Short-range Correlation Effects Research Articles

A density-fitting implementation of the density-based basis-set correction method.

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order Møller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

Ion Steric Effect Induces Giant Enhancement of Thermoelectric Conversion in Electrolyte-Filled Nanochannels.

Ionic thermoelectricity in nanochannels has received increasing attention because of its advantages, such as high Seebeck coefficient and low cost. However, most studies have focused on dilute simple electrolytes that neglect the effects of finite ion sizes and short-range electrostatic correlation. Here, we reveal a new thermoelectric mechanism arising from the coupling of the ion steric effect due to finite ion sizes and ion thermodiffusion in electric double layers, using both theoretical and numerical methods. We show that this mechanism can significantly enhance the thermoelectric response in nanoconfined electrolytes depending on the properties of electrolytes and nanochannels. Compared to the previously known mechanisms, the new mechanism can increase the Seebeck coefficient by 100% or even 1 order of magnitude enhancement under optimal conditions. Moreover, we demonstrate that the short-range electrostatic correlation can help preserve the Seebeck coefficient enhancement in a weaker confinement or in more concentrated electrolytes.

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies.

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

Recent astrophysical observations reproduced by a short-range correlated van der Waals-type model?

ABSTRACT We perform an improvement in a van der Waals-type model by including its effects of short-range correlations (SRCs). Attractive and repulsive parts of the nucleon–nucleon interaction are assumed to be density-dependent functions, more specifically, we adopt the Carnahan–Starling (CS) method for the latter, and a suitable expression for the former in order to reproduce the structure of the Clausius (C) real gas model. The parametrizations of the resulting model, named as Clausius-–Carnahan–Starling (CCS)-SRC model, are shown to be capable of reproducing the flow constraint at the high-density regime of symmetric nuclear matter for incompressibility values inside the range of K0 = (240 ± 20) MeV. In the context of stellar matter, our findings point out a good agreement of the CCS-SRC model with recent astrophysical observational data, namely, mass–radius contours and dimensionless tidal deformability regions and values, coming from gravitational waves data related to the GW170817 and GW190425 events, and from the NASA’s Neutron star Interior Composition Explorer mission. Furthermore, the values for the symmetry energy slope of the model (L0) are in agreement with a recent range found for this quantity, claimed to be consistent with results reported by the updated lead radius experiment (PREX-2) collaboration. In this case, higher values of L0 are favoured, while the opposite scenario does not allow simultaneous compatibility between the model and the astrophysical data.

Impacts of symmetry energy slope on the oscillation frequencies of neutron stars with short-range correlation and admixed dark matter

Oscillation modes of compact stars, in general, can serve as a fingerprint in determining the equation of state (EOS) of dense matter. In this study, we examine the impact of symmetry energy slope (L) on the oscillation frequencies of neutron stars (NSs) with nucleon–nucleon short range correlation (SRC) and admixed dark matter (DM) for the first time within the relativistic mean-field theory. By adjusting the L, we revise the EOS and coupling parameters in light of the SRC and DM effects, and construct the new sets. The results reveal that NSs containing SRC and DM inside are more likely to satisfy the observational constraints, and we find that smaller L exhibits larger fundamental non-radial and radial frequencies, and that the effect on large separation is also mainly concentrated in the low-mass region. Moreover, we update the linear relationship between the non-radial frequency and mean density, and we further give empirical relations between non-radial and radial frequencies and tidal deformability at different L for 1.4 and 2. These findings will enable us to more effectively confine the NS EOSs, in turn, also provide a strategy to place constraints on the L.

