Models for nulear reactions:
No single reaction mechanism or model can explain all features of different types of nuclear reactions. Three well-known proposed mechanism of nuclear reactions are-
1. The optical model
2. Liquid-drop model or compound nucleus model
3. Direct interaction model
The Optical Model of Nuclear Reaction
This model uses the principle of optics. When light shines on a transparent crystal ball, maximum portion of incident ray is transmitted with some scattering and reflection but no absorption. But in case of black crystal ball, all absorbed and there is no transmission or scattering.
In case of nuclear reactions the incoming particles are scattered in elastic scattering and are absorbed in induced transmutations. If the nucleus is considered as a crystal ball it can be neither totally transparent nor totally black. The optical model of the nucleus is also known as the cloudy crystal ball model, indicating that nuclei both scatter and absorb the incoming particles.
Calculation of nuclear potential consist of both absorption and scattering. This model is in excellent agreement with experiments for scattering. Unfortunately, this model does not allow us to obtain much information about the fate of the absorption of the particles which lead to inelastic scattering and transmutation.
Liquid-drop Model or Compound Nucleus Model of Nuclear Reaction
Bohr proposed a mechanism to explain nuclear reactions in which a compound nucleus is formed by incoming particle and target nucleus.
40 19 K + 42He à 44 21Sc*
The compound nucleus might be in an excited state, added by kinetic energy of the incoming particles and binding energy of incoming particles in the compound nucleus.
The energy brought in by the incoming particle is transferred to the other nucleons through frequent collisions until a state of statistical equilibrium is reached. During this time, there is an increase in the probability that at least one nucleon will gain kinetic energy in excess of its binding energy and will be evaporated (i.e. leaves the nucleus)
The excitation energy of residual nucleus decreases due to the evaporation of nucleons equivalent to the summation of binding energy and kinetic energy of released nucleon.
The evaporation process continues until the residual excitation energy is less than the binding energy of a nucleon. Left over excitation energy might be removed from the nucleus by emission of-y-rays.
According to this mechanism, nuclear reaction take places in two steps.
1. Formation of compound nucleus
2. Evaporation or product nucleus formation
Second step is relatively slower means that compound nucleus has a relatively long life time.
Same compound nucleus may be formed by different set of projectile and target nucleus.
In the same way, decay of similar compound nucleus yields different products.
Direct Interaction Model of Nuclear Reaction
This model is proposed by Serber, for high energy projectile ( > 50 MeV).
At high energies the relative speed between projectile and target nuclei is so high
that the time available for distribution of energy between all nucleons is too short means that we can initially consider projectile and target nuclei as consisting of fairly isolated nucleons. Serber proposed that high energy reactions occur in two stages.
(i) At first stage the nucleons in the incoming particle undergoes direct collision with individual target nucleons. In these collisions the struck nucleon often receives energy
much in excess of its binding energy. Consequently, after each collision both the nucleons belonging initially to the bombarding particle and the struck nucleon have some probability of escaping the nucleus since their kinetic energies are greater than their binding energies. If both particles escape, the nucleus is usually left with only a small amount of excitation energy. The residual excitation energy is uniformly distributed among the residual nucleons.
ii. On the contrary at slower second stage residual excitation energy is escaped by nucleon evaporation. This stage closely resemble the compound nucleus theory.