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Discrepancy between experimental and theoretical β-decay rates resolved from first principles


The dominant decay mode of atomic nuclei is beta decay (β-decay), a process that changes a neutron into a proton (and vice versa). This decay offers a window to physics beyond the standard model, and is at the heart of microphysical processes in stellar explosions and element synthesis in the Universe1,2,3. However, observed β-decay rates in nuclei have been found to be systematically smaller than for free neutrons: this 50-year-old puzzle about the apparent quenching of the fundamental coupling constant by a factor of about 0.75 (ref. 4) is without a first-principles theoretical explanation. Here, we demonstrate that this quenching arises to a large extent from the coupling of the weak force to two nucleons as well as from strong correlations in the nucleus. We present state-of-the-art computations of β-decays from light- and medium-mass nuclei to 100Sn by combining effective field theories of the strong and weak forces5 with powerful quantum many-body techniques6,7,8. Our results are consistent with experimental data and have implications for heavy element synthesis in neutron star mergers9,10,11 and predictions for the neutrino-less double-β-decay3, where an analogous quenching puzzle is a source of uncertainty in extracting the neutrino mass scale12.

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Fig. 1: Gamow–Teller strength in 100Sn.
Fig. 2: Gamow–Teller strengths in light nuclei.
Fig. 3: Gamow–Teller strengths in medium-mass nuclei.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Janka, H.-T., Langanke, K., Marek, A., Martínez-Pinedo, G. & Müller, B. Theory of core-collapse supernovae. Phys. Rep. 442, 38–74 (2007).

    ADS  Article  Google Scholar 

  2. 2.

    Schatz, H. et al. Strong neutrino cooling by cycles of electron capture and β-decay in neutron star crusts. Nature 505, 62–65 (2013).

    ADS  Article  Google Scholar 

  3. 3.

    Engel, J. & Menéndez, J. Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review. Rep. Prog. Phys. 80, 046301 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    Towner, I. S. Quenching of spin matrix elements in nuclei. Phys. Rep. 155, 263–377 (1987).

    ADS  Article  Google Scholar 

  5. 5.

    Epelbaum, E., Hammer, H.-W. & Meißner, U.-G. Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009).

    ADS  Article  Google Scholar 

  6. 6.

    Barrett, B. R., Navrátil, P. & Vary, J. P. Ab initio no core shell model. Prog. Part. Nucl. Phys. 69, 131–181 (2013).

    ADS  Article  Google Scholar 

  7. 7.

    Hagen, G. et al. Neutron and weak-charge distributions of the 48Ca nucleus. Nat. Phys. 12, 186–190 (2016).

    Article  Google Scholar 

  8. 8.

    Stroberg, S. R. et al. Nucleus-dependent valence-space approach to nuclear structure. Phys. Rev. Lett. 118, 032502 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Korobkin, O., Rosswog, S., Arcones, A. & Winteler, C. On the astrophysical robustness of the neutron star merger r-process. Mon. Not. R. Astron. Soc. 426, 1940–1949 (2012).

    ADS  Article  Google Scholar 

  10. 10.

    Mumpower, M. R., Surman, R., McLaughlin, G. C. & Aprahamian, A. The impact of individual nuclear properties on r-process nucleosynthesis. Prog. Part. Nucl. Phys. 86, 86–126 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    Pian, E. et al. Spectroscopic identification of r-process nucleosynthesis in a double neutron-star merger. Nature 551, 67–70 (2017).

    ADS  Article  Google Scholar 

  12. 12.

    Barea, J., Kotila, J. & Iachello, F. Limits on neutrino masses from neutrinoless double-β decay. Phys. Rev. Lett. 109, 042501 (2012).

    ADS  Article  Google Scholar 

  13. 13.

    Wilkinson, D. H. Renormalization of the axial-vector coupling constant in nuclear β-decay (II). Nucl. Phys. A 209, 470–484 (1973).

    ADS  Article  Google Scholar 

  14. 14.

    Brown, B. A. & Wildenthal, B. H. Experimental and theoretical Gamow–Teller beta-decay observables for the sd-shell nuclei. At. Data Nucl. Data Tables 33, 347–404 (1985).

    ADS  Article  Google Scholar 

  15. 15.

    Chou, W.-T., Warburton, E. K. & Brown, B. A. Gamow–Teller beta-decay rates for A ≤ 18 nuclei. Phys. Rev. C 47, 163–177 (1993).

    ADS  Article  Google Scholar 

  16. 16.

    Martínez-Pinedo, G., Poves, A., Caurier, E. & Zuker, A. P. Effective G A in the pf shell. Phys. Rev. C 53, R2602–R2605 (1996).

