Natural nuclear reactions occur in the interaction between cosmic rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy, at an adjustable rate, on demand. Perhaps the most notable nuclear reactions are the nuclear chain reactions in fissionable materials that produces induced nuclear fission, and the various nuclear fusion reactions of light elements that power the energy production of the Sun and stars. Both of these types of reactions are employed in nuclear weapons.-obtained from Wikipedia.
The Nuclear reactors generally for Power Generation like the ones in Bombay are of Fission type.,
Two types of breeder reactors are possible:
Fast breeder reactor or FBR which uses fast (unmoderated) neutrons to breed fissile plutonium from fertile uranium-238 (it can also breed fissile uranium-233 from thorium)
Thermal breeder reactor which uses thermal spectrum (moderated) neutrons to breed fissile uranium-233 from thorium (thorium fuel cycle)
Hard to say. There are thousands of nuclear reactions possible. Also, its hard to say which reaction is most well known. People know of fission reactions because of their energy applications. If you are astrophysicist, two protons fusing to form deuteron, positron and neutrino is the most common (weak) nuclear reaction occuring in the universe.
In point of view, Heavy ion reactions are interesting and including unknown various aspects to the following reasons:
1- Production of new super heavy nuclei by various heavy ion reactions. There are very modern heavy ion accelerators in nuclear research centers.
2- Although induced fission reactions by light projectiles and heavy ions are studied by researcher more than 50 years, this reaction is very complicated and the dynamics as well as statics properties are not determined, completely.
3- One of the interesting kind of heavy ion reactions is deep inelastic reactions.
4- As a result due to the above reasons and another evidences these reactions are very interesting. Several reactions depends on the kinetic energy of the projectile and the nature of the projectile and of the target can be occurred.
To some degree this has been answered, but from your question, it seems you are more interested in fission (i.e., rather than fusion). To really understand fission, you need to understand the specific details (see, e.g., C. Wagemans' book "The Nuclear Fission Process"), which are really quite complicated.
For example, the "x" and "y" in your equation are both parts of probability distributions. The physics and mathematics behind those distributions are not trivial.
If you are asking "how many elements spontaneously fission," and you want a practical answer, then it's anything with an atomic mass greater than or equal to 232 (mathematically, the criterion is for Z^2/A >= 47).
If you are asking about fissionable or fissile materials, you'll have to define your terms a bit better (see Pruvost, Lynn, & Harmon 2004).
If you are asking about decay modes in general, you'll have to stare at the chart of the nuclides for a long time -- that number is very large.
Perhaps if you're willing to clarify your question, we can generate a more helpful answer.
A nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle (such as a proton, neutron, or high energy electron) from outside the atom, collide to produce one or more nuclides that are different from the nuclide(s) that began the process.
In principle, a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare. "Nuclear reaction" is a term implying an induced change in a nuclide, and thus it does not apply to any type of radioactive decay (which by definition is a spontaneous process).
Natural nuclear reactions occur in the interaction between cosmic rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy, at an adjustable rate, on demand. Perhaps the most notable nuclear reactions are the nuclear chain reactions in fissionable materials that produces induced nuclear fission, and the various nuclear fusion reactions of light elements that power the energy production of the Sun and stars. Both of these types of reactions are employed in nuclear weapons.
The following is a summary of the nuclear reactions:
Elastic Scattering
When no energy is transferred between the target nucleus and the incident particle, the process is known as 208Pb elastic scattering
Inelastic Scattering
When energy is transferred, the process is called inelastic scattering
In cases when the incident particle is a complicated nuclide, it may also be left in excited state. This process is called mutual excitation.
Capture Reactions
Both charged and neutral particles can be captured by nuclei. Neutron capture reactions are used to produce many radioactive nuclides.
Rearrangement Reactions
The absorption of a particle accompanied by the emission of one or more particles is called a rearrangement reaction. Various rearrangement reactions change the number of neutrons and the number of protons of the target nuclide.
Fission Reactions
Typical and well-known neutron-induced fission reactions. These reactions release energy. The released neutrons induce further reactions, causing contineous chain reactions.
Fusion Reactions
The fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future.
For the generation of electricity the most common nuclear reactions knows today is the fission reactions, which is the typical reactions that occurred within nuclear power reactors.