1st Week: Introduction to Nuclear Physics & Abundance Determination in Astrophysics B

The Standard Model

The current picture of fundamental particles consists of leptons, quarks, and gauge bosons.

The family of leptons consist of 6 different particles. These particles are the $\nu _{e}$ , e, $\nu _{\mu }$ , $\mu$ , $\nu _{\tau }$ , and $\tau$ . The $\nu 's$ , until rather recently were thought to be massless particles. However, experiments have shown that they are able to oscillate between flavors, which is only possible if they have mass. Some of these experiments such as LSND also suggest the possibility of a possible fourth $\nu$ that is sterile, meaning that it does not interact via the weak nuclear force (see gauge bosons below).

The family of quarks also consists of 6 different flavors. These flavors are: the up, down, charm, strange, top and bottom quarks. Quarks cannot be studied individually, but in one of the two known types of particles they join together to create: mesons and baryons. Mesons are particles that consist of a certain flavor of quark and an anti-quark of another flavor. Baryons consist of 3 quarks of any flavor together. Other particles such as pentaquarks (5 quark particles), have been theorized, but not yet seen.

There are five known types of gauge bosons, and a sixth theorized type that has yet to be seen. The role that gauge bosons play is that of carrying out the four fundamental forces. These forces are: Gravitation, Electro-Magnetic, Weak Nuclear, and Strong Nuclear. (One can find a summary of the forces here.) The gauge boson for the gravitational force is the graviton, a particle that has yet to be seen by researchers. The electro-magnetic force is carried out via the photon. The weak nuclear force has 3 different gauge bosons, the $W^{-}$ , $W^{+}$ , and $Z^{o}$ . Lastly, the gauge boson for the strong nuclear force is the gluon.

Important Particles

The universe is made up of:

60% Dark Energy
38% Dark Matter
2% Nuclei and Electrons

In this course, one is mostly concerned with the last category. Specifically one is interested how the structure of these particles changes when undergoing an astrophysical process. A list of these particles (and their interactions) can be found in the table of the nuclides. Usually one is concerned with atoms. Atoms consist of three smaller particles: the positively charged protons and the neutral neutrons in the central nucleus and the negatively charged electrons orbiting the nucleus. These atoms come in various sizes and are usually listed in the periodic table in order of increasing proton number. So atoms of the the same proton number are of the same element. However, some elements have different numbers of neutrons. These two atoms are known as isotopes of the particular element. To differentiate among these different particles a system was developed which looks like: $_{A}Y$ where A is the mass number and Y is the element name. From this one can find the number of protons (Z) from the name of the element and the number of neutrons (N) from the mass number (A-Z=N). The actual mass of the atom is slightly less than the mass number. The actual mass of the atom can be found by A = Z + N - binding energy.

Nucleosynthesis, or where do elements come from?

Since the Big Bang there have been a wide variety of nuclear reactions in the Universe. At the beginning of times there was only a gas of gluons and quarks. The interaction of these particles gave raise to the formation of the first three elements of the periodic table: Hydrogen (H), Helium (He) and Lithium (Li). From then on, the process of nulceosynthesis has taken place in the formation an life of stars, supernova explosions or the interaction of matter with cosmic rays. Nucleosynthesis can be understood as the process of creating new nuclei with preexisting ones.

Abundances in Nuclear Astrophysics

The solar system is believed to have formed from a nebula that consisted of an isotropic distribution of chemical and isotopic abundances. The chemical elements and molecules in stars can be identified since each element chemical compound has unique energy levels. Therefore, individual elements and chemical compounds produce their own unique absorption and emission lines. It is then possible to observe the spectra from the stars to see what patterns are present and therefore be able to determine elements and chemical compounds in stars. It was found that the abundances observed in stars were quite similar to those found in our solar system. Many had believed that if we knew the abundances in our solar system then this would provide an understanding of a "cosmic" distribution. This was disproved after the study of pre-solar grains found in ancient meteorites which showed large differences in isotopic abundances. Other methods of determining solar abundances included looking at the isotopic content of the earth (as this data has been largely unaffected). As mentioned before, certain meteorites can give quite a large amount of information about abundances if the meteorite is not fractionated.

Definitions

Some physical quantities used in nuclear astrophysics are defined below:

Particle density of isotope i: $n_{i}$

This quantity has units of number of particles per $cm^{3}$ .

Particle abundance

$X_{i}={n_{i} \over \sum _{j}n_{j}}$

where the sum is over all the isotopes $j$ . From this definition we get the formula $\sum _{i}X_{i}=1$

Logarithmic and normalized to Hydrogen relative abundance: $\epsilon _{i}=\log _{10}X_{i}+12$ .

The mass fraction X_i is a fraction of the total mass of a sample that is made up by nucleus of species i

$n_{i}={X_{i}\rho \over m_{i}}$

where $\rho$ is the mass density in $g/cm^{3}$ and $m_{i}$ is the mass of the nucleus of species i. This can also be expressed as

$n_{i}={X_{i} \over A_{i}}\rho N_{A}$ .

From this equation we get $Y_{i}=X_{i}/A_{i}$ . Here $N_{A}$ is Avogadro's number. We have used the approximation $m_{i}\approx A_{i}m_{u}$ , and $m_{u}=1/N_{A}$ .