Quasiboson Approximation Research Articles

Quasi-boson approximation yields accurate correlation energy in the 2D electron gas

We report the successful adaptation of the quasi-boson approximation, a technique traditionally employed in nuclear physics, to the analysis of the two-dimensional electron gas. We show that the correlation energy estimated from this approximation agrees closely with the results obtained from quantum Monte Carlo simulations. Our methodology comprehensively incorporates the exchange self-energy, direct scattering, and exchange scattering for a particle-hole pair excited out of the mean-field ground state within the equation-of-motion framework. The linearization of the equation of motion leads to a generalized random phase approximation (gRPA) eigenvalue equation whose spectrum indicates that the plasmon dispersion remains unaffected by exchange effects, while the particle-hole continuum experiences a marked upward shift due to the exchange self-energy. Using the gRPA excitation spectrum, we calculate the zero-point energy of the quasi-boson Hamiltonian, thereby approximating the correlation energy of the original Hamiltonian. This research highlights the potential and effectiveness of applying the quasi-boson approximation to the gRPA spectrum, a fundamental technique in nuclear physics, to extended condensed matter systems. Published by the American Physical Society 2024

Many body phenomenon within multiple scattering approach in PEELS

SynopsisPlasmon excitation within multiple scattering approach is being explored. The plasmon loss is described within the so-called quasi-boson approximation, originally proposed by Hedin and further extended by Fujikawa. We compare the different fluctuation potentials i.e. Plasmon-pole model, Bechstedt model and other available potentials based on beyond-RPA dielectric functions and use either the exact core state wave function or more accurate model than a simple delta function used previously for total energy loss in Aluminium targets.

Restoring the Pauli principle in the random phase approximation ground state

Random phase approximation ground state contains electronic configurations where two (and more) identical electrons can occupy the same molecular spin-orbital violating the Pauli exclusion principle. This overcounting of electronic configurations happens due to quasiboson approximation in the treatment of electron-hole pair operators. We describe the method to restore the Pauli principle in the RPA wavefunction. The proposed theory is illustrated by the calculations of molecular dipole moments and electronic kinetic energies. The Hartree–Fock based RPA, which is corrected for the Pauli principle, gives the results of comparable accuracy with Møller-Plesset second order perturbation theory and coupled-cluster singles and doubles method.

Particle-hole cumulant approach for inelastic losses in x-ray spectra

Inelastic losses in core level x-ray spectra arise from many-body excitations, leading to broadening and damping as well as satellite peaks in x-ray photoemission (XPS) and x-ray absorption (XAS) spectra. Here we present a practical approach for calculating these losses based on a cumulant representation of the particle-hole Green's function, a quasi-boson approximation, and a partition of the cumulant into extrinsic, intrinsic and interference terms. The intrinsic losses are calculated using real-time, time-dependent density functional theory while the extrinsic losses are obtained from the GW approximation of the photo-electron self-energy and the interference terms are approximated. These effects are included in the spectra using a convolution with an energy dependent particle-hole spectral function. The approach elucidates the nature of the spectral functions in XPS and XAS and explains the significant cancellation between extrinsic and intrinsic losses. Edge-singularity effects in metals are also accounted for. Illustrative results are presented for the XPS and XAS for both weakly and more correlated systems.

Effect of the Pauli principle on the deformed quasiparticle random-phase approximation calculations and its consequence forβ-decay calculations of deformed even-even nuclei

In this work, I take into consideration the Pauli exclusion principle (PEP) in the quasiparticle random-phase approximation (QRPA) calculations for the deformed systems by replacing the traditional quasiboson approximation (QBA) with the renormalized one. With this new formalism, the parametrization of QRPA calculations has been changed and the collapse of QRPA solutions could be avoid for realistic ${g}_{pp}$ values. I further find that the necessity of the renormalization parameter of particle-particle residual interaction ${g}_{pp}$ in QRPA calculations is due to the exclusion of PEP. So with the inclusion of PEP, I could easily extend the deformed QRPA calculations to the less-explored region where lack of experimental data prevent effective parametrization of ${g}_{pp}$ for QRPA methods. With this theoretical improvement, I give predictions of weak decay rates for even-even isotopes in the rare-earth region and compare the results with existing calculations.

Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fullfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green's function approach can be formulated.

Collective excitations in Random Phase Approximation and beyond

Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.

