JP2002090318A - Method and device for positron annihilation gamma-ray spectrum analysis - Google Patents

Abstract

PROBLEM TO BE SOLVED: To correctly evaluate the energy distribution form of annihilation gamma-ray by obtaining a measured result reflecting only the properties of a sample without depending on the gamma-ray energy resolution and energy calibration of a measuring device. SOLUTION: A function obtained by convoluting a model function to the true energy distribution of positron annihilation gamma-ray by a distribution function with a width equivalent to energy resolution, or its approximate function is fitted as a model to the spectrum data of the measured positron annihilation gamma-ray.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a positron annihilation gamma ray spectrum analysis method and apparatus for examining the properties of a positron annihilation partner electron or a material containing the same from the positron annihilation gamma ray energy distribution.

[0002]

2. Description of the Related Art As one of the methods for evaluating the properties of materials using positron annihilation gamma rays, the Doppler method utilizing the energy of an annihilation gamma ray by Doppler shift due to the momentum of an electron pair at the time of annihilation is known. is there. In this method, the Doppler shift width in the case of annihilation with free electrons is small, the Doppler shift is large in the case of annihilation with bound electrons, and the annihilation ratio with free electrons increases when the number of defects in the sample increases. I use.

FIG. 6 is an explanatory diagram of a conventional example of a positron annihilation γ-ray spectrum analysis method. In FIG. 6, reference numeral 11 denotes positron annihilation γ-ray spectrum measurement data, reference numeral 12 denotes a peak central region, and reference numeral 13 denotes a peak peripheral region. The ratio of the count of the peak center 12 to the sum of the count of the peak center region 12 and the count of the peak peripheral region 13 in the positron annihilation γ-ray energy distribution is used as an evaluation index of the sample material and is called an S parameter. I have.

[0004] However, the energy resolution of the measuring device and the 1
Depending on the energy width per channel, etc., the energy spectrum of the measured annihilation gamma ray and the aforementioned S
Since the parameters change, it is impossible to compare the evaluation results between measurement data having different energy resolutions or the like due to measurements under different conditions. Furthermore, accidental variations in energy resolution and the like cause accidental errors in the evaluation results.

[0005] In addition, when an operation is performed between measurement data in order to remove the background or to combine a plurality of measurement data, the operation is generally performed between the same channels of each data. Measurement often evaluates the energy distribution shape, slight energy calibration deviation between each data will damage the energy distribution shape information, and the difference in energy resolution should be normal distribution The energy measurement error is regarded as the synthesis of normal distributions having different widths, which makes it more difficult to evaluate the energy distribution shape of the annihilation gamma rays.

In addition, in the case of background removal or the like, a correct result cannot be obtained by subtracting data having different effective measurement times or positron source intensities. Processing is required.

[0007]

In the above-described conventional positron annihilation γ-ray spectrum analysis method, the energy distribution of the annihilation γ-rays to be measured depends on the energy resolution of the measuring device, and the measured energy distribution differs between the measurement data having different energy resolutions. The problem was to solve the problem that the evaluation results could not be compared with each other.

In addition, when an operation is performed between measurement data for background removal or for synthesizing a plurality of measurement data, the background positron annihilation γ-rays cannot be accurately removed or the positron annihilation γ-ray energy distribution The shape information is damaged or the energy measurement error distribution is no longer a normal distribution, making it difficult to obtain measurement results that reflect only the properties of the sample and to correctly evaluate the energy distribution shape of annihilation gamma rays. In some cases, solving this was also an issue.

The present invention has been made in view of such conventional circumstances, and it is possible to obtain a measurement result that reflects only the properties of a sample without depending on the γ-ray energy resolution or energy calibration of a measuring apparatus. It is an object of the present invention to provide a positron annihilation γ-ray spectrum analysis method and apparatus capable of correctly evaluating the energy distribution shape of annihilation γ-rays.

[0010]

In order to achieve the above object, according to the first aspect of the present invention, the measured positron annihilation γ
Fitting a model function for the true energy distribution of positron annihilation γ-rays with the distribution function of the width corresponding to the energy resolution to the spectral data of the line, or a function approximating the function And a positron annihilation γ-ray spectrum analysis method characterized by the following.

