Radiative lifetime and energy of the low-energy isomeric level in $^{229}\mathrm{Th}$

Radiative lifetime and energy of the low-energy isomeric level in ${}^{229}{Th}$

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 92, 054324 – Published 25 November 2015; Erratum Phys. Rev. C 95, 039902 (2017)

Abstract

We estimate the range of the radiative lifetime and energy of the anomalous, low-energy $3 / 2^{+} (7.8 \pm 0.5$ eV) state in the ${}^{229}{Th}$ nucleus. Our phenomenological calculations are based on the available experimental data for the intensities of $M 1$ and $E 2$ transitions between excited levels of the ${}^{229}{Th}$ nucleus in the $K^{π} [N n_{Z} Λ] = 5 / 2^{+} [633]$ and $3 / 2^{+} [631]$ rotational bands. We also discuss the influence of certain branching coefficients, which affect the currently accepted measured energy of the isomeric state. From this work, we establish a favored region, $0.66 \times 10^{6} {s eV}^{3} / ω^{3} \leq τ \leq 2.2 \times 10^{6} {s eV}^{3} / ω^{3}$ , where the transition lifetime $τ$ as a function of transition energy $ω$ should lie at roughly the 95% confidence level. Together with the result of Beck et al. [LLNL-PROC-415170 (2009)], we establish a favored area where transition lifetime and energy should lie at roughly the 90% confidence level. We also suggest new nuclear physics measurements, which would significantly reduce the ambiguity in the present data.

Received 28 September 2015

DOI:https://doi.org/10.1103/PhysRevC.92.054324

Physics Subject Headings (PhySH)

Electromagnetic transitions Isomer decays Lifetimes & widths Nuclear structure & decays

A ≥ 220

Nuclear Physics

Erratum

Erratum: Radiative lifetime and energy of the low-energy isomeric level in $^{229} Th$ [Phys. Rev. C 92, 054324 (2015)]

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 95, 039902 (2017)

Authors & Affiliations

E. V. Tkalya^*

Skobeltsyn Institute of Nuclear Physics Lomonosov Moscow State University, Leninskie gory, Moscow 119991, Russia and Nuclear Safety Institute of Russian Academy of Science, Bol'shaya Tulskaya 52, Moscow 115191, Russia

Christian Schneider, Justin Jeet, and Eric R. Hudson

Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA

^*eugene.tkalya@mail.ru

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Vol. 92, Iss. 5 — November 2015

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Figure 1
The experimental values for the reduced probability of the nuclear (a) $9 / 2^{+} (97.14 keV) \to 7 / 2^{+} (71.83 keV)$ , and (b) $9 / 2^{+} (97.14 keV) \to 5 / 2^{+} (29.19 keV)$ transitions. The relevant level scheme of the ${}^{229}{Th}$ nucleus is shown in (c). Data for the transitions were taken from: 1 [47], 2 [48], 3 [49], and 4 [50].
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Figure 2
The range of possible radiative linewidths $Γ_{rad}$ (upper scale) and half-lives $T_{1 / 2}$ (lower scale) of the isomeric state $3 / 2^{+} 3 / 2 [631] (7.8 \pm 0.5 eV)$ in the ${}^{229}{Th}$ nucleus. Calculations are based on values for $B_{W . u .} (M 1; 3 / 2^{+} 3 / 2 [631] \to 5 / 2^{+} 5 / 2 [633])$ from Table 1 (calculated from: 1 [47], 2 [48], 3 [49], 4 [50]) and, for completeness, Table 2 (5 [43]; 6 [49]). The refractive index $n \approx 1.5$ increases the probability of the $M 1$ transition by a factor $n^{3}$ (third row). The Coriolis interaction can lead to a slight increase of the linewidth by a factor of 1.2–1.3 [13] (fourth row).
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Figure 3
The ranges of possible conversion widths (upper scale) and lifetimes (lower scale) of the isomeric nuclear state in a neutral isolated Th atom. The designations are identical with designations in Fig. 2.
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Figure 4
Relevant part of the level scheme of ${}^{229}{Th}$ with transitions and branching ratios $b^{*}, b_{29}$ , and $b_{42}$ used in the works [23, 42] to determine the energy of the isomeric level. Energies of the levels and transitions are given in keV.
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Figure 5
Favored region and experimentally excluded regions for the nuclear isomeric transition as a function of transition energy (wavelength) and radiative lifetime. (Left) The favored region (dash-dotted blue line; 95% confidence level; see text) and currently accepted energy of the isomeric transition (dotted blue lines) according to Ref. [24] [label: Beck (2009); 2 standard deviations $\approx 95$ % confidence level] are recommended as primary region of interest for current searches (blue shaded area). Experimentally excluded areas according to Ref. [67] (green shaded area between circles; label: Moore (2004); 99.7% confidence level; adopted from [67], Fig. 4]) and Ref. [2] [red shaded area between solid red lines; label: Jeet (2015); 90% confidence level] exclude parts of the favored region. Also shown are the more conservative bounds (outer dash-dotted yellow lines; see text). The point at 7.8 eV (blue circle) shows exemplarily the weighted average of the radiative lifetimes from reduced transition probabilities in Table 1 with 1.96 standard deviations including a Birge ratio of 3.4. (Right) Radiative lifetimes at 7.8 eV for individual values of the reduced transition probability with 1.96 standard deviations (corresponding to a 95% confidence level) according to Table 1 (circles, blue; labels: Bemis (1988): [47]; Gulda (2002): [48]; Barci (2003): [49]; Ruchowska (2006): [50]) and Table 2 (squares, red; labels: ${Barci}^{☆}$ (2003): [49]; Singh (2005): [43]). (The latter are only shown for completeness and do not enter into the construction of the favored region.)
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Physical Review C

covering nuclear physics

Radiative lifetime and energy of the low-energy isomeric level in ${}^{229}{Th}$

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 92, 054324 – Published 25 November 2015; Erratum Phys. Rev. C 95, 039902 (2017)

Abstract

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Erratum

Erratum: Radiative lifetime and energy of the low-energy isomeric level in $^{229} Th$ [Phys. Rev. C 92, 054324 (2015)]

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 95, 039902 (2017)

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Physical Review C

covering nuclear physics

Radiative lifetime and energy of the low-energy isomeric level in Th229

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 92, 054324 – Published 25 November 2015; Erratum Phys. Rev. C 95, 039902 (2017)

Abstract

Physics Subject Headings (PhySH)

Erratum

Erratum: Radiative lifetime and energy of the low-energy isomeric level in 229Th [Phys. Rev. C 92, 054324 (2015)]

E. V. Tkalya, Christian Schneider, Justin Jeet, and Eric R. Hudson

Phys. Rev. C 95, 039902 (2017)

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Radiative lifetime and energy of the low-energy isomeric level in ${}^{229}{Th}$

Erratum: Radiative lifetime and energy of the low-energy isomeric level in $^{229} Th$ [Phys. Rev. C 92, 054324 (2015)]