Extended second random phase approximation applied to metallic clusters

The coupling to two particle-two hole configurations is at the basis of the calculations of the spreading width of the collective excitations that in random phase approximation (RPA) are described as superpositions of one particle-one hole elementary modes. Second RPA (SRPA) is just the extension of RPA including both kinds of configurations. In SRPA use is made of the quasiboson approximation (QBA) as in RPA. It has been found that this is at the origin of the fact that the coupling among them strongly lowers the RPA collective excitations, both in metallic clusters and in nuclei. When the coupling of the two particle-two hole configurations among themselves is also included, as it has to be done in order to be consistent, this effect is even enhanced. Thus the reasonably good description of the collective vibrational states obtained at the RPA level (as expected on physical grounds, for example, for the dipole modes) is completely spoiled in SRPA. In the present paper we show quantitatively, for metallic clusters, that this disturbing behavior is eliminated when no use is made of QBA and a better description of ground-state correlations is introduced.

Self-consistent extension of random-phase approximation enlarged beyond particle-hole configurations

We present a new extension of the random-phase approximation method: the quasiboson approximation is avoided and correlations are included in the ground state without resorting to renormalized operators or renormalized matrix elements; the configuration space is enlarged by considering also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state, together with the particle-hole ones. Two new and relevant advantages of this method with respect to the existing extensions of random-phase approximation are highlighted: (i) the energy weighted sum rules are completely satisfied; (ii) the problem of the existence of nonphysical states in the spectrum, related to the inclusion of particle-particle and hole-hole configurations, is solved: a way to unambiguously disentangle physical from nonphysical states in the excitation spectrum is presented. The method is applied here to a three-level Lipkin model where its quality can be judged by comparing with the exact results. Both advantages (i) and (ii) shall lead to feasible future applications of this extended RPA to several realistic cases.

An exact microscopic multiphonon approach to collective modes in nuclei

We propose a method for solving the nuclear eigenvalue problem using a Hamiltonian of general form in a space spanned by multiphonon states built out of particle-hole TammDancoff phonons. The method consists in deriving for a given n-phonon subspace a set of equations of motion of simple structure, where all quantities are expressed in terms of energies and one-body density matrices determined in the (n − 1)-phonon subspace. Their solution, therefore, yields states built out of particle-hole operators applied on top of the (n−1)phonons basis states. Because of this peculiar structure, the states so generated form an overcomplete set. The redundancy, however, is removed completely and efficiently by a procedure based on the Choleski decomposition. The phonon composition of the basis states allows to remove naturally and maximally the spurious admixtures induced by the center of mass motion. The iteration of the equations from n = 0 up to an arbitrary number N of phonons generates an orthogonal basis spanning a space which is the direct sum of 0+1+..+N phonon subspaces. This basis decomposes the full Hamiltonian into N diagonal blocks plus off-diagonal terms coupling the n-phonons with the (n ± 1)and (n ± 2)-phonon subspaces. These off-diagonal terms are easily computed by recursive relations. The Hamiltonian can, therefore, be easily diagonalized by resorting to importance sampling techniques [1,2], which allow to truncate the multiphonon space while monitoring the accuracy of the solutions. The method can be easily upgraded so as to generate a particle-hole or quasiparticle RPA multiphonon basis. It is suitable for describing with high accuracy low-lying multiphonon spectra, whose experimental evidence is rapidly growing, as well as high-energy resonances like the recently discovered double dipole giant resonance. It can account with great accuracy for the anharmonicities associated to all collective modes. Last, but not least, it yields a highly correlated ground state which contains explicitly up to N particle N hole configurations and, therefore, applies to the cases where the quasiboson approximation breaks down. For illustrative purposes, we apply the method to 16O, whose low-lying states are dominated by complex configurations containing up to 4 particle 4 hole states. Such a calculation probes the extreme accuracy of the method, on the one hand, and, on the other hand, provides a complete and exhaustive information on the microscopic structure of low and high energy states in 16O.

THE NUMBER SELF-CONSISTENT RENORMALIZED RANDOM PHASE APPROXIMATION

RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigen-values for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

Evolution of 2+ γ wave functions and gamma-stiffness in well-deformed rare-earth nuclei

The evolution of the structure of the gamma-vibrational band head 2+ γ in well-deformed rare-earth nuclei is studied within the framework of RPA calculations using a quasiboson approximation based on the Nilsson model. The obtained evolution of the quasiparticle structure of the gamma-vibrational band head is shown to correlate well with the evolution of the same nuclei within the IBA symmetry triangle when described in the extended consistent-Q formalism. An empirical relation is presented that links the IBA parameter χ with the quasiparticle structure of the gamma-vibrational band head.

Extension of the second random-phase approximation

The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.

Scalar ground-state observables in the random phase approximation

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in $0\ensuremath{\Elzxh}\ensuremath{\omega}$ shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.

The exotic μ−→ e− conversion rates by explicit renormalized quasiparticle RPA calculations.

