Question #10120

discuss energy levels of light nuclei & hypothesis of charge independence of nuclear force

Expert's answer

The atomic nucleus is a system of A particles (Z protons and N neutrons) the motion of which is governed by their mutual interactions. The exact description of the behavior of this system is equivalent to the solution of the n-body problem in quantum mechanics. Recently, several attempts have been made to obtain approximate solutions to the nuclear problem but we are still far from an accurate description. Although qualitative understanding was gained, exact eigenfunctions canot be calculated for any given (finite) nucleus. In the past, various models were proposed, some very successful. These models replace the nuclei by greatly simplifies systems which can be handles mathematically. The wave functions of the successful models can be used to calculate many properties of nuclei to a high degree of accuracy.

The theory of heavy electrons recently developed by several authors may be considered to give a satisfactory account of the empirically known neutron-proton interaction. However, it now seems well established that there exists a proton-proton interaction of comparable magnitude which is not accounted for equally well. Owing to the fact that the emission of a heavy electron involves the change of a neutron into a proton or vice versa, the first approximation of this theory gives only an exchange force between unlike particles, whereas a force between like particles must be due to double transitions and thus only appears in the second approximation. It is true that the expansion in terms of the number of particles emitted is actually so badly convergent that the second order proton-proton force at distances of about 10^−13 cm. is found to be not essentially smaller than the first order neutron-proton force, but nevertheless this does not explain experimental facts, since the calculated second order force is always repulsive.

The theory of heavy electrons recently developed by several authors may be considered to give a satisfactory account of the empirically known neutron-proton interaction. However, it now seems well established that there exists a proton-proton interaction of comparable magnitude which is not accounted for equally well. Owing to the fact that the emission of a heavy electron involves the change of a neutron into a proton or vice versa, the first approximation of this theory gives only an exchange force between unlike particles, whereas a force between like particles must be due to double transitions and thus only appears in the second approximation. It is true that the expansion in terms of the number of particles emitted is actually so badly convergent that the second order proton-proton force at distances of about 10^−13 cm. is found to be not essentially smaller than the first order neutron-proton force, but nevertheless this does not explain experimental facts, since the calculated second order force is always repulsive.

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