Abstract. The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
The fluctuation properties of energy spectrum, electromagnetic transition intensities and electromagnetic moments in nucleus are investigated with realistic shell model calculations. We find that the spectral fluctuations of are consistent with the Gaussian orthogonal ensemble of random matrices. Besides, we observe a transition from an order to chaos when the excitation energy is increased and a clear quantum signature of the breaking of chaoticity when the single-particle energies are increased. The distributions of the transition intensities and of the electromagnetic moments are well described by a Porter-Thomas distribution. The statistics of electromagnetic transition intensities clearly deviate from a Porter-Thomas distribution (i.e., a transition towards regularity is observed) when the single-particle energies are increased whereas the statistics of electromagnetic moments are not affected by the change of the single-particle energies.
The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the
J−T scheme for 12 particles in the
sd-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.
Background: In quantum mechanics, entanglement is the most striking phenomenon which has no counterpart in classical systems. Although different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics.Purpose: We aim to study mode entanglement in the seniority model, derive analytic formulas for the one-body reduced density matrix of states with seniority $\ensuremath{\nu}=0,\phantom{\rule{0.16em}{0ex}}1,\phantom{\rule{0.16em}{0ex}}2$, and 3, and also determine the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, we compare the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states.Methods: In the seniority model the analytic results are calculated using the quasispin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the
G-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies.Results: In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states is revealed. Numerical results are presented for the lightest stable calcium isotopes and for
94Ru nucleus.Conclusions: For
94Ru, the seniority model accounts for the
0g9/2 mode entropies, but seniority mixing is important for certain yrast states. Interaction induced quantum fluctuations decrease the occupation of the
0f5/2,
1p3/2, and
1p1/2 shells, and result in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple
(0g9/2)4 seniority model. The
0f7/2 shell based seniority model is more accurate for the
Ca isotopes, but seniority mixing is substantial for some
44Ca yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.