Resonance parameters of the reaction 12C(d,p[gamma])13C in the vicinity of 1450 keV for accelerator energy calibration

1 Resonance parameters of the reaction 12C(d,p)13C in the vicinity of 1450 keV for accelerator energy calibration L. Csedreki1*, G. Á. Szíki2, Z. Szikszai1, I. Kocsis2 1Institute for Nuclear Research, Hungarian Academy of Sciences, MTA Atomki H-4001 Debrecen, P.O. Box 51, Hungary 2University of Debrecen, Faculty of Engineering, Department of Basic Technical Studies, H4028 Debrecen, Ótemető u. 2-4, Hungary *) Corresponding author. Tel.: +36 52 509200; fax: +36 52 416181. E-mail address: c[email protected] (L. Csedreki). Abstract The observed resonance parameters of the 12C(d,p)13C reaction in the vicinity of 1450 keV deuteron energy have been determined in a thorough procedure, fitting our recent experimental excitation curve, as well as earlier literature data with the Root Software Package. The resulting energy and width (FWHM) of resonance are 1445.8 ± 0.2 keV and 5.3±0.4 keV, respectively. We propose the application of this resonance as a precise and simple method for accelerator energy calibration when performing DIGE analysis. PACS: 29.30.-h; 25.45.-z; 82.80.Ej; 25.45.De Keywords: 12C(d,p)13C reaction, resonance parameters, accelerator calibration, DIGE Introduction and motivation The accurate energy calibration of low energy particle accelerators is a basic requirement in the field of Ion Beam Analysis (IBA) and low energy nuclear physics. Several absolute methods can be applied for particle accelerator energy calibration, for example measuring narrow nuclear reaction resonances and/or neutron threshold [1], using 2 non-resonant nuclear reactions [2], cross over techniques at higher energies [3], and techniques based on Rutherford backscattering spectrometry (RBS) [4]. To our best knowledge, using deuteron beams, only the 16O(d,n)17F reaction at 1829.2±0.6 keV threshold energy has been applied for the precise absolute energy calibration of accelerators [5]. The implementation of the neutron threshold reaction is rather complicated since the high background of neutrons from d+d reactions can hide the small neutron yield around the threshold energy, as we observed earlier [6]. Therefore, a narrow nuclear reaction resonance, detecting gamma-rays, is preferable. In our laboratory, we are continuously working on the precise determination of thick target gamma ray yields and excitation functions of several nuclear reactions for analytical purposes [7-12]. In the framework of a Coordinated Research Project organized by the International Atomic Energy Agency (IAEA-CRP) [13], we measured the excitation function for the 3089 keV gamma line of the 12C(d,pγ)13C reaction, as well as for the particles from the 12C(d,p1)13C, 12C(d,p0)13C and 12C(d,d0)12C reactions in the 0.74-2.0 MeV energy range. The results were presented in ref. [12]. For the 12C+d nuclear reactions in the studied energy range, a pronounced compound nucleus mechanism is present besides the direct mechanism. Consequently, certain resonances appear in the excitation function. Close to 1450 keV deuteron energy, a fairly narrow and quite intense resonance can be observed. The existence of this kind of narrow and strong resonance with well-defined energy is unique among the deuteron induced nuclear reactions. As the preparation of a carbon target is simple, this nuclear resonance is a possible option for accelerator energy calibration using gamma-ray detection. With this method, the necessity of measuring a narrow proton resonance before switching to a deuteron beam can be avoided. Nevertheless, to apply this resonance for energy calibration, its position has to be determined as accurately as possible. The energy of this resonance had been established earlier as 1449.5±1.5 keV with a width of 7.0±0.5 keV [14] based on the work of Tryti et al. [15]. Tryti’s work focused on the angular distributions of protons, obtained from the shape of the Doppler-shifted γ-lines, aiming to gain insight to the complex character of the reaction. The resonance energy parameters were obtained by a meticulous procedure of expressing the differential cross-sections in terms of Legendre polynomials and studying the energy dependence of the polynomial coefficients [15, 16]. This work gave invaluable information on the nature of the reaction; however, looking at all the present time available experimental data, we think that it is indispensable to re-assess this resonance and establish the resonance 3 energy (and the other resonance parameters) anew, with a straightforward approach which is also applicable in a routine analytical setting. The observed shape of resonance in the excitation function depends on several parameters, such as the energy of resonance (ER), the width of the resonance (Γ), the cross section at the resonance energy (σR) and the loss of energy in the target (ξ). The dependence of the excitation function of these parameters was given in ref. [17], and a detailed mathematical description of the problem was also presented there. Beside the compilation and evaluation