The nuclear charge radius of 13C

Patrick Müller; Matthias Heinz; Phillip Imgram; Kristian König; Bernhard Maass; Takayuki Miyagi; Wilfried Nörtershäuser; Robert Roth; Achim Schwenk

doi:10.1038/s41467-025-60280-9

The nuclear charge radius of ¹³C

Patrick Müller
, Matthias Heinz
, Phillip Imgram
, Kristian König
, Bernhard Maass
, Takayuki Miyagi
, Wilfried Nörtershäuser
, Robert Roth
, Achim Schwenk

Advanced Computing for Nuclear, Particle

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of ¹³C and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the 2 ³S → 2 ³P fine-structure triplet in ¹³C⁴⁺ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than 2 MHz although second-order hyperfine-structure effects shift individual lines by several GHz. We improved the uncertainty of R_c(¹³C) determined with electrons by a factor of 6 and found a 3σ discrepancy with the muonic atom result of similar accuracy.

Original language	English
Article number	6234
Journal	Nature Communications
Volume	16
Issue number	1
DOIs	https://doi.org/10.1038/s41467-025-60280-9
State	Published - Dec 2025

Funding

We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 279384907—SFB 1245. The experiment (P.I., K.K., B.M., P.M., W.N.) was also supported in part by the BMBF under Contract Nos. 05P19RDFN1 and 05P21RDFNA. P.M. and P.I. acknowledge support from HGS-HIRE. M.H., T.M., and A.S. were supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 101020842).

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title = "The nuclear charge radius of 13C",

abstract = "The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of 13C and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the 2 3S → 2 3P fine-structure triplet in 13C4+ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than 2 MHz although second-order hyperfine-structure effects shift individual lines by several GHz. We improved the uncertainty of Rc(13C) determined with electrons by a factor of 6 and found a 3σ discrepancy with the muonic atom result of similar accuracy.",

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AU - Müller, Patrick

AU - Heinz, Matthias

AU - Imgram, Phillip

AU - König, Kristian

AU - Maass, Bernhard

AU - Miyagi, Takayuki

AU - Nörtershäuser, Wilfried

AU - Roth, Robert

AU - Schwenk, Achim

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AB - The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of 13C and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the 2 3S → 2 3P fine-structure triplet in 13C4+ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than 2 MHz although second-order hyperfine-structure effects shift individual lines by several GHz. We improved the uncertainty of Rc(13C) determined with electrons by a factor of 6 and found a 3σ discrepancy with the muonic atom result of similar accuracy.

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The nuclear charge radius of ¹³C

Abstract

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