Observations on the long-lived Mossbauer effects of 93mNb

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.

of γ γ s 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 γ s give rise to a multiplet rather than a simple triplet. The central energy of the pairing γ γ s is one quarter of the transition energy, which is 7.71 keV for 93m Nb with E 0 = 30.82 keV 4 . Figure 1 shows the decays of four x-rays, where Ta γ @ 67.8 keV represents the β decay of 182 Ta and Zr Kα represents the electron capture + β + decay of 92m Nb. X-rays have two characteristic time constants corresponding to 92m Nb and 182 Ta. The contributions of the slow 93m Nb (half-life of 16 years) and 94 Nb (half-life of 2 × 10 4 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.

Results
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 statistics 2 is not caused by the phenomenon discussed here.
The first 7 data points of Ta γ shown in Fig. 1 depict a chaotic decay of 182 Ta, 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 182 Ta decay. An α branching channel to reach a stable 178 Hf from 182 Ta is considered.
With some care we inspected the high-energy γ s using an HPGe detector. Only the characteristic γ s emitted from the 182 Ta and the 94 Nb decays were found (see Figures S6 and S7 in the Supplementary information). The readings of two γ s @ 706.2 keV and @ 871.1 keV reveal the major excitation of 94 Nb in the sample, the density of which was ∼ 1000 times higher than the 182 Ta density at day one. Neither the MeV α particle nor the characteristic γ s of 178 Hf or 178 Lu 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 92m Nb 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 2012 1 . At around the same time, the ratio of W Kα /Ta γ increased from 0.70 to 3.9 after day 116.
The 92m Nb 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. 92m Nb is an isomeric γ excitation of J π = 2 + . The 135-keV M5 transition to the 92 Nb ground state of J π = 7 + is negligible with respect to the major β decay channel 4 . The Nb K-lines with a half-life of 4.2 days strictly follow the 92m Nb decay.
where Spectra(i) are the count rates in the 8192 channels, Ta(i) are x-rays contributed by the 182 Ta decay, Zr(i) are x-rays contributed by the 92m Nb decay of, i is the index of 160 data points, and t(i) is the time of measurement. No x-rays strictly depend on 92m Nb, 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 182 Ta 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 work 2 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 work 2 (see Fig. S2 in the Supplementary information).
Two pronounced peaks, i.e., γ γ @ 15.4 keV (E 0 /2) and Quad @ 7.5 keV, emerge in Fig. 4, the time constant of which strictly matches the 182 Ta decay, except for the first 7 data points. The Quad peak is apparently not the Ni Kα in previous work 2 , because the corresponding Ni Kβ is entirely absent. Furthermore, the broadband x-rays spread over the entire spectrum also follow the 182 Ta decay. Two peaks of γ γ 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 γ s isotopically emitted into the 4π solid angle, which are probably generated by multipolar γ s after day 116. The short burst lasted less than 120 ns. Multiple γ s 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.
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-μ m 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 γ γ and Quad are obviously abnormal. We conclude that these represent entangled γ s emitted from 93m Nb.
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 γ γ 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 γ γ was ∼ 600 eV (see Fig. 2).
We applied three multipolar MeV γ s from 137 Cs and 60 Co, 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 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 182 Ta 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 γ γ peak just at the moment, at which the spectral change took place. The vertical black line highlights the γ γ 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 γ γ FWHM of ∼ 600 eV, which then gives a true γ γ FWHM of ∼ 400 eV.
depended on the multipolarities of impinging γ s. The dead time of detector in Table 2 reelected the total incoming counts. The impinging E2 γ s increased 10% of the internal γ @ 1121 keV from the 182 Ta 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 137 Cs is also a long-lived Mossbauer γ with a half-life of 2.55 minutes, the first-order thermal Doppler shift of which vanishes 11 . We estimate its coherent length ∼ 100 m using the second-order Doppler shift. In contrast, the coherent lengths of E2 γ s from 60 Co are on the μ m order, as restricted by the first-order Doppler shift.