of the existing literature data, we measured the excitation function of the 12C(d,pγ)13C, 12C(d,p1)13C and 12C(d,d0)12C reactions in the 14101500 keV energy range using a self-supporting carbon foil with 20 µg/cm2 thickness. Moreover, in order to check the reliability of our experimental set-up and the applied fitting and evaluating process, the excitation function of the 23Na(p,p’γ)23Na reaction was measured in the 1900-1959 keV energy range and the parameters of the 1931 keV resonance were determined and compared with literature data. This work was carried out as a part of the measurement of the excitation function of the 23Na(p,p’γ)23Na reaction in the 1800-3000 keV energy range. The final excitation function with the detailed description of the experimental condition will be published later. Experimental procedure The measurements were carried out at the 5 MV Van de Graaff accelerator of MTA Atomki. The available ions for analysis are H +, D +, and 4He +. The assortment of ions and their energy range provided by the accelerator make it possible to apply most of the ion beam analytical techniques: PIXE, PIGE, RBS, Scanning Transmission Ion Microscopy (STIM), Elastic Recoil Detection Analysis (ERDA) etc. A self-supporting carbon foil (thickness: 1.0×1018 atom/cm2) with an evaporated palladium layer on its surface (thickness: 2.2×1017 atom/cm2) was used as a target for the measurement of the excitation functions of 12C+d reaction. Due to some properties of the sample, the measurements of the 12C+d reaction were carried out on the target with the top of the Pd layer, which caused a systematic alteration in the resonance parameters. Therefore, the correction of the resonance energy was necessary based on the stopping power of deuteron beam in the Pd layer. The energy loss (4.4 keV) was calculated with the SRIM code [18]. 4 Moreover, a thin film of NaCl (thickness: 8.4×1017 atom/cm2) evaporated on a self-supported thin film of Ag was used for the measurement of the excitation function of the 23Na(p,p’γ)23Na reaction in the 1900-1959 keV energy range. Since the parameters of the included 1931 keV resonance have well established values in the literature, the reliability of our experimental arrangement, fitting and evaluating process could be checked. The number of target nuclei was determined with RBS technique using alpha beam of 1.5MeV energy. The uncertainty of target thickness determination was 2.5%. For the detection of gamma-rays, a Canberra Model GR4025-7600SL coaxial type HPGe detector (crystal: 59.5 mm diameter, 170 cm3 volume) was applied at an angle of 55° relative to the incident beam direction with a distance of 9.5 cm between the front face of the crystal and the target. Particles from Rutherford backscattering and nuclear reaction were detected with an ORTEC Ion Implanted Silicon detector with 13 keV energy resolution. For the elimination of high intensity backscattered particles, we used a copper collimator with a diameter of 3 mm in front of the particle detector. The number of bombarding particles (Np) was determined via the measurement of the incident charge on the target chamber, which was an ideal Faraday cup. For a more detailed description of the experimental setup and also for the procedure of the determination of the absolute efficiency of HPGe detector (εabs) and the solid angle of the Si detector (Ω), see ref. [11]. The uncertainty of the determination of Np (stochastic and systematic uncertainties together) was taken into account with 3%. The uncertainty of εabs and Ω were taken into account also with 3%. The energy of the beam, as well as its energy stability was regularly assessed measuring the 991.81±0.04 keV resonances in the 27Al(p,γ)28Si reaction. Data fitting process The fitting process of the excitation function of the 12C+d and 23Na(p,p’γ)23Na reactions around the resonance energies (~1450 keV and ~1931 keV, respectively) was performed using the Minuit part of the Root Software Package [19] after careful background subtraction. This software is capable to take the uncertainties of cross section data into account, thus to calculate the uncertainties of the fitted resonance parameters. We followed basically two different ways of background subtraction. In the case of the 12C+d reaction, the excitation function was fitted with the model function p(E) given by Equation 1 typically in the 1440-1470 keV energy range using linear background subtraction (see Equation 2). 5 𝑝(𝐸)=  𝑅  2(𝑡𝑎𝑛−1𝐸−𝐸𝑅  /2 −𝑡𝑎𝑛−1𝐸−𝐸𝑅−   /2 )  (1), 𝐼𝑖𝑛𝑏𝑔(𝐸)=𝑎𝐸+𝑏 (2) where E is the incident particle energy, Γ is the full width of resonance at half maximum intensity, ER is the resonance energy, σR is the cross section at the resonance energy and ξ is the loss of energy in the target. Figure 1 shows an example for the fitted excitation function in the case of 12C(d,pγ)13C reaction (our measurement). Thus the excitation function (excit (E)) can be modelled as: 𝑒𝑥𝑐𝑖𝑡(𝐸)=𝑝(𝐸)+𝑙𝑖𝑛𝑏𝑔(𝐸) (3) We derived Equation 1 from Equation 14 in literature [17] converting the expressions to give cross section values instead of yields. In the case of the 23Na(p,p’γ)23Na reaction, the excitation function was also fitted with the model function p(E) (equation 1.) typically in the 1900-1959 keV energy range after the subtraction of a two order polynomial background (equation 4., Figure 2). 