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Observation of the competitive double-gamma nuclear decay

Abstract

The double-gamma (γγ)-decay of a quantum system in an excited state is a fundamental second-order process of quantum electrodynamics. In contrast to the well-known single-gamma (γ)-decay, the γγ-decay is characterized by the simultaneous emission of two γ quanta, each with a continuous energy spectrum. In nuclear physics, this exotic decay mode has only been observed for transitions between states with spin-parity quantum numbers Jπ = 0+ (refs 1, 2, 3). Single-gamma decays—the main experimental obstacle to observing the γγ-decay—are strictly forbidden for these 0+ → 0+ transitions. Here we report the observation of the γγ-decay of an excited nuclear state (Jπ = 11/2) that is directly competing with an allowed γ-decay (to ground state Jπ = 3/2+). The branching ratio of the competitive γγ-decay of the 11/2 isomer of 137Ba to the ground state relative to its single γ-decay was determined to be (2.05 ± 0.37) × 10−6. From the measured angular correlation and the shape of the energy spectra of the individual γ-rays, the contributing combinations of multipolarities of the γ radiation were determined. Transition matrix elements calculated using the quasiparticle–phonon model reproduce our measurements well. The γγ-decay rate gives access to so far unexplored important nuclear structure information, such as the generalized (off-diagonal) nuclear electric polarizabilities and magnetic susceptibilities3.

Main

Two-photon processes, that is, excitation and decay of a quantum state simultaneously involving two photons whose energy sum E1 + E2 matches the transition energy E0, have been studied intensely in the past two decades in atomic physics4,5 and are now routinely applied in spectroscopic studies. These processes were first discussed theoretically in 19296,7, and the same approach predicted the existence of the rare double-β-decay of atomic nuclei as the analogous second-order process for the electroweak interaction8. In contrast to the situation in atomic physics, data on the γγ-decay of atomic nuclei are very sparse. Up to now, γγ-decays of nuclear states have only been observed for the special cases of the first excited states of the ‘doubly-magic’ nuclei 16O, 40Ca and 90Zr (refs 1, 2, 3, 9). The first excited states of these nuclei have the unusual property of having spin-parity quantum numbers Jπ = 0+, which is also the case for their ground states. Hence, γ-decays are strictly forbidden for these transitions. For almost all other nuclei, the first excited states have spin quantum numbers larger than zero, making γ-decays possible. Despite several searches10,11, the γγ-decay has never been observed in a situation where a single γ-ray transition is allowed, a situation we call the competitive γγ-decay, denoted by ‘γγ/γ-decay’. Preliminary evidence for the γγ/γ-process obtained by other groups in parallel with our work has been announced elsewhere (ref. 12, and D. J. Millener and R. J. Sutter (personal communication); ref. 13, and C. J. Lister (personal communication)). In the present work, the experimental difficulties have been overcome and we report here firm observation of the γγ/γ-decay of a nuclear state.

The experimental challenge to the observation of the competitive γγ-decay arises from its decay rate, which is more than five orders of magnitude smaller than that of the allowed γ-decay. In an ensemble of nuclei undergoing γ-decay from a given excited state, there are a large number of γ quanta being emitted, which cause two basic challenges, illustrated in Fig. 1. First, a γ quantum with transition energy E0 can deposit part of its energy in one detector and then scatter into the second detector, depositing there its remaining energy. The sum of the energies registered in both detectors equals the transition energy, which is the signature of the γγ-decay. Second, two γ quanta, each with energy E0, can be emitted independently by two nuclei at almost the same time, and deposit a fraction of their energy in two detectors, such that the energy sum is again close to E0. Although these random coincidences can be subtracted from truly simultaneous events, they cause a substantial statistical uncertainty, thereby preventing the observation of the much rarer γγ/γ-decay unless they are suppressed properly.