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 93m Nb decay in the old single-crystal sample 2 , when 182 Ta vanished in 2015. 93m Nb cannot provide x-rays > 30 keV, so we must have a coincident arrival of multiple γ s, 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 94 Nb.
One 94 Nb decay gave roughly one 92m Nb decay probably via a Raman branching at day one. Two E2 γ s from 94 Nb scatter the 92m Nb to the virtual 4 + or 6 + states, which return to the 92 Nb ground state shortly. A similar Raman scheme doesn't apply for 93m Nb, because there is no available 6 − state of 92 Nb 4 . It requires an extreme Raman cross-section to double the 92m Nb 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 γ s emitted from the 92m Nb decay or the 92m Nb excitations themselves cooperated with each other. The E2 γ s @ 0.93 MeV emitted from the 92m Nb decay has a near-resonant coupling with the E2 transition @ 0.95 MeV of 93 Nb. Coherent 93 Nb nuclei in an exciton provide a collective scattering, which is amplified by a factor of ∼ 10 10 giving rise to a strong exciton-field coupling with a Ω R ≫ 1 MeV 5,6 . MeV E2 γ s are therefore stored in a small "cavity" of the μ m-size exciton. Note that E2 γ s in Table 2 are from an external source. The internal E2 γ sources shall coherently 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 γ γ @15.4, Zr Kα @15.7, Nb Kα @16.6, Zr Kβ @17.7, Nb Kβ @18.6, Hf Kα 2 @54.6, Hf Kα 1 @55.8, W Kα 2 @58.0, W Kα 1 @59.3, Hf Kβ 3 @63.0, Hf Kβ 1 @63.2, Hf Kβ 2 @65.0, Ta γ @65.7, W Kβ 3 @67.0, W Kβ 1 @67.2, Ta γ @67.8, W Kβ 2 @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. move with the surrounding nuclei, that tremendously enhance the coupling strength. The photonic reservoir may thus provide a spontaneous cooperation to terminate the accelerated 92m Nb decay. This strong coupling also  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 γ γ , 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 γ γ increased on insertion of Al foils. Decreasing broadband x-rays all over the spectral range reveals they are coincident arrivals of multiple γ s. We failed to identify a peak located @ 6.39 keV. applies to the E2 γ s emitted from 94 Nb, which induce broadband x-rays following the 93m Nb decay. Annihilation of one 93m Nb exciton releases the storing E2 γ s, which create a short burst of isotropic γ s.
We have observed three phases of the 182 Ta 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 92m Nb after day 116; 3) appearance of Ta K-lines with 1% branching 2 in the coming year.
Note that the parity of dilute 92m Nb dictates 182 Ta that is 1000 times denser. The M4 γ s from 93m Nb probably changes the 182 Ta 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 182 Ta, which appears to be a pathological conclusion made in the previous report 2 . Although the α branching of 182 Ta releases energy, the same pathology remains. Roughly 4 MeV is required to make the 3% α tunnelling observable 4 . We speculate that several MeV E2 γ s from 94 Nb stored in a photonic reservoir cause the α tunnelling out of 182 Ta in phase 1 and the photo-neutron in phase 3.
No γ γ @ 15.4 keV and Quad @ 7.5 keV were seen previously 2 and γ γ now disappear together with the Hf K-lines. We therefore suggest that the α particle creates an umklapp phonon to release γ γ and Quad.
The 92m Nb decay dominated the day-one Nb x-rays. Later on, these are contributed wholly by the 182 Ta decay. Two β decays were in competition with each other, and even their decay rates at day 16 and their β stopping powers were similar 4 . The vanishing 92m Nb contribution of the 160 data points reveals weak β activity in ejecting Nb K electrons. Instead, we consider the enhanced Raman scattering by multipolar γ s.
The ratio of Nb Kα /Ta γ was 4.5 in the presence of Ta K-lines 2 but 6 before and after day 116. It increases to more than 8 if the sample is rotated through 90 degrees (Fig. 2). One 92m Nb decay created one Nb K x-ray at day one, while one 182 Ta decay created more than two Nb K x-rays. Multipolar γ s emitted from 182 Ta 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 γ s emitted within nanoseconds, several cps of which hardly co-exist at all according to conventional wisdom. High-energy multipolar γ s are easy to be stored by the near-resonant 93 Nb. In contrast, the low-energy spin-1 x-rays are difficult to be hold by the 93 Nb 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 γ s.
The Quad peak deviates from the 7.71-keV 4γ s 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 γ s rather than just 2 γ s, the long-observed puzzle of the missing Ta L-lines 2 is then resolved. The Nb standing wave between two nearest neighbouring Nb atoms (2.86 Å) is 4.34 keV (see the 103m Rh 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 γ γ is usually very broad 4 , 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 γ γ width further increased to 400 eV at the longitudinal position (Fig. 2). According to our theory, the γ γ width will be the 0.03-eV Debye energy. The γ γ 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 γ γ FWHM in the longitudinal position reveals the anisotropic γ γ 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 γ s 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 γ s from 94 Nb stored in a photonic reservoir accelerate two different β decays. 182 Ta β decay abruptly switches its branching channels, as dictated by the parity of diluted 92m Nb. Multipolar γ s 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 93m Nb excitation in the crystal 1 . The superradiance of 10 36 ≫ 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 92m Nb 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 report 1 , 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-μ m Al foil, the other was a 0.1-mm Pb foil. Their photo-electric attenuations were verified by the calibration sources of 241 AM and 55 Fe.
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 137 Cs (10 μ Ci), 60 Co (1 μ Ci) and 241 AM (1 μ Ci) 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 182 Ta decay in the samples, when 20% dead time appeared in Table 2.