Probing heavy-ion collisions with the yield ratios of neutron-proton at intermediate energy

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we investigate effects of nucleon-nucleon short-range correlations (SRCs) and the nuclear symmetry energy on the yield ratios of neutron-proton (n/p) in four reaction systems K94r+94Kr, Z94r+94Zr, M94o+94Mo and R94u+94Ru. It is found that effects of the symmetry energy and the high momentum tails (HMTs), caused by the SRCs of nucleon-nucleon in the target and projectile, on the kinetic energy distribution of n/p yield ratio are almost same in four reaction systems. While the effect of the HMTs on the double ratio of n/p from neutron-rich and neutron-deficient reaction systems K94r+94Kr and R94u+94Ru is enlarged, and it is about two times than that of the symmetry energy in the high kinetic energies. Meanwhile, we find that the dependence of isospin-fractionation (i.e., the double ratio of n/p of gas-liquid phase) on the isospin asymmetry of reaction system is completely not sensitive to the HMTs but keeping high sensitivity to the symmetry energy. It indicates that the distribution of isospin-fractionation on the isospin asymmetry of reaction system can be taken as an experimental observable to extract information on nuclear symmetry energy.

CALCULATION OF THE INELASTIC LONGITUDINAL ELECTRON SCATTERING OF 20Ne AND 24Mg NUCLEI

The inelastic longitudinal electron scattering form factors F(q)'s, an expression for the transition charge density are studied where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The core polarization transition density is evaluated by adopting the shape of Tassie model together with form of the ground state two-body charge density distributions which included the effect of short range correlation(SRC). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a good agreement between the calculated inelastic longitudinal F(q)'s and those of experimental data for 20Ne and 24Mg nuclei.

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the equation of state (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both nonrelativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and nonrelativistic free Fermi gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering short-range correlations (SRCs) as well as nonlinear relativistic mean field models, we study effects of relativistic kinematics, dimensionality, interactions, and SRC on the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal three-dimensional space, it could be even smaller in spaces with reduced dimensions for subsystems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities, and/or symmetries. We also found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ could theoretically become very large only at the ultrarelativistic limit far above the density reachable in neutron stars. However, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affects significantly the density dependence of $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ compared to the relativistic FFG model prediction. The SRCs affect significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ while the relativistic corrections are found negligible. Although we found no fundamental physics reason for the $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ to be very small especially at high densities, the results may help better understand the EOS of dense neutron-rich matter.

Effects of nucleon-nucleon short-range correlations on inclusive electron scattering

The nucleon-nucleon short-range correlation (NN-SRC) is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this paper, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $(e,{e}^{\ensuremath{'}})$ cross sections are calculated within the plane-wave impulse approximation (PWIA) framework, including the quasielastic (QE) part and $\mathrm{\ensuremath{\Delta}}$ production part. Especially in the $\mathrm{\ensuremath{\Delta}}$ production region, we reconsider the electromagnetic structures of the nucleon resonance $\mathrm{\ensuremath{\Delta}}$(1232) and the scattering mechanisms, and thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $(e,{e}^{\ensuremath{'}})$ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $0.5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}<{Q}^{2}<1\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$, the QE peak and $\mathrm{\ensuremath{\Delta}}$ production peak not only reflect the mean-field structure but also are sensitive to the NN-SRC information. Finally, we provide another method to extract the strengths of NN-SRC from experimental cross sections for selected nuclei at the suitable kinematics.

Many-body approximations to the superfluid gap and critical temperature in pure neutron matter

We compute singlet pairing gaps and critical temperatures in pure neutron matter with different many-body approximations. Medium effects tend to reduce gaps and critical temperatures compared to the standard BCS ansatz. In the mean-field approximation, the ratio of these two quantities remains constant across a wide range of densities. This constant ratio is close to the universal prediction of BCS theory, whether three-neutron interactions are included or not. Using a more sophisticated many-body approach that incorporates the effect of short-range correlations in pairing properties, we find that the gap to critical temperature ratio in the low-density regime is substantially larger than the BCS prediction, independently of the interaction. In this region, our results are relatively close to experiments and theoretical calculations from the unitary Fermi gas. We also find evidence for a different density dependence of zero-temperature gaps and critical temperatures in neutron matter.

