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Application of the method of adding amplitudes of coincident pulses to study the cascaded gamma decay of YB and SM nuclei at the Dalat-2 nuclear reactor

formation and decay to lower levels. Experimental information is the basis for evaluating and verifying theoretical models of nuclear data and structure. Currently, nuclear data and structure studies based on the (n, ) reaction are mainly conducted on nuclear reactors and on some accelerators. The problem can be divided into two directions:

- Theoretical calculation direction: organize editing, re-evaluate reaction data, evaluate verification and develop theoretical models to describe reaction cross-section, level density, level width, gamma decay force function,...

- Experimental direction: conduct experimental measurements on neutron beams of different energies, on sample targets to determine the energy, intensity and lifetime of excited states with the best possible accuracy.

The results of experimental studies depend almost entirely on the quality of the spectrometer systems.

Because the interaction of gamma radiation with matter - specifically with the detector material - is subject to three main effects: photoelectric absorption, Compton scattering and pair production, the gamma radiation spectrum obtained is always complex. For that reason, there are several different types of gamma spectrometers aimed at reducing background, eliminating the influence of unwanted effects to obtain useful information. In the general review of research methods, some commonly used gamma spectrometers and their advantages and disadvantages will be presented.

I.1.1. Single crystal gamma spectrometer with ultrapure semiconductor detector


The HPGe ultra-pure semiconductor detector has the obvious advantages of not having to be continuously stored in liquid nitrogen, and at the same time the energy resolution and recording efficiency are also much higher than diffuse semiconductor detectors of the same volume.

The use of a semiconductor detector in a single-crystal gamma spectrometer is very simple. The main configuration of the measuring system is shown in Figure 1.2:


Figure 1.2: Block diagram of a single crystal semiconductor gamma spectrometer .

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The semiconductor detector is coupled to a spectrum amplifier. The signal at the output of the detector is amplified in amplitude and shaped appropriately for the ADC to analyze the peak amplitude of the pulse. The MCD coupling system will collect the data after the ADC has finished converting and put it into the memory cell. The number of pulses with the same amplitude value corresponds to the number of energy values ​​of gamma quanta absorbed by the detector. When gamma radiation interacts with the detector, the amount of energy absorbed by the detector depends on the interaction process that occurs. Usually, the interaction process is one of the three interaction effects below:

- The detector completely absorbs the energy of the gamma quantum according to the

photoelectric effect


- The detector absorbs only a part of the gamma energy according to the compton effect - because the compton scattering angle changes in a wide range from 0 to 180 0 , the absorbed energy is also in a wide range and does not form a peak (here there may also be multiple compton scattering leading to the entire energy of the gamma quantum being absorbed and this process also contributes to the peaks appearing due to the photoelectric effect).

- The pair production effect appears when the gamma quantum energy is greater than 1022 keV. The interaction process according to the pair production effect produces electron - positron pairs. Inside the detector, the electron's travel distance is very short and the electron's energy will be quickly absorbed. The positron, after slowing down, will quickly annihilate, creating two 511 keV gamma quanta. If both

If both gamma quanta are absorbed, this process is equivalent to photoelectric absorption. If one of the two gamma quanta is released, the absorbed energy will form a single escape peak, if both gamma quanta are released, the absorbed energy will form a double escape peak. Thus, the pair creation process of a transition will contribute two more peaks in addition to the total absorption peak and a continuous background due to Compton scattering when there is pair annihilation. Figure 1.3 shows the gamma radiation spectrum of 35 Cl(n, ) 36 Cl. To evaluate the quality of the peak, people often use the ratio of peak area to background and many times the count of the Compton background is many times larger than the peak area. Therefore, the error in determining the peak cross section - transition intensity increases significantly.


Figure 1.3: Instantaneous gamma emission spectrum of 36 Cl measured with a single crystal spectrometer .


The gamma radiation spectrum in Figure 1.3 shows: The Compton background is large and complex, not simply decreasing linearly with increasing energy. The number of peaks is very large, including single and double escape peaks that are very strong and often much stronger than the total absorption peaks with nearby energies. Thus, the determination of small-intensity transitions will be subject to two major sources of error: Error due to the background and error due to the influence of strong transitions.

In the study of nuclear structure from the transitions obtained in the single crystal gamma radiation spectrum, it is impossible to arrange the excitation level diagram because the order of the transitions is not known. With the transitions measured in this spectrum, it is impossible to determine which transitions are primary, which are secondary, which transitions belong to the cascade decay pair... Therefore, it is also impossible to evaluate parameters such as nuclear level density, gamma transition force function... In addition to the reasons of peak-to-background area ratio, the complexity of the spectrum, the above-mentioned reason is the most important for developing research methods using semiconductor detectors to record gamma radiation.

I.1.2. Compton background-reduced gamma spectrometer

Compton background-reduced tandem gamma spectrometers have a simple structure as shown in Figure 1.4. The system consists of a main detector, surrounding auxiliary detectors and electronic blocks to control the gamma radiation recording process according to the signals from the detectors. Because the information obtained about the measured object is mainly located in the photoelectric absorption peaks, Compton background-reduced tandem spectrometer systems are widely used.


Figure 1.4: Compton background-reduced tandem spectrometer [69].

