Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Thermonuclear reactions probed at stellar-core conditions with laser-based inertial-confinement fusion


Stars are giant thermonuclear plasma furnaces that slowly fuse the lighter elements in the universe into heavier elements, releasing energy, and generating the pressure required to prevent collapse. To understand stars, we must rely on nuclear reaction rate data obtained, up to now, under conditions very different from those of stellar cores. Here we show thermonuclear measurements of the 2H(d, n)3He and 3H(t,2n)4He S-factors at a range of densities (1.2–16?g?cm−3) and temperatures (2.1–5.4?keV) that allow us to test the conditions of the hydrogen-burning phase of main-sequence stars. The relevant conditions are created using inertial-confinement fusion implosions at the National Ignition Facility. Our data agree within uncertainty with previous accelerator-based measurements and establish this approach for future experiments to measure other reactions and to test plasma-nuclear effects present in stellar interiors, such as plasma electron screening, directly in the environments where they occur.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 2: Comparison of the core conditions of several stellar systems to those achieved in the experiments described herein.
Figure 1: Experimental setup and conditions achieved at peak burn.
Figure 3: Thermonuclear reactivity and S-factor data for 2H(d, n)3He and 3H(t,2n)4He.


  1. 1

    Bethe, H. A. Energy production in stars. Phys. Rev. 55, 434–456 (1939).

    Article  ADS  MATH  Google Scholar 

  2. 2

    Clayton, D. D. Principles of Stellar Evolution and Nucleosynthesis: With a New Preface (University of Chicago Press, 1968).

    Google Scholar 

  3. 3

    Junker, M. et al. Cross section of 3He(3He,2p)4He measured at solar energies. Phys. Rev. C 57, 2700–2710 (1998).

    Article  ADS  Google Scholar 

  4. 4

    Bonetti, R. et al. First measurement of the 3He(3He,2p)4He cross section down to the lower edge of the solar Gamow peak. Phys. Rev. Lett. 82, 5205–5208 (1999).

    Article  ADS  Google Scholar 

  5. 5

    Dzitko, H., Turck-Chieze, S., Delbourgo-Salvador, P. & Lagrange, C. The screened nuclear reaction rates and the solar neutrino puzzle. Astrophys. J. 447, 428–442 (1995).

    Article  ADS  Google Scholar 

  6. 6

    Adelberger, E. G. et al. Solar fusion cross sections. Rev. Mod. Phys. 70, 1265–1291 (1998).

    Article  ADS  Google Scholar 

  7. 7

    Fowler, W. A. What cooks with solar neutrinos? Nature 238, 24–26 (1972).

    Article  ADS  Google Scholar 

  8. 8

    Super-Kamiokande, C. et al. Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett. 81, 1562–1567 (1998).

    Article  Google Scholar 

  9. 9

    Ahmad, Q. R. et al. Measurement of the rate of ν e + dp + p + e interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory. Phys. Rev. Lett. 87, 071301 (2001).

    Article  ADS  Google Scholar 

  10. 10

    Ahmad, Q. R. et al. Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory. Phys. Rev. Lett. 89, 011301 (2002).

    Article  ADS  Google Scholar 

  11. 11

    Csótó, A. & Langanke, K. Large-space cluster model calculations for the 3He(3He,2p)4He and 3H(3H,2n)4He reactions. Nucl. Phys. A 646, 387–396 (1999).

    Article  ADS  Google Scholar 

  12. 12

    Moses, E. I., Boyd, R. N., Remington, B. A., Keane, C. J. & Al-Ayat, R. The National Ignition Facility: ushering in a new age for high energy density science. Phys. Plasmas 16, 041006 (2009).

    Article  ADS  Google Scholar 

  13. 13

    Eggleton, P. P., Dearborn, D. S. P. & Lattanzio, J. C. Deep mixing of 3He: reconciling Big Bang and stellar nucleosynthesis. Science 314, 1580–1583 (2006).

    Article  ADS  Google Scholar 

  14. 14

    Stahler, S. W. Deuterium and the stellar birthline. Astrophys. J. 332, 804–825 (1988).

    Article  ADS  Google Scholar 

  15. 15

    Spiegel, D. S., Burrows, A. & Milsom, J. A. The deuterium-burning mass limit for brown dwarfs and giant planets. Astrophys. J. 727, 57 (2011).