    ADS  Article  Google Scholar 

  17. 17.

    Machleidt, R. & Entem, D. R. Chiral effective field theory and nuclear forces. Phys. Rep. 503, 1–75 (2011).

    ADS  Article  Google Scholar 

  18. 18.

    Holt, J. W., Kaiser, N. & Weise, W. Chiral three-nucleon interaction and the 14C-dating β decay. Phys. Rev. C 79, 054331 (2009).

    ADS  Article  Google Scholar 

  19. 19.

    Maris, P. et al. Origin of the anomalous long lifetime of 14C. Phys. Rev. Lett. 106, 202502 (2011).

    ADS  Article  Google Scholar 

  20. 20.

    Hinke, C. B. et al. Superallowed Gamow–Teller decay of the doubly magic nucleus 100Sn. Nature 486, 341–345 (2012).

    ADS  Article  Google Scholar 

  21. 21.

    Morris, T. D. et al. Structure of the lightest tin isotopes. Phys. Rev. Lett. 120, 152503 (2018).

    ADS  Article  Google Scholar 

  22. 22.

    Hebeler, K., Bogner, S. K., Furnstahl, R. J., Nogga, A. & Schwenk, A. Improved nuclear matter calculations from chiral low-momentum interactions. Phys. Rev. C 83, 031301 (2011).

    ADS  Article  Google Scholar 

  23. 23.

    Ekström, A. et al. Accurate nuclear radii and binding energies from a chiral interaction. Phys. Rev. C 91, 051301 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Leistenschneider, E. et al. Dawning of the N = 32 shell closure seen through precision mass measurements of neutron-rich titanium isotopes. Phys. Rev. Lett. 120, 062503 (2018).

    ADS  Article  Google Scholar 

  25. 25.

    Batist, L. et al. Systematics of Gamow–Teller beta decay ‘southeast’ of 100Sn. Eur. Phys. J. A 46, 45–53 (2010).

    ADS  Article  Google Scholar 

  26. 26.

    Pastore, S. et al. Quantum Monte Carlo calculations of weak transitions in A = 6–10 nuclei. Phys. Rev. C 97, 022501 (2018).

    ADS  Article  Google Scholar 

  27. 27.

    Langanke, K., Dean, D. J., Radha, P. B., Alhassid, Y. & Koonin, S. E. Shell-model Monte Carlo studies of fp-shell nuclei. Phys. Rev. C 52, 718–725 (1995).

    ADS  Article  Google Scholar 

  28. 28.

    Gaarde, C. et al. Excitation of giant spin–isospin multipole vibrations. Nucl. Phys. A 369, 258–280 (1981).

    ADS  Article  Google Scholar 

  29. 29.

    Wakasa, T. et al. Gamow–Teller strength of 90Nb in the continuum studied via multipole decomposition analysis of the 90Zr(p,n) reaction at 295 MeV. Phys. Rev. C 55, 2909–2922 (1997).

    ADS  Article  Google Scholar 

  30. 30.

    Bhat, M. R. in Qaim, S. M. (ed.) Nuclear Data for Science and Technology, 817 (Springer, Berlin, 1992).

  31. 31.

    Brown, B. A. & Richter, W. A. New ‘USD’ Hamiltonians for the sd shell. Phys. Rev. C 74, 034315 (2006).

    ADS  Article  Google Scholar 

  32. 32.

    Entem, D. R. & Machleidt, R. Accurate charge-dependent nucleon–nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001 (2003).

    ADS  Article  Google Scholar 

  33. 33.

    Bogner, S. K., Furnstahl, R. J. & Perry, R. J. Similarity renormalization group for nucleon–nucleon interactions. Phys. Rev. C 75, 061001 (2007).

    ADS  Article  Google Scholar 

  34. 34.

    Hagen, G., Jansen, G. R. & Papenbrock, T. Structure of 78Ni from first-principles computations. Phys. Rev. Lett. 117, 172501 (2016).

    ADS  Article  Google Scholar 

  35. 35.

    Simonis, J., Stroberg, S. R., Hebeler, K., Holt, J. D. & Schwenk, A. Saturation with chiral interactions and consequences for finite nuclei. Phys. Rev. C 96, 014303 (2017).

    ADS  Article  Google Scholar 

  36. 36.

    Entem, D. R., Machleidt, R. & Nosyk, Y. High-quality two-nucleon potentials up to fifth order of the chiral expansion. Phys. Rev. C 96, 024004 (2017).

    ADS  Article  Google Scholar 

  37. 37.

    Navrátil, P. Local three-nucleon interaction from chiral effective field theory. Few-Body Systems 41, 117–140 (2007).

    ADS  Article  Google Scholar 

  38. 38.

    Edmonds, A. R. Angular Momentum in Quantum Mechanics (Princeton Univ. Press, Princeton, NJ, 1957).

  39. 39.

    Krebs, H., Epelbaum, E. & Meißner, U.-G. Nuclear axial current operators to fourth order in chiral effective field theory. Ann. Phys. 378, 317–395 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  40. 40.

    Park, T.-S. et al. Parameter-free effective field theory calculation for the solar proton-fusion and hep processes. Phys. Rev. C 67, 055206 (2003).

    ADS  Article  Google Scholar 

  41. 41.

    Gazit, D., Quaglioni, S. & Navrátil, P. Three-nucleon low-energy constants from the consistency of interactions and currents in chiral effective field theory. Phys. Rev. Lett. 103, 102502 (2009).

    ADS  Article  Google Scholar 

  42. 42.

    Hagen, G. et al. Coupled-cluster theory for three-body Hamiltonians. Phys. Rev. C 76, 034302 (2007).

    ADS  Article  Google Scholar 

  43. 43.

    Roth, R. et al. Medium-mass nuclei with normal-ordered chiral NN + 3N interactions. Phys. Rev. Lett. 109, 052501 (2012).

    ADS  Article  Google Scholar 

  44. 44.

    Hergert, H. et al. In-medium similarity renormalization group with chiral two- plus three-nucleon interactions. Phys. Rev. C 87, 034307 (2013).

    ADS  Article  Google Scholar 

  45. 45.

    Bartlett, R. J. & Musiał, M. Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 79, 291–352 (2007).

    ADS  Article  Google Scholar 

  46. 46.

    Hagen, G., Papenbrock, T., Hjorth-Jensen, M. & Dean, D. J. Coupled-cluster computations of atomic nuclei. Rep. Prog. Phys. 77, 096302 (2014).

    ADS  Article  Google Scholar 

  47. 47.

    Lee, Y. S., Kucharski, S. A. & Bartlett, R. J. A coupled cluster approach with triple excitations. J. Chem. Phys. 81, 5906–5912 (1984).

    ADS  Article  Google Scholar 

  48. 48.

    Watts, J. D. & Bartlett, R. J. Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies. Chem. Phys. Lett. 233, 81–87 (1995).

    ADS  Article  Google Scholar 

  49. 49.

    Ekström, A. et al. Effects of three-nucleon forces and two-body currents on Gamow–Teller strengths. Phys. Rev. Lett. 113, 262504 (2014).

    ADS  Article  Google Scholar 

  50. 50.

    Menéndez, J., Gazit, D. & Schwenk, A. Chiral two-body currents in nuclei: Gamow–Teller transitions and neutrinoless double-beta decay. Phys. Rev. Lett. 107, 062501 (2011).

    ADS  Article  Google Scholar 

  51. 51.

    Miorelli, M., Bacca, S., Hagen, G. & Papenbrock, T. Computing the dipole polarizability of 48Ca with increased precision. Phys. Rev. C 98, 014324 (2018).

    ADS  Article  Google Scholar 

  52. 52.

    Ikeda, K., Fujii, S. & Fujita, J. The (p,n) reactions and beta decays. Phys. Lett. 3, 271–272 (1963).

    ADS  Article  Google Scholar 

  53. 53.

    Yako, K. et al. Gamow–Teller strength distributions in 48Sc by the 48Ca(p,n) and 48Ti(n,p) reactions and two-neutrino double-β decay nuclear matrix elements. Phys. Rev. Lett. 103, 012503 (2009).

  54. 54.

    Smith, C. E., King, R. A. & Crawford, T. D. Coupled cluster methods including triple excitations for excited states of radicals. J. Chem. Phys. 122, 054110 (2005).

    ADS  Article  Google Scholar 

  55. 55.

    Faestermann, T., Górska, M. & Grawe, H. The structure of 100Sn and neighbouring nuclei. Prog. Part. Nucl. Phys. 69, 85–130 (2013).

    ADS  Article  Google Scholar 

  56. 56.

    Shen, J. & Piecuch, P. Biorthogonal moment expansions in coupled-cluster theory: review of key concepts and merging the renormalized and active-space coupled-cluster methods. Chem. Phys. 401, 180–202 (2012).

    Article  Google Scholar 

  57. 57.

    Shen, J. & Piecuch, P. Combining active-space coupled-cluster methods with moment energy corrections via the CC(P;Q) methodology, with benchmark calculations for biradical transition states. J. Chem. Phys. 136, 144104 (2012).

