Comment on "First Observation of Multiple Transverse Wobbling Bands of Different Kinds in 183 Au [Phys. Rev. Lett. 125, 132501 (2015)]"
CComment on “First Observation of Multiple Transverse Wobbling Bands of DifferentKinds in
Au [Phys. Rev. Lett. 125, 132501 (2020)]”
S. Guo
1, 2 and C. M. Petrache 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. Nandi et al., Phys. Rev. Lett. 125, 132501 (2020)] two transverse wobbling bands werereported in
Au. The critical experimental proof for this assignment is the E M PACS numbers: 21.10.Re, 21.60.Ev, 23.20.Lv, 27.60.+j
This comment quests on the reliability of the reportedtransverse wobbling bands in Ref. [1] via an analysis ofthe statistical error.To deduce the mixing ratio [2], the polarization ( P ) isextracted using the formula P = A/Q = aC ⊥ − C (cid:107) aC ⊥ + C (cid:107) /Q, (1)where C ⊥ and C (cid:107) denote the number of coincidencecounts between the segments of the clover detector inthe direction perpendicular and parallel to the emis-sion plane, respectively. Polarization sensitivity ( Q ) andasymmetry correction ( a ) were two necessary calibrationsabsent in Ref. [1].Here we examine the statistical error on the P of the495-keV transition, based on the corresponding spectrashown in Fig. 1. Surprisingly apparent backgrounds ex-ist below the 495-keV peaks in both perpendicular andparallel spectra.According to the spectra, C ⊥ = N ⊥ − N b ∼ ,C (cid:107) = N (cid:107) − N b ∼ . (2)One should not neglect the errors induced by subtract-ing the spectra gated by the Compton platform near tothe gating transition (marked by an extra subscript “ b ”),from that gated by the peak channels of the gating tran-sition (marked by an extra subscript “ p ”). Therefore thecounts can be further written as N ⊥ = N ⊥ p − N ⊥ b ∼ ,N (cid:107) = N (cid:107) p − N (cid:107) b ∼ ,N b = N bp − N bb ∼ . (3)
480 5000306090
N ~250 b N ~462 N ~449495 C oun t s Energy (keV)
FIG. 1. (Color online) Partial γ -ray spectra gated by 502-keVtransition extracted from Fig. 1c of Ref. [1]. The counts areobtained by summing the areas between the orange lines. Thebackground is estimated as shown in blue. Their statistical errors are σ ( N ⊥ ) = (cid:112)
462 + 2 σ ( N ⊥ b ) ,σ ( N (cid:107) ) = (cid:113)
449 + 2 σ ( N (cid:107) b ) ,σ ( N b ) = (cid:112)
250 + 2 σ ( N bb ) . (4)According to error propagation formulas in textbookssuch as Ref. [3], σ u ≈ (cid:115) σ x + σ y ( x + y ) , ( u = x − yx + y , x ≈ y ) . (5)Assuming a = 1 and imposing Q = 0.233 (using thecalibration in Ref. [2]) into Eqs. 1-5, a r X i v : . [ nu c l - e x ] D ec σ P (495) ≈ (cid:112) σ ( C ⊥ ) + σ ( C (cid:107) )( C ⊥ + C (cid:107) ) Q = (cid:112) σ ( N ⊥ b ) + 2 σ ( N (cid:107) b ) + 4 σ ( N bb )(212 + 199)0 . . (6)As a conservative estimation, one can assume that theerrors on N ⊥ b , N (cid:107) b , and N bb are all around √ N b ( √ σ P (495) ≈ .
61, which is much larger thanthe underestimated reported error σ P ≈ .
09. Accordingto the PDCO curves plotted in Fig. 2 of Ref. [1], it isimpossible to exclude one of the two solutions with anerror of ≈ .
61, and therefore to definitely establish thecharacter of the 495-keV transition.In addition, the wobbling nature to the h / band wasalso supported by the deduced mixing ratio of another498-keV connecting transition. However, the contamina-tion from another adjacent 498-keV E [1] S. Nandi, G. Mukherjee, Q. B. Chen, S. Frauendorf,R. Banik, and S. Bhattacharya et al. , Phys. Rev. Lett. , 132501 (2020).[2] K. Starosta, T. Morek, C. Droste, S. Rohozi´ n ski, J. Sre-brny, and A. Wierzchucka et al. , Nucl. Instrum. MethodsPhys. Res., Sect. A , 16 (1999).[3] G. F. Knoll, editor John Wiley & Sons, Inc., Third Edi-tion.114