Observations on the long-lived Mossbauer effects of ^93mNb

Abstract

Several observations of the Nb long-lived Mossbauer phenomena are presented, in consequence of an irradiation increased by an order of magnitude compared with previous work. These are 1) two β decays of ¹⁸²Ta and ^92mNb are enhanced, i.e., ¹⁸²Ta is now 200 times faster than in previous results while ^92mNb is twice as fast as normal; 2) γs emitted from two β decays compete to eject electrons in a winner-takes-all rule, rather than by superposition; 3) abrupt spectral changes reveal three decay phases of ¹⁸²Ta; 4) the biphoton γγ of ^93mNb is released from the sample for the first time; 5) the γγ distribution is narrow, in contrast to the broad γγ spectrum obtained from independent nuclei; 6) Nb K-lines super-radiate along the long sample axis; 7) collective scattering of multipolar MeV γs. The manipulation of nuclear decay speeds demonstrated here highlights a potential application of this work in cleaning up the nuclear wastes.

Introduction

To explain the resonant absorption of long-lived Mossbauer effects mediated by the biphoton γγ^1,2,3, a theory has been developed to interpret the variety of available experimental observations. A brief introduction to the physics of this theory and its extension to 4 entangled γs is required. Results of ^93mNb experiments presented now reconfirm the large number of ^103mRh observations made before 2008^1,3, which are briefly summarized in the Supplementary information.

In the multipolar nuclear transition of long-lived Mossbauer nuclides⁴, simultaneous γγ occur in opposite directions to preserve the γ energy by eliminating their recoil energy. Once resonant absorption occurs between two identical nuclei in the same neighbourhood, the probability of spontaneous γ emission yields a superradiant factor of ⁵. The spontaneous γγ emission thus becomes -fold effective in a crystal containing N identical nuclei in resonance⁶.

Delocalised γγ absorb N phonons to acquire a mass, in the form of the so-called nuclear exciton¹, having an emerging magnetic quantum number of m = 0⁷. The exciton spreads in a region containing N/M identical nuclei in a micron range with M (∼10¹²) excitons and N (∼10²²) nuclei in a crystal.

The AC Stark effect produces Rabi sidebands around the characteristic γs, regardless of atomic or nuclear transitions^1,3. Mollow triplets³ were observed for Rh K-lines and ^103mRh γ at 39.8 keV. The vacuum Rabi oscillation Ω_R for M/N ≪ 1/2 is so fast that the recoil phonon never leaves, leading to an entanglement between γγ and the phonon². The superradiance has an Avogadro number of N rather than N^1/2, resulting from the superposition of N nuclei × N phonons in resonance¹. A detailed evaluation provided in the Supplementary information reveals the ^103mRh superradiance ∼10²⁸ ≫ N. The old model of ^103mRh given in the previous report¹ is therefore incomplete.

Neither ^93mNb γγ nor its Rabi splitting has previously been observed^1,2, and till now the exact value of Ω_R has not been known. Nevertheless, Ω_R must be greater than 30 meV in order to survive the thermal agitation at room temperature. Assuming that the M4 Γ_γγ/Γ_γ branching ratio is mainly attributed to the low-lying E2 Raman transition as well as the nuclear size^8,9, we fine-tuned the value of the ¹³⁷Ba 11/2⁻ excited state for ^93mNb to 10⁻⁶. Four factors, i.e., the 30-meV Ω_R, the 16-year half-life, the internal conversion, and the Γ_γγ/Γ_γ branching ratio, give a γγ superradiance ∼10³³. The rotational symmetry of ^93mNb is spontaneously broken by the absorption of N nuclear magnons¹⁰.