    ADS  Article  Google Scholar 

  58. 58.

    Navrátil, P., Vary, J. P. & Barrett, B. R. Large-basis ab initio no-core shell model and its application to 12C. Phys. Rev. C 62, 054311 (2000).

    ADS  Article  Google Scholar 

  59. 59.

    Roth, R. & Navrátil, P. Ab Initio study of 40Ca with an importance-truncated no-core shell model. Phys. Rev. Lett. 99, 092501 (2007).

    ADS  Article  Google Scholar 

  60. 60.

    Tsukiyama, K., Bogner, S. K. & Schwenk, A. In-medium similarity renormalization group for nuclei. Phys. Rev. Lett. 106, 222502 (2011).

    ADS  Article  Google Scholar 

  61. 61.

    Hergert, H., Bogner, S. K., Morris, T. D., Schwenk, A. & Tsukiyama, K. The in-medium similarity renormalization group: a novel ab initio method for nuclei. Phys. Rep. 621, 165–222 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  62. 62.

    Morris, T. D., Parzuchowski, N. M. & Bogner, S. K. Magnus expansion and in-medium similarity renormalization group. Phys. Rev. C 92, 034331 (2015).

    ADS  Article  Google Scholar 

  63. 63.

    Bogner, S. K. et al. Nonperturbative shell-model interactions from the in-medium similarity renormalization group. Phys. Rev. Lett. 113, 142501 (2014).

    ADS  Article  Google Scholar 

  64. 64.

    Parzuchowski, N. M., Stroberg, S. R., Navrátil, P., Hergert, H. & Bogner, S. K. Ab initio electromagnetic observables with the in-medium similarity renormalization group. Phys. Rev. C 96, 034324 (2017).

    ADS  Article  Google Scholar 

  65. 65.

    Brown, B. A. & Wildenthal, B. H. Status of the nuclear shell model. Annu. Rev. Nucl. Part. Sci. 38, 29–66 (1988).

    ADS  Article  Google Scholar 

  66. 66.

    Wildenthal, B. H., Curtin, M. S. & Brown, B. A. Predicted features of the beta decay of neutron-rich sd-shell nuclei. Phys. Rev. C 28, 1343–1366 (1983).

    ADS  Article  Google Scholar 

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The authors thank H. Grawe and T. Faestermann for useful correspondence, J. Engel, E. Epelbaum, D. Gazit, H. Krebs, D. Lubos, S. Pastore and R. Schiavilla for useful discussions and K. Hebeler for providing us with matrix elements in Jacobi coordinates for the three-nucleon interaction at next-to-next-to-leading order22. This work was prepared in part by Lawrence Livermore National Laboratory (LLNL) under contract DE-AC52-07NA27344 and was supported by the Office of Nuclear Physics, US Department of Energy, under grants DE-FG02-96ER40963, DE-FG02-97ER41014, DE-SC0008499, DE-SC0018223 and DE-SC0015376, the Field Work Proposals ERKBP57 and ERKBP72 at Oak Ridge National Laboratory (ORNL), the FWP SCW1579, LDRD projects 18-ERD-008 and 18-ERD-058 and the Lawrence Fellowship Program at LLNL, and by NSERC grant no. SAPIN-2016-00033, ERC grant no. 307986 STRONGINT and the DFG under grant SFB 1245. TRIUMF receives federal funding through a contribution agreement with the National Research Council of Canada. Computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) programme. This research used resources of the Oak Ridge Leadership Computing Facility located at ORNL, which is supported by the Office of Science of the Department of Energy under contract no. DE-AC05-00OR22725. Computations were also performed at LLNL Livermore Computing under the institutional Computing Grand Challenge Program, at Calcul Quebec, Westgrid and Compute Canada, and at the Jülich Supercomputing Center (JURECA).

Author information




G.H., T.D.M. and T.P. performed the coupled-cluster calculations. G.R.J. computed three-nucleon forces for the coupled-cluster calculations. P.G., S.Q., P.N. and K.A.W. performed calculations for the two-body currents. P.N. developed the higher-precision chiral three-nucleon interactions used in this work and performed no-core shell model calculations. G.H. and T.D.M. derived and implemented the new formalism to incorporate higher-order excitations in coupled-cluster theory. S.R.S. and J.D.H. performed VS-IMSRG calculations. All authors discussed the results and contributed to the manuscript at all stages.

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Correspondence to G. Hagen.

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Gysbers, P., Hagen, G., Holt, J.D. et al. Discrepancy between experimental and theoretical β-decay rates resolved from first principles. Nat. Phys. 15, 428–431 (2019).

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