In such a positron annihilation γ-ray spectrum analysis method, the positron annihilation γ-ray is measured by convoluting a model function for the true energy distribution with a distribution function having a width corresponding to the energy resolution. A fitting model for the annihilation γ-ray spectrum data is obtained.

In the present invention, it is desirable that the model function for the true energy distribution of the positron annihilation gamma ray is composed of two or more components having different energy distribution widths.

In the above positron annihilation γ-ray spectrum analysis method, when two or more components having different distributions are present in the momentum of the electron as the positron annihilation partner, fitting is performed on the measured positron annihilation γ-ray spectrum data. A model is obtained.

According to the second aspect of the present invention, the model function for the distribution of the peak value of the γ-ray detection signal is integrated with the measured positron annihilation γ-ray spectrum data by the width of each channel of the pulse height analyzer. A positron annihilation γ-ray spectrum analysis method characterized by fitting a function obtained by the above or an approximate function thereof as a model.

In such a positron annihilation γ-ray spectrum analysis method, the measured positron annihilation γ is obtained by integrating the model function for the distribution of the peak value of the γ-ray detection signal with the width of each channel of the peak analyzer. A fitting model for the line spectral data is obtained.

In addition, in addition to the invention described in claim 2, the model function for the distribution of the peak values of the γ-ray detection signal can be a model for the spectrum data of the positron annihilation γ-ray described in claim 1.

In such a positron annihilation γ-ray spectrum analysis method, a model function for the true energy distribution of the positron annihilation γ-rays is convoluted with a distribution function having a width corresponding to the energy resolution. By integrating with the width of the channel, a fitting model for the measured positron annihilation γ-ray spectrum data is obtained.

According to the third aspect of the invention, the count of each channel of the measured positron annihilation γ-ray spectrum data is calculated by approximating a continuous distribution before the peak value is quantized, which is obtained from data near the channel. A positron annihilation γ-ray spectrum analysis method is characterized in that a curve is converted into a value in the channel, and the distribution of the peak value is subjected to fitting by a model function.

In such a positron annihilation γ-ray spectrum analysis method, the count of each channel of the spectrum data is converted into the value of the approximate curve of the continuous distribution before the peak value is quantized in the channel. Data suitable for fitting with a model for the peak value can be obtained.

In the present invention, in addition to the means according to the third aspect, the model function for the distribution of peak values of the γ-ray detection signal is a model for the spectrum data of the positron annihilation γ-rays according to the first aspect. Can be.

In such a positron annihilation γ-ray measurement spectrum analysis method, when there are two or more components having different distributions in the momentum of the electron as the positron annihilation partner, the method is suitable for fitting with a model to the peak value. Data can be obtained.

In the present invention, in addition to the above, in addition to the above, γ other than positron annihilation γ-rays measured simultaneously with positron annihilation γ-rays
The energy resolution at the positron annihilation γ-ray energy can be estimated from the line spectral data.

In such a positron annihilation γ-ray spectrum analysis method, the value of the energy resolution used in the analysis can be measured for each measurement.

Also, in the present invention, the energy resolution is estimated by using 10 Ge ke ray of ⁶⁸ Ge or
It may be used γ-rays of 1274keV of ²² Na.

In such a positron annihilation γ-ray spectrum analysis method, the value of the energy resolution used in the analysis can be measured for each measurement without preparing a separate γ-ray source.

According to the fourth aspect of the present invention, when calculating spectral data such as background subtraction, for each channel of both or one of the spectral data, a peak value obtained from data near the channel is quantized. Positron annihilation γ-rays, characterized in that an approximate curve of a continuous distribution before being performed is a distribution within a peak range corresponding to the channel, and peak values in these are requantized by an energy calibration common to both spectral data. A spectrum analysis method is provided.

According to the present invention, the energy calibration of both spectral data to be operated can be matched by conversion of energy calibration in consideration of the wave height distribution inside the channel.

According to the fifth aspect of the present invention, when calculating spectral data such as background subtraction, the energy resolution of each spectral data is calculated from the variance corresponding to a predetermined energy resolution or the worse of the two resolutions. A positron annihilation γ-ray spectrum analysis method characterized in that each spectrum data is convoluted with a distribution function having a variance obtained by subtracting a variance corresponding to (1).