Short-range correlation effects in neutron star's radial and non-radial oscillations * *Supported by the National Key Research and Development Program of China (2017YFA0402600, 2016YFE0129300), the National SKA Program of China (2020SKA0120300) and the National Natural Science Foundation of China (11833003, 11947211, 119051)

In this study, we determine the influence of the nucleon-nucleon short range correlation (SRC) on static spherically symmetric neutron stars (NSs) from the perspectives of radial and nonradial oscillations for the first time. We revise the equation of state and coupling parameters in the relativistic mean field theory after considering the SRC effect, and select the hyperon coupling parameters as the SU(3) model. For the non-radial oscillations, the SRC effect decreases the -mode frequency by kHz. For the radial oscillations, it decreases the fundamental radial frequency by 0.75 ~ 0.85 kHz. Additionally, we refit the linear relationship between the average density and -mode frequency for SRC. Combining the characteristics of the radial and non-radial frequencies, we provide a view of inferring the maximum mass of NSs. Owing to the characteristics of the SRC influence on the radial frequency, we expect that the SRC can be tested by future observation and can also be used as a probe for the structure inside NSs.

Short-range correlations in the extended quantum molecular dynamics model

Short-range potential has been added into an extended quantum molecular dynamics (EQMD) model. The rms radius, binding energy, and momentum distribution of $^{12}\mathrm{C}$ with different initial structures and short-range potential parameters have been checked. The separation energy of $^{12}\mathrm{C}(p,2p)^{11}\mathrm{B}$ reaction is calculated and compared with the experimental data, which indicates that our modified EQMD model can be taken as a reliable tool for studying proton pair knock-out reaction. Furthermore, the short-range correlation effects on emission time and momentum spectrum of two protons are discussed. Finally, the momentum correlation function of the emitted proton pair is calculated by Lednicky and Lyuboshitz's analytical method. The result explains that short-range repulsion causes high momentum tail and weakens the momentum correlation function.

Elastic and inelastic C2 form factors of nickel isotopes and two-body correlations

The inelastic form factors for C2 transition have been studied for even nickel isotopes ([Formula: see text]Ni) using the form of Tassie shape for ground state charge density distribution. The charge density distribution is investigated using the one- and two-body terms in the cluster expansion. The effect of short-range correlations is included using Jastrow-type correlation function into the two-body density term of the cluster expansion. This concludes that the inserting of the influence of short-range correlations is required for reaching an important adjustment in the calculated elastic and inelastic form factors which explain the data very well at the high momentum transfers ([Formula: see text][Formula: see text]fm[Formula: see text].

Nuclear effects in neutrino-nucleus DIS and a probe for short-range correlations

We investigate charged-current neutrino-nucleus deep inelastic scattering with particular interests in relationship of short range correlation (SRC) and EMC effect. The structure functions $F^A_2(x,Q^2)$, $x F^A_3(x,Q^2)$ and ratios of differential cross sections are presented where the nuclei $A$ are chosen to be carbon, iron and lead. We propose a kind of universal modification functions which would provide a nontrivial test of SRC universality on the platform of neutrino-nucleus scattering and improve our understanding of nucleon structure substantially.

Elastic and inelastic form factors including 2-body short-range correlation effect

The charge distributions and elastic electron form factors for 18O, 42,44Ca, 58Ni, and 118Sn nuclei were considered using the cluster expansion of the 1- and 2-body terms. Inelastic electron form factors to 2+ states with core-polarization effects were studied, where the nuclear collective modes were considered alongside the shell model transition density. The influence of short-range correlations (SRCs) was calculated by the parameter β, which was introduced into the ground-state charge distribution and concluded the Jastrow-type function. It is found that the inclusion of 2-body correlations is necessary to describe the observed data of elastic and inelastic form factors at high momentum transfer q > 3 fm–1.