Applying the new observation of Ω_R∼100 eV, the superradiance becomes ≫ N^3/2 and the above-mentioned ^93mNb model is again incomplete. Bosonic excitons prefer antiferromagnetic ordering to lower the energy. There are two magnon polarizations in the antiferromagnetic ordering. The M4 exciton of ^93mNb may consist of a pair of γγs that acquire one more degree of freedom to absorb the residual magnon polarization. The exciton chains align themselves in the direction of the long sample axis. The photon flux therefore depends on the sample geometry. The emerging magnetic quanta of pairing 4 γs give rise to a multiplet rather than a simple triplet. The central energy of the pairing γγs is one quarter of the transition energy, which is 7.71 keV for ^93mNb with E₀ = 30.82 keV⁴.

Results

Figure 1 shows the decays of four x-rays, where Ta γ @ 67.8 keV represents the β decay of ¹⁸²Ta and Zr Kα represents the electron capture + β⁺ decay of ^92mNb. X-rays have two characteristic time constants corresponding to ^92mNb and ¹⁸²Ta. The contributions of the slow ^93mNb (half-life of 16 years) and ⁹⁴Nb (half-life of 2 × 10⁴ years) are negligible. The varying time constants are demonstrated by the initial 9 data points of the four decays shown in Fig. 1, which were taken in the same position during the period of hazardous radioactivity.

Figure 1

Decays of four x-rays in counts per second (cps) against their reference lines of half-lives listed below.

The left-hand axis shows the rates of Nb Kα (black dot, 111.4 d), Nb Kβ (orange square, 111.4 d), Ta γ (blue diamond, 111.4 d), and the right-hand axis shows the rates of Zr Kα (green star, 10.15 d). Removing its contamination makes Zr Kα very sensitive to the temperature shift of the spectra. Data points of Zr Kα after day 51 are deleted because of their overly large fluctuation. The hollow symbols show data points measured at the incline position highlighted by the gray background, while the solid symbols show data points measured at the contact position. The data points taken at the incline position are multiplied by a factor of calibration using the detected total counts (see Fig. S1 in the Supplementary information). The insets show the calibration between two measuring positions, where the K x-rays of Nb and Zr are anisotropic. The details of the first 7 data points and their reference lines are shown in the insets blow.

The initial sample position with inclination was replaced by a contact position at day 12. The calibration between the two positions using the same activated sample (Fig. 1) demonstrates an interesting anisotropy at about 20%. More anisotropic x-rays are shown in the Supplementary information. We conclude that the main fluxes of the Nb K-lines and the Zr K-lines do not run along the 1-mm axis of the sample. Instead, x-rays super-radiate along the 3-cm axis, where the Nb Kα increased by more than 40% (see Fig. 2). It is worth noting that the anisotropic impurity channel of Ni revealed by the sub-Poissonian photon statistics² is not caused by the phenomenon discussed here.

Figure 2

Superradiance of Nb K-lines along the long sample axis.

Two spectra of LP1 and LP2 were taken in the longitudinal position and one spectrum of CP was taken in the contact position at day 116. LP1 was taken during the transition of ¹⁸²Ta decay from phase 1 to phase 2. One inset gives the detailed superradiance of Nb Kα. The Nb Kα/Ta γ ratio is ∼6 for the contact position. The Nb Kα/Ta γ ratio is ∼8 for the longitudinal position, which equates to >8, because the Pb wrapping foils block Nb K-lines but do not block Ta γ. The other inset shows the broadened γγ peak just at the moment, at which the spectral change took place. The vertical black line highlights the γγ energy of 15.4 keV. Another peak is probably located @ 15.9 keV (see Fig. S3 and Fig. S4 in the Supplementary information). Therefore, a conservative estimate gives the γγ FWHM of ∼600 eV, which then gives a true γγ FWHM of ∼400 eV.

The first 7 data points of Ta γ shown in Fig. 1 depict a chaotic decay of ¹⁸²Ta, which is, however, at least three times faster than the normal half-life of 114.43 days. This enhanced decay then relaxes within 10 days. Taken together, the 160 data points give a 3% enhanced half-life of 111.4 ± 0.3 d. The Hf K-lines (see Fig. 3 and Fig. S2 in the Supplementary information) appear to follow the ¹⁸²Ta decay. An α branching channel to reach a stable ¹⁷⁸Hf from ¹⁸²Ta is considered.

