REVIEWS OF MODERN PHYSICS VoLUME 29, NuMBER 4 OcroBER, 1957 Synthesis of the Elements in Stars* E. MARGARET BURBIDGE, G. R. BURBIDGE, WILLIAM: A. FOWLER, AND F. HOYLE Kellogg Radiation1Laboratory, California Institute of Technology, and M aunt Wilson and Palomar Observatories, Carnegie Institution of Washington, California Institute of Technology, Pasadena, California "It is the stars, The stars above us, govern our conditions"; (King Lear, Act IV, Scene 3) but perhaps "The fault, dear Brutus, is not in our stars, But in ourselves," (Julius Caesar, Act I, Scene 2) TABLE OF CONTENTS Page I. Introduction ...............................................................· ............... 548 A. Element Abundances and Nuclear Structure. 548 B. Four Theories of the Origin of the Elements ............................................... 550 C. General Features of Stellar Synthesis ..................................................... 550 II. Physical Processes Involved in Stellar Synthesis, Their Place of Occurrence, and the Time-Scales Associated with Them ...............· ..................... · ................................. 551 A. Modes of Element Synthesis ............................................................. 551 B. Method of Assignment of Isotopes among Processes (i) to (viii) .............................. 553 C. Abundances and Synthesis Assignments Given in the Appendix. 555 D. Time-Scales for Different Modes of Synthesis .............................................. 556 III. Hydrogen Burning, Helium Burning, the a Process, and Neutron Production ..................... 559 A. Cross-Section Factor and Reaction Rates .................................................. 559 B. Pure Hydrogen Burning ................... ; ............................................... 562 C. Pure Helium Burning ................................................................... 565 D. a Process ................................... :· ........................................... 567 E. Succession of Nuclear Fuels in an Evolving Star ....... , ................................... 568 F. Burning of Hydrogen and Helium with Mixtures of Other Elements; Stellar Neutron Sources .... 569 IV. e Process. 577 V. s and r Processes: General Considerations. 580 A. "Shielded" and "Shielding" Isobars and the s, r, p Processes ................................. 580 B. Neutron-Capture Cross Sections ........... , .............................................. 581 C. General Dynamics of the s and r Processes . 583 VI. Details of the s Process . 583 *Supported in part by the joint program of the Office of Naval Research and the U. S. Atomic Energy Commission. 547 'Cqpyrlght © 1957 by the American Physical Society 548 BURBIDGE, BURBIDGE, FOWLER, AND HOYLE VII. Details of the r Process . 587 A. Path of the r Process ................................................................... 588 B. Calculation of the r-Process Abundances .................................................. 593 C. Time for the r Process: Steady Flow and Cycling. 596 D. Freezing of the r-Process Abundances ........................................... ·.......... 597 VIII. Extension and Termination of the r Process and s Process ..................................... 598 A. Synthesis of the Naturally Radioactive Elements .......................................... 598 B. Extension and Termination of the r Process .............................................. 598 C. Age of the Elements and of the Galaxy .................................................. 605 D. Termination of the s Process; the Abundances of Lead, Bismuth, Thorium, and Uranium ...... 608 IX. p Process ................................................................................ 615 X. x Process ................................................................................ 618 A. Observational Evidence for Presence of Deuterium, Lithium, Beryllium, and Boron in our Galaxy 618 B. Nuclear Reactions which Destroy Deuterium, Lithium, Beryllium, and Boron ................. 618 C. Synthesis of Deuterium, Lithium, Beryllium, and Boron . 618 D. Preservation of Lithium in Stars ......................................................... 620 XI. Variations in Chemical Composition among Stars, and Their Bearing on the Various Synthesizing Processes. 620 A. Hydrogen Burning and Helium Burning ................................................... 621 B. a Process .............................................................................. 626 C. Synthesis of Elements in the Iron Peak of the Abundance Curve, and the Aging Effect as It Is Related to This and Other Types of Element Synthesis . 626 D. s Process .............................................................................. 