𝑝𝑜𝑙𝑏𝑔(𝐸)=𝑐𝐸2+𝑑𝐸+𝑓, (4) Thus, the excitation function can be modelled as: 𝑒𝑥𝑐𝑖𝑡(𝐸)=𝑝(𝐸)+𝑝𝑜𝑙𝑏𝑔(𝐸), (5) In the case of the excitation function of Tryti [15, 16] and Elekes [20], all the parameters (ER, σR, Γ, ξ) were fitted together due to the uncontrolled or obviously incorrect target thicknesses (ξ). In the case of our recent measurement and ref [12], because of the reliable experimental target thickness data, only three parameters (ER, σR, Γ) were fitted and ξ was a fixed parameter. For the details of the computations we refer to the software manual, available online [Minuit 2, Fred James and Matthias Winkler, CERN, Geneva/http://root.cern.ch/drupal/content/minuit2-manual-600]. Results and discussion 6 Table 1 shows the integrated result of the fitting process in the case of the ~1450 keV and ~1931 keV resonance of the 12C+d and 23Na(p,p’γ)23Na reactions, respectively, complemented with some other experimental and literature data. The data included in Table 1 are the following:  source of data,  type of nuclear reaction,  energy loss in the target at 1450 keV or 1931 keV incident particle energy calculated from published or measured experimental thickness data using SRIM 2013 software (the given uncertainties include the uncertainty of thickness measurement (~3%) and SRIM calculation (<4%).  number of data points in the resonant peak (expected minimum number for the fitting process is 4),  parameters fitted with Root Software: resonance energy, resonance width, cross section at the resonance energy, energy loss in the target at 1450 keV or 1931 keV particle energy, square of the correlation coefficient (R2). We note that in the case of our measurements, the resonance energies were corrected with the energy loss in the palladium layer. The calculated values of ER=1931.80.1and Γ=5.70.2 in the case of the 23Na(p,p’γ)23Na reaction are consistent (within two sigma uncertainty) with the literature data (ER=1930.70.8 and Γ=6.90.5 [21]). This result confirms the reliability of our experimental set-up and the applied fitting and evaluating process. From the data for the 12C(d,pγ)13C reaction (ref. 12, 15, 16, 20 and Csedreki et al.) in Table 1, we determined the resonance energy and width (FWHM) of the ~1450 keV resonance calculating the weighted averages. The final uncertainty of the resonance energy and width was calculated as: 𝜎=√1 ∑1 𝜎𝑖2 𝑛 𝑖=1 (7) where σ is the error of the weighted average, σi is the uncertainty of each parameters. The final, accepted data are the following: 7 𝐸𝑅=1445.8 ± 0.2 keV ,  =5.3 ± 0.4 keV To determine these new values, all the available, well-established experimental data that we could find in the literature and we succeeded to fit were taken into account. Some data were omitted from the fitting process because of the obviously incorrect energy calibration or insufficient number of data points in the resonant peak. Moreover, in one case we were unable to fit the excitation function. The omitted data are presented in Table 2. In the case of particle production cross sections, the angular dependence of the reactions may affect the observed resonance parameters through the interference of different resonances. Thus, to determine the resonance parameters, the complex description of the reaction is necessary, using R-matrix calculations. However, this time-consuming and indepth approach is hardly applicable in the IBA practice. Conclusion In this work, we systematically studied the resonance of the 12C(d,pγ)13C reaction in the vicinity of 1450 keV as a potential choice for accelerator energy calibration for deuterons. On the one hand, we measured the excitation functions of the 12C(d,pγ)13C, 12C(d,p1)13C and 12C(d,d0)12C reactions, simultaneously detecting the resulting particles and gamma-rays. On the other hand, we collected the literature data on the ~1450 keV resonance of the above reactions. On the basis of 5 different datasets (3 from literature and 2 from our own measurements, using gamma-ray detection) for the region around 1450 keV, applying a fitting and weighted averaging process, we obtained 1445.8± 0.2 keV and 5.3±0.4 keV for the resonance energy and width, respectively. 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The experimental data are from our own measurements detecting gamma rays from the 3089 keV line. The obtained ER=1451.3±0.2 keV should be corrected with the Pd layer thickness. The correction resulted in the value ER=1446.90.2 keV. Error A and B dashed lines show the 1sigma uncertainty of the resonance energy. Fig. 2 Fitting process of the excitation function of the 23Na(p,p’γ)23Na reaction at ~1931 keV. The figure includes the results of the fitting process with the calculated and literature data of resonance parameters and also the polynomial background. Error A and B dashed lines correspond to the 1sigma uncertainty of the resonance energy.