Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2000-07-27
Phys.Rev. C63 (2001) 064307
Physics
Nuclear Physics
Nuclear Theory
9 pages, latex, 6 figures
Scientific paper
10.1103/PhysRevC.63.064307
We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $\Lambda$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \ln (\mu E +\nu)$. This relation holds for all the systems under consideration.
Koutroulos C. G.
Massen S. E.
Panos C. P.
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