We investigate the μ− e conversion matrix elements by explicit calculations within the renormalized quasiparticle random phase approximation (RQRPA). In this approach, by promoting the quasi-Boson approximation mostly used in ordinary QRPA, the Pauli-principle is restored to a large extent and the nucleon-nucleon ground state correlations are reliably taken into account. We have pointed out that the usual QRPA includes quite strong ground state correlations and it, therefore, overestimates their effect on the μ− e conversion rates and especially on the coherent mode, which is the most important μ− e conversion channel. The rate of this channel is currently measured in the SINDRUM II experiment at PSI and is expected to be extracted in the designed MECO experiment at Brookhaven. By combining our nuclear calculations with the existing experimental limits on the branching ratio R μe − for 208 Pb and 48 Ti we put constraints on the flavour violating parameters entering the μ− e conversion effective currents in modern gauge theories.

Recent developments in theoretical description of two-neutrino double beta decay

Some recent developments in the theoretical description of the two-neutrino double beta decay (2ν2β-decay) matrix elements are presented. We discuss the intermediate nucleus approach (INA), theS-matrix approach and the Operator Expansion Method (OEM), which offer different insight into the problem of 2ν2β-decay. From a detailed study within the OEM it follows that one of the basic features of 2ν2β-decay is the energy difference of the initial and final nuclei. The decisive role of the Coulomb interaction within the OEM is exhibited. The introduction of the time integral representation for the 2ν2β-decay matrix element, which is derived within the field theory approach, allows a more consistent analysis. It is shown that the results obtained within the INA in the quasiboson approximation scheme are questionable from the physics point of view and that higher order approximations are important. From a field theory analysis of the 2ν2β-decay amplitude it follows that the summation over the intermediate nuclear states corresponds to a summation over a class of meson exchange diagrams. A new electron-gamma exchange mechanism for 2ν2β-decay is proposed.

Non-collapsing renormalized QRPA with proton-neutron pairing for neutrinoless double beta decay

Using the renormalized quasiparticle random phase approximation (RQRPA), we calculate the light neutrino mass mediated mode of neutrinoless double beta decay (0νββ-decay) of 76Ge, 100Mo, 128Te and 130Te. Our results indicate that the simple quasiboson approximation is not good enough to study the 0νββ-decay, because its solutions collapse for physical values of g pp. We find that extension of the Hilbert space and inclusion of the Pauli principle in the QRPA with proton-neutron pairing, allows us to extend our calculations beyond the point of collapse, for physical values of the nuclear force strength. As a consequence one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half-life of 0νββ-decay.

Extended quasiparticle RPA and double-beta-decay nuclear matrix elements

The quasiparticle random-phase-approximation model is extended toward restoration of fermion anticommutation relations for quasiparticle operators, beyond the quasi-boson approximation, within the framework of equation-of-motion method. The restoration of broken symmetries avoids an unreasonable enhancement of quasiparticle correlations in the ground state, and enables to make more reliable predictions. By the extended model, somewhat larger bounds are deduced on the neutrino mass and right-handed current parameters, compared to ordinary quasiparticle calculations, for a given half-life limit of the neutrinoless double beta decay.

Towards a self-consistent random-phase approximation for Fermi systems.

We present a method which allows us to treat correlations in finite Fermi systems in a more consistent way than the random-phase approximation (RPA). The quasiboson approximation (QBA), where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state, is avoided in our approach where the correlated ground state is always used. We derive a closed, nonlinear set of equations which determines the energies and wave functions of the excited states as well as the single-particle occupation numbers in the ground state. As an example we apply to metallic clusters a simplified version of the approach which represents, however, a significant improvement over previous attempts to go towards a self-consistent RPA. We show that our method allows one to correct for the inadequacy of standard RPA in cases where the use of QBA becomes questionable.

The Pauli principle, QRPA and the two-neutrino double beta decay

We examine the violation of the Pauli exclusion principle in the Quasiparticle Random Phase Approximation (QRPA) calculation of the two-neutrino double beta decay matrix elements, which has its origin in the quasi-boson approximation. For that purpose we propose a new renormalized QRPA with proton-neutron pairing method (full-RQRPA) for nuclear structure studies, which includes ground state correlation beyond the QRPA. This is achieved by using of renormalized quasi-boson approximation, in which the Pauli exclusion principle is taken into account more carefully. The full-RQRPA has been applied to two-neutrino double beta decay of $^{76}Ge$, $^{82}Se$, $^{128}Te$ and $^{130}Te$. The nuclear matrix elements have been found significantly less sensitive to the increasing strength of particle-particle interaction in the physically interesting region in comparison with QRPA results. The strong differences between the results of both methods indicate that the Pauli exclusion principle plays an important role in the evaluation of the double beta decay. The inclusion of the Pauli principle removes the difficulties with the strong dependence on the particle-particle strength $g_{pp}$ in the QRPA on the two-neutrino double beta decay.