Explicitly correlated Fock-space coupled-cluster singles and doubles method for (1,1), (0,2), and (2,0) sectors

A linearly approximated explicitly correlated coupled-cluster singles and doubles model for the Fock-space coupled-cluster method has been formulated and implemented. An extension of the Fock-space wave operators is introduced in order to treat the short-range correlation effects for excited and doubly electron-attached states. We show that an effective reduction in the number of active virtuals can also be obtained by improving how the short-range correlation is treated. Numerical results to gauge the performance for valence and Rydberg excitation energies, double ionization potentials, and double electron attachment energies of several molecules are obtained. Statistical measures of the errors in excitation energies show that the explicitly correlated results are within 0.1eV from the complete basis set limit already at the double-ζ level unless the excitation energies are too close to the ionization thresholds. Similar accuracy is seen for the double ionization potentials and double electron attachment energies.

Examining the EMC effect using the F2n neutron structure function

The persistently mysterious deviations from unity of the ratio of nuclear target structure functions to those of deuterium as measured in deep inelastic scattering (often termed the "EMC Effect") have become the canonical observable for studies of nuclear medium modifications to free nucleon structure in the valence regime. The structure function of the free proton is well known from numerous experiments spanning decades. The free neutron structure function, however, has remained difficult to access. Recently it has been extracted in a systematic study of the global data within a parton distribution function extraction framework and is available from the CTEQ-Jefferson Lab (CJ) Collaboration. Here, we leverage the latter to introduce a new method to study the EMC Effect in nuclei by re-examining existing data in light of the the magnitude of the medium modifications to the free neutron and proton structure functions independently. From the extraction of the free neutron from world data, it is possible to examine the nuclear effects in deuterium and their contribution to our interpretation of the EMC Effect. In this study, we observe that the ratio of the deuteron to the sum of the free neutron and proton structure functions has some $x_{B}$ and $Q^{2}$ dependencies that impact the magnitude of the EMC Effect as typically observed. Specifically, different EMC slopes are obtained when data from different $x_{B}$ and $Q^{2}$ values are utilized. While a linear correlation persists between the EMC and short range correlation effects, the slope is modified when deuteron nuclear effects are removed.

Taming the fixed-node error in diffusion Monte Carlo via range separation.

By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of μ = 0.5 bohr-1 provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.

Electron Scattering from Some Fp- Shell Nuclei with Inclusion the Effect of Short-Range Correlation

The effects of short-range correlation on elastic Coulomb (charge) form factors, charge density distributions as well as root mean square charge radii of various nuclei (for instance, 46, 48, 50Ti, 52, 54Cr, 56, 58Fe, and 72, 74, 76Ge nuclei) are examined. The one- and two body terms of the cluster expansion together with the single-particle harmonic oscillator wave functions are utilized. For the purpose of embedding these effects into the formulae of charge density and form factor we employ the correlation function of Jastrow-type. These formulae depend upon the short-range correlation parameter (which instigates from the Jastrow function) and the oscillator size parameter Both and are found by the fitting to the measured elastic form factors. It is noticed that the embedding of short-range correlation effects into the calculations of and is a requisite for the achievement of a vital change in the computed results and remarkably vital for the characterization of the measured data.

Effects of short-range nuclear correlations on the deformability of neutron stars

In the present work, we investigate the effects of short-range correlations (SRC) on the dimensionless deformability of the binary neutron system related to the GW170817 event. We implemented phenomenological SRC in a relativistic mean-field model in which the bulk parameters, namely, incompressibility ($K_0$), effective nucleon mass ratio ($m^*$), symmetry energy ($J$) and its slope ($J_0$), are independently controlled. Our results point out that the SRC favor the model to pass through the constraints, established by the LIGO/Virgo Collaboration, on the values of $\Lambda_{1.4}$ and on the $\Lambda_1\times\Lambda_2$ region. We also found a clear linear correlation between $\Lambda_{1.4}$ with $K_0$ and $L_0$ (increasing dependence), and with $m^*$ and $J$ (decreasing dependence). Finally, we also obtained compatible numbers for $R_{1.4}$ (model with and without SRC) in comparison with recent data from the neutron star interior composition explorer mission.