Introduction:

Photonuclear reaction (PNR) is useful in many applications of nuclear science. Obtained data from PNRs are important for a variety of current applications of nuclear technology such as radiation shielding, radiation transport analyses, calculations of absorbed radiation doses for the human body, physics of fusion reactors, activation analyses, nuclear waste transmutation, astrophysical nucleosynthesis, and reactor core design as well as in nuclear physics research fields such as nuclear resonances, nuclear state excitation mechanism, identification of nuclear levels and deformations [1-6]. In PNR, target materials are bombarded by high energy photons produced as bremsstrahlung radiation by electron accelerators. These accelerators are relatively small machines. Generally, they are present in many laboratories and hospitals. Irradiation of materials by photon leads to the excitation of nucleus in material. The excited nucleus decays by emitting a particle or photons. At this stage, the residual activity of the final nucleus is measured by a detector system. Determination of the multiple elements, deeper penetrating capability of the photon on the target, and non-destructive structure of the process are the advantages of PNR [7].

The experimental studies on the photon induced reactions began in 1934 [8]. In the past, several activities were carried out which aimed to provide photonuclear data [4] and references therein. However, there are still lack of experimental data. Currently, the Extreme Light Infrastructure – Nuclear Physics (ELI-NP) facility puts it in perspective for more precise data [9]. Beside there can be found an effort of NUBA (Akdeniz University Nuclear Sciences Research and Application Center) for compilation of photonuclear data [6, 10-12]. Within this context the aim of the present study is the contribution of photonuclear data of erbium nuclei. As will be explained later, the neutron capture process of erbium target has been observed in our experiment because of the nature of our experimental setup.

Erbium element, which was used as a target material in this study, has six stable isotopes (¹⁶²Er, ¹⁶⁴Er, ¹⁶⁶Er, ¹⁶⁷Er, ¹⁶⁸Er, and ¹⁷⁰Er). Er isotopes are used in nuclear reactor control rods as a good neutron absorber. Also, erbium is used in yttrium aluminum garnet medical lasers for some medical procedures. In photonuclear reaction processes in which clinical electron linear accelerators (cLINAC) are used, one can expect the capture of the neutrons by the target nuclei because of the abundances of the neutrons in the environment of the experimental area. Because of this reason, we have focused on the possible capture of neutrons by the Er target in our experiment. By analyzing the residual activity of the Er target after bombardment by using cLINAC, the possible neutron capture of ¹⁷⁰Er nucleus in our experiment has been verified. The half-life of the ¹⁷¹Er nucleus and five transition energies of its daughter nucleus have been determined as consistent with adopted values in literature.

Experimental Section:

The experiment consists of two steps, including the irradiation of Er target and measurement of residual activity. For the activation of the Er target a cLINAC (ElektaTM SynergyTM) of NUBA (Akdeniz University Nuclear Sciences Research and Application Center) is used. The generated primary electrons (50 keV) are accelerated in a cooper cavity by 30 GHz RF with about 5 MW peak power. The bremsstrahlung photons are produced in such a way that electrons in the beam hit the tungsten target and are stopped there. Uniform and forward focused photons can be obtained by its flattening and collimating. In these type of experiments, about a half of the kinetic energy of electrons is converted to the bremsstrahlung photons [2]. In the second step of the experiment, an HpGe (AMATEK-ORTEC) p-type coaxial detector with an electrical cooling system is used for measurement of residual activity. The detector system is connected to the bias supply, an amplifier, an analog-to-digital converter, and a computer. The detector is placed into a 10 cm thick lead shield and the inner surface of the shield is covered by a 2 mm thick copper foil in order to protect the detector from X-rays arising in lead. The FWHM values are 0.77 keV for 122 keV of ⁵⁷Co and 1.85 keV for 1332 keV of ⁶⁰Co. The relative efficiency of the detector is 40%. The energy calibration of the detector is done by using the standard Na, Mn, Ba, Cs, and Co calibration sources.