Figure 1: The two main experimental obstacles to measuring the γγ/γ-decay.
figure1

a, Schematic illustration of the experimental set-up. A 661.66-keV γ-ray (green wavy line) emitted from the central source (black dot) can deposit part of its energy in detector 1 (labelled red square) and then be scattered into detector 2 where it deposits its remaining energy. Lead (grey) is used to suppress this effect relative to the γγ-events (blue wavy lines). Lead collimators (dark grey) are used for background suppression. b, Energy-sum spectra of the 72°-group with time gates on the prompt coincidence peak (orange filled circles; |Δt| ≤ 1.2 ns) and on the random coincidences (green filled triangles; 20 ns ≤ |Δt| ≤ 76 ns). The ordinate values should be multiplied by the given factor. Inset, time difference spectrum (red trace) and parts of the imposed time gates (orange bar (prompt) and green areas (random)) used to obtain the energy-sum spectra of b. The energy condition |E1E2| < 300 keV was imposed on data reported in b as well as on that shown in the inset. Error bars, ±1 s.d.

PowerPoint slide

In our experiment, the first excited 11/2 state of 137Ba was populated through β decays of 137Cs nuclei, a well known γ-ray calibration standard. This isomer decays dominantly via a single-γ magnetic hexadecapole (M4) transition to the 3/2+ ground state, emitting a γ-ray with an energy of 661.66 keV (Fig. 2a inset). The emitted γ-rays were detected using five large-volume LaBr3:Ce (Ce-activated LaBr3) detectors positioned in a planar fashion symmetrically around the 137Cs γ-ray source (Fig. 1a). Thus, the angle between two adjacent detectors amounted to 72°, and two groups of five detector pairs can be formed with relative angles of 72° (‘72°-group’) and 144° (‘144°-group’). The undesired Compton scattering of 661.66-keV γ-rays between two detectors was suppressed by thick lead shields. Data were recorded for a measurement time of 52.7 days.

Figure 2: Energy-sum spectrum and energy-gated time spectra of the 72°-group.
figure2

a, Energy-sum spectrum E1 + E2 after subtraction of the random coincidences (requiring the energy condition |E1E2| < 300 keV). The spectrum is fitted with a superposition of a Gaussian and an exponential function to describe the peak and the background, respectively. The orange (647 keV < E1 + E2 < 677 keV) and green areas (582 keV < E1 + E2 < 632 keV and 692 keV < E1 + E2 < 742 keV) represent the energy conditions employed to obtain the time-difference spectra displayed in b. Inset, level scheme of 137Ba with level energies in keV on the left and spin-parity Jπ quantum numbers on the right. The solid red arrow labels the single-γ transition of the 11/2 state to the ground state. The dashed blue arrows illustrate the structure of the matrix element of the γγ/γ-decay involving the lowest 7/2+ state. b, Time difference spectra. The orange data points correspond to the orange region in a, while the green solid line with surrounding shading shows the background corresponding to the green area in a. The solid orange curve shows the expected time spectrum for γγ-decay, while the solid red curve shows the expected time spectrum, assuming the peak at 661.66 keV was caused by Compton-scattered γ-rays. Error bars in a, b are ±1 s.d.

PowerPoint slide

The spectrum of the time-difference (Δt) between two hits in two detectors of the 72°-group is presented in Fig. 1b inset. The prompt time-coincidence peak centred at Δt = 0 sits on a flat background caused by random coincidences. The time condition |Δt| ≤ 1.2 ns selects true (prompt) as well as random coincidences, resulting in the energy-sum spectrum E1 + E2 shown in Fig. 1b (orange filled circles). The contribution of random coincidences is determined by imposing a wide time gate on the flat background and scaling the corresponding energy-sum spectrum with a factor of 0.0214 to correct for the different widths of both conditions (Fig. 1b, green filled triangles). The random coincidences dominate the statistical uncertainty.

The final energy-sum spectrum of the 72°-group—after subtraction of random coincidences—is shown in Fig. 2a. We imposed the energy condition |E1 − E2| < 300 keV to obtain further background suppression (see Supplementary Information). The spectrum is well described by assuming a superposition of an exponential background and a Gaussian peak at 661.6(1.6) keV in agreement with the expected energy sum (here and elsewhere, numerals in parentheses indicate the 1σ uncertainty). It has an area of 693(95) counts, establishing the observation of the competitive γγ-decay.

