Ground state correlations in the BCS treatment of a monopole pairing Hamiltonian

The treatment of a monopole pairing Hamiltonian, in the quasiparticle basis and with the inclusion of ground state correlations, is discussed. The theoretical procedure is based on the BCS method supplemented by a variational treatment of ground state correlations. A significant improvement in the results is found, for ground state energies, when the comparison between correlated, BCS and exact values is performed. Results are discussed for one and two level model configurations.     

The use of coherent states in the variational treatment of proton-neutron interactions

Coherent states are used as trial states to determine, variationally, the structure of the eigenvectors belonging to a schematic Hamiltonian consisting of single-particle, pairing and residual proton-neutron interaction terms. It is shown that the standard proton-neutron quasiparticle random-phase approximation (pn-QRPA) is recovered, as a variational theory, by replacing quasiparticle pair creation and annihilation operators by bosons. It is also shown that an exact, algebra preserving, mapping of the Hamiltonian is needed to describe the spectrum beyond the QRPA phase transition. The role of the spurious components of the trial wave functions is discussed. Received: 19 February 2002 / Accepted: 3 May 2002     

Exact solution of the spin-isospin proton-neutron pairing Hamiltonian

The exact solution of the proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with nondegenerate single-particle orbits and equal pairing strengths is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled nonlinear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for a system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.     

Validity of an algebraic-variational approach to the theory of collective motion for an exactly soluble shell model with R(5) symmetry

An algebraic-variational approach to the theory of collective motion previously applied in variant forms to pairing and monopole interaction models is here developed for an exactly soluble shell model Hamiltonian with R(5) symmetry. The spectrum of this class of Hamiltonian operators has previously been shown to represent a two-dimensional vibrator-rotator. The approximation scheme developed yields almost exact results up to the two-phonon level in the spherical region and goes over smoothly into a theory of the lowest states of the ground state rotational band in the deformed regime.     

Pair-vibrational states in the presence of neutron–proton pairing

Pair vibrations are studied for a Hamiltonian with neutron–neutron, proton–proton and neutron–proton pairing. The spectrum is found to be rich in strongly correlated, low-lying excited states. Changing the ratio of diagonal to off-diagonal pairing matrix elements is found to have a large impact on the excited-state spectrum. The variational configuration interaction (VCI) method, used to calculate the excitation spectrum, is found to be in very good agreement with exact solutions for systems with large degeneracies having equal T=0$T=0$ and T=1$T=1$ pairing strengths.     

重夸克偶素的高阶变分-积分微扰修正

利用基于积分方程的改进的变分微扰方法(变分-积分微扰法)求解重夸克偶素激发态.设置含有变分参数的母哈密顿量作为零级哈密顿量,选择该母哈密顿系统的精确解作为试探波函数,得到了只有几项的高阶修正波函数和高阶能量修正.该计算结果更接近精确能量值,修正波函数的有界性和收敛性也得到了证明.结果表明,这种方法不仅可提高计算结果的精度,而且可确保微扰级数解的收敛性. 关键词： 重夸克偶素 变分-积分微扰法 高阶能量修正     

A microscopic description of the vibrational spectra in even spherical nuclei

The previously developed multiphonon method is applied to the study of the quadrupole vibrational motion in even-even spherical nuclei. For the first time calculations with a model Hamiltonian containing pairing and quadrupole-quadrupole interactions are performed up to four phonons. The contributions of all the parts of the Hamiltonian are analyzed and it is shown that some terms generally omitted cannot be neglected.     

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Summary In the present work we have applied the correlated squeezed-state approach to investigate the ground state of the extended Hubbard model which is coupled to local Holstein phonons. Our study begins with decoupling the electron and phonon subsystems approximately by introducing a variational correlated squeezed-state ansatz for the phonons. Then assuming the renormalized intersite electron correlation of the effective electronic Hamiltonian to be attractive and the renormalized on-site correlation repulsive, we have applied the generalized Hartree-Fock approximation to obtain the ground state of the system, which is a superconducting state with intersite pairing. With optimal values of the variational parameters the correlated squeezed-state approach will by construction yield a ground-state energy lower than those obtained in previous studies. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is noticeably weakened. This weakening of the reduction effect should, in turn, significantly affect other physical properties of the system.     

Lattice calculation of the vector mass in the Schwinger model

Using the variational method, we calculate the mass of the vector meson in the Hamiltonian lattice Schwinger model. Our results are consistent with the exact value in the continuum.     

A particle number projection study with the generator coordinate method

The generator coordinate method (GCM) is used in order to describe pairing vibrations. The generating wave functions are particle-number-projected BCS-wave functions. With the conventional pairing Hamiltonian the method is tested in some simple models and applied also to the even Nickel isotopes. The results obtained can be regarded as encouraging ones.     

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.     

Theory of oxide high temperature superconductivity

We propose a model Hamiltonian for the high temperature superconductivity from the analogy of the BCS model hamiltonian. We seek a possibility of real space electron pairing. It follows then the magnetic exchange interaction is not a source of pairing and we propose a form of pairing interaction from the argument of the broken symmetry of electron number conservation. Based on a variational wave function, the ground state energy of our model is studied.     

Exact solution of the isovector neutron-proton pairing Hamiltonian

The complete exact solution of the T = 1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with nondegenerate single-particle levels and including isospin symmetry-breaking terms. The power of the method is illustrated with a numerical calculation for for 64Ge for a pf + g9/2 model space which is out of reach of modern shell-model codes.     

Integrable model for interacting electrons in metallic grains.

We find an integrable generalization of the BCS model with nonuniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe ansatz. Uniform pairing and Coulomb interaction are obtained as the "isotropic limit" of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.     

Pairing effects in Sn isotopes

An extensive study of pairing effects in the Sn isotopes is carried out. The pairing Hamiltonian is treated by the chain-calculation method which provides practically exact solutions while involving less computational work than a complete-basis diagonalization. The coupling strength is fixed by reproducing the energy of the 9^? state in¹¹⁶Sn, while the single-particle energies have been determined by an analysis of the experimental low-energy spectra of the odd-A isotopes. A detailed comparison of the calculated results with experimental data evidences the importance of neutron pairing correlations in the 50–82 shell. The results of this paper complement those of our previous study of theN=82 isotones. It turns out that the role of pairing correlations is similar to a large extent in both cases.     

Exactness of two-body cluster expansions in many-body quantum theory

The Horn-Weinstein formula and the variational principle, combined with numerical results for a few many-electron systems, are used to provide support for a conjecture that the exact ground-state wave function for a Hamiltonian system containing up to two-body terms may be represented by an exponential cluster expansion employing a finite two-body operator.     

Condensate fragmentation in a new exactly solvable model for confined bosons

Based on Richardson's exact solution of the multilevel pairing model we derive a new class of exactly solvable models for the finite boson system. As an example we solve a particular Hamiltonian which displays a transition to a fragmented condensate for repulsive pairing interaction.     

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non-degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.     

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.