In the present invention, by convoluting spectral data with a distribution function having a variance corresponding to the difference in variance corresponding to the energy resolution, the energy resolutions of the two spectral data to be operated can be made coincident with each other. The energy calibration of the data can be matched.

Further, in the present invention, when the positron annihilation γ-ray generated by the positron emitted from the positron source annihilating outside the sample is subtracted as a background, the positron annihilation γ-ray is measured simultaneously with the positron annihilation γ-ray. Alternatively, the counting of each spectrum data may be normalized by counting the γ-rays emitted from the positron source.

In such a positron annihilation γ-ray spectrum analysis method, it is possible to correct the difference between the effective measurement time and the positron source intensity of both spectral data to be operated.

Further, in the present invention, when the positron annihilation γ-rays generated from everywhere due to the generation of electron pairs by the γ-rays emitted from the sample or the environment are subtracted as a background, the positron annihilation γ-rays are measured simultaneously with the positron annihilation γ-rays. The counting of each spectrum data may be normalized by the counting of γ-rays emitted from the sample or the environment other than γ-rays.

In such a positron annihilation γ-ray spectrum analysis method, the difference between the effective measurement time of both spectral data to be operated and the γ-ray intensity emitted from the sample or the environment to generate an electron pair is corrected. Can be.

According to the sixth aspect of the present invention, the first to fifth aspects are described.
A positron annihilation γ-ray spectrum analyzing apparatus, comprising: a calculation means for performing the positron annihilation γ-ray spectrum analysis according to any one of the above.

According to the seventh aspect of the present invention, the first to fifth aspects are provided.
A recording medium characterized by recording a calculation program for performing positron annihilation γ-ray spectrum analysis according to any one of the above.

[0036]

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, the positron annihilation γ according to the present invention will be described.
One embodiment of a line spectrum analysis method and apparatus will be described with reference to FIGS.

FIG. 5 shows the structure of the apparatus. As shown in FIG. 5, in the electron annihilation γ-ray spectrum analyzer 8, a computer program is read from a floppy disk 9 as a recording medium on which a calculation program for performing analysis to be described later is recorded, and the positron annihilation γ-ray measurement is performed. Apparatus 10
The following analysis is performed on the spectrum data measured by the above-mentioned method.

FIG. 2 shows the spectrum data obtained by setting a radioactive sample containing ⁶⁰ Co to ⁶⁸ Ge, which is a positron source. As shown in FIG. 2, the positron annihilation gamma ray peak 5 and the positron source emits 10
A γ-ray peak 6 of 77 keV and a γ-ray peak 7 of 1173 keV emitted from the sample to be measured are observed.

FIG. 3 shows spectral data obtained by measurement without setting the sample to be measured in the positron source. As shown in FIG. 3, a positron annihilation gamma ray peak 5 and a 1077 keV gamma ray peak 6 emitted from the positron source are observed.

FIG. 4 shows the spectrum data obtained by the measurement with the sample to be measured set in a dummy having the same shape as the positron source. As shown in FIG. 4, the positron annihilation γ-ray peak 5 and the 1
A gamma ray peak 7 of 173 keV is observed.

More specifically, for each of the spectral data shown in FIGS. 2, 3 and 4, a relational expression between the channel and the energy, that is, energy calibration, is obtained from the channel at the center of each γ-ray peak and its energy. Derive. For γ-ray peaks other than positron annihilation γ-rays, the total count and the width, that is, the resolution, of each peak are calculated.

Next, the resolution at the positron annihilation γ-ray energy is calculated for each spectrum data. In general, the square of the resolution is a linear function of energy, and its gradient is specific to the detector.Therefore, the positron annihilation γ-ray is calculated from the resolution at energies other than the positron annihilation γ-ray using the gradient determined in advance by calibration measurement. It is possible to estimate the resolution in energy.

