Pairing vibrational and isospin rotational states in a particle number and isospin projected generator coordinate method

Pairing vibrational and isospin rotational states are described in different approximations based on particle number and isospin projected, proton-proton, neutron-neutron and proton-neutron pairing wave functions and on the generator coordinate method (GCM). The investigations are performed in models for which an exact group theoretical solution exists. It turns out that a particle number and isospin projection is essential to yield a good approximation to the ground state or isospin yrast state energies. For strong pairing correlations (pairing force constant equal to the single-particle level distance) isospin cranking (-ωT_x) yields with particle number projected pairing wave function also good agreement with the exact energies. GCM wave functions generated by particle number and isospin projected BCS functions with different amounts of pairing correlations yield for the lowest T = 0 and T = 2 states energies which are practically indistinguishable from the exact solutions. But even the second and third lowest energies of charge-symmetric states are still very reliable. Thus we conclude that also in realistic cases isospin rotational and pairing vibrational states may be described in the framework of the GCM method with isospin and particle number projected generating wave functions.     

Variational approach to configuration interaction

A variational method is developed to determine configuration interaction wave functions. The method is straightforward and is applied to a pairing Hamiltonian with constant matrix elements, for which exact eigenvalues are available. Comparisons are made with the exact results. Calculations can be carried out to any desired degree of accuracy. The method is also applied to a Hamiltonian that has neutron-neutron, proton-proton, and neutron-proton pairing. No difficulties are found in extending the method to this Hamiltonian that has many collective modes. In practice, the method scales linearly with , where is the number of variational basis states.     

The pairing correlations and nuclear shapes at very high angular momenta

The usual Strutinsky shell corrections include the pairing correlations in the BCS approach. At high-spin states the cranked intrinsic wave functions are not symmetric or antisymmetric under time reversal symmetry for general triaxial shapes. On the basis of the Hartree-Fock-Bogoliubov (HFB) approach two generalizations of the Strutinsky procedure are given to describe pairing correlations also for high-spin states and triaxial shapes. The method is applied to the neutron-deficient rare earth nucleus ¹⁵⁰Gd. It is found that pairing has an important effect on the change of nuclear deformation with increasing angular momentum. The proton pairing persists at least up to I ≈ 40.     

Local energy density functional and density-dependent pairing in nuclear systems

An approach based on the local energy density functional method for describing the ground-state properties of superfluid nuclei is presented. A generalized variational principle is formulated which corresponds, in the weak pairing approximation, to a full treatment of the Hartree-Fock-Bogoliubov problem with an effective contact pairing interaction. The Gor’kov equations for generalized Green’s functions are treated exactly in the coordinate-space representation. The method is used to calculate the differential observables including odd-even mass differences and odd-even effects in charge radii which turn out to be very sensitive to the density dependence of the effective pairing force. A better knowledge of this density dependence allows one to make predictions for the pairing gap at the Fermi surface as a function of nuclear matter density. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 260–265 (25 August 1998)     

Study of weak pairing correlations in aluminum nanograins

Weak pairing correlations in aluminum nanograins have been investigated using a symmetrical polynomial method based on the wave functions projected onto states with a fixed number of electrons. It is shown that this approach does not lead to a sharp transition from the superconducting to normal state with an increase in temperature, and the intensity of the pairing correlations exceeds that obtained using traditional BCS theory.     

Study ofpf-shell nuclei with a symmetry conserving generator coordinate method

Bands based on the 0⁺ ground state and the first excited 0⁺ pairing vibrational state of⁴⁸Ti,⁵²Cr and⁵⁶Fe are studied with the generator coordinate method. The generating wave functions for each value of the angular momentumJ are angular momentum and particle number projected selfconsistent Hartree-Fock-Bogoliubov states where the constrained amount of pairing correlations serves as the generator coordinate. The interaction is given by reaction matrix elements derived from the Hamada-Johnston force. The basis includes the four lowest oscillator shells. The excitation energies of the pairing vibrational states can be reproduced fairly well by the present choice of the generating wave functions, whereas the ground band is not much improved compared to projected Hartree-Bogoliubov calculations. We find that the strength of the pairing correlations in the 0⁺ and 2⁺ states of the ground state and the pairing vibrational bands can be related to data of two-particle transfer reactions. The angular momentum dependence of the pairing correlations and of the moments of inertia are studied. The results show that for a strongly paired ground state the ground state band and the pairing vibrational band intersect. This may produce in the yrast band the anomaly of the moment of inertia known from rare earth nuclei.     

