Neutron capture
A direct way to produce neutron-rich nuclides is neutron capture. Most of the heavier nuclear species in the universe have been produced in cosmic scenarios by this reaction mechanism. Roughly two scenarios are considered according to the magnitude of the neutron flux. The s process ("slow" process) evolves close to the valley of beta stability. Since the time delay between two consecutive capture reactions is longer than most of the beta half-lives, the beta-unstable capture product decays, before the next neutron is captured. The r process ("rapid" process) evolves far from the valley of beta stability. The time between two consecutive capture reactions is smaller than the beta half-lives of the nuclei close to beta stability.
The application of neutron capture in laboratory under controlled conditions for the production of very neutron-rich nuclei is not possible, because too high neutron fluxes would be needed. A technical application, with or without explicit intention, is the production of plutonium and minor actinides (actinides with small production yields) in fission reactors. They are formed by consecutive neutron capture and beta decay from ²³⁸U nuclei. However, the production follows closely the valley of beta stability.
 

Fusion
Two nuclei, gently brought into contact, may fuse due to the attractive nuclear forces. For lighter systems, this is the most important reaction mechanism at energies close to the Coulomb barrier. In very heavy systems, however, the Coulomb force tends to destabilise the merged system so that they re-separate immediately with higher probability.
Fusion reactions, in particular using heavy-ion beams, have proven to be well suited for the production of proton-rich nuclei up to the proton drip line. They have been an important tool for exploring the properties of exotic nuclei on the neutron-deficient side of the chart of the nuclides. Furthermore, fusion is the only tool applied to produce super-heavy elements.
Since the nucleons of projectile and target just add up, the nuclear composition of the fusion product is well defined. Only the evaporation process leads to a loss of a few nucleons.
Due to the curvature of the line of beta-stability, fusion is not suited for the production of neutron-rich nuclides. Another draw-back of fusion reactions is the low beam energy required which only allows for the application of thin targets, because the energy of the projectiles would become too low in a thicker target due to electronic interactions. Therefore, only a very small fraction of the projectiles goes into nuclear reactions, thus resulting in low intensities of secondary beams.
 

Fission
Fission can be considered in some sense as the reverse of fusion. Here the process starts from heavy rather neutron-rich nuclei. As a consequence, the fission products  are normally situated on the neutron-rich side of the chart of nuclides. The production of nuclides which are more neutron rich than the fissioning system is only possible due to charge polarisation, that means that the two fission fragments are formed with different N-over-Z ratios. Fluctuation phenomena as well shell effects might be responsible for charge polarisation. However, the restoring force due to the nuclear asymmetry energy is very strong. This limits the polarisation to rather low values.
Most fission fragments are formed with appreciable excitation energies, leading to neutron evaporation very shortly after fission. Therefore, the average N-over-Z ratio of the fission fragments is below the value of the fissioning nucleus.
 

Fragmentation
Nuclear collisions at bombarding energies well above the Fermi energy can be considered as quasi-free nucleon-nucleon collisions. The collisions essentially remove a number of nucleons from the projectile respectively target nucleus. Collisions at large impact parameters are an interesting tool for the production of exotic nuclides. We use the term fragmentation for these reactions in which a large part of the projectile respectively target survives. This should not be confounded with multi-fragmentation in which very light nuclei are produced at more central collisions.
An important feature of fragmentation reactions is the strong statistical fluctuation. This leads to large variations in the N-over-Z ratio of the reaction products. Also the energy induced in the collision is subject to a large fluctuation and extends to rather high values. Therefore, the consecutive evaporation cascade has an important influence on the nuclear composition of the fragmentation products observed.
Fragmentation is a mechanism which produces a large number of nuclides, scattered over an extended region of the chart of the nuclides.

Estimation of production rates in an in-flight secondary-beam facility

Estimation of production rates in an ISOL secondary-beam facility