

以长的时间间隔t1，t2，t3，t4，t5，t6为测量周期，时间t1，t2，t3，t4，t5，t6的值分别为10-120分钟，测量周期为6个。Taking the long time interval t 1 , t 2 , t 3 , t 4 , t 5 , t 6 as the measurement cycle, the values of time t 1 , t 2 , t 3 , t 4 , t 5 , t 6 are respectively 10- 120 minutes, 6 measurement cycles.

其计算方法为：Its calculation method is:

6个测量周期的计数分别为n(1)，n(2)，n(3)，n(4)，n(5)，n(6)。The counts of the 6 measurement cycles are n(1), n(2), n(3), n(4), n(5), n(6) respectively.

nno (( 11 )) == EE. ∫∫ 00 tt 11 AA αα (( tt )) dtdt -- -- -- (( 1717 ))

nno (( 22 )) == EE. ∫∫ tt 11 tt 11 ++ tt 22 AA αα (( tt )) dtdt -- -- -- (( 1818 ))

nno (( 33 )) == EE. ∫∫ tt 11 ++ tt 22 tt 11 ++ tt 22 ++ tt 33 AA αα (( tt )) dtdt -- -- -- (( 1919 ))

nno (( 44 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 AA αα (( tt )) dtdt -- -- -- (( 2020 ))

nno (( 55 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 ++ tt 44 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 AA αα (( tt )) dtdt -- -- -- (( 21twenty one ))

nno (( 66 )) == EE. ∫∫ tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 tt 11 ++ tt 22 ++ tt 33 ++ tt 44 ++ tt 55 ++ tt 66 AA αα (( tt )) dtdt -- -- -- (( 22twenty two ))

将n(1)，n(2)，n(3)，n(4)，n(5)，n(6)值带入式（17）、（18）、（19）、（20）、（21）、（22），解得NRaA1、NRaB1 NRaC1、NThB1、NThC1、A0的值的值，然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度。Put the values of n(1), n(2), n(3), n(4), n(5), and n(6) into formulas (17), (18), (19), (20), (21) and (22), get the values of N RaA1 , N RaB1 N RaC1 , N ThB1 , N ThC1 , and A 0 , and then get RaA, RaB, RaC, ThB, ThC activity concentration.

Claims (2)

