Abstract
Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schrodinger equation, nonlinear terms appear in the neighborhood of the singular points.
Highlights
In 1936, Niels Bohr wrote in the address delivered on January 27 before the Copenhagen Academy [1,2]: In the atom and in the nucleus we have to do with two extreme cases of mechanical many-body problems for which a procedure of approximation resting on a combination of one-body problems, so effective in the former case, loses any validity in the latter where we, from the very beginning, have to do with essential collective aspects of the interplay between the constituent particles
It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus
Dynamical phase transitions are caused by singular points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross
Summary
In medium-mass nuclei, the first (elastic) decay threshold is at a comparably low excitation energy of the nucleus where the level density is still relatively low These nuclei are characterized by overlapping resonance states with different lifetimes. Dynamical phase transitions in quantum systems will be discussed They are directly related to the existence of exceptional points the mathematical properties of which are known for more than 40 years [13]. The narrow compound nucleus resonances in heavy nuclei (well known at that time) are the result of a dynamical phase transition They are characterized by essential collective aspects of the interplay between the constituent particles and not by a combination of one-body problems.
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