Then, for each spectrum data, the energy calibration is converted to a predetermined one, and the energy resolution is converted to the worst one among the three. This conversion creates a function that approximates the distribution of peak values before AD conversion of each spectrum data, that is, before quantization, and calculates the square of the worst of the three resolutions of the spectrum data and the resolution of the spectrum data. The approximation function is convoluted with a normal distribution function having a resolution based on the square root of the square difference, and the result is requantized in accordance with a predetermined energy calibration.

The function for approximating the distribution of peak values before quantization is to create an approximate function within the range of the peak value corresponding to each channel before conversion from data including the channels before and after each channel. By connecting these, it is possible to define the entire required peak value range.

The approximation function in the range of the peak value corresponding to each channel is based on the condition that the integration in the range of the peak value corresponding to the channel and the channels before and after the channel is equal to the count of the channel. It is obtained as the solution of the equation Requantization is performed by integrating an approximate function within a range of peak values corresponding to each channel after the conversion.

Next, the spectral data obtained by the measurement with the sample set in the positron source was subjected to the above-mentioned conversion. From the counting of each channel, the spectral data obtained by the measurement without setting the sample in the positron source was converted. The count of the same channel is multiplied by the count of the entire 1077 keV γ-ray peak in the spectrum data obtained by setting the sample in the positron source, and 1077 k in the spectrum data obtained by measurement without setting the sample in the positron source.
Subtract the count for the entire eV gamma ray peak.

From the results obtained here, the spectrum data obtained by performing the above-described conversion on the spectrum data obtained by setting the sample on the dummy of the positron source and then counting the same channel, and calculating the spectrum data obtained by setting the sample on the positron source. Is multiplied by the total count of 1173 keV γ-ray peaks, and the value obtained by dividing the total count of 1173 keV γ-ray peaks in the spectrum data obtained by setting the sample on the dummy of the positron source is subtracted.

The spectral data of the positron annihilation γ-rays obtained by the above processing is fitted by a model function shown in the following equation (1), and the obtained coefficient A
The ratio A / B of the values of A and B or A / (A + B) is used as the evaluation index of the sample.

The equation (1) will be described with reference to FIG. 1. The first term of the equation (1) is obtained by convolving the true sharp component model 3 with the resolution. This corresponds to the component model 4.

The second term is a true broad component model 1.
Is convoluted with the resolution, and corresponds to the broad component model 2 convolved with the resolution. Since the model function shown in the equation (1) includes an indefinite integral that is difficult to obtain analytically, a numerical approximation calculation method such as Taylor expansion of the integrand is used.

[0051]

(Equation 1)

Next, another embodiment of the positron annihilation γ-ray spectrum analyzing method according to the present invention will be described. In this embodiment, the energy calibration of each measured spectrum data and the requantization at the time of the conversion of the energy resolution in the above-described embodiment are performed by approximating the peak value distribution function at each channel center value. And the fitting model function for this is changed to the following equation (2).

[0053]

(Equation 2)

In the embodiment of the positron annihilation gamma ray measuring method and apparatus according to the present invention described above, the following operation and effect can be obtained.

By convoluting the model function for the true energy distribution of the positron annihilation γ-ray with a distribution function having a width corresponding to the energy resolution, a fitting model for the measured positron annihilation γ-ray spectrum data can be obtained. In addition, the evaluation of the true energy distribution can be performed without being affected by the energy resolution, and the accuracy and universality of the evaluation can be improved.

In the case where the momentum of the electron as the positron annihilation partner has two or more components having different distributions, a fitting model for the measured positron annihilation γ-ray spectrum data is obtained, and thus the influence of the energy resolution is obtained. The evaluation of the true energy distribution can be performed without the need, and this has the effect of improving the accuracy and universality of the evaluation.

By integrating the model function for the distribution of the peak value of the γ-ray detection signal by the width of each channel of the peak analyzer, a fitting model for the measured positron annihilation γ-ray spectrum data is obtained. It is possible to evaluate the true energy distribution without being affected by the quantization by the analyzer, which has the effect of improving the accuracy and universality of the evaluation.

The model function for the true energy distribution of the positron annihilation gamma ray is convoluted with a distribution function having a width corresponding to the energy resolution, and further integrated by the width of each channel of the pulse height analyzer to obtain the measured positron energy. Annihilation γ
Since a fitting model is obtained for the line spectral data, it is possible to evaluate the true energy distribution without being affected by the energy resolution and quantization by the pulse height analyzer, which has the effect of improving the accuracy and universality of the evaluation. .

