Comparison of the decay constants of ⁵¹Cr with metal, oxide, and chromate chemical states

Abstract

Chromium-51 decays through electron capture, the probability of which is perturbed by its electronic state. We have precisely measured the decay constants (${\lambda}$) of ⁵¹Cr with metal (Cr⁰), oxide (Cr³⁺), and chromate (Cr⁶⁺) to investigate the effects of chemical states on the decay constants of ⁵¹Cr. The value of ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$ was determined to be (6.4 ± 3.7) × 10⁻⁴, whereas the difference less than 1.4 × 10⁻⁴ was observed for ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$.

Introduction

The decay constants of more than ten nuclides from ⁷Be to ²³⁵U^m have been found to be changed with changing environmental factors such as its chemical state [1]. Kakiuchi and Mukoyama [2] reported the change in the decay constant of the electron capture decay nuclide ⁵¹Cr between the two chemical forms CrCl₃ (valence state +3) and Na₂CrO₄ (valence state +6). They also estimated the value for the relative change in the decay constant among Cr⁰, Cr³⁺, and Cr⁶⁺ valence states with a simple theoretical model. The estimation shows that the relative change in the decay constant between Cr⁰ and Cr³⁺ state is approximately equal to that between the Cr³⁺ and Cr⁶⁺ state. However, there is no experimental value of the decay constant of Cr⁰ state so far. In this study, the decay constants of ⁵¹Cr have been precisely measured with Cr⁰, Cr³⁺, and Cr⁶⁺ valence states to investigate the effects of chemical states on the decay constants of ⁵¹Cr.

Experimental

The decay constants of ⁵¹Cr were measured for three chemical forms: chromium metal (Cr⁰), chromium (III) oxide Cr₂O₃ (Cr³⁺), and potassium chromate K₂CrO₄ (Cr⁶⁺). The isotope ⁵¹Cr was produced in the ^natCr(γ, xn)⁵¹Cr reaction.

Target materials were about 100 mg each of Cr metal, Cr₂O₃, and potassium dichromate K₂Cr₂O₇. Each target material was sealed in a quartz tube and irradiated with bremsstrahlung photons. The irradiation was carried out with the electron linear accelerator at Tohoku University. The accelerator was operated at an electron energy of 30 MeV with a mean current of around 0.12 mA during the 8 h irradiation.

After the irradiation, the metal and Cr₂O₃ targets were maintained at 800 °C for 5 h in argon and atmosphere, respectively, with an electric furnace. The K₂Cr₂O₇ target was mixed into 250 mg of a non-radioactive K₂Cr₂O₇ reagent and then dissolved in 3 mL of distillated water. The solution was heated on a hot-plate and alkalified with potassium carbonate to produce ${\text{CrO}}_{4}^{2 - }$. The solution was filtered and the filtrate was evaporated to less than 1 mL on a hot-plate. Finally, a K₂CrO₄ sample was prepared by recrystallization from the solution. The metal, Cr₂O₃, and K₂CrO₄ samples were placed in aluminum cups separately and sealed with an epoxy resin adhesive.

These samples were measured in pairs of Cr₂O₃-metal and K₂CrO₄-metal to reduce the influence caused by the difference of detectors. The sample pairs were set in automated sample changers [3] and alternately placed in front of a high-purity Ge (HP-Ge) detector at intervals of 7,200 s. The procedures were repeated over at least 95 days, which is longer than 3.4 times of the half-life of ⁵¹Cr (27.702 days [4]). A ¹³⁷Cs source was positioned close to the HP-Ge detector as a reference source to correct for influential factors for determination of the half-life such as pile-up effects [5]. The dead-time of the measurement system was from 4 to 8 % at the beginning of the measurement. The internal clock time of the computer for data acquisition was constantly calibrated by a time-standard signal distributed via a long-wave radio transmission station in Japan.

The experiments for each of the sample pair were separately conducted two times.

