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Register a new userVariational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei
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Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like correlations in the ground states of $ ^{116}$Sn,$ ^{106}$Sn and $ ^{100}$Sn. The same effective nucleon-nucleon interaction namely, the D1S parameterization of the Gogny force is used to derive both the mean field and correlation components of nuclear wave functions. Calculations are performed using an axially symetric representation. The structure of correlated wave functions, their convergence with respect to the number of particle-hole excitations and the influence of correlations on single-particle level spectra and occupation probabilities are analyzed and compared with results obtained with the same two-body effective interaction from BCS, Hartree-Fock-Bogoliubov and particle number projected after variation BCS approaches. Calculations of nuclear radii and the first theoretical excited $0^+$ states are compared with experimental data.
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In a previous paper we proposed a Projected Configuration Interaction method that uses sets of axially deformed single particle states to build up the many body basis. We show that the choice of the basis set is essential for the efficiency of the method, and we propose a newly improved algorithm of selecting the projected basis states. We also extend our method to model spaces that can accomodate both parities, and can include odd-multipole terms in the effective interaction, such as the octupole contributions. %A universal algorithm of the choice of the PCI basis was presented in details. Examples of $^{52}$Fe, $^{56}$Ni, $^{68}$Se, $^{70}$Se and $^{76}$Se are calcualted showing good agreement with the full Configuration Interaction results.
Background: The nuclear many-body system is a strongly correlated quantum system, posing serious challenges for perturbative approaches starting from uncorrelated reference states. The last decade has witnessed considerable progress in the accurate treatment of pairing correlations, one of the major components in medium-sized nuclei, reaching accuracies below the 1% level of the correlation energy. Purpose: Development of a quantum many-body method for pairing correlations that is (a) competitive in the 1% error range, and (b) can be systematically improved with a fast (exponential) convergence rate. Method: The present paper capitalizes upon ideas from Richardson-Gaudin integrability. The proposed method is a two-step approach. The first step consists of the optimization of a Richardson-Gaudin ground state as variational trial state. At the second step, the complete set of excited states on top of this Richardson-Gaudin ground state is used as an optimal basis for a Configuration Interaction method in an increasingly large effective Hilbert space. Results: The performance of the variational Richardson-Gaudin (varRG) and Richardson-Gaudin Configuration Interaction (RGCI) method is benchmarked against exact results using an effective $G$-matrix interaction for the Sn region. The varRG already reaches accuracies around the 1% level of the correlation energies, and the RGCI step sees an additional improvement scaling exponentially with the size of the effective Hilbert space. Conclusions: The Richardson-Gaudin models of integrability provide an optimized complete basis set for pairing correlations.
Recently we have proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration-mixing of several cranked mean-field wave functions after the angular-momentum-projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in $^{164}$Er, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for study of the nuclear rotational motion.
Simple generic aspects of nuclear pairing in homogeneous medium as well as in finite nuclei are discussed. It is argued that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon-nucleon (NN) interaction in general and pairing NN interaction in particular what allows for regularization of the ultraviolet (high-momentum) divergences and a consistent formulation of effective superfluid local theory. Some aspects of (dis)entanglement of pairing with various other effects as well as forefront ideas concerning isoscalar pairing are also briefly discussed.
We analyze the localization properties of two-body correlations induced by pairing in the framework of relativistic mean field (RMF) models. The spatial properties of two-body correlations are studied for the pairing tensor in coordinate space and for the Cooper pair wave function. The calculations are performed both with Relativistic-Hatree-Bogoliubov (RHB) and RMF+Projected-BCS (PBCS) models and taking as examples the nuclei $^{66}$Ni, $^{124}$Sn and $^{200}$Pb. It is shown that the coherence length have the same pattern as in previous non-relativistic HFB calculations, i.e., it is maximum in the interior of the nucleus and drops to a minimum in the surface region. In the framework of RMF+PBCS we have also analysed, for the particular case of $^{120}$Sn, the dependence of the coherence length on the intensity of the pairing force. This analysis indicates that pairing is reducing the coherence length by about 25-30 $%$ compared to the RMF limit.
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