Reasonable explanations other than γγ/γ-decay can be excluded. First, let us assume that despite our careful assembly of the lead shields, the peak is caused by Compton-scattered 661.66-keV γ-rays (due, for example, to a small hole in the absorptive lead shields). The additional flight path of the γ quantum from one detector to the other would cause a time delay to which the LaBr3:Ce detectors are sensitive. Hence, this possibility can be excluded by investigating the shape of the time-difference spectra. A narrow energy gate on the γγ/γ-sum-energy peak results in the time-difference spectrum presented in Fig. 2b (orange filled circles). The contribution of the background counts (solid green curve) is determined with energy gates on the background. The time-difference spectrum follows a Gaussian distribution centred at Δt = 0 (solid orange curve) with a full-width at half-maximum that is in agreement with the time resolution of our LaBr3:Ce detectors, namely 1 ns. In the case of Compton scattering, a superposition of two Gaussians with centroids at Δt = ±0.8 ns (solid red curve in Fig. 2b) would be expected, in contradiction to the observed time spectrum.

A second possibility for the origin of the peak is a sequential decay via the 1/2+ state at an excitation energy of 283.5 keV (Fig. 2a inset), corresponding to two subsequent γ-decays. Our observed γ-ray energy spectra of individual photons—gated on γγ/γ-events—are continuous and do not peak at the transition energies to and from the 1/2+ state, thereby excluding sequential decay. In addition, the γ-branch to the 1/2+ state has been measured recently and amounts to only 1.12(9) × 10−7 (ref. 14), less than 6% of our measured γγ/γ-branching ratio.

In addition, data were recorded for the detector group forming opening angles of 144°. A Gaussian peak is found in the corresponding energy-sum spectrum at an energy of 664.2(28) keV and with an area of 307(78) counts (Fig. 3). This shows that the γγ/γ-decay of the 11/2 isomer of 137Ba exhibits a very pronounced angular correlation of the two emitted γ quanta, characteristic of the multipolarities involved in the transition.

Figure 3: Energy-sum spectrum of the 144°-group.
figure3

The energy-sum spectrum E1 + E2 of the 144°-group after subtraction of the random coincidences (with the energy condition |E1 − E2| < 250 keV) is shown by the red data points. The Gaussian (solid blue curve) on top of an exponential background (dashed-blue curve) with a peak area of 307(78) counts is located at an energy of 664.2(28) keV, in agreement with the transition energy of 661.66 keV. Error bars, ±1 s.d.

PowerPoint slide

In the theoretical treatment of the γγ-decay process, it follows from second-order perturbation theory that the calculation of the γγ-decay transition rate3,15 involves a summation over a complete set of states, subject to well known electromagnetic selection rules based on the multipolarity and character of the transition. In a reasonable approximation, the possible decay paths can be restricted to two cases (see Supplementary Information for a justification of this approximation), which we will describe here in the language of ‘Feynman diagrams’: in the first case, the nucleus undergoes virtual M2 transitions from the 11/2 state to intermediate 7/2+ states (Fig. 2a inset), which are coupled by E2 transitions to the 3/2+ ground state. The final matrix element is obtained by a summation over all intermediate 7/2+ states of 137Ba, whose contributions add up coherently. The second possibility is an E3M1 transition through intermediate 5/2+ states. The theory of the γγ-decay is fully developed (see, for example, the Appendix of ref. 3; a first application of the formalism to 137Ba was performed by D.J. Millener (personal communication)), and the differential branching ratio for the current case is approximately given by

where Γγγ is the decay width for two-photon emission, and s stands for {L, L′, In, ω, θ12}; here L and L′ label the multipoles of the two virtual transitions involved, In is the spin of the intermediate state n, ω is the energy of one of the γ-rays, θ12 denotes the angle between the two emitted γ-rays (that is, in our experiment θ12 = 72° and 144°) and dΩ and dΩ′ are their solid angle elements. The coefficients αE2M2 and αM1E3 contain the nuclear structure information and are defined as

where S and S′ are the multipole characters. Each intermediate state |In〉 contributes with a product of matrix elements connecting it to the ground state (〈3/2+||SL′||In〉) and to the 11/2 isomer (〈In||SL||11/2〉) weighted approximately with the inverse of its excitation energy En. The quadrupole–quadrupole (Aqq) and octupole–dipole (Aod) terms of equation (1) depend only on and , respectively, while the interference term Ax depends on their product. Each term has a characteristic dependence on θ12 and the γ-ray energy ω. Thus, the values of αE2M2, αM1E3 and the sign of αE2M2αM1E3 can be determined from an analysis of the measured angular correlation and the energy spectra of the emitted γ-rays. More information and the full form of equation (1) is given in Supplementary Information.

In Fig. 4, the result of a simultaneous fit to the energy spectrum (Fig. 4a) and angular correlation (Fig. 4b) is presented. The available data are well described by equation (1) (solid blue curve), and the contribution of the Aqq term (dashed blue curve) dominates in comparison to the Aod term (dotted blue curve). The angular correlation is very sensitive to the product of αE2M2 and αM1E3. The final branching ratio amounts to Γγγ/Γγ = 2.05(37) × 10−6, and the values for the two matrix elements are given in Table 1.

Figure 4: Measured energy spectrum and angular correlation.
figure4

δ (δ′) is the differential γγ-decay width from equation (1) integrated over the corresponding energy bin, divided by the γ-decay width Γγ and evaluated at the average emission angles θ12 = 72° and 144° (see Supplementary Information equation (2) for details of δ and δ′). a, Data points, dependence of δ on the energy E1 of the lower-energy γ-ray for θ12 = 72°. Also shown are the results of the fit of equation (1) (solid blue curve) and the contributions of the Aqq (dashed blue curve), Aod (blue dotted curve) and Ax terms (blue dash-dotted curve). Results of the QPM calculation (orange solid curve) are compared to the data. b, Data points, dependence of δ′ on θ12 integrated over the energy bin |E1E2| < 250 keV. Other curves as in a. All values are corrected for the small contribution of the cascade of the decay via the 1/2+ state. Error bars, ±1 s.d.

PowerPoint slide

Table 1 Measured and theoretical parameter values

In Fig. 4 and Table 1 our data are also compared to predictions of the microscopic quasiparticle–phonon model (QPM)16 (solid orange curves). Further details of the QPM calculation are given in Supplementary Information. The QPM reproduces the experimental branching ratio and the two matrix elements rather well. As experimentally observed, it predicts a dominant Aqq term and a positive sign for αE2M2αM1E3. According to the QPM results, the value of αE2M2 is dominated by the matrix element coupled to the lowest 7/2+ state at an excitation energy of 1,252 keV (Supplementary Information). The reason is twofold: the lowest 7/2+ is close in energy to the 11/2 state, reducing the size of the denominator in equation (2), and almost all of the low-lying E2-strength is concentrated in the transition, resulting in a large matrix element.

In conclusion, we have observed the γγ-decay of a nuclear transition in competition with an allowed γ-decay. Our results demonstrate that theory provides a realistic description of the double-photon decay, and that the present state of the art of experimental equipment allows such a process to be measured even in the presence of the direct one-photon decay. This opens a new field of studies that were not previously possible. While the branching ratio is probably too small for the observation of the γγ-decay of a first excited 2+ state, which is present in nearly all even–even nuclei, we expect that there are other odd-A nuclei where the competitive γγ-decay can be measured. Such experiments will be difficult and time-consuming, and the number of suitable nuclides obtainable in an isomeric state is limited. Nevertheless, the sensitivity of the experiment is now sufficient to enable investigation of so-far-unexplored nuclear structure observables, namely the (off-diagonal) nuclear electric and magnetic polarizabilities.

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Acknowledgements

This work was supported by the State of Hesse under the Helmholtz International Center for FAIR (HIC for FAIR) and by the German Research Council (DFG) under grant no. SFB 634. We thank D. J. Millener, R. J. Sutter for an open discussion and for generously sharing their preliminary results before publication, and C. J. Lister for discussions. H.S. thanks Dirk Schwalm for raising interest in this topic.

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C.W. and H.S. performed the data analysis and derived the equations given in Supplementary Information. C.W., H.S. and N.P. contributed to the interpretation of the results. C.W. and R.L. were responsible for the set-up of the LaBr3:Ce detector array and the data acquisition system. V.Yu.P. performed the QPM calculation. C.W., H.S., N.P. and T.A. prepared the manuscript. All authors discussed the results, commented on and contributed to the manuscript.

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Correspondence to H. Scheit.

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This file contains Supplementary Text and Data, Supplementary Figure 1, Supplementary Tables 1-4 and Supplementary References. (PDF 273 kb)

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Walz, C., Scheit, H., Pietralla, N. et al. Observation of the competitive double-gamma nuclear decay. Nature 526, 406–409 (2015). https://doi.org/10.1038/nature15543

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