Figure 3

Spectral evolutions.

Line B1: accumulation of the first 7 data points; line B2: accumulation of the first 80 data points; line B3: accumulation of the next 80 data points. Major x-rays are identified, i.e., V Kα @5.0, V Kβ @5.4, Quad @7.5, W Lα @8.4, W Lβ @9.7, W Lγ @11.3, biphoton γγ @15.4, Zr Kα @15.7, Nb Kα @16.6, Zr Kβ @17.7, Nb Kβ @18.6, Hf Kα₂ @54.6, Hf Kα₁ @55.8, W Kα₂ @58.0, W Kα₁ @59.3, Hf Kβ₃ @63.0, Hf Kβ₁ @63.2, Hf Kβ₂ @65.0, Ta γ @65.7, W Kβ₃ @67.0, W Kβ₁ @67.2, Ta γ @67.8, W Kβ₂ @69.1 in keV. It should be noted that the measured energy of Hf Kα is 400 eV lower than normal. Several peaks in the energy ranging from 22 to 29 keV are not identified but have frequently been observed before^1,2. These peaks disappear after one year and are probably due to radioactive impurities.

With some care we inspected the high-energy γs using an HPGe detector. Only the characteristic γs emitted from the ¹⁸²Ta and the ⁹⁴Nb decays were found (see Figures S6 and S7 in the Supplementary information). The readings of two γs @ 706.2 keV and @ 871.1 keV reveal the major excitation of ⁹⁴Nb in the sample, the density of which was ∼1000 times higher than the ¹⁸²Ta density at day one. Neither the MeV α particle nor the characteristic γs of ¹⁷⁸Hf or ¹⁷⁸Lu were found. The MeV α particles escaping from the sample were probably too rare to be caught by the α-particle detector used. Figure 2 shows that the Hf K-lines disappeared after day 116, when the Zr Kα from ^92mNb decayed to 0.03 counts per second (cps). We observed the same transition at 0.02-cps Zr Kα using the same detector from the sample of a similar size in 2012¹. At around the same time, the ratio of W Kα/Ta γ increased from 0.70 to 3.9 after day 116.

The ^92mNb decay is characterized by the Zr Kα in Fig. 1. Again, the first 7 data points reveal a doubled decay speed, which recovered to the normal half-life of 10.15 d within 10 days. ^92mNb is an isomeric γ excitation of J^π = 2⁺. The 135-keV M5 transition to the ⁹²Nb ground state of J^π = 7⁺ is negligible with respect to the major β decay channel⁴. The Nb K-lines with a half-life of 4.2 days strictly follow the ^92mNb decay.

Figure 3 shows the spectral evolution in two periods. We decomposed the 160 spectra in the contact position using two characteristic half-lives (111.4 and 10.15 d), as shown in Fig. 4 using the equation

Figure 4

Accumulation of the decomposed spectra.

Line C1 obtained using differential mapping between lines B1 and B2 + B3 under the condition of cancelling Ta γ @ 67.8 keV; line C2 is the spectrum Ta(i) decomposed using eq. 1 with a half-life of 111.4 d; line C3 is the spectrum Zr(i) decomposed using eq. 1 with a half-life of 10.15 d. C2 contains x-rays following the ¹⁸²Ta decay. C3 contains x-rays following the ^92mNb decay. Note that the left Rabi sideband of Nb Kα shows up at right hand side of the non-Gaussian γγ peak @15.4 keV of C2 line. Two figures C1 and C3 are very different, i.e., C1 contains Nb x-rays and the biphoton γγ, while C3 does not.