1.一种利用a粒子总计数测量空气中222Rn、220Rn子体的方法，通过空气采样泵将空气中氡子体采集到滤膜上，然后测量滤膜上的α衰变总计数，从而计算得到氡子体空气浓度；本测量方法基于以下条件： 1. a kind of method utilizing α particle total count to measure 222 Rn, 220 Rn daughter body in the air, radon daughter body in the air is collected on the filter membrane by air sampling pump, then measure the α decay total count on the filter membrane, thereby The air concentration of radon daughters is calculated; this measurement method is based on the following conditions: 1) 采样过程中222Rn、220Rn子体浓度和空气采样泵采样流率恒定不变； 1) The concentration of 222 Rn, 220 Rn daughters and the sampling flow rate of the air sampling pump are constant during the sampling process; 2) 滤膜的过滤效率和自吸收因子均为恒定常数，且不依气溶胶粒径改变，在使用微孔滤膜时，没有自吸收； 2) The filtration efficiency and self-absorption factor of the filter membrane are constant and do not change according to the particle size of the aerosol. When using a microporous filter membrane, there is no self-absorption; 3) 探测器的探测效率为恒定常数，且不依α粒子能量改变，依赖于滤膜具有较小的自吸收和滤膜到探测器距离较小； 3) The detection efficiency of the detector is a constant constant, and does not change according to the energy of α particles, and depends on the small self-absorption of the filter membrane and the small distance from the filter membrane to the detector; 在222Rn、220Rn子体采样过程中，滤膜上的氡子体数量随着采样而不断增长，其数量还会由于从母体核素衰变而增加和自身衰变而减少，用下述微分方程组表述： During the sampling process of 222 Rn and 220 Rn daughters, the number of radon daughters on the filter membrane will continue to increase with the sampling, and its number will also increase due to the decay of the parent nuclide and decrease due to its own decay, using the following differential equation Group representation:
Figure 113583DEST_PATH_IMAGE001
               (1)
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(1) 式中G为过滤效率，Q为采样流率，
Figure 2013100697035100001DEST_PATH_IMAGE002
、
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、
Figure 935094DEST_PATH_IMAGE005
、
Figure 2013100697035100001DEST_PATH_IMAGE006
分别为RaA、RaB、RaC、ThB、ThC活度浓度，
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、
Figure 2013100697035100001DEST_PATH_IMAGE008
Figure 331626DEST_PATH_IMAGE009
、
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、
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分别为RaA、RaB、RaC、ThB、ThC的半衰期，、
Figure 545756DEST_PATH_IMAGE013
Figure DEST_PATH_IMAGE014
、
Figure 682339DEST_PATH_IMAGE015
、分别为采样过程中滤膜上积累的RaA、RaB、RaC、ThB、ThC的原子数； Where G is the filtration efficiency, Q is the sampling flow rate,
Figure 2013100697035100001DEST_PATH_IMAGE002
,
Figure 217674DEST_PATH_IMAGE003
,
Figure 935094DEST_PATH_IMAGE005
,
Figure 2013100697035100001DEST_PATH_IMAGE006
are the activity concentrations of RaA, RaB, RaC, ThB, and ThC, respectively,
Figure 330303DEST_PATH_IMAGE007
,
Figure 2013100697035100001DEST_PATH_IMAGE008
Figure 331626DEST_PATH_IMAGE009
,
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,
Figure 91772DEST_PATH_IMAGE011
are the half-lives of RaA, RaB, RaC, ThB, and ThC, respectively, ,
Figure 545756DEST_PATH_IMAGE013
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,
Figure 682339DEST_PATH_IMAGE015
, Respectively, the atomic numbers of RaA, RaB, RaC, ThB, and ThC accumulated on the filter membrane during the sampling process; 对式（1）求解得到：采样时间T1结束时滤膜上积累的RaA、RaB、RaC、ThB、ThC的原子数与空气中RaA、RaB、RaC、ThB、ThC活度浓度的关系； Solve formula (1) to get: the relationship between the number of atoms of RaA, RaB, RaC, ThB, ThC accumulated on the filter membrane at the end of sampling time T1 and the activity concentration of RaA, RaB, RaC, ThB, ThC in the air; 采样结束后，取下滤膜送入a计数测量仪进行测量，该时间间隔为T2，滤膜上的222Rn、220Rn子体以采样结束时刻的数量为初始值开始衰变，同时子体核素还由于母体核素的衰变而增加，用下述微分方程组表述： After the sampling is over, remove the filter membrane and send it to a counting instrument for measurement. The time interval is T 2 . The 222 Rn and 220 Rn daughters on the filter membrane begin to decay with the number at the end of sampling as the initial value, and at the same time the daughters The nuclide also increases due to the decay of the parent nuclide, expressed by the following differential equations:
Figure 538169DEST_PATH_IMAGE017
               (2)
Figure 538169DEST_PATH_IMAGE017
(2) 对式（2）求解得到采样结束后经过T2时间衰变，滤膜上的RaA、RaB、RaC、ThB、ThC的原子数与采样结束时刻的RaA、RaB、RaC、ThB、ThC的原子数的关系； Solve the formula (2) to get T2 time decay after the end of sampling. relation; 利用a计数测量仪开始对滤膜测量瞬间，滤膜上的RaA、RaB、RaC、ThB、ThC的原子数分别为
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、
Figure 469216DEST_PATH_IMAGE019
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、
Figure 246433DEST_PATH_IMAGE021
、
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，根据式（1）、（2）倒推得到空气中的RaA、RaB、RaC、ThB、ThC活度浓度； At the moment when the filter membrane is measured by a counting instrument, the atomic numbers of RaA, RaB, RaC, ThB, and ThC on the filter membrane are respectively
Figure DEST_PATH_IMAGE018
,
Figure 469216DEST_PATH_IMAGE019
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,
Figure 246433DEST_PATH_IMAGE021
,
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, according to formulas (1) and (2), the activity concentrations of RaA, RaB, RaC, ThB, and ThC in the air can be obtained by deduction; 采样后，将滤膜送入a计数测量仪，开始测量总a计数，222Rn子体的a衰变包括：RaA 6.0MeV、RaC` 7.69MeV；220Rn子体的a衰变包括：ThC 6.05MeV、ThC`  8.78MeV； After sampling, send the filter membrane to the a count measuring instrument to start measuring the total a count. The a decay of 222 Rn daughters includes: RaA 6.0MeV, RaC` 7.69MeV; the alpha decay of 220 Rn daughters includes: ThC 6.05MeV, ThC` 8.78 MeV; a计数测量仪开始测量后，滤膜上的222Rn、220Rn子体仍然按式（2）衰变，对式（2）求解，解得测量过程中滤膜上任意时刻的RaA、RaB、RaC、ThB、ThC的原子数为： After the counting measuring instrument starts to measure, the 222 Rn and 220 Rn daughters on the filter membrane still decay according to the formula (2), solve the formula (2), and solve the RaA, RaB, RaC on the filter membrane at any time during the measurement process , ThB, ThC atomic numbers are:                              （3） (3)