    Article  ADS  Google Scholar 

  16. 16

    Serpico, P. D. et al. Nuclear reaction network for primordial nucleosynthesis: a detailed analysis of rates, uncertainties and light nuclei yields. J. Cosmol. Astropart. Phys. 2004, 010 (2004).

    Article  Google Scholar 

  17. 17

    Cook, A. W. Artificial fluid properties for large-eddy simulation of compressible turbulent mixing. Phys. Fluids 19, 055103 (2007).

    Article  ADS  MATH  Google Scholar 

  18. 18

    Weber, C. R. et al. Three-dimensional hydrodynamics of the deceleration stage in inertial confinement fusion. Phys. Plasmas 22, 032702 (2015).

    Article  ADS  Google Scholar 

  19. 19

    Marinak, M. M. et al. Three-dimensional HYDRA simulations of National Ignition Facility targets. Phys. Plasmas 8, 2275–2280 (2001).

    Article  ADS  Google Scholar 

  20. 20

    Smalyuk, V. A. et al. Measurements of an ablator-gas atomic mix in indirectly driven implosions at the National Ignition Facility. Phys. Rev. Lett. 112, 025002 (2014).

    Article  ADS  Google Scholar 

  21. 21

    Casey, D. T. et al. Development of the CD Symcap platform to study gas-shell mix in implosions at the National Ignition Facility. Phys. Plasmas 21, 092705 (2014).

    Article  ADS  Google Scholar 

  22. 22

    Chadwick, M. B. et al. ENDF/B-VII.0: next generation evaluated nuclear data library for nuclear science and technology. Nucl. Data Sheets 107, 2931–3060 (2006).

    Article  ADS  Google Scholar 

  23. 23

    Adelberger, E. G. et al. Solar fusion cross sections. II. The pp chain and CNO cycles. Rev. Mod. Phys. 83, 195–245 (2011).

    Article  ADS  Google Scholar 

  24. 24

    Patel, P. et al. Bull. Am. Phys. Soc. 55th Annu. Meeting APS Div. Plasma Phys. Vol. 58, 16 (American Physical Society, 2013).

    Google Scholar 

  25. 25

    Atzeni, S. & Meyer-ter-Vehn, J. The Physics of Inertial Fusion (Oxford Univ. Press, 2004).

    Book  Google Scholar 

  26. 26

    Angulo, C. et al. A compilation of charged-particle induced thermonuclear reaction rates. Nucl. Phys. A 656, 3–183 (1999).

    Article  ADS  Google Scholar 

  27. 27

    Kim, Y. et al. D-T gamma-to-neutron branching ratio determined from inertial confinement fusion plasmas. Phys. Plasmas 19, 056313 (2012).

    Article  ADS  Google Scholar 

  28. 28

    Zylstra, A. B. et al. Using inertial fusion implosions to measure the T + 3He fusion cross section at nucleosynthesis-relevant energies. Phys. Rev. Lett. 117, 035002 (2016).

    Article  ADS  Google Scholar 

  29. 29

    Data retrieved from the EXFOR database website on Jul 23, 2015.

  30. 30

    McNeill, K. G. & Keyser, G. M. The relative probabilities and absolute cross sections of the D − D reactions. Phys. Rev. 81, 602–606 (1951).

    Article  ADS  Google Scholar 

  31. 31

    Preston, G., Shaw, P. F. D. & Young, S. A. The cross-sections and angular distributions of the D+D reactions between 150 and 450 keV. Proc. R. Soc. Lond. A 226, 206–216 (1954).

    Article  ADS  Google Scholar 

  32. 32

    Booth, D. L., Preston, G. & Shaw, P. F. D. The cross section and angular distributions of the D-D reactions between 40 and 90 keV. Proc. Phys. Soc. A 69, 265–270 (1956).

    Article  ADS  Google Scholar 

  33. 33

    Ganeev, A. S. et al. The D-D reaction in the deuteron energy range 100-1000 kev. Sov. J. At. Energy 5, 21–36 (1958).

    Google Scholar 

  34. 34

    Davidenko, V. A., Kucher, A. M., Pogrebov, I. S. & Tuturov, I. F. Nuclear reactions in light nuclei. Sov. J. At. Energy Suppl. No 5, 7 (1957).

