Nucleosynthesis

Reading Assignment

Synthesis of the elements in stars: forty years of progress, George Wallerstein, Icko Iben, , Jr., Peter Parker, Ann Merchant Boesgaard, Gerald M. Hale, Arthur E. Champagne, Charles A. Barnes, Franz Käppeler, Verne V. Smith, Robert D. Hoffman, Frank X. Timmes, Chris Sneden, Richard N. Boyd, Bradley S. Meyer, and David L. Lambert Rev. Mod. Phys. 69, 995 – Published 1 October 1997

Introduction

Nuclide Chart

http://adsabs.harvard.edu/abs/1957RvMP...29..547B

http://adsabs.harvard.edu/abs/1965ApJS...11..121S

http://adsabs.harvard.edu/abs/1999PrPNP..43..419K

http://adsabs.harvard.edu/abs/2007PhR...450...97A

α-process

The alpha process is one of two classes of nuclear fusion reactions by which stars convert helium into heavier elements, the other being the triple-alpha process. While the triple-alpha process only requires helium, once some carbon is present, these other reactions that consume helium are possible:

{\begin{array}{ll}\mathrm {{_{6}^{12}C}+{_{2}^{4}He}->{_{8}^{16}O}+\gamma } &E=7.16\ \mathrm {MeV} \\\mathrm {{_{8}^{16}O}+{_{2}^{4}He}->{_{10}^{20}Ne}+\gamma } &E=4.73\ \mathrm {MeV} \\\mathrm {{_{10}^{20}Ne}+{_{2}^{4}He}->{_{12}^{24}Mg}+\gamma } &E=9.32\ \mathrm {MeV} \\\mathrm {{_{12}^{24}Mg}+{_{2}^{4}He}->{_{14}^{28}Si}+\gamma } &E=9.98\ \mathrm {MeV} \\\mathrm {{_{14}^{28}Si}+{_{2}^{4}He}->{_{16}^{32}S}+\gamma } &E=6.95\ \mathrm {MeV} \\\mathrm {{_{16}^{32}S}+{_{2}^{4}He}->{_{18}^{36}Ar}+\gamma } &E=6.64\ \mathrm {MeV} \\\mathrm {{_{18}^{36}Ar}+{_{2}^{4}He}->{_{20}^{40}Ca}+\gamma } &E=7.04\ \mathrm {MeV} \\\mathrm {{_{20}^{40}Ca}+{_{2}^{4}He}->{_{22}^{44}Ti}+\gamma } &E=5.13\ \mathrm {MeV} \\\mathrm {{_{22}^{44}Ti}+{_{2}^{4}He}->{_{24}^{48}Cr}+\gamma } &E=7.70\ \mathrm {MeV} \\\mathrm {{_{24}^{48}Cr}+{_{2}^{4}He}->{_{26}^{52}Fe}+\gamma } &E=7.94\ \mathrm {MeV} \\\mathrm {{_{26}^{52}Fe}+{_{2}^{4}He}->{_{28}^{56}Ni}+\gamma } &E=8.00\ \mathrm {MeV} \end{array}}

E is the energy produced by the reaction, released primarily as gamma rays (Template:Mvar).

This sequence ends at $\mathrm {_{28}^{56}Ni}$ because it is the most stable (i.e., it has the highest nuclear binding energy per nucleon) in the chain. $\mathrm {_{28}^{62}Ni}$ has the most binding energy per nucleon and $\mathrm {_{26}^{56}Fe}$ has the least mass per nucleon. Therefore, production of heavier nuclei requires energy instead of releasing it.

All these reactions have a very low rate at the temperatures and densities in stars and therefore do not contribute significantly to a star's energy production; with elements heavier than neon (atomic number > 10), they occur even less easily due to the increasing Coulomb barrier.

Alpha process elements (or alpha elements) are so-called since their most abundant isotopes are integer multiples of four, the mass of the helium nucleus (the alpha particle). They are synthesized by alpha capture prior to silicon burning a precursor to Type II supernovae. Silicon and calcium are purely alpha process elements. Magnesium can be burned by proton capture reactions. As for oxygen, some authorsTemplate:Which consider it an alpha element, while others do not. Oxygen is surely an alpha element in low-metallicity population II stars. It is produced in Type II supernovae and its enhancement is well correlated with an enhancement of other alpha process elements. Sometimes carbon and nitrogen are considered alpha process elements, since they are synthesized in nuclear alpha-capture reactions.

The abundance of alpha elements in stars is usually expressed in a logarithmic manner:

[\alpha /\mathrm {Fe} ]=\log _{10}{\left({\frac {N_{\alpha }}{N_{\mathrm {Fe} }}}\right)_{Star}}-\log _{10}{\left({\frac {N_{\alpha }}{N_{\mathrm {Fe} }}}\right)_{Sun}}

,

Here $N_{\alpha }$ and $N_{\mathrm {Fe} }$ are the number of alpha elements and iron nuclei per unit volume. Theoretical galactic evolution models predict that early in the universe there were more alpha elements relative to iron. Type II supernovae mainly synthesize oxygen and the alpha-elements (Ne, Mg, Si, S, Ar, Ca and Ti) while Type Ia supernovae mainly produce elements of the iron peak: TI, V, Cr, Mn, Fe, Co and Ni, but also alpha-elements

s-process

Carbon-13 pocket

r-process

r-process simulation

Another r-process simulation

p-process

rp-process

Cosmic-Ray Spallation

Assignment

For elements with atomic numbers less than that of calcium, the most abundant isotope of each element with an even number of protons has Z=N, e.g. ⁴He, ¹²C, ¹⁶O, ⁴⁰Ca, ... and those with odd proton numbers, N, Na, Al ... have Z nearly equal to N. When one goes to heavier nuclei however there is a surplus of neutrons in the most abundant isotopes; iron-56 has 26 protons and 30 neutrons. Explain both these trends why light nuclei have Z about equal to N while heavy nuclei have Z less than N.
Why is combination of a single neutron and a single proton stable but two protons is not?
Calculate the energy released in erg/g when a composition of pure helium burns to pure carbon-12 and to 50/50 carbon-12 and oxygen 16. What is the energy released when each of these mixtures is burned to Nickel-56? In both cases how much nickel has to be made to produce 10⁵¹ erg?
The neutron capture cross sections at 30 keV for the stable isotopes of barium are ¹³⁰Ba, 715 mb ¹³²Ba, 447mb, ¹³⁴Ba, 221 mb ¹³⁵Ba, 457 mb, ¹³⁶Ba, 69 mb, ¹³⁷Ba, 57 mb, and ¹³⁸Ba, 3.9 mb. The s-only isotopes of barium are 134 and 136 and the nuclear charge is 56. a) Why is the cross section of ¹³⁵Ba greater than that of ¹³⁴Ba or ¹³⁶Ba? Why is the cross section of ¹³⁸Ba so small? What do you expect for the solar ratio of the abundance of ¹³⁴Ba to that of ¹³⁶Ba? Your discussion should at least mention why reactions with large releases of energy have large cross-sections.