Comment on "Longitudinal wobbling in 133 La [Eur. Phys. J. A 55, 159 (2019)]"
CComment on “Longitudinal wobbling in
La [Eur. Phys. J. A 55, 159 (2019)]”
W. Hua, S. Guo,
2, 3, ∗ and C. M. Petrache Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China CAS Key Laboratory of High Precision Nuclear Spectroscopy,Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China School of Nuclear Science and Technology, University of ChineseAcademy of Science, Beijing 100049, People’s Republic of China Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France (Dated:)In [S. Biswas et al., Eur. Phys. J. A 55, 159 (2019)] a longitudinal wobbling band was reportedin
La. The critical experimental proof for this assignment is the E2 dominated linking transi-tions between the wobbling and normal bands, which are supported by angular distribution andlinear polarization measurements. However, severe problems are found in the reported experimentalinformation, indicating that the assignment of wobbling band was not firmly established.
PACS numbers: 21.10.Re, 21.60.Ev, 23.20.Lv, 27.60.+j
The band built on the 17/2 − state at 1738 keV in Lawhich has been interpreted as the signature partner of theband built on the 11/2 − state at 536 keV in Ref. [1], hasbeen reinterpreted as longitudinal wobbling in Ref. [2]based on angular distribution and polarization measure-ments. As the first experimental candidate for low-spinlongitudinal wobbling, this work is rather important, anddeserves a careful examination on the reliability of the re-ported results.After evaluating the reported experimental informa-tion carefully, some problems are found. To establisha wobbling band, the key experimental criterion is the E I = 1 linking transitions. In the com-mented work [2], E /M δ ) were deducedby the angular distribution and linear polarization mea-surements. For three linking transitions with energies of758, 874, and 982 keV, the mixing ratios are all deducedwith absolute values larger than 1, leading to a predom-inantly electric nature.For the angular distribution, estimated curves with fit-ted a and a coefficients were shown in comparison withthe experimental results, and the mixing ratios were de-duced based on the a and a coefficients (see Fig. 2 inRef. [2]). The same curves are produced in the presentcomment, using the data of Ref. [2] and a direct method[3], and adding an extra curve for each transition pro-duced by using small mixing ratios ( | δ | <
1) (see Fig. 1).It is found that the curves with larger and smaller mixingratios are quite similar, and are hardly distinguishablewithin the reported error bars. It appears therefore thatthe dominating M I = 2 pure E − is higher by about an order of mag- θ(°)
758 keV 874 keV 982 keVExp. δ=0δ=-0.3δ=-1.96
Exp. δ=0δ=-0.3δ=-2.24
Exp. δ=0δ=-0.28δ=-2.9
FIG. 1. (Color online) Estimated angular distribution curvesand experimental results for the reported longitudinal wob-bling band in
La. The experimental results and the curvesfor pure M δ (in red) are takenfrom the Fig. 2 in Ref. [2], and those with smaller mixingratios and same σ /I are also plotted (in green) for comparison. nitude relative to the linking transitions of the yrare band(see Fig. 2 and Fig. 3 in Ref. [2]). However, the rela-tive errors of the counts on the 789-keV transition areeven slightly higher than those on the three linking tran-sitions. In addition, for each transition, the number ofcounts at different angles is different. This is in contrastwith the relative errors of the three linking transitionswhich are almost identical. We also checked the devia-tion between the experimental results and the estimatedcurve, which for the 789-keV transition is expected tobe smaller than for the linking transitions, because itsstatistics is higher. Based on the errors and the devia-tions between the experimental and calculated angulardistribution, the reported results of Ref. [2] appear tobe questionable, and for the three linking transitions inparticular, significantly underestimated.Another problem exists in the extraction of the polar-ization values from the coincidence events between thesegments of the Clover detector in the direction perpen-dicular ( N ⊥ ) and parallel ( N (cid:107) ) to the emission plane.According to Ref. [4], a r X i v : . [ nu c l - e x ] D ec C oun t -1 -0.5 0 0.500.040.08 E rr o r / C oun t -0.5 0 0.5 1cos( )θ 00.040.08 D e vu a ti on / C oun t FIG. 2. (Color online) The counts, relative errors and relativedeviations for the experimental results on the 789-, 758-, 874-,and 982-keV transitions in Ref. [2]. Q = aR − aR + 1 /P. (1)where Q denotes the polarization sensitivity of theCLOVER detectors, P denotes the polarization values, R denotes the ratio between N ⊥ and N (cid:107) , and a denotescorrection due to the asymmetry in response of the Cloversegments.According to the Fig. 4 in Ref. [2], the R values arededuced assuming a zero background (see Fig. 3). Wealso extracted the polarization values from the data inFig. 4 of Ref. [2] and list them in Fig. 4.It is found that the R value for the 874-keV transitionis much lower than those for the 758- and 982-keV tran-sitions, while the P values are only slightly different. Ac-cording to the Eq. 1, only two coefficients, Q and a , areinvolved in the deduction of P . The parameter a is cali-brated to increase or decrease linearly, while Q decreasesslightly with increasing γ energies in the 700-1000 keV in-terval. The curves in Fig. 4 are plotted according to Eq.1. For each transition, the suitable Q and a values shouldbe close to the corresponding curves. The calibration ofthe polarization sensitivity was not mentioned in Ref. [2].One observes that the curve for the 874-keV transition iswell below those for the 758- and 982-keV transitions. It
750 7600500100015002000 C oun t s Energy (keV) ┴ N /N ~1.27 ┴ N /N ~1.07 ┴ FIG. 3. (Color online) The spectra taken from Fig. 4 in Ref.[2]. The R values are deduced within the range between theorange dash lines assuming the a zero background (green dashlines). Asymmetry correction ( a ) P o l a r i za ti on S e n s iti v it y ( Q ) FIG. 4. (Color online) Each curve shows possible solutions ofasymmetry correction ( a ) and polarization sensitivity ( Q ) todeduce the reported polarization values ( P ) from the reportedspectra for the three linking transitions of 758, 874 and 982keV. As a reference, the area between two green lines showthe reasonable values for Q according to a calibration in Ref.[4]. is therefore impossible to find three points on the threecurves which would induce a monotonic change of a and Q values with decreasing transition energy. Therefore itis questionable how the polarization values were deduced.In conclusion, severe problems have been found in thereported experimental results in Ref. [2], which shedsdoubts on the existence of the reported longitudinal wob-bling. Meanwhile, considering the importance of the ex-perimental observation on the low-spin longitudinal wob-bling, another experimental work and reliable data anal-ysis would be very welcome to clarify the identified in-congruences in Ref. [2].This work has been partly supported by the NationalNatural Science Foundation of China, under contractsNo. 11805289 and U1932137. ∗ Corresponding author ; [email protected][1] C.M. Petrache et al. Phys. Rev. C , 94, 064309, (2016).[2] S. Biswas et al. Eur. Phys. J. A , 55, 159, (2019).[3] J. T. Matta et al. Phys. Rev. Lett. , 114, 082501, (2015).[4] K. Starosta et al. Nucl. Instrum. Methods Phys. Res. Sect.Aet al. Nucl. Instrum. Methods Phys. Res. Sect.A