    Google Scholar 

  35. 35

    Belov, A. S., Kusik, V. E. & Ryabov, Yu. V. The nuclear fusion for the reactions 2H(d, n)3He,2H(d,γ)4He at low deuterons energy and cold nuclear fusion. Il Nuovo Cimento A 103, 1647–1650 (1990).

    Article  ADS  Google Scholar 

  36. 36

    Brown, R. E. & Jarmie, N. Differential cross sections at low energies for 2H(d,p)3H and 2H(d,n)3He. Phys. Rev. C 41, 1391–1400 (1990).

    Article  ADS  Google Scholar 

  37. 37

    Greife, U., Gorris, F., Junker, M., Rolfs, C. & Zahnow, D. Oppenheimer–Phillips effect and electron screening in d + d fusion reactions. Z. Phys. A 351, 107–112 (1995).

    Article  ADS  Google Scholar 

  38. 38

    Leonard, D. S., Karwowski, H. J., Brune, C. R., Fisher, B. M. & Ludwig, E. J. Precision measurements of 2H(d, p)3H and 2H(d, n)3He total cross sections at Big Bang nucleosynthesis energies. Phys. Rev. C 73, 045801 (2006).

    Article  ADS  Google Scholar 

  39. 39

    Bystritsky, V. M. et al. Using a Hall accelerator to investigate d(d, n)3He and d(p, γ)3He reactions in the astrophysical energy region. Bull. Russ. Acad. Sci. Phys. 74, 531–534 (2010).

    Article  Google Scholar 

  40. 40

    Serov, V. I., Abramovich, S. N. & Morkin, L. A. Total cross section measurement for the reaction T(t, 2n)4He. At. Energy 42, 66–69 (1977).

    Article  Google Scholar 

  41. 41

    Govorov, A. M., Li, K.-Y., Osetinskii, G. M., Salatskii, V. I. & Sizov, I. V. Total cross section of the T + T reaction in the 60–1140 keV energy range. Sov. Phys. JETP 15, 266–267 (1962).

    Google Scholar 

  42. 42

    Jarmie, N. & Allen, R. C. T(t, α)n, n reaction. Phys. Rev. 111, 1121–1128 (1958).

    Article  ADS  Google Scholar 

  43. 43

    Agnew, H. M. et al. Measurement of the cross section for the reaction T + T → He4+2n+11.4?Mev. Phys. Rev. 84, 862–863 (1951).

    Article  ADS  Google Scholar 

  44. 44

    Krauss, A., Becker, H. W., Trautvetter, H. P., Rolfs, C. & Brand, K. Low-energy fusion cross sections of D + D and D + 3He reactions. Nucl. Phys. A 465, 150–172 (1987).

    Article  ADS  Google Scholar 

  45. 45

    Data retrieved from website on Jul 23, 2015.

  46. 46

    Assenbaum, H. J., Langanke, K. & Rolfs, C. Effects of electron screening on low-energy fusion cross sections. Z. Phys. A 327, 461–468 (1987).

    ADS  Google Scholar 

  47. 47

    Salpeter, E. E. Electron screening and thermonuclear reactions. Aust. J. Phys. 7, 373–388 (1954).

    Article  ADS  MATH  Google Scholar 

  48. 48

    Brown, L. S. & Sawyer, R. F. Nuclear reaction rates in a plasma. Rev. Mod. Phys. 69, 411–436 (1997).

    Article  ADS  Google Scholar 

  49. 49

    Graboske, H. C., Dewitt, H. E., Grossman, A. S. & Cooper, M. S. Screening factors for nuclear reactions. II. Intermediate screening and astrophysical applications. Astrophys. J. 181, 457–474 (1973).

    Article  ADS  Google Scholar 

  50. 50

    Bahcall, J. N. Non-resonant nuclear reactions at stellar temperatures. Astrophys. J. 143, 259–261 (1966).

    Article  ADS  Google Scholar 

  51. 51

    Casey, D. T. et al. Measuring the absolute deuterium–tritium neutron yield using the magnetic recoil spectrometer at OMEGA and the NIF. Rev. Sci. Instrum. 83, 10D912 (2012).

    Article  Google Scholar 

  52. 52

    Cooper, G. W. et al. Copper activation deuterium-tritium neutron yield measurements at the National Ignition Facility. Rev. Sci. Instrum. 83, 10D918 (2012).