where Spectra(i) are the count rates in the 8192 channels, Ta(i) are x-rays contributed by the ¹⁸²Ta decay, Zr(i) are x-rays contributed by the ^92mNb decay of, i is the index of 160 data points, and t(i) is the time of measurement. No x-rays strictly depend on ^92mNb, except the Zr K-lines and a peak @ 14.7 keV (see Fig. 4). We failed to identify this γ @ 14.7 keV to be the left Rabi sideband of Zr Kα, because its right Rabi sideband is invisible beneath the Nb Kα peak. Another small peak @ 17.5 keV follows the ¹⁸²Ta decay, which may be the right Rabi sideband of Nb Kα. Its left counterpart @ 15.9 keV is difficult to identify in Fig. S3 and S4 of the Supplementary information. The two sidebands disappeared together after day 116 (see Fig. 2). No pronounced spectral migration of Nb K-lines given in previous work² was found in these 160 data points.

V Kα (4.95 keV) and V Kβ (5.43 keV) with a branching ratio of 10:1 are identified to be the impurity channel of V, which has a similar time-varying time constant to that observed for the Ni impurity channel in previous work² (see Fig. S2 in the Supplementary information).

Two pronounced peaks, i.e., γγ @ 15.4 keV (E₀/2) and Quad @ 7.5 keV, emerge in Fig. 4, the time constant of which strictly matches the ¹⁸²Ta decay, except for the first 7 data points. The Quad peak is apparently not the Ni Kα in previous work², because the corresponding Ni Kβ is entirely absent. Furthermore, the broadband x-rays spread over the entire spectrum also follow the ¹⁸²Ta decay. Two peaks of γγ and Quad disappeared with the Hf K-lines together after day 116 (see Fig. 2), when the low-energy broad-band x-rays between 2 and 5 keV abruptly increased by a factor of more than three, from 9 cps to 30 cps.

The low-energy broadband x-rays remained unchanged on insertion of a 0.1-mm Pb foil after day 116 (see Fig. S5 in the Supplementary information), while they are reduced overall following insertion of a thin Al foil before day 116 (see Fig. 5). The exponential shape seen in Fig. S5 (not a Compton plateau) reveals the random arrivals of a short-burst γs isotopically emitted into the 4π solid angle, which are probably generated by multipolar γs after day 116. The short burst lasted less than 120 ns. Multiple γs arriving at the detector are thus treated as a single count by the multi-channel analyzer, which reports a 100% live-time. The 70% live-time before day 116 reveals a long burst of a γ train, which is probably generated by the speculated α particle.

Figure 5

Coincident arrival of multiple γs at the detector.

The spectral ratio between no-layer and 3-layer Al foils is obtained by normalizing the Ta γ @ 67.8 keV and an average of Gaussian with a sigma of 10 channels. The energy positions of the Quad, the W Lα, the γγ, and the Ta γ are highlighted by the vertical lines. The inset shows the development of the highlighted peaks by inserting Al foil layer by layer, the numbers of which are given in Table 1. Note the Quad count @ 7.5 keV deceased much less than the W Lα count, while the γγ increased on insertion of Al foils. Decreasing broadband x-rays all over the spectral range reveals they are coincident arrivals of multiple γs. We failed to identify a peak located @ 6.39 keV.

We inserted the Al filter layer by layer just one week before the spontaneous spectral change at day 116. The photo-electric attenuations of one 25-μm Al foil are roughly 30% @ 7.5 keV and 6% @ 15 keV, respectively. Figure 5 and Table 1 show the results obtained using increasing numbers of Al layers. The photo-electric attenuations of γγ and Quad are obviously abnormal. We conclude that these represent entangled γs emitted from ^93mNb.

Table 1 The photo-electric attenuations of six x-rays, i.e., Nb Kα, Nb Kβ, γγ, W Lα, W Lβ, and Quad, by comparing their ratios between inserting 1, 2, 3 layers of Al foil and no Al foil.