627 E. r Process ....................................................... ~ ...................... 629 F. p Process .............................................................................. 629 G. x Process .............................................................................. 629 H. Nuclear Reactions and Element Synthesis in Surfaces of Stars. 629 XU. General Astrophysics . 630 A. Ejection of Material from Stars and the Enrichment of the Galaxy in Heavy Elements ......... 63Q B. Supernova Outbursts. 633 C. Supernova Light Curves. 635 D. Origin of the r-Process Isotopes in the Solar System ....................................... 639 XIII. Conclusion . 639 Acknowledgments. 641 Appendix. 641 Bibliography. 647 I. INTRODUCTION of known nuclear species is almost 1200, with some 327 A. Element Abundances and Nuclear Structure of this number known to occur in nature. In spite of this, the situation is not as complex as it might seem. AN inhabits a universe composed of a great Research in "classical" nuclear physics since 1932 has M variety of elements and their isotopes. In Table shown that all nuclei consist of two fundamental build­ I,1 a count of the stable and radioactive elements and ing blocks. These are the proton and the neutron which isotopes is listed. Ninety elements are found terrestrially are called nucleons in this context. As long as energies and one more, technetium, is found in stars; only pro­ below the meson production threshold are not exceeded, methium has not been found in nature. Some 272 stable all "prompt" nuclear processes can be described as the and 55 naturally radioactive isotopes occur on the earth. shuffling and reshuffling of protons and neutrons into In addition, man has been able to produce artificially the variety of nucleonic packs called nuclei. Only in the the neutron, technetium, promethium, and ten trans­ slow beta-decay processes is there any interchange be­ manic elements. The number of radioactive isotopes he tween protons and neutrons at low energies, and even has produced now numbers 871 and this number is there, as in the prompt reactions, the number of nu­ gradually increasing. cleons remains constant. Only at very high energies Each isotopic form of an element contains a nucleus can nucleons be produced or annihilated. Prompt with its own characteristic nuclear properties which are nuclear processes plus the slow beta reactions make different from those of all other nuclei. Thus the total it possible in principle to transmute any one type of SYNTHESIS OF ELEMENTS IN STARS 549 TABLE 1,1. Table of elements and isotopes [compiled from Chart of the Nuclides (Knolls Atomic Power Laboratory, April, 1956)]. H Elements Isotopes 10 Stable 81 Stable 272 He Radioactive: Radioactive: Natural (Z~83) 1• Natural (A <206) 11d (Z>83) 9b . (A~206) 44 Natural: Natural: Stable and Radioactive 91 Stable and Radioactive 327 Radioactive: Radioactive: Artificial (Z ~ 83) 1• Artificial (A <206) 702 (Z>83) 10 (A~206) 169 Total 102 Total 1198 Neutron 1 Neutron 1 103 1199 N•82 N=l26 • Tc, observed in S-type stars. b Including At and Fr produced in weak side links of natural radioactivity e Pm, not observed in nature. d Including H•, Cl•, and Tc••. -2 nuclear material into any other even at low energies of interaction. With this relatively simple picture of the structure 100 .150 and interactions of the nuclei of the elements in mind, ATOMIC WEIGHT it is natural to attempt to explain their origin by a FIG. 1,1. Schematic curve of atomic abundances as a function synthesis or buildup starting with one or the other or of atomic weight based on the data of Suess and Urey (Su56). Suess and· Urey have employed relative isotopic abundances to both of the fundamental building blocks. The following determine the slope and general trend of the curve. There is still question can be asked: What has been the history of considerable spread of the individual abundances about the curve the matter, on which we can make observations, which illustrated, but the general features shown are now fairly well established. These features are outlined in Table 1,2. Note the produced the elements and isotopes of that matter in overabundances relative to their neighbors of the alpha-particle the abundance distribution which observation yields? nuclei A= 16, 20, · · ·40, the peak at the iron group nuclei, and the This history is hidden in the abundance distribution of twin peaks at A= 80 and 90, at 130 and 138, and at 194 and 208. the elements. To attempt to understand the sequence of events leading to the formation of the elements it is the sun were :first derived by Russell (Ru29) and the necessary to study the so-called universal or cosmic most recent work is due to Goldberg, Aller, and Miiller abundance curve. (Go57). Accurate relative isotopic abundances