The Unknown Nuclear Forces
The interactions between the nucleons inside the nucleus has been a hard physical reality to describe. We have different models describing the model of forces inside the nucleus and the interactions of the nucleons with the force. However the base of description with the Schrodinger equation remains utterly valid until dealing with small number of particles. When we have many number of particles included, we run out of clue on which equation to solve and which to take as a reference. Despite the consistency of the nuclear density and binding energy nucleon it is very hard to figure out the interaction between neutrons and protons within the force field as described by the theory of interaction due to exchange forces.
For simple nuclei like hydrogen , the problems are easy as they involve 1 nucleon(1 proton and 1 neutron) and which can be solved using the one body, two body or many body theorems. As the number of nucleon rises the number of force experienced by a single nucleon is due to a number of other nucleons and same case applies to all of the others. If using the Shell model of distribution of nucleons, still the density of the nucleus is consistent as the distribution of the nucleons along the nuclear volume. We may assume that the nucleons will be in well defined orbits and at well-defined distances.
The above facts thus does not mean that a pair of nucleons will thus be similar to other as the particles are identical. This is not allowed by ‘Pauli exclusion principle’ that two similar bodies with same spin and angular momentum can be found in the same state. Thus there rises a contradiction and we will have to keep the nucleons at formidable distances to allow them to exist inside the nucleus and not violate the principles of quantum mechanics. So, solving the Schrodinger equation for the n body problem does not prove to solve the problem of nuclear force fields.
Further the observed values of saturation in the density of nucleons and binding energy per nucleon suggested the use of exchange forces in describing the nuclear forces. Still by no means it is established that the nuclear forces are of exchange types and the high energy scattering of nucleons indicate that the potential between two exchange nucleons has less exchange characters in order to explain the saturation.
Thus these complexities of the nucleus and the nucleon interaction have resulted in many hypothesis and none describing the forces accurately. Each set of nucleon in each atom has to be dealt with different case of hypothesis. Due to this problem, further analysis of the properties of nuclei cannot be done. Some properties of the nucleus which are experimentally proved and well known like the distribution of nucleons, uniform potential, density, uniform binding energy all are on the basis of per nucleon thus cannot be interpreted as a whole to describe the nuclear forces. The complexity in the interactive forces of the different sets of nucleons and further complexity added by the charge of the electron and coulomb forces that has to be taken into account makes it hard to properly describe the strong and short ranged nuclear force.