Results and discussion

The decay constant of ⁵¹Cr was determined based on a reference method using a ¹³⁷Cs source. The ratio R(t) is given by the following equation:

$$ \begin{gathered} R\left( t \right) = \frac{{C_{\text{sample}} (t)}}{{C_{\text{ref}} (t)}}, \hfill \\ C_{\text{sample(ref)}} \left( t \right) = \frac{{\lambda_{\text{sample(ref)}} N}}{{(1 - e^{{ - \lambda_{\text{sample(ref)}} t_{\text{R}} }} )}}\frac{{t_{\text{R}} }}{{t_{\text{L}} }}, \hfill \\ \end{gathered} $$

where C _sample(ref)(t) and $\uplambda_{sample(ref)}$ are count rates of a sample (reference source) at the beginning of each data acquisition and decay constant, respectively. N is the net counts in the objective peak. t _R and t _L are real time and live time, respectively. The decay constant t _sample is described in the following equation:

$$ \lambda_{\text{sample}} = \lambda_{\text{ref}} - a_{\text{slope}} , $$

where a _slope is the slope of the graph of ln R(t) against time.

A typical γ-ray spectrum for a Cr-metal sample measured for the first 7,150 s is shown in the Fig. 1. The ⁵¹Cr γ peak at Eγ = 320.1 keV and the ¹³⁷Cs γ peak at Eγ = 661.7 keV can be observed as two prominent peaks. Other peaks in the spectrum are ascribed to ⁴⁸Cr, which is produced in the ⁵⁰Cr(γ, 2n) reaction, ⁴⁸V, in the ⁵⁰Cr(γ, pn) reaction, and natural background radiations.

Fig. 1

A typical γ-ray spectrum for a Cr metal sample measured for 7,150 s

A typical decay curve for the R(t) obtained using a least-squares fitting procedure and their residuals are shown in the upper and lower panel of Fig. 2, respectively. The residuals of the fit of all the data are within the limit of approximately 0.6 %. The half-life of ⁵¹Cr with the metal form is determined to be 27.68 ± 0.02 days by the weighted average of four samples, which is in good agreement with literature value 27.702 ± 0.004 days [4].

Fig. 2

An example of the decay curve for the 320 keV γ line of ⁵¹Cr (upper panel) and the normalized residuals (lower panel)

Relative differences in the decay constant of ⁵¹Cr obtained from this work and the previous research [2] are shown in the Fig. 3. The relative difference ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$ was determined to be (6.4 ± 3.7) × 10⁻⁴. On the other hand, the difference less than 1.4 × 10⁻⁴ at a 68 % confidence level was observed for ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$. Kakiuchi and Mukoyama [2] reported the value of (5.3 ± 2.1) × 10⁻⁴ for ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$, which is in good agreement with the our value of ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$. It follows from the results that the magnitude of the correlation of the decay constants of ⁵¹Cr with Cr metal, Cr₂O₃, and K₂CrO₄ chemical forms, respectively, are determined to be $\lambda ({\text{Cr}}^{0} ) \approx \lambda ({\text{Cr}}^{3 + } ) < \lambda ({\text{Cr}}^{6 + } )$. In Ref. [2], the relative difference ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 6 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$ and ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$ were estimated to be 2.63 × 10⁻³ and (1.22–1.65) × 10⁻³, respectively, based on a Hartree–Fock-Slater approximation. There is a discrepancy between the simple theoretical estimation and our results not only of quantitative degree but also the qualitative tendency.

Fig. 3

Relative differences in the decay constant of ⁵¹Cr between Cr metal, Cr₂O₃, and K₂CrO₄ chemical forms, respectively

In conclusion, we measured the decay constants of ⁵¹Cr with the Cr metal, Cr₂O₃, and K₂CrO₄ chemical form. The difference less than 1.4 × 10⁻⁴ at a 68 % confidence level was observed for ${{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} \mathord{\left/ {\vphantom {{\left\{ {\lambda \left( {{\text{Cr}}^{{ 3 { + }}} } \right) - \lambda \left( {{\text{Cr}}^{ 0} } \right)} \right\}} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}} \right. \kern-0pt} {\lambda \left( {{\text{Cr}}^{ 0} } \right)}}$, which disagrees with the theoretical estimation in Ref. [2]. For further discussion on the relation between the decay constant and the electron state, higher-accuracy experimental data and more realistic model are required.