Addendum: The observation of vibrating pear-shapes in radon nuclei

Abstract

We would like to make readers aware that after the publication of this article the sort code was updated. This resulted in more gamma-gamma data, particularly for high-spin transitions. By performing additional analysis we confirm the energies of most of the states, have identified several new states, and have updated one of the states that was incorrectly represented in its energy in the original paper. The figures (Figs. 1-4) and table (Table 1) are updated along with their captions. The overall conclusions of the paper remain unaffected. The new data confirm our original finding, that 224,226 Rn behave as octupole vibrators in which the octupole phonon is aligned to the rotational axis. We conclude that there are no isotopes of radon that have static octupole deformation, so that any parity doublets in the odd-mass neighbours will not be closely spaced in energy. This means that radon atoms will provide less favourable conditions for the enhancement of a measurable atomic electric-dipole moment. Prior to this work, less was known about the energies and spins of excited states in 224,226 Rn. The spectra of γ-rays time-correlated with scattered beam and target recoils are shown in Fig. 1. The E2 γ-ray transitions within the ground-state positive-parity band can be clearly identified. The other relatively intense γ-rays observed in these spectra are assumed to have E1 multipolarity, depopulating the odd-spin negative-parity members of the octupole band. In order to determine which states are connected by these transitions, pairs of time-correlated ('coincident') γ-rays were examined. In this analysis, the energy spectrum of γ-rays coincident with one particular transition is generated by requiring that the energy of this gating transition lies in a specific range. Typical spectra obtained this way are shown in Fig. 2. Each spectrum corresponds to a particular gating transition, background subtracted, so that the peaks observed in the spectrum arise from γ-ray transitions in coincidence with that transition. The data in these γ-γ spectra have been significantly enhanced by modifying the sort code that converts raw data from the Miniball spectrometer to Root analysis files. This modification enables γ-γ data to be included when both heavy ions are detected in the silicon detector array, in addition to single-ion events. Since both conditions for ion detection were already considered for single γ-ray events, this modification does not affect the total spectra shown in (Fig. 1), but considerably enhances the statistics of the γ-γ gated spectra shown in Fig. 2. The additional γ-γ data have allowed the authors to extend the level schemes by one additional state in each of the positive-parity bands in 224,226 Rn and in the negative-parity band in 224 Rn over that reported originally. More importantly, we are able to determine the probable energy of the 7 − , 9 − and 11 − states in 226 Rn, see Fig. 2. By extrapolating this band to lower spin states on the basis of its rotational-like behaviour, we are able to estimate th...

Pear-shaped atomic nuclei

“…For the source of the data shown here, see figs. 7,8 in [12], and see [17][18][19]. (Online version in colour.…”

“…To explore further required the development of accelerated radioactive ion beams (RIBs), which enables a much larger range of isotopes to be studied using the method of Coulomb excitation. In this manner, measurements of E3 matrix elements have been performed in recent years for 220 [7,17] of energy levels of 224,226 Rn presented in figure 2 also exploited Coulomb excitation of accelerated radon ions, but at higher energies where the interaction is not purely electromagnetic. )…”

“…The study of the rotational behaviour of reflection-asymmetric nuclei has been hampered by their inaccessibility using conventional spectroscopic techniques. Nevertheless, the development of highly efficient germanium detector arrays (for review, see [ 13 ]) has revealed cascades of γ -rays de-exciting quantum states in nuclei weakly populated by spontaneous fission [ 14 ] and multi-nucleon transfer reactions [ 15 ], in rare compound nucleus channels [ 16 ], and in inelastically scattered radioactive nuclei (see next section) [ 7 , 17 ]. The outcome of these studies for the Z ≈ 88, N ≈ 134 mass region is shown in figure 2 , and for nuclei in the Z ≈ 56, N ≈ 88 mass region in figure 3 .…”

“…In this manner, measurements of E 3 matrix elements have been performed in recent years for 220 Rn [ 32 ], 224 Ra [ 32 ], 144 Ba [ 33 ], 146 Ba [ 34 ] and 222,228 Ra [ 35 ], using the RIB accelerators REX- and HIE-ISOLDE, CERN, Geneva, Switzerland, and CARIBU, Argonne National Laboratory, Lemont, IL, USA. (It should be noted that the measurements [ 7 , 17 ] of energy levels of 224,226 Rn presented in figure 2 also exploited Coulomb excitation of accelerated radon ions, but at higher energies where the interaction is not purely electromagnetic.)…”

“…Measurements of the E 3 strength in odd- A nuclei have yet to be carried out, however. For radon isotopes, it appears unlikely that odd- A nuclei such as 223,225 Rn will have low-lying parity doublets [ 7 , 17 ], and any enhancement of the Schiff moment will be smaller in radon atoms than for radium atoms. Realistic estimates of Schiff moments for octupole-vibrational systems have yet to be made [ 55 , 56 ].…”