The ratio of Nb Kα/Ta γ in Fig. 2 increased from 6 to 8 by rotating the sample to the longitudinal position, while the broadband x-rays between 2 and 5 keV increased by 50%. The 15.4-keV γγ was just disappearing at the moment of rotation of the sample, and it disappeared altogether on rotation back to the contact position half an hour later. The FWHM of γγ was ∼600 eV (see Fig. 2).

We applied three multipolar MeV γs from ¹³⁷Cs and ⁶⁰Co, i.e., 662 keV (M4), 1173 keV (E2), and 1333 keV (E2), to demonstrate the collective scattering of nuclear exciton in Table 2. The collective scattering strongly depended on the multipolarities of impinging γs. The dead time of detector in Table 2 reelected the total incoming counts. The impinging E2 γs increased 10% of the internal γ @ 1121 keV from the ¹⁸²Ta decay, while only increased 1% of the total counts. The M4 γ did not change the total counts and the internal γ counts too much. Instead, more M4 γ was scattered away by the nuclear exciton. The M4 γ @ 662 keV from ¹³⁷Cs is also a long-lived Mossbauer γ with a half-life of 2.55 minutes, the first-order thermal Doppler shift of which vanishes¹¹. We estimate its coherent length ∼100 m using the second-order Doppler shift. In contrast, the coherent lengths of E2 γs from ⁶⁰Co are on the μm order, as restricted by the first-order Doppler shift.

Table 2 Collective scattering of multipolar MeV γs.

Discussion

Although no atomic transition emits x-rays >120 keV, we observe broadband x-rays over a wide range of energies beyond 200 keV, the distribution of which contains no Compton plateau (see Fig. 2). These broadband x-rays followed the slow ^93mNb decay in the old single-crystal sample², when ¹⁸²Ta vanished in 2015. ^93mNb cannot provide x-rays >30 keV, so we must have a coincident arrival of multiple γs, as revealed by inserting a filter (see Fig. 5 and Fig. S5 in the Supplementary information). These facts reveal the presence of a high-energy source in the sample, which we then identify as ⁹⁴Nb.

One ⁹⁴Nb decay gave roughly one ^92mNb decay probably via a Raman branching at day one. Two E2 γs from ⁹⁴Nb scatter the ^92mNb to the virtual 4⁺ or 6⁺ states, which return to the ⁹²Nb ground state shortly. A similar Raman scheme doesn’t apply for ^93mNb, because there is no available 6⁻ state of ⁹²Nb⁴. It requires an extreme Raman cross-section to double the ^92mNb decay speed. The following discussions are an attempt to shed some light on these matters.

This enhanced Raman scattering should not spontaneously stop within 10 days, unless the multipolar γs emitted from the ^92mNb decay or the ^92mNb excitations themselves cooperated with each other. The E2 γs @ 0.93 MeV emitted from the ^92mNb decay has a near-resonant coupling with the E2 transition @ 0.95 MeV of ⁹³Nb. Coherent ⁹³Nb nuclei in an exciton provide a collective scattering, which is amplified by a factor of ∼10¹⁰ giving rise to a strong exciton-field coupling with a Ω_R ≫ 1 MeV^5,6. MeV E2 γs are therefore stored in a small “cavity” of the μm-size exciton. Note that E2 γs in Table 2 are from an external source. The internal E2 γ sources shall coherently move with the surrounding nuclei, that tremendously enhance the coupling strength. The photonic reservoir may thus provide a spontaneous cooperation to terminate the accelerated ^92mNb decay. This strong coupling also applies to the E2 γs emitted from ⁹⁴Nb, which induce broadband x-rays following the ^93mNb decay. Annihilation of one ^93mNb exciton releases the storing E2 γs, which create a short burst of isotropic γs.

We have observed three phases of the ¹⁸²Ta decay in the past ten years. Now they are 1) appearance of Hf K-lines with the 3% branching before day 116; 2) disappearance of Hf K-lines triggered by the vanishing ^92mNb after day 116; 3) appearance of Ta K-lines with 1% branching² in the coming year.

Note that the parity of dilute ^92mNb dictates ¹⁸²Ta that is 1000 times denser. The M4 γs from ^93mNb probably changes the ¹⁸²Ta parity (J^π = 3⁻) by Raman accelerating the β decay in phase 2, i.e., via the 1^{+ 182}Ta state @ 593 keV to the 2^{+ 182}W state @100 keV, as revealed by the ratios between 100 keV/113 keV in two phases (Figures S6 and S7 in the Supplementary information). No other branching channel has yet been found.

6 MeV is required to emit a neutron from the ¹⁸²Ta, which appears to be a pathological conclusion made in the previous report². Although the α branching of ¹⁸²Ta releases energy, the same pathology remains. Roughly 4 MeV is required to make the 3% α tunnelling observable⁴. We speculate that several MeV E2 γs from ⁹⁴Nb stored in a photonic reservoir cause the α tunnelling out of ¹⁸²Ta in phase 1 and the photo-neutron in phase 3.

No γγ @ 15.4 keV and Quad @ 7.5 keV were seen previously² and γγ now disappear together with the Hf K-lines. We therefore suggest that the α particle creates an umklapp phonon to release γγ and Quad.

The ^92mNb decay dominated the day-one Nb x-rays. Later on, these are contributed wholly by the ¹⁸²Ta decay. Two β decays were in competition with each other, and even their decay rates at day 16 and their β stopping powers were similar⁴. The vanishing ^92mNb contribution of the 160 data points reveals weak β activity in ejecting Nb K electrons. Instead, we consider the enhanced Raman scattering by multipolar γs.

The ratio of Nb Kα/Ta γ was 4.5 in the presence of Ta K-lines² but 6 before and after day 116. It increases to more than 8 if the sample is rotated through 90 degrees (Fig. 2). One ^92mNb decay created one Nb K x-ray at day one, while one ¹⁸²Ta decay created more than two Nb K x-rays. Multipolar γs emitted from ¹⁸²Ta exhibit multiple inelastic scatterings featured by the macroscopic cross-sections.

Taking two independent radioactivities together produces a superposition of their spectra. The winner-takes-all interference between two different β decays reveals the spontaneous cooperation of multipolar γs emitted within nanoseconds, several cps of which hardly co-exist at all according to conventional wisdom. High-energy multipolar γs are easy to be stored by the near-resonant ⁹³Nb. In contrast, the low-energy spin-1 x-rays are difficult to be hold by the ⁹³Nb nuclei. The spin-1 Nb K-lines along the long sample axis also reveals the same result that the superradiance is established among emitters of the same kind. The 100-ps propagation time of Nb K-lines is too short to give the co-existing K-lines in sample. The sample must contain a photonic reservoir to maintain the traces of all superradiant γs.

The Quad peak deviates from the 7.71-keV 4γs by 200 eV. Further investigation is required to understand whether the energy reductions of Quad and Hf Kα (Fig. 3) are actually two sides of the same coin. If the exciton contains 4 γs rather than just 2 γs, the long-observed puzzle of the missing Ta L-lines² is then resolved. The Nb standing wave between two nearest neighbouring Nb atoms (2.86 Å) is 4.34 keV (see the ^103mRh results in the Supplementary information). Two defect modes locate @ 9.87 + δ and @ 5.54-δ keV. Assuming δ∼0.2 keV, the 10-keV γ is not enough to eject electrons on the L1 and L2 shells of Ta, while the rapid Rabi oscillations inhibit the photoelectric ejection of the Ta L3 electrons with an ionization energy of 9.881 keV.

