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At least 343 records · Page 19
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DOE OSTI2021

Redshift space power spectrum beyond Einstein-de Sitter kernels

Abstract We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc -1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

Astronomy & Astrophysics↗
DOE OSTI2021

Multi-tracer intensity mapping: cross-correlations, line noise & decorrelation

Line intensity mapping (LIM) is a rapidly emerging technique for constraining cosmology and galaxy formation using multi-frequency, low angular resolution maps. Many LIM applications crucially rely on cross-correlations of two line intensity maps, or of intensity maps with galaxy surveys or galaxy/CMB lensing. We present a consistent halo model to predict all these cross-correlations and enable joint analyses, in 3D redshift-space and for 2D projected maps. We extend the conditional luminosity function formalism to the multi-line case, to consistently account for correlated scatter between multiple galaxy line luminosities. This allows us to model the scale-dependent decorrelation between two line intensity maps, a key input for foreground rejection and for approaches that estimate auto-spectra from cross-spectra. This also enables LIM cross-correlations to reveal astrophysical properties of the interstellar medium inacessible with LIM auto-spectra. We expose the different sources of luminosity scatter or "line noise" in LIM, and clarify their effects on the 1-halo and galaxy shot noise terms. In particular, we show that the effective number density of halos can in some cases exceed that of galaxies, counterintuitively. Using observational and simulation input, we implement this halo model for the Hα, [Oiii], Lyman-α, CO and [Cii] lines. Here, we encourage observers and simulators to measure galaxy luminosity correlation coefficients for pairs of lines whenever possible. Our code is publicly available at https://github.com/EmmanuelSchaan/HaloGen/tree/LIM. In a companion paper, we use this halo model formalism and code to highlight the degeneracies between cosmology and astrophysics in LIM, and to compare the LIM observables to galaxy detection for a number of surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Effects of overlapping sources on cosmic shear estimation: Statistical sensitivity and pixel-noise bias

The next generation of dark-energy imaging surveys — so called “Stage-IV” surveys, such as that of the Rubin Observatory Legacy Survey of Space and Time (LSST) — will cross a threshold in the number density of detected sources on the sky that requires qualitatively different image analysis and measurement techniques compared to the current generation of Stage-III surveys. In Stage-IV surveys, a significant amount of the cosmologically useful information is due to sources whose images overlap with those of other sources on the sky. Here, we focus on the weak gravitational lensing probe, for which we expect the largest impact since the cosmic shear signal is primarily encoded in the estimated shapes of observed galaxies and thus directly impacted by overlaps. We introduce a framework based on the Fisher formalism to analyze the effect of the overlapping sources (“blending”) on the estimation of cosmic shear. This method gives concrete predictions for the minimum loss of information due to noise and blending for any choice of “deblending” scheme and shape-measurement algorithm. Our studies account for undetected sources but do not address their full effects and biases they may introduce. We use simulated images and predict this impact of blending for three surveys: the Dark Energy Survey (DES), the Hyper-Suprime Cam Subaru Strategic Program (HSC-SSP), and the Rubin LSST. Our methodology successfully estimates the statistical sensitivity to weak lensing for DES and HSC early results. For LSST, we present the expected loss in statistical sensitivity for the ten-year survey due to blending. We find that for approximately 62% of galaxies that are likely to be detected in full-depth LSST images, at least 1% of the flux in their pixels is from overlapping sources. We also find that the statistical correlations between measures of overlapping galaxies and, to a much lesser extent (0.2%) the higher shot noise level due to their presence, decrease the effective number density of galaxies, N eff , by ~ 18%. We calculate an upper limit on N eff of 39.4 galaxies per arcmin 2 in r band. We study the impact of stars on as a function of stellar density and illustrate the diminishing returns of extending the survey into lower Galactic latitudes. We extend the simulation-based Fisher formalism to predict the expected increase in pixel-noise bias due to blending for maximum-likelihood (ML) shape estimators. We find that noise bias depends sensitively on the particular shape estimator and measure of ensemble-average shape that is used, and properties of the galaxy that include redshift-dependent quantities such as size and luminosity. The source code for these studies is available online.[The documented software developed for the catalog-level studies are available in the open-source LSST DESC github repository https://github.com/LSSTDESC/WeakLensingDeblending. The software for analyzing one or two galaxies with user-defined parameters is in the open-source github repository https://github.com/ismael-mendoza/ShapeMeasurementFisherFormalism.]

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Cosmological analysis of three-dimensional BOSS galaxy clustering and Planck CMB lensing cross correlations via Lagrangian perturbation theory

In this work, we present a formalism for jointly fitting pre- and post-reconstruction redshift-space clustering (RSD) and baryon acoustic oscillations (BAO) plus gravitational lensing (of the CMB) that works directly with the observed 2-point statistics. The formalism is based upon (effective) Lagrangian