Abstract
The g factor of the \(12^+\) K-isomer in \(^{174}\)W has been measured by means of the time-differential perturbed angular distribution technique as \(g(12^+)=+0.304(11)\). In addition, the half-life of the isomer has been remeasured as \(T_{1/2}(12^+)=124(8)\) ns, in agreement with the literature value and confirming the anomalous hindrance F of the E2 transition to the \(10^+\) level of the ground state band with respect to the \(\gamma \)-tunnelling model prediction. The measured g factor has been compared with estimates based on experimental g factors from odd-mass isotopes in the same mass region and with Nilsson model calculations. The results establish unique features of the \(12^+\) K-isomer in \(^{174}\)W, which can possess a non-pure intrinsic configuration and/or can be characterised by values of the intrinsic quadrupole moment \(Q_0\) and the rotational g factor \(g_R\) significantly different with respect to the majority of K-isomers at mass \(A \approx 180\).
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The dataset analyzed during the current study is available from the corresponding author on reasonable request.]
Notes
The \(8^-\) level at 2268 keV with \(T_{1/2} = 158(3)\) ns [18] is fed from the the \(K=12^+\) isomer (see Fig. 1). For this reason, and also because of the chosen value of the magnetic field (optimized for the \(K=12^+\) isomer), the level of statistics achieved in the present experiment prevented the determination of the g factor for the \(K=8^-\) isomer.
In the case of a state with \(K=1/2\), instead of using Eq. 4, the g factor is calculated with the equation 4-88 of Ref. [33]:
$$\begin{aligned} g=g_R+\frac{g_K-g_R}{4I(I+1)}\left[ 1+\left( 2I+1\right) \left( -1\right) ^{I+\frac{1}{2}}b_0\right] \end{aligned}$$(6)where \(b_0\) is the magnetic decoupling parameter.
It should be noted that if the band built on the \(K=12^+\) isomer is affected by Coriolis mixing, the \(\left| (g_K-g_R) /Q_0\right| \) ratio determined from the excited states in the band in Ref. [18] could be different than the one of the band head. This would be particularly true if the \(K=12^+\) isomer configuration includes orbits with \(i_{13/2}\) neutron parentage, such as \(7/2^+[633]\) or \(5/2^+[642]\). As discussed in Ref. [36], the effect of Coriolis interactions could manifest as a renormalization of the \(g_R\) value. However, in the present discussion, it is assumed that the effect of the Coriolis mixing in the band built on the \(K=12^+\) isomer is negligible and that \(g_R\) is the same in Eqs. 4 and 7.
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Acknowledgements
We thankfully acknowledge the staff of the LNL Tandem-XTU accelerator for the high quality of the delivered \(^{16}\)O beam, M. Loriggiola for producing the target and the mechanical workshops of the INFN division of Florence for their crucial contribution. The contribution of A. Stuchbery in producing Table 1 and Fig. 6 is gratefully acknowledged. We are also grateful to M. Ionescu-Bujor and P.M. Walker for the fruitful discussions on both the data analysis and the interpretation.
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Rocchini, M., Nannini, A., Benzoni, G. et al. g factor of the \(12^+\) K-isomer in \(^{174}\)W. Eur. Phys. J. A 56, 289 (2020). https://doi.org/10.1140/epja/s10050-020-00298-3
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DOI: https://doi.org/10.1140/epja/s10050-020-00298-3