Universal trend of the information entropy of a fermion in a mean field
Abstract
We calculate the information entropy of singleparticle states in position space S_{r} and momentum space S_{k} for a nucleon in a nucleus, a Λ 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} (or S_{k})=a+bN^{1/3} in all of the above manybody 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 a uniform scaling of coordinates, and is a characteristic of the singleparticle states of a specific system. The order of singleparticle states according to S_{r}+S_{k} is the same as their classification according to energy, keeping the quantum number n constant. The spinorbit partners are ordered correctly. It is also seen that S_{r}+S_{k} is enhanced by the excitation of a fermion in a quantummechanical system. Finally, we obtain a relationship of S_{r}+S_{k} with the energy of the corresponding singleparticle state, i.e., S_{r}+S_{k}=k ln(μE+ν). This relation holds for all systems under consideration.
 Publication:

Physical Review C
 Pub Date:
 June 2001
 DOI:
 10.1103/PhysRevC.63.064307
 arXiv:
 arXiv:nuclth/0007064
 Bibcode:
 2001PhRvC..63f4307P
 Keywords:

 21.10.k;
 21.80.+a;
 89.70.+c;
 Properties of nuclei;
 nuclear energy levels;
 Hypernuclei;
 Information theory and communication theory;
 Nuclear Theory;
 Quantum Physics
 EPrint:
 9 pages, latex, 6 figures