I. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 55 (2022)

RIKEN Accel. Prog. Rep. 55 (2022)

Estimation of radiative half-life of 229m Th by half-life measurement ofother nuclear excited states in 229 Th†
Y. Shigekawa,∗1 A. Yamaguchi,∗2,∗3 K. Suzuki,∗4 H. Haba,∗1 T. Hiraki,∗4 H. Kikunaga,∗5 T. Masuda,∗4
S. Nishimura,∗1 N. Sasao,∗4 A. Yoshimi,∗4 and K. Yoshimura∗4
The ﬁrst excited state in the 229 Th nucleus (229m Th)
has an excitation energy of ∼8 eV.1–4) This low-lying isomeric state allows the laser excitation and spectroscopyof the nucleus, potentially leading to an ultraprecise optical nuclear clock.5) This radiative half-life of 229m Th,
which determines the natural linewidth of the nuclear
transition between the ground state and 229m Th, is an
important parameter to estimate the performance of thenuclear clock. The radiative half-life has yet to be determined experimentally; however, it can be estimated fromthe reduced transition probabilities B(Xλ) of the interband transitions between the 5/2+ [633] and 3/2+ [631]rotational bands beginning with higher excited states
than 229m Th by applying the Alaga rule.6) The Alaga
rule states that the ratio of two B(Xλ) values for a pairof intra- or inter-band transitions equals the ratio of thesquares of Clebsch-Gordan coeﬃcients based on the assumption of the separable rotational motion of a nucleus.
In this study, we measured the half-lives of the excitedstates in the 5/2+ [633] and 3/2+ [631] bands to determine
the B(Xλ) values required to estimate the radiative halflive of 229m Th.
To determine the half-lives, we performed a coincidence measurement between γ rays and α particles emitted from a 233 U source, as described in Ref. 7). First, we
obtained the time trace of the 42.43-keV γ rays following the 4783.5-keV α particles (see Fig. 1 in this paperand Fig. 2 in Ref. 7)). By ﬁtting a single exponential
decay function convoluted with a Gaussian function to
the time trace, the half-life of the 42.43-keV state wasdetermined to be 169(4) ps, which is consistent with thevalue of 172(6) ps reported previously.8) Next, we performed ﬁtting to the time trace of the 54.70-keV γ rays
following the 4729-keV α particles, yielding a half-life of103(12) ps. Moreover, by selecting the 97.14-keV γ rays,
we obtained a half-life of 88(9) ps. From the weighted average of these values, the half-life of the 97.14-keV state
was determined to be 93(7) ps. In the same manner, thehalf-life of the 71.82- and 163.25-keV states were determined for the ﬁrst time to be 120(40) and 220(30) ps by
ﬁtting to the time traces of the 71.82- and 66.12-keV γrays following the 4754-keV and 4664-keV α particles,
respectively.
We derived the B(Xλ) values using the obtained halflives, experimental γ branching ratios,1,9,10) mixing ra†
∗1
∗2
∗3
∗4
∗5

Condensed from the article in Phys. Rev. C 104, 024306 (2021)
RIKEN Nishina Center
Quantum Metrology Laboratory, RIKENPRESTO, Japan Science and Technology Agency
Research Institute for Interdisciplinary Science, Okayama University
Research Center for Electron-Photon Science, Tohoku UniversityFig. 1. Energy levels of the 229 Th nucleus grouped into rotational bands, as well as the α and γ transitions used
for determining the half-lives of the excited states (units:keV).

tios,9,10) and internal conversion coeﬃcients.10,11) First,
for the intra-band transitions, we found that the B(M1)and B(E2) values of the transitions starting with the29.19-, 42.43-, 71.83-, and 97.14-keV states were consistent with the values estimated from the Alaga rule.
By contrast, for the transitions starting with the 163.25keV state, the B(M1) and B(E2) values deviated fromthe estimation based on the Alaga rule, as it often appears with increasing nuclear spins. Next, to investigate
the validity of the Alaga rule for the inter-band transitions, we calculated the B(M1; 229m Th→229g Th) values
from the B(M1) values of the 29.19→0, 71.83→42.43,
and 97.14→71.83 keV transitions based on the Alaga
rule. The values obtained from the 29.19→0 and71.83→42.43 keV transitions agreed with each other(0.014(4) and 0.013(4) μN 2 , respectively). This indicatesthat the contribution of the Coriolis interactions is insigniﬁcant and the Alaga rule is applicable for the interband transitions between those low-spin states. The
weighted average of B(M1; 229m Th→229g Th) obtained
from these transitions was 0.014(3) μN 2 , from which
we estimated the radiative half-life of 229m Th to be
5.0(11) × 103 s.
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