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.     

Statistical description of the nuclear fermi liquid drop

The Thomas-Fermi method with applications to the nucleus is revisited. Incorporation of new developments like the treatment of fluctuations and correlations and nuclear pairing will be described. Level densities, response functions and density-density correlations are presented explicitly.     

Critical-point description of the transition from vibrational to rotational regimes in the pairing phase

An approximate solution at the critical point of the pairing transition from harmonic vibration to deformed rotation in gauge space is found by analytic solution of the collective pairing Hamiltonian. The eigenvalues are expressed in terms of the zeros of Bessel functions of integer order. The results are compared to the pairing bands based on the Pb isotopes.     

The pairing correlations in the phased t－U Hubbard model

In this paper we have studied the phased t－U Hubbard model. Using the constrained path Monte Carlo method, we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.     

Formal solutions for response functions of superconductors and 3He(B). I

The superfluid Fermi liquids with BCS and BW pairing are considered in the collisionless regime and with the effective quasiparticle interaction in the pairing channel, restricted to only one Legendre harmonic. In such a case, the density-density, density-current and current-current correlation functions are expressed in terms of matrix elements of some scalar operator and the gauge invariance of such expressions is proved. The expressions obtained for autocorrelation functions are discussed and some of their limiting values are established.     

Spin polaron approach to superconductivity

Superconducting pairing is considered for a two-dimensional system with strong correlation between the carrier subsystem and the subsystem of localized spins. The Kondo lattice model is analyzed for the case where spin polarons are the elementary excitations. It is shown that taking into account only the anomalous Green’s functions for bare holes is insufficient for superconducting pairing to occur; it arises only after the introduction of the anomalous Green’s functions for spin-polaron operators.     

Pairing vibrational states and the generator coordinate method

The pairing vibrational states and the two-neutron transfer cross sections between these states are calculated in Ni, Sn and Pb isotopes by the generator coordinate method (GCM). The particle number fluctuation of the BCS functions is handled by projecting in a good approximation on sharp particle numbers. The results agree quite well with the experimental data.     

Shell effects in a paired nucleus for finite excitation energies

Shell effects are considered as functions of the excitation energy of the nucleus. The effects of pairing are included and studied in the BCS approximation. Some numerical results, based on the single-particle spectrum of a Woods-Saxon potential, are given. In the limit of zero excitation the shell correction to the energy is compared with the results obtained by the Strutinsky method.     

Pairing correlations in finite systems: from the weak to the strong fluctuations regime

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.     

Composite boson dominance in many-fermion systems

I recently proposed a method of bosonization based on the use of coherent states of fermion composites, whose validity was restricted to smooth structure functions. In the present paper I remove this limitation and derive results which hold for arbitrary interactions and structure functions. The method respects all symmetries and in particular fermion number conservation. It reproduces exactly the results of the pairing model of atomic nuclei and of the BCS model of superconductivity in the number conserving form of the quasi-chemical equilibrium theory.     

标准对力模型的新迭代方法(英文)

建立了一种求解标准对力模型的新迭代方法。该方法基于标准对力模型的多项式方案,为球形和形变系统提供了方便的初始值预测。特别是对于大尺寸系统,该方法将求解k对多项式的系统方程式简化为分步求解1对多项式系统的迭代过程,并通过快速Newton-Raphson以及Monte Carlo采样算法逐步提供初始值预测。通过扩展,本算法还可用于解决Gaudin型量子多体问题,例如考虑超过100条轨道、50对的大尺寸系统,以及超形变核、核裂变的研究中。A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.     

Die experimentelle Bestimmung der Neutronenstreulänge für das Wismutatom mit Hilfe der Totalreflexion an einem flüssigen Wismutspiegel

We construct generalized HF- and HB-equations fitted for building the symmetry properties of the Hamiltonian into. Therefore we use the method of Green's functions for condensed systems. The structure of HF- and HB-equations is conserved, only the density and pairing matrices change. Physical quantities may easily be calculated.