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

## Abstract

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.

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## References

1. 1

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

2. 2

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

3. 3

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

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).

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).

6. 6

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

7. 7

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

8. 8

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

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).

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).

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).

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).

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).

14. 14

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

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).

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).

17. 17

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

18. 18

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

19. 19

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

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).

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).

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).

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).

24. 24

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

25. 25

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

26. 26

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

27. 27

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

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).

29. 29

Data retrieved from the EXFOR database http://www.nndc.bnl.gov/EXFOR 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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

42. 42

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

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).

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).

45. 45

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).

47. 47

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

48. 48

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

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).

50. 50

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

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).

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).

53. 53

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

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).

55. 55

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

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).

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).

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).

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).

60. 60

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

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).

## Acknowledgements

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

Authors

### Contributions

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)

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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). https://doi.org/10.1038/nphys4220

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