Immediately before and after sample counting, a set of calibration sources were measured. The aim of second calibration-sources measurement was to check the stability of the electronics and the measurements. In this way, we were able to track any channel shift during the measurement and also, through combining the before and after calibration results, eliminate or reduce any systematic errors coming from the channel shift. The data acquisition was performed with MAESTRO software, the peak analysis was performed with RadWare code [13], and the energy calibration was performed in ROOT [14]. With these three programs we determined the centroids, areas, and energies as well as their respective uncertainties for all peaks found in a spectrum. We note that the ROOT fitting procedure takes into account both the uncertainties in energy as well as the centroid according to the effective variance method. In this experiment, the Er powder sample is used as a target material. It consists of a mixture of six stable isotopes ¹⁶²Er, ¹⁶⁴Er, ¹⁶⁶Er, ¹⁶⁷Er, ¹⁶⁸Er, and ¹⁷⁰Er with 0.14%, 1.61%, 33.61%, 22.93%, 26.78% and 14.93% natural abundances, respectively. 25 g powder sample of Er in a small isinglass is placed 60 cm away from the photon source and it is bombarded with continuous bremsstrahlung photons with 14 MeV endpoint energy and with neutrons from a tungsten target after (γ,n) photonuclear reactions. The exposure time was 45 minutes and purification was not considered.

A clinical linear accelerator is a tool that provides sufficient photon intensity for performing photonuclear reactions. Clinical linear accelerators have been used for many experimental studies in literature [10-12, 15-20]. On the other hand, a clinical electron accelerator is a good neutron source. We get about 9000 neutron/cm²s at 100 cm distance for the clinical electron accelerator used in the present experiment. In Fig. 1, our measurement of the thermal neutron flux is shown. About 30-50% of neutrons come from the tungsten target where neutron flux is about 10¹⁰-10¹¹ neutrons/s. Besides, possible (γ,n) photonuclear reactions in our experiment can release neutrons and this can be thought of as an additional neutron source. There are about 1000 times less photons hitting the erbium than tungsten so if tungsten contributes 9000 neutron/cm²s, erbium will contribute ~9. Thus, these neutrons can lead neutron bombardment of Er material and stable Er isotopes can absorb neutrons. Because ¹⁶²Er and ¹⁷⁰Er in Er target material can convert into unstable isotopes ¹⁶³Er and ¹⁷¹Er, after absorbing a neutron in this experiment, neutron absorption of two stable isotopes ¹⁶²Er and ¹⁷⁰Er are candidates for observation. However, observing of neutron absorption of ¹⁷⁰Er is the most possible one when low natural abundance of ¹⁶²Er (0.14%) in sample is considered. After a neutron capture of ¹⁷⁰Er, it is converted to ¹⁷¹Er. ¹⁷¹Er decays into ¹⁷¹Tm with beta decay. Adopted half-life for this decay is 7.516 hours [21]. In our experiment, total counting time is 75.98 hours which can be enough for determination of ¹⁷¹Er half-life. For this purpose, counts of gamma peaks of ¹⁷¹Tm are used.

Fig. 1Full-screen View

(Color online) Thermal neutron flux of the clinical electron accelerator used in the experiment as a function of distance (as determined by an independent In-Cd foil measurement).

Results and Discussion:

For our experiment, a possible path for observing neutron absorbtion of ¹⁷⁰Er is given in Eqs. (1-3). A stable ¹⁷⁰Er nucleus is converted into an unstable ¹⁷⁰Er^* nucleus after absorption of a neutron. The ¹⁷¹Er^* nucleus transforms to ¹⁷¹Tm^* by beta decay. The half-life of ¹⁷¹Tm is 1.92 years and it transforms to ¹⁷¹Yb by beta decay [21]. Because of this long half-life of ¹⁷¹Tm, the half-life of ¹⁷¹Er can be determined by analyzing the corresponding gamma-ray peaks of ¹⁷¹Tm. In the present study, the analyses have been made by using the RadWare package [13]. It shows the gamma ray spectra and gives possibility to fit each peaks. The energy, centroid, FWHM, area, background, and errors information can be obtained from the RadWare program after fitting desired peaks. Statistical errors represent the uncertainty in both the photopeak position and energy calibration where systematic error come from the difference in the before and after calibrations caused by the channel drift during the experiment. Statistical errors dominate in most of the cases. Detailed analysis on calibration and how the transition energies and corresponding uncertainties are obtained can be found in Ref.[11].

