To do nuclear astrophysics, one must have a broad understanding of both nuclear physics (how the atomic nucleus works) and astrophysics (to understand the types of environments where energies are sufficient that the nuclear structure can undergo change). In graduate school, my nuclear astrophysics classes were taught by the man that wrote the book. In this case, Principles of stellar evolution and nucleosynthesis, by Donald Clayton.
However, Don Clayton's interests were in later stages of stellar nucleosynthesis, the formation of the heavier elements. In situations I deal with, crank claims usually try to claim few to no nuclear reactions are taking place in stars. For that case, I needed a book that placed more emphasis on the nuclear reactions earlier in the star's life. It would be even better if I could find a book that covered the status of experimental verification of stellar nuclear reactions.
The book I found which did an excellent job of covering these two topics was
C. E. Rolfs and W. S. Rodney. Cauldrons in the cosmos: Nuclear astrophysics. 1988.
This book presented a lot of material on theoretical and experimental nuclear astrophysics, and a number of items I had not seen covered to the level of detail before.
Going Backwards to Go Forwards
One of the major difficulties in doing experimental nuclear astrophysics is that it is very difficult to reproduce stellar interior conditions in Earth laboratories. But sometimes nature provides a 'back door' on the process. We have yet to find a violation of the principle of microscopic reversibility - that all atomic and subatomic reactions can run backwards and forwards. If we can have the reaction
A + B -> X + Y
thenX + Y -> A + B
is also possible. As in chemistry, there are physical principles we can use to mathematically relate the reaction rates in the forward and reverse reaction.Photodisintegration, where a high-energy photon 'breaks' a nucleus into smaller components, is very hard to measure. It requires a high density of high-energy photons that is very difficult to produce in a lab but easy to occur at the center of a million kilometers of hydrogen (for an example where the lab is reaching the capabilities of the stellar environment, see 'Out There' Astrophysics Impacts Technology (again)). In some of these cases, we can measure the capture cross-section of the particles created in the original reaction and then compute the photoionization rate using quantum mechanics (pg 148).
Similarly, the very important triple-alpha reaction (wikipedia), where three helium nuclei (alpha particles) collide to form a carbon nucleus, be examined by exploring the reaction from the opposite direction (pg 282):
Proton+Proton Reaction
One nice part of Rolfs and Rodney text is the level of detail it covers on the theoretical AND experimental aspects of nuclear reactions in stars, starting with the proton-proton chain and covering the individual reactions. The reaction at the base of the chain,
has never been observed under laboratory conditions. The reason why is that the coulombic repulsion between two protons at stellar core temperatures is too large to be overcome by the classical mechanical means of overcoming an energy barrier. However, quantum mechanics gives the process a very small probability of the two protons tunneling through the coulombic barrier to interact (the same process used with electrons in the tunnel diode). The tunneling probability is LOW. At a temperature of 10,000,000K, this probability is 9e-10 (pg 155). Yet even with this low probability, there is so much hydrogen at the center of the Sun, at sufficient density, that the interaction rate makes up for this low probability and accounts for the energy release we measure from the Sun.
In terms of measuring this reaction rate in the laboratory, the calculation on pg 334 puts this in perspective. The total cross-section for the reaction at a lab energy of 1 MeV is about 1e-47 cm^2. With a proton beam of 1 milliamperes on a THICK target of pure hydrogen with 10^23 atoms/cm^2 in the beam, the time between reactions would be 1 MILLION YEARS. This experiment is clearly impractical to do with current technology.
If the proton+proton reaction had a much higher reaction probability, sufficient for us to measure in current laboratories, then the reaction rate at the centers of stars would be so high that stars would have burned out long ago.
While there are very few nuclear reactions which we can measure in the laboratory at relevant stellar energies, the practice is calibrate the data to the cross-section computation in the energy ranges where we can measure, and then extrapolate this function to lower energies. The advantage of this is that any other interactions which could influence the reaction rate would increase the reaction cross-section (pg 189).