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   （4）
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(4)
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             （5）
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(5)
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                             （6）
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(6)
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    （7）
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(7) 将式（3）、（4）、（5）、（6）、（7）转换为活度形式： Convert formulas (3), (4), (5), (6), and (7) into activity forms:
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                          （8）
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(8) （9） (9)
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      （10）
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(10)
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                         （11）
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(11)
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（12）
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(12) 滤膜上的RaA、RaB、RaC、ThB、ThC的活度分别为
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、
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、
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、； The activities of RaA, RaB, RaC, ThB and ThC on the filter membrane are respectively
Figure 283845DEST_PATH_IMAGE033
,
Figure 805962DEST_PATH_IMAGE035
,
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, ; 根据222Rn、220Rn放射性衰变规律知道，滤膜上任意时刻的总的a衰变活度
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为： According to the law of radioactive decay of 222 Rn and 220 Rn, the total alpha decay activity at any time on the filter membrane
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for:               （13） (13) 式中A0为a计数测量仪的本底计数率； In the formula, A 0 is the background counting rate of the a counting measuring instrument; 其特征是：以短时间间隔t为测量周期，时间t为1-10分钟，周期数量大于或等于6个； Its characteristics are: the short time interval t is used as the measurement cycle, the time t is 1-10 minutes, and the number of cycles is greater than or equal to 6; 其计算方法有两种： There are two calculation methods: A、根据第i个测量周期的总a计数
Figure DEST_PATH_IMAGE040
，求得第i个测量周期的单位时间的平均计数，由于测量周期较短，这些平均计数与在该测量周期中点的值近似相等，有： A. According to the total a count of the i-th measurement cycle
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, to obtain the average count per unit time of the i-th measurement cycle, due to the short measurement cycle, these average counts are related to The values at the points in the middle of the measurement period are approximately equal, with:
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                          （14）
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(14) E为a计数测量仪对a粒子的探测效率； E is the detection efficiency of a counting instrument to a particle;     利用式（14）对
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的数据进行非线性拟合，能得到
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、
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、、
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、A0的值；然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度； Use formula (14) to
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Non-linear fitting of the data, we can get
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,
Figure 903417DEST_PATH_IMAGE019
Figure 255901DEST_PATH_IMAGE020
, ,
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, the value of A 0 ; then according to the formula (1), (2), the activity concentration of RaA, RaB, RaC, ThB, ThC in the air can be obtained by deduction; B、求
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在第i个测量周期的积分： B. ask
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Integration at the i-th measurement cycle:
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                               （15）
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(15) 应用最小二乘法求解222Rn,220Rn子体浓度，引入残差
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： Apply the least square method to solve the concentration of 222 Rn, 220 Rn daughters, and introduce the residual
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:
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                            （16）
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(16) 式中w i 是i计数段的权重因子，权重因子的引入是考虑每个计数段的计数统计误差不同对拟合结果的误差影响； In the formula, w i is the weight factor of the i counting segment, and the introduction of the weighting factor is to consider the error impact of the different counting statistics errors of each counting segment on the fitting result; 根据最小二乘法原理，使得残差
Figure 879835DEST_PATH_IMAGE044
取最小值，能得到
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、
Figure 103323DEST_PATH_IMAGE019
Figure 387674DEST_PATH_IMAGE020
、
Figure 987151DEST_PATH_IMAGE021
、、A0的值，然后根据式（1）、（2）倒推得到空气RaA、RaB、RaC、ThB、ThC活度浓度； According to the principle of the least squares method, the residual
Figure 879835DEST_PATH_IMAGE044
Taking the minimum value, we can get
Figure 41826DEST_PATH_IMAGE018
,
Figure 103323DEST_PATH_IMAGE019
Figure 387674DEST_PATH_IMAGE020
,
Figure 987151DEST_PATH_IMAGE021
, , the value of A 0 , and then according to the formula (1), (2), the activity concentration of air RaA, RaB, RaC, ThB, ThC can be obtained; 上述方法采用的222Rn、220Rn子体采集系统由带有滤膜的采样头、采样杆、流量计、连接管和空气采样泵组成，采样头和采样杆连接，采样杆和流量计连接，流量计通过连接管和空气采样泵连接。 The 222 Rn, 220 Rn progeny collection system adopted by the above method is composed of a sampling head with a filter membrane, a sampling rod, a flow meter, a connecting pipe and an air sampling pump, the sampling head is connected with the sampling rod, and the sampling rod is connected with the flow meter. The flow meter is connected to the air sampling pump through the connecting pipe. 2.根据权利要求1所述的一种利用a粒子总计数测量空气中222Rn、220Rn子体的方法，其特征是：用以长时间间隔t1，t2，t3，t4，t5，t6为测量周期取代短时间间隔t为测量周期，时间t1，t2，t3，t4，t5，t6的值分别为10-120分钟，测量周期为6个，其计算方法为：  2. a kind of method according to claim 1 utilizing alpha particle total count to measure 222 Rn, the method of 220 Rn daughter body in the air is characterized in that: for long time interval t 1 , t 2 , t 3 , t 4 , t 5 , t 6 is the measurement cycle instead of the short time interval t as the measurement cycle, the values of time t 1 , t 2 , t 3 , t 4 , t 5 , and t 6 are 10-120 minutes respectively, and the measurement cycle is 6, Its calculation method is: 6个测量周期的计数分别为
Figure DEST_PATH_IMAGE046
，
Figure 259050DEST_PATH_IMAGE047
，
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，
Figure 635673DEST_PATH_IMAGE049
，
Figure DEST_PATH_IMAGE050
，
Figure 473179DEST_PATH_IMAGE051
， The counts of the 6 measurement cycles are
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,
Figure 259050DEST_PATH_IMAGE047
,
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,
Figure 635673DEST_PATH_IMAGE049
,
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,
Figure 473179DEST_PATH_IMAGE051
,
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                              （17）
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(17)
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                            （18）
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(18)                                    （19） (19)
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                                （20）
Figure 465592DEST_PATH_IMAGE055
(20)
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                              （21） 
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(twenty one)
Figure 13117DEST_PATH_IMAGE057
                              （22）
Figure 13117DEST_PATH_IMAGE057
(twenty two) 将
Figure 337919DEST_PATH_IMAGE046
，
Figure 894671DEST_PATH_IMAGE047
，，
Figure 520005DEST_PATH_IMAGE049
，
Figure 128841DEST_PATH_IMAGE050
，
Figure 489284DEST_PATH_IMAGE051
值带入式（17）、（18）、（19）、（20）、（21）、（22），解得、
Figure 405604DEST_PATH_IMAGE019
Figure 688687DEST_PATH_IMAGE020
、
Figure 400291DEST_PATH_IMAGE021
、
Figure 203162DEST_PATH_IMAGE022
、A0的值的值，然后根据式（1）、（2）倒推得到空气中RaA、RaB、RaC、ThB、ThC活度浓度。 Will
Figure 337919DEST_PATH_IMAGE046
,
Figure 894671DEST_PATH_IMAGE047
, ,
Figure 520005DEST_PATH_IMAGE049
,
Figure 128841DEST_PATH_IMAGE050
,
Figure 489284DEST_PATH_IMAGE051
Put the value into formula (17), (18), (19), (20), (21), (22), and solve ,
Figure 405604DEST_PATH_IMAGE019
Figure 688687DEST_PATH_IMAGE020
,
Figure 400291DEST_PATH_IMAGE021
,
Figure 203162DEST_PATH_IMAGE022
, A 0 value, and then according to the formula (1), (2) inversely get the activity concentration of RaA, RaB, RaC, ThB, ThC in the air.
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US20160091614A1 (en) * 2014-09-29 2016-03-31 Battelle Energy Alliance, Llc Radioactive waste screening systems, and related methods
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CN103439734A (en) * 2013-09-05 2013-12-11 衡阳师范学院 A method for synchronously measuring the concentrations of 222Rn, 220Rn and their daughters
CN103439734B (en) * 2013-09-05 2016-09-14 衡阳师范学院 A method for synchronously measuring the concentrations of 222Rn, 220Rn and their daughters
US20160091614A1 (en) * 2014-09-29 2016-03-31 Battelle Energy Alliance, Llc Radioactive waste screening systems, and related methods
CN104360370A (en) * 2014-11-11 2015-02-18 南华大学 Method for continuously measuring concentrations of thoron daughters
CN105954789A (en) * 2016-04-20 2016-09-21 南华大学 Accurate calibration method for alpha spectrometry peak overlap correction factor of radon daughter measuring instrument
CN105954789B (en) * 2016-04-20 2018-05-01 南华大学 A kind of accurate calibration method of measurement of radon daughters instrument alpha energy spectrum overlap of peaks modifying factor
CN106019354A (en) * 2016-06-07 2016-10-12 南华大学 Artificial radionuclide dissolvability monitoring method and apparatus
CN106019354B (en) * 2016-06-07 2018-10-30 南华大学 Artificial radionuclide concentration monitoring method and device
CN107024710A (en) * 2017-05-12 2017-08-08 国网吉林省电力有限公司电力科学研究院 222Rn radon daughter radioactive levels cumulative effect determines device and method
CN112733068A (en) * 2021-01-08 2021-04-30 中国辐射防护研究院 Method for calculating activity of each generation of daughter of radionuclide decay chain
CN112733068B (en) * 2021-01-08 2023-07-25 中国辐射防护研究院 Method for calculating activity of each daughter of radionuclide decay chain

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