In Fig. 2, the gamma-ray spectrum of photonuclear reaction products of Er nuclei is shown. Five gamma peaks of ¹⁷¹Tm (111.63 keV, 124.07 keV, 277.50 keV, 308.314 keV, and 907.7 keV) are visible in the spectrum. The energy peak of 308.314 keV arising from the 7/2^- to 5/2⁺ transition in ¹⁷¹Tm has been analyzed by using RadWare package. It has been fitted to the skewed Gaussian shape and smoothed with step function.

Fig. 2Full-screen View

Gamma-ray spectrum of photonuclear reaction products of erbium obtained from the HPGe detector.

Thus, the peak value of this transition originated from ¹⁷¹Tm has been determined as 308.314 keV. By the similar way, the energy peaks arising from 5/2⁺ to 3/2⁺, 7/2⁺ to 3/2⁺, 5/2⁺ to 7/2⁺, and 5/2⁺ to 3/2⁺ transitions in ¹⁷¹Tm have been also analyzed. The gamma-ray energy peaks belonging to ¹⁷¹Tm with their error values are listed in Table 1. Also, Table 1 includes present adopted values with systematic errors in literature [19]. The uncertainties are shown in brackets by considering the last significant digit. As can be understood from Table 1, the results are found in good agreement with adopted values in the literature. It should be noted that the errors of gamma peaks of 277.50 keV, 308.314 keV, and 907.7 keV obtained in the present study are less than those of literature value.

The half-life value can be determined by looking at the peak area change at constant time intervals [11]. The evolution of the peak counts with time have been analyzed for determination of the half-life of the parent nucleus (¹⁷¹Er), after accurate determination of the peaks. For this purpose, the most intensive peak of ¹⁷¹Tm (308.11 keV) originating from 7/2⁺ to 5/2⁺ transition has been chosen (Fig. 3).

Fig. 3Full-screen View

The most intense 308.314 keV peak used for determination of ¹⁷¹Er half-life.

The growth curve of the counts in the peaks belonging to the daughter nucleus is related to the decay curve of the unstable parent nucleus. The change of peak area obtained in this way exhibits the same functional dependence as the activity and can thus be fitted with a simple exponential function (A(t) = A₀e^{- λ t}). By considering logarithmic values of the counts, a simple linear fit has been used to determine the half-life (T_1/2=ln2/λ). The fit for the 308.314 keV peak of ¹⁷¹Tm is shown in Fig. 4. The half-life value shown in the present study has statistical uncertainty only since all of the uncertainty is provided by a single fitting procedure. The value 7.48(6) h for the half-life of ¹⁷¹Er has been obtained by taking the formula T_1/2=ln2/λ into account in the present study. This result is in harmony with the literature value 7.516(2) [21].

Fig. 4Full-screen View

The decay curve of ¹⁷¹Er obtained from the 308.314 keV peak.

Conclusion:

In conclusion, one neutron absorption of the ¹⁷⁰Er nucleus has been observed in our experiment by activation of stable Er nuclei with bremsstrahlung photons. This absorption leads to the transformation of ¹⁷⁰Er to ¹⁷¹Er^*. Later ¹⁷¹Er^* decays into the unstable ¹⁷¹Tm^* nucleus with beta decay and unstable ¹⁷¹Tm^* releases gamma rays to be stable. Five gamma-ray peaks of the ¹⁷¹Tm nucleus (111.63 keV, 124.07 keV, 277.50 keV, 308.314 keV, and 907.7 keV) have been determined in the present study. The half-life of ¹⁷¹Er isotope has been found as 7.48 h by analyzing the decay curve of ¹⁷¹Er obtained from the 308.314 keV gamma peak. The gamma-ray energies of ¹⁷¹Tm and the half-life of ¹⁷¹Er have been determined in agreement with the literature values. Furthermore, this study shows usefulness of the method and equipment, i.e. cLINAC, in determination of the energies and half-lives of the isotopes. And this method can be used in education and training young physicists when we do not have a nuclear reactor.