Over 100 pages of the book (pg 190-327) is devoted to descriptions of experimental nuclear astrophysics techniques.
Once some of the techniques are described, the book goes into more detailed explorations of nuclear reactions with more complex nuclei heavier than helium. There is discussion of the nuclear reactions around Be7, which decays via electron capture. This creates the interesting effect that the beryllium-7 nucleus is stable, while the beryllium-7 atom is not. This is because the electron wave-function in the innermost electrons has a significant amplitude in the nucleus itself, increasing the probability of electron can react with the protons for the inverse-beta decay reaction (pg 346):
Modern experiments with this method of altering radioactive decay rates have occasionally been invoked by Young-Earth Creationists as evidence that nuclear decay rates could have been significantly higher in the past (See Accelerated Radioactive Decay According to Answers in Genesis)
The theoretical and experimental work around more complex reactions is explored as well. I was surprised to find how many of the heavier nuclei experiments so important for described the steps of stellar reactions beyond hydrogen and helium burning actually have significant laboratory experiments behind them.
Because researchers don't have the resources to explore EVERY possible nuclear reaction hypothesized to occur in stars, they must rely on nuclear models to compute the structure of the nuclei of interest and then compute the cross sections of the reaction of interest. One model that has found successful use is the Hauser-Feschback statistical model which can be used to compute an energy-averaged cross-section for nuclei were there are many resonances (pg 432). While these models are used for reactions where we don't have data, they are often tested and calibrated by applying them to reactions where we can obtain experimental data (pg 434).
Pages 493-495 covered some of the early ideas (about 1988) for solving the solar neutrino problem which was still unsolved at that time.
Stellar Composition Effects
One of the other interesting applications in the book was a discussion of limiting cases in stellar composition. In a simple case of a chemically homogeneous star, the structure is largely determined by the mean molecular weight, mu. This value can be approximated in atomic mass units, by the equation
mu= 1/(2X+0.75Y+0.5Z)
where X is the mass fraction of hydrogen, Y is the mass fraction of helium, and Z is the mass fraction of every element with an atomic mass greater than helium, often referred to as 'metals'. Since everything must add up to 1.0, we require that Z = 1-X-Y. In the text, the authors examined two interesting limiting cases, a star of all iron (Z=1, X=Y=0) and all hydrogen (X=1, Y=Z=0). In the early 1900s, it was believed that stars were largely iron due to the large number of iron lines in the Sun's spectra. However, once astronomers understood how spectral lines were formed, largely through the work of Cecilia Payne, it was eventually understood that they were largely hydrogen. In the example, we see that the mean molecular weight of an all hydrogen star is mu=0.5, while for an all iron star it is mu=2.0. In terms of gas pressure, this means that the iron star must have about four times higher pressure than a hydrogen star to maintain hydrostatic balance (pg 96).
Applications
One of my motivations for reading this book was to refresh my nuclear physics background but also to explore possible alternative sources of information for dealing with the cranks that claim the Sun and other stars are not nuclear powered. While the book is now over 20 years old, it directed me to some of the earlier research in experimental nuclear astrophysics from which I was able to track more modern work and updates via ADS.
One of the most useful items I found was the computation of what was required to produce the proton+proton -> deuteron reaction in the laboratory. While various cranks like to claim that the failure to produce the reaction in the laboratory is a failure of nuclear astrophysics, the facts paint a different picture. It is not that researchers tried to produce the reaction and failed, but they probably have never tried to produce that reaction specifically because it had such a low probability at the energies available in the Sun's core. There have been many experiments in the late 1930s to the 1950s colliding protons together over a broad range of energies (refs).
While this twenty-year old book provided an excellent overview of stellar nuclear reactions, I suspect significant revision of some experimental results will take place as the National Ignition Facility (link) enables these reactions to be explored at significantly higher densities.
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