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R. N. Mohapatra
Clearly, for this process to occur, one just cannot have one extra neutron
around a nucleus. The fusion process will then take too long. The key question
then is how many neutrons must be there per cubic centimeter surrounding a
nucleus (N, Z) for this neutron absorption process to occur in a short time? It
turns out that if the number of neutrons per cubic centimeter is in excess of
millions to billions, with a temperature of 100 million degrees Celsius, then
the process of generating the heavier nucleus is possible in a short time span. If
the neutron capture process is slow compared to the beta decay process, only
certain nuclei are produced and this process is called an s-process (slow process)
for short. This generates only about half the elements beyond iron. This can
happen in the later stages in the evolution of stars with a mass up to 10 solar
masses. The s-process is successful because there is enough time for the isotope
formed from the capture of a single neutron to decay before another neutron is
captured, altering the radioactive property of the isotope. To remind the reader,
an isotope of an element has more neutrons in the nucleus of that element than
the usually more abundant nucleus with the same number of protons. Iron,
for example, has four naturally occurring isotopes and several unstable ones.
If the building up process reaches a stage such that the nucleus undergoes
alpha decay, then we come back to a lighter element and the s-process stops.
Typically an s-process stops with elements lead, bismuth, and polonium. Lead
has Z = 82, bismuth has Z = 83 and polonium has Z = 84. Recall that iron has
Z = 26. That is quite a progress though still not a complete understanding of
the element formation, since it does not explain many familiar heavier nuclei
seen in nature such as radium (Z = 88), thorium (Z = 90), uranium (Z = 92),
plutonium (Z = 94), etc (Fig. 19.4).
When in an astrophysical environment, the number of neutrons per cubic
centimeters is a lot higher than a million, say about 10
20 neutrons (i.e. 100
million trillion) per cubic centimeter; there, the neutron absorption process
occurs more rapidly. This is called r-process (r-for rapid) and this environment
generates the remaining half of the nuclei. Such environments are possible only
inside supernovae or inside binary neutron star mergers. For a long time it
was believed that supernovae were the main sites for r-process nucleosynthesis
since calculations showed that there were a huge number of neutrons in them.
However, supernovae have a lot of neutrinos as well in their mantle. These
neutrinos convert most of these neutrons to protons, which then fuse with two
more neutrons to make an alpha particle. This so-called alpha effect depletes
the number of neutrons that could have helped the r-process. This makes the
buildup of heavier elements difficult in a supernova. There are suggestions
that if there is a sterile neutrino (dark neutrino, see below), then many of the
active neutrinos could oscillate to the sterile neutrino, reducing the number
of neutrinos and thence preventing the so-called alpha effect. Lately, evidence
R. N. Mohapatra
Clearly, for this process to occur, one just cannot have one extra neutron
around a nucleus. The fusion process will then take too long. The key question
then is how many neutrons must be there per cubic centimeter surrounding a
nucleus (N, Z) for this neutron absorption process to occur in a short time? It
turns out that if the number of neutrons per cubic centimeter is in excess of
millions to billions, with a temperature of 100 million degrees Celsius, then
the process of generating the heavier nucleus is possible in a short time span. If
the neutron capture process is slow compared to the beta decay process, only
certain nuclei are produced and this process is called an s-process (slow process)
for short. This generates only about half the elements beyond iron. This can
happen in the later stages in the evolution of stars with a mass up to 10 solar
masses. The s-process is successful because there is enough time for the isotope
formed from the capture of a single neutron to decay before another neutron is
captured, altering the radioactive property of the isotope. To remind the reader,
an isotope of an element has more neutrons in the nucleus of that element than
the usually more abundant nucleus with the same number of protons. Iron,
for example, has four naturally occurring isotopes and several unstable ones.
If the building up process reaches a stage such that the nucleus undergoes
alpha decay, then we come back to a lighter element and the s-process stops.
Typically an s-process stops with elements lead, bismuth, and polonium. Lead
has Z = 82, bismuth has Z = 83 and polonium has Z = 84. Recall that iron has
Z = 26. That is quite a progress though still not a complete understanding of
the element formation, since it does not explain many familiar heavier nuclei
seen in nature such as radium (Z = 88), thorium (Z = 90), uranium (Z = 92),
plutonium (Z = 94), etc (Fig. 19.4).
When in an astrophysical environment, the number of neutrons per cubic
centimeters is a lot higher than a million, say about 10
20 neutrons (i.e. 100
million trillion) per cubic centimeter; there, the neutron absorption process
occurs more rapidly. This is called r-process (r-for rapid) and this environment
generates the remaining half of the nuclei. Such environments are possible only
inside supernovae or inside binary neutron star mergers. For a long time it
was believed that supernovae were the main sites for r-process nucleosynthesis
since calculations showed that there were a huge number of neutrons in them.
However, supernovae have a lot of neutrinos as well in their mantle. These
neutrinos convert most of these neutrons to protons, which then fuse with two
more neutrons to make an alpha particle. This so-called alpha effect depletes
the number of neutrons that could have helped the r-process. This makes the
buildup of heavier elements difficult in a supernova. There are suggestions
that if there is a sterile neutrino (dark neutrino, see below), then many of the
active neutrinos could oscillate to the sterile neutrino, reducing the number
of neutrinos and thence preventing the so-called alpha effect. Lately, evidence