The operating principle of the complex measuring system as shown in Figure 1.4 is that the Compton scattered gamma quanta leaving the main detector will be covered by the auxiliary detectors.

surrounding detectors. Pulses from the surrounding detectors will block the main detector from being recorded for a certain period of time depending on the time resolution of the system. If there is no pulse from the surrounding detectors, the main detector pulse will be recorded (which is considered to correspond to complete absorption). To improve the ability to reduce background in the spectrum, attention should be paid to the following two important issues:

* The more efficient the surrounding detector system is, the better: If 30% of the gamma quanta after Compton scattering are absorbed, the background is reduced by 30%. With the best systems today, the Compton background is reduced by about 30 to 50%.

* The system needs to be carefully shielded because high gamma background will lead to a reduction in the ability to record useful events due to random coincidences. At the same time, the time resolution of the system must also be increased to reduce random coincidences. We know that the random coincidence rate N nn = 2 N 1 .N 2 . where N 1 is the counting rate at detector 1, N 2 is the counting rate at detector 2, is the width of the coincidence (or anti-coincidence) time window. Thus, to reduce the influence of random coincidences, we need to reduce all 3 parameters above by shielding and increase the working speed of the electronic system. Of course, due to the nature of the interaction process, with semiconductor detectors, the coincidence window cannot be smaller than a certain value that is specific to the measurement system. Since the speed of the electronic system is usually very large, the effect on the time resolution of the electronic system is negligible compared to the travel time of the electrical load elements in the detector; the minimum value of is usually taken to be about 3 times the detector time (the distance between the two electrodes divided by the drift speed of the main electrical load elements corresponding to the selected working high voltage value of the detector).

I.1.3. Compton spectrometer

Compton scattering can also be used in another way to measure the radiant energy of gamma rays. When an incident gamma ray with energy h 0 interacts with an electron by Compton scattering, the energy of the recoil electron (which the detector absorbs part of the energy) corresponding to the scattered gamma quantum that flies out at a fixed angle is determined as follows:

E h ⎡

1 ⎤ MeV;


with 0 =

h 0


(1.1)

0 ⎢ 1

⎣

1 0

(1 cos ) ⎥


0

MC 2


⎦

Thus, the energy of the recoil electron depends only on the energy h 0 of the incident gamma quantum when the scattering angle remains constant. Constructing the measuring system in this direction also allows to reduce the background due to Compton scattering. Figure 1.5 shows the arrangement of the detectors in a Compton spectrometer.


Figure 1.5: Detector arrangement in a compton spectrometer .

Two detectors I and II are placed so that the line connecting the centers of the two crystals forms an angle with the direction of the original gamma ray beam. Detector I is called the analyzing detector, it records the recoil electrons in the Compton scattering effect. Detector II is called the control detector, it records the gamma quanta scattered from detector I with the scattering angle . The process of generating flashes in the control crystal and the analyzing crystal is simultaneous. Therefore, thanks to the diagram

For analysis, it is possible to select the pulses caused by recoil electrons with scattered gamma quanta flying out at angle . The energy of the recoil electrons depends monotonically on the energy of the initial gamma quanta when the scattering angle is fixed, so it is possible to determine the energy of the initial gamma quanta according to the energy of the recoil electrons. In Figure 1.6 are spectra illustrating the background reduction capability of the Compton spectrometer with NaI(Tl) scintillation detectors [69].

Figure 1.6: Spectra measured with a single crystal spectrometer (a, b) and spectra measured with a Compton spectrometer (c, d) of Cs 137 and Mn 54 .

From the diagram in Figure 1.5 we see that the scattered gamma quanta fall on the control detector not only at angle but also at  . Therefore, fluctuations will appear in

the energy spectrum of the recoil electron and thus introduces additional error in determining the energy of the initial gamma quantum.

To reduce fluctuations when determining the recoil electron energy, it is necessary to reduce the solid angle  , and to increase the recording efficiency, this solid angle must be increased. To reduce the error in determining the recoil electron energy, the authors in [4] placed the control detector at an angle greater than 150 0 .

I.1.4. Paired generation spectrometer

In some cases of recording high-energy gamma radiation, a pair-forming spectrometer can be used to improve recording efficiency and reduce background. The physical process occurring in the recording detector is as follows: The electron-positron pair generation phenomenon occurs in the recording detector. Due to the high density of the material that makes up the detector, after losing energy, the positron will quickly annihilate and create two 511 keV gamma quanta flying in opposite directions. If the pairs of detectors are placed 180 0 opposite to each other around the main detector, when the pair generation phenomenon occurs, the recording detector will produce an electric pulse with an amplitude proportional to

E - 1022 keV (if two gamma quanta annihilate at 511 keV leaving the detector) or E - 511 keV (if only one 511 keV gamma quantum leaves the detector) or E (if no 511 keV gamma quanta are emitted from the main detector). Thus, choosing the recording method of 2 pulses from opposite pairs of detectors (corresponding to 511 keV gamma quanta) unlocking the coincidence allows the analysis of the pulse amplitude from the main detector. Only pulses with amplitudes corresponding to the energy E - 1022 keV (corresponding to the occurrence of the pair phenomenon) is recorded. This allows to completely reduce the compton background, single escape peaks and complete absorption peaks in the obtained gamma spectrum. Thus, the gamma spectrum will be much simpler and when processing the spectrum, it is necessary to add 1022 keV to the position of each peak.

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