By converting the count of each channel of the spectral data into the value of the channel of the approximate curve of the continuous distribution before the peak value is quantized, data suitable for fitting a model to the peak value is obtained. It is possible to evaluate the true energy distribution without being affected by quantization by the pulse height analyzer,
This has the effect of improving the accuracy and universality of the evaluation.

When there are two or more components having different distributions in the momentum of the electron as the positron annihilation partner, data suitable for fitting a model to the peak value can be obtained. It is possible to evaluate the true energy distribution without being affected by the above, and this has the effect of improving the accuracy and universality of the evaluation.

Since the value of the energy resolution used for the analysis can be actually measured for each measurement, it is possible to evaluate the true energy distribution without being affected by the energy resolution for each measurement, thereby improving the accuracy and universality of the evaluation. There is.

Since the value of the energy resolution used for analysis can be measured for each measurement without preparing a separate γ-ray source, it is possible to evaluate the true energy distribution without being affected by the energy resolution for each measurement. This has the effect of improving the accuracy and universality of the data.

The conversion of the energy calibration in consideration of the wave height distribution inside the channel makes it possible to make the energy calibrations of both the spectral data for performing the calculation such as background subtraction coincide with each other. The evaluation of the true energy distribution can be performed without receiving the effect, and the accuracy and universality of the evaluation can be improved.

By convolving the spectrum data with a distribution function having a variance corresponding to the difference in variance corresponding to the energy resolution, the energy resolutions of the two spectral data for which operations such as background subtraction are performed can be matched. The evaluation of the true energy distribution can be performed without being affected by the fluctuation of the energy resolution, and the accuracy and universality of the evaluation can be improved.

When subtracting the positron annihilation γ-rays generated by the positron emitted from the positron source excluding the sample other than the sample as a background, it is possible to correct the difference between the effective measurement time and the positron source intensity of the two spectral data to be operated. Thus, the evaluation of the true energy distribution can be performed without being affected by these factors, and the accuracy and universality of the evaluation can be improved.

When the positron annihilation γ-rays generated everywhere due to the generation of electron pairs by the γ-rays emitted from the sample or the environment are subtracted as a background, the effective measurement time of both spectral data to be operated and the emission from the sample or the environment are reduced. To correct the difference in gamma-ray intensity that causes electron pair generation,
It is possible to evaluate the true energy distribution without being affected by the influence, and it is possible to improve the accuracy and universality of the evaluation.

[0067]

As described in detail above, according to the present invention, it is possible to obtain a measurement result that reflects only the properties of a sample without depending on the γ-ray energy resolution or energy calibration of the measurement apparatus. In addition, the energy distribution shape of the annihilation gamma ray can be correctly evaluated.

That is, according to the first aspect of the present invention,
By convoluting the model function for the true energy distribution of the positron annihilation γ-ray with a distribution function having a width corresponding to the energy resolution, a fitting model for the measured positron annihilation γ-ray spectrum data is obtained. It is possible to evaluate the true energy distribution without being affected by the above, and this has the effect of improving the accuracy and universality of the evaluation.

According to the second aspect of the present invention, the measured positron annihilation γ-ray spectrum is integrated by integrating the model function for the peak value distribution of the γ-ray detection signal with the width of each channel of the pulse height analyzer. Since a fitting model for the data is obtained, it is possible to evaluate the true energy distribution without being affected by the quantization by the pulse height analyzer, which has the effect of improving the accuracy and universality of the evaluation.

According to the third aspect of the present invention, the count of each channel of the spectrum data is converted into a value of the approximate curve of the continuous distribution before the peak value is quantized in the channel, thereby obtaining a value corresponding to the peak value. Since data suitable for fitting with the model can be obtained, it is possible to evaluate the true energy distribution without being affected by quantization by the pulse height analyzer, which has the effect of improving the accuracy and universality of the evaluation .