    Article  Google Scholar 

  53. 53

    Bleuel, D. L. et al. Neutron activation diagnostics at the National Ignition Facility (invited). Rev. Sci. Instrum. 83, 10D313 (2012).

    Article  Google Scholar 

  54. 54

    Johnson, M. G. et al. Neutron spectrometry—an essential tool for diagnosing implosions at the National Ignition Facility (invited). Rev. Sci. Instrum. 83, 10D308 (2012).

    Article  Google Scholar 

  55. 55

    Yeamans, C. B., Bleuel, D. L. & Bernstein, L. A. Enhanced NIF neutron activation diagnostics. Rev. Sci. Instrum. 83, 10D315 (2012).

    Article  Google Scholar 

  56. 56

    Frenje, J. A. et al. First measurements of the absolute neutron spectrum using the magnetic recoil spectrometer at OMEGA (invited). Rev. Sci. Instrum. 79, 10E502 (2008).

    Article  Google Scholar 

  57. 57

    Sayre, D. B. et al. Measurement of the T + T neutron spectrum using the National Ignition Facility. Phys. Rev. Lett. 111, 052501 (2013).

    Article  ADS  Google Scholar 

  58. 58

    Casey, D. T. et al. Measurements of the T(t,2n)4He neutron spectrum at low reactant energies from inertial confinement implosions. Phys. Rev. Lett. 109, 025003 (2012).

    Article  ADS  Google Scholar 

  59. 59

    Allen, K. W., Almqvist, E., Dewan, J. T., Pepper, T. P. & Sanders, J. H. The T + T reactions. Phys. Rev. 82, 262–263 (1951).

    Article  ADS  Google Scholar 

  60. 60

    Wong, C., Anderson, J. D. & McClure, J. W. Neutron spectrum from the T + T reaction. Nucl. Phys. 71, 106–112 (1965).

    Article  Google Scholar 

  61. 61

    Brune, C. R. et al. R-matrix description of particle energy spectra produced by low-energy 3H + 3H reactions. Phys. Rev. C 92, 014003 (2015).

    Article  ADS  Google Scholar 

Download references


The authors sincerely thank the NIF operations staff who supported this work. The authors also thank N. Kabadi for discovering an error in equation (9) in an earlier version of the manuscript. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and by Ohio University under US Department of Energy grant number DE-FG02-88ER40387 and DE-NA0002905.

Author information




D.T.C. shot (experiments) RI (responsible individual), stagnation campaign lead, and nuclear data analysis. D.B.S. nTOF (neutron time of flight) instrument analysis and nuclear data analysis. C.R.B. nuclear data analysis. V.A.S. shot RI and CD symcap campaign lead. C.R.W. three dimensional hydrodynamic simulations. R.E.T. experiment design and one dimensional hydrodynamic simulations. J.E.P. experiment design, CD symcap campaign lead, and two dimensional hydrodynamic simulations. G.P.G. shot RI and nTOF analysis. B.A.R. mix campaign lead. D.D. stellar evolution simulations. L.R.B. shot RI and X-ray image analysis. J.A.F. Magnetic Recoil Spectrometer (MRS) analysis. M.G.-J. MRS analysis. R.H. nTOF analysis. N.I. shot RI and X-ray image analysis. J.M.M. shot RI and nTOF analysis. T.M. shot RI and X-ray image analysis. G.A.K. shot RI and X-ray image analysis. S.M. experiment design and 2shock campaign lead. J.S. experiment design. S.F.K. shot RI and X-ray image analysis. A.P. shot RI and X-ray image analysis. L.B.H. experiment design. S.L. shot RI. B.K.S. experiment design and stagnation campaign lead. N.B.M. experiment design and IDEP campaign lead. L.D. experiment design. C.B.Y. shot RI and activation diagnostics analysis. J.A.C. nTOF analysis. D.P.M. nuclear data analysis. D.M.H. deuterium and tritium operations. M.C.-Z. mass spectrometer data analysis. T.R.K. deuterium and tritium operations. T.G.P. deuterium and tritium operations.

Corresponding author

Correspondence to D. T. Casey.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 689 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Casey, D., Sayre, D., Brune, C. et al. Thermonuclear reactions probed at stellar-core conditions with laser-based inertial-confinement fusion. Nature Phys 13, 1227–1231 (2017).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing