For this purpose, δ from Eq. The full data set, as well as the different angular groups, were used to construct the summed energy spectra. The contours are separated by one standard deviation. From Eqs. This gave five independent γγ-correlation angles centred at:
The error bars represent the one standard-deviation statistical uncertainty. Given an angle, θ1,2, the differential decay is integrated over the frequency of the γ ray, ω.
The frequency is proportional to the energy, and the integration limits are taken as the edges of the energy bin of interest. In the experimental spectrum, a natural low-energy limit comes from the low-energy threshold of the detectors around keV. The upper limit was chosen as half of the total energy as we are not able to distinguish any relative ordering of the γ rays.
This procedure was performed for all combinations of θ1,2 and δ was evaluated as a function of angle. The results of this evaluation are shown in Fig. The angular correlation of the two photons emitted in the double-γ decay from this work and reference 11compared with the expected angular distributions of pure M2E2 and E3M1 decay. Full size image This data can be directly fitted to the generalised polarisability functions of Eq. Other components like αE2M2 or αM3E1 could, in principle, also contribute.
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However, the general polarisability functions are linearly dependent in the exchange of terms, weighted by the coefficients given by the Wigner 6j symbols, and this experiment is not sensitive to this ordering.
These additional components are, furthermore, expected to be small. Thus, we restrict the discussion to the αM2E2 and αE3M1 polarisabilities from here on. Energy-sharing distributions The angular distributions themselves are not enough to completely distinguish between the contribution from the different polarisabilities. When calculating the goodness-of-fit χ2two local minima corresponding to either a large αM2E2 component or a large αE3M1 component appear.
Instead, it is necessary to study the energy-sharing distributions between the two individual γ-rays.
From Eqs. For this purpose, δ from Eq. Figure 5 a shows the results of these evaluations. When including the data from Walz et al.
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The resulting χ2 surface is shown in Fig. As seen here, the χ2 analysis from this data favours a large αE3M1 component, in contradiction with both the experimental interpretation and theoretical conclusions reported in ref. The data points correspond to the sum of the differential branching ratio defined in Eq.
The contours are separated by one standard deviation.
The data from the present work is shown as a black point, data from reference 11 is shown as a red point, and a fit with the two data sets combines is shown as a purple point. The error bars represent the one standard-deviation statistical uncertainty, except the error bars in Eγ,low that represent the width of the energy bin.
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Full size image Discussion To understand these results, we performed theoretical calculations of the polarisation functions from Eq. The application of the QPM in the case of odd-mass spherical nuclei is discussed in detail in reference In particular, the nuclear structure of Ba was studied within the framework of this model in references 2728 and in reference In the work presented here, the calculations were built on the EDF theory coupled with the QPM 29 to obtain magnetic and electric spectral distributions.
To understand the origin of this discrepancy, the properties of the dominant, low-lying, states were investigated from another perspective using the state-of-the-art nuclear MCSM 33 This can explain the observed suppression of αE2M2.
Table 2 lists the contributing low-lying matrix elements discussed here. Table 2 Calculated matrix elements.
The digitisers were controlled using the Multi Instance Data Acquisition System software and triggered individually. Each event consisted of the energy, the time-stamp, and the the digitised voltage pulse from the detector.
The sub-nanosecond time information was obtained from the value of the time-stamp corrected by a digital interpolation of the sampling points in the recorded pulse, at half of the maximum value of the pulse and interpolated using a quadratic polynomial.
The general polarisability functions in Eq. The quasiparticle-phonon model The QPM Hamiltonian includes mean field, pairing interaction and separable multipole and spin-multipole interactions The mean field for protons and neutrons is defined as a Woods-Saxon potential with parameter sets derived self-consistently from a fully microscopic Hartree-Fock-Bogoljubov HFB calculations described in 29 The method assures a good description of nuclear ground-state properties by enforcing that measured separation energies and nuclear radii are reproduced as close as possible The pairing and residual interaction parameters are fitted to reproduce the odd-even mass differences of neighbouring nuclei as well as the experimental values of the excitation energies and reduced transition probabilities of low-lying collective and non-collective states in the even-even core nucleus Of particular importance in these studies is the determination of the isovector spin-dipole coupling constant which is extracted from comparison to data from ref.
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Single-particle s. We point out that the s.
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The exact commutation relations between quasiparticle and phonon operators are used to solve this problem. The properties of the phonons are determined by solving QRPA equations from refs.
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Theoretical nuclear physics Abstract Second-order processes in physics is a research topic focusing attention from several fields worldwide including, for example, non-linear quantum electrodynamics with high-power lasers, neutrinoless double-β decay, and stimulated atomic two-photon transitions. For the electromagnetic nuclear interaction, the observation of the competitive double-γ decay from mBa has opened up the nuclear structure field for detailed investigation of second-order processes through the manifestation of off-diagonal nuclear polarisability. Here, we confirm this observation with an 8.
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