According to the fourth aspect of the present invention, the energy calibration of both spectral data for performing calculations such as subtraction of the background can be matched by conversion of energy calibration in consideration of the wave height distribution inside the channel. Therefore, it is possible to evaluate the true energy distribution without being affected by the deviation of the energy calibration, which has the effect of improving the accuracy and universality of the evaluation.

According to the fifth aspect of the present invention, the spectral data is convoluted with a distribution function having a variance corresponding to a difference in variance corresponding to the energy resolution. Since the energy resolutions can be matched, it is possible to evaluate the true energy distribution without being affected by energy resolution fluctuations, and there is an effect of improving the accuracy and universality of the evaluation.

According to a sixth aspect of the present invention, the method is specifically implemented by providing the calculation means for performing the positron annihilation γ-ray spectrum analysis according to any one of the first to fifth aspects. Can be.

According to a seventh aspect of the present invention, there is provided a recording medium storing a calculation program for performing the positron annihilation γ-ray spectrum analysis according to any one of the first to fifth aspects. The above method can be effectively implemented when used in combination with the calculation means.

[Brief description of the drawings]

FIG. 1 shows an embodiment of the present invention, in which a positron annihilation γ is shown.
FIG. 4 is an explanatory diagram of a line spectrum data fitting model.

FIG. 2 illustrates an embodiment of the present invention, and is an explanatory diagram of spectrum data measured by setting a sample in a positron source.

FIG. 3, showing the embodiment of the present invention, is an explanatory diagram of spectrum data measured without setting a sample in a positron source.

FIG. 4 illustrates an embodiment of the present invention, and is an explanatory diagram of spectrum data measured by setting a sample on a dummy of a positron source.

FIG. 5 is an explanatory view showing an embodiment of the present invention and showing a device configuration.

FIG. 6 is an explanatory view of a positron annihilation γ-ray spectrum shape evaluation method according to a conventional technique.

[Description of Signs] 1 True broad component model 2 Broad component model convolved with resolution 3 True sharp component model S 4 Sharp component model convolved with resolution 5 Positron annihilation γ-ray peak 6 1077 keV γ-ray peak of Ge-68 7 1173 keV γ-ray peak of Co-60 11 Positron annihilation γ-ray spectrum measurement data 12 Peak central region 13 Peak peripheral region

Claims (7)

[Claims] 1. A function obtained by convoluting a model function for a true energy distribution of a positron annihilation gamma ray with a distribution function having a width corresponding to an energy resolution with respect to measured spectrum data of the annihilation gamma ray. Or a positron annihilation γ-ray spectrum analysis method, characterized by fitting an approximate function of the positron as a model. 2. A function obtained by integrating a model function for the distribution of peak values of a γ-ray detection signal with respect to measured spectrum data of positron annihilation γ-rays by the width of each channel of a pulse height analyzer, or A positron annihilation γ-ray spectrum analysis method characterized by fitting the approximate function as a model. 3. The count of each channel of the measured positron annihilation γ-ray spectrum data in each channel is calculated from the data in the vicinity of the channel, and the value in the channel of the approximate curve of the continuous distribution before the peak value is quantized. To
On the other hand, a positron annihilation γ-ray spectrum analysis method characterized by performing a fitting to a distribution of peak values by a model function. 4. When calculating spectral data such as background subtraction, continuous distribution before peak value quantization is performed on each or both channels of spectral data, obtained from data near the channel. A positron annihilation γ-ray spectrum analysis method, characterized in that the approximation curve is distributed within a peak range corresponding to the channel, and the peak values in these are requantized by an energy calibration common to both spectrum data. 5. When calculating spectral data such as background subtraction, the variance corresponding to the energy resolution of each spectrum data is subtracted from the variance corresponding to the predetermined energy resolution or the worse of the two resolutions. A positron annihilation γ-ray spectrum analysis method, wherein each spectrum data is convoluted with a distribution function having a variance of the measured values. 6. A positron annihilation γ-ray spectrum analyzer, comprising a calculation means for performing positron annihilation γ-ray spectrum analysis according to any one of claims 1 to 5. 7. A recording medium having recorded thereon a calculation program for performing positron annihilation γ-ray spectrum analysis according to any one of claims 1 to 5.