To explain the resonant absorption of long-lived Mossbauer effects mediated by the biphoton γγ1,2,3, 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 20081,3, 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 transitions1,3. Mollow triplets3 were observed for Rh K-lines and 103mRh γ at 39.8 keV. The vacuum Rabi oscillation ΩR 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 N1/2, 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 observed1,2, and till now the exact value of ΩR has not been known. Nevertheless, ΩR must be greater than 30 meV in order to survive the thermal agitation at room temperature. Assuming that the M4 Γγγγ branching ratio is mainly attributed to the low-lying E2 Raman transition as well as the nuclear size8,9, we fine-tuned the value of the 137Ba 11/2 excited state for 93mNb to 10−6. Four factors, i.e., the 30-meV ΩR, the 16-year half-life, the internal conversion, and the Γγγγ 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 ΩR100 eV, the superradiance becomes  N3/2 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.


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
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
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
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 before1,2. 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 Jπ = 2+. The 135-keV M5 transition to the 92Nb ground state of Jπ = 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
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
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.


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 ΩR 1 MeV5,6. 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 (Jπ = 3) by Raman accelerating the β decay in phase 2, i.e., via the 1+ 182Ta state @ 593 keV to the 2+ 182W 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 δ0.2 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 ΩR100 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 ΩR200 eV. The speculated 800-eV Rabi sidebands around Nb Kα in Fig. S3 is probably driven by 4 γs with a 200-eV ΩR, which disappear most likely due to the parity change after day 116.


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 N3/2 gives rise to the reported 4γ model.


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.

Additional Information

How to cite this article: Cheng, Y. et al. Observations on the long-lived Mossbauer effects of 93mNb. Sci. Rep. 6, 36144; doi: 10.1038/srep36144 (2016).

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.