The energy distribution of an individual γγ is usually very broad⁴, while a narrow width shows up the non-Gaussian FWHM of 130 eV and 170 eV at the contact and incline positions, respectively (see Fig. S3 in the Supplementary information). The γγ width further increased to 400 eV at the longitudinal position (Fig. 2). According to our theory, the γγ width will be the 0.03-eV Debye energy. The γγ peak is thus a quintuplet mainly contributed by a Ω_R∼100 eV of m =± 1 at the contact position. The pronounced broadening of the γγ FWHM in the longitudinal position reveals the anisotropic γγ of m = ± 2 with a Ω_R∼200 eV. The speculated 800-eV Rabi sidebands around Nb Kα in Fig. S3 is probably driven by 4 γs with a 200-eV Ω_R, which disappear most likely due to the parity change after day 116.

Conclusions

The well-known photonic physics as promoted by the AMO society has been extended to the realm of nuclear physics in this report. We suggest that multipolar γs from ⁹⁴Nb stored in a photonic reservoir accelerate two different β decays. ¹⁸²Ta β decay abruptly switches its branching channels, as dictated by the parity of diluted ^92mNb. Multipolar γs emitted from two different β decays compete with each other, rather than superposing together to eject the Nb K electron. Their Raman cross-sections are extremely large. The superradiance along the long sample axis reveals a coherent enhancement of Nb K-lines, which have no intrinsic coherence at all. The Nb K-lines cannot leave the coherent trace-records in the sample, unless a photonic reservoir exists. Taking these observations together leads us to a long-predicted coherence for all ^93mNb excitation in the crystal¹. The superradiance of 10³⁶ ≫ N^3/2 gives rise to the reported 4γ model.

Methods

In a set of experiments, we newly activated four niobium polycrystalline sheets of 99.99% purity (3 cm × 1.5 cm × 1 mm). We refer to sample No. 3 in this work. The method is as detailed in the reference 1, except that the irradiation time was two hours without the Cd shielding. The ^92mNb density was thus increased by a factor of 20 compared with the previous result. We used the same silicon detectors located at Hsinchu in the previous report¹, which are the Si-PIN type (XR-100CR) manufactured by AMPTEK in Bedford, MA 01730, USA. The day-one measurement started at 2016/2/4.

There are 3 different measuring positions, i.e., 1) an incline position before day 12: the sample is 1-cm away with a 30-degree angle of inclination; 2) a contact position after day 12: the sample is directly in contact with the beryllium window of the detector; and 3) a longitudinal position: the 3-cm long sample axis is parallel to the normal vector of the beryllium window. The sample area fully covers the 0.5-inch ϕ beryllium widow of detector at the contact position. Three samples (No. 1, No. 2, and No. 3) were wrapped by 5 layers of 0.1-mm Pb foil together, such that the Pb shielding opened an area of three surfaces (1 mm × 1.5 cm) in contact with the beryllium window in the longitudinal position.

Two kinds of filter were inserted between the sample and the beryllium widow. One was a 25-μm Al foil, the other was a 0.1-mm Pb foil. Their photo-electric attenuations were verified by the calibration sources of ²⁴¹AM and ⁵⁵Fe.

The live-times of detector were insensitive to the incoming rate during the calibration between incline position and contact position, i.e. 70% for 120 cps and 230 cps, respectively. However, it changed to 100% after day 116.

We cooled the sample in liquid nitrogen between day 53 and day 81. Two detectors of the same type are applied, i.e., one for the measurements before day 116 and the other for the measurements after day 116. The first detector failed to work at day 116 and it was replaced by the second detector.

The high-energy x-rays were taken by a HPGe detector (CANBERRA GC0518, Coaxial-Ge type) with ϕ 4.25 cm and a length of 4.1 cm, which was calibrated by ¹³⁷Cs (10 μCi), ⁶⁰Co (1 μCi) and ²⁴¹AM (1 μCi) and located in a box of the 3-cm Pb shielding. The temperature of measuring environment was stable (27 ± 0.5 °C). We manipulated the dead time of HPGe detector to avoid any possible pile-up errors induced by the ¹⁸²Ta decay in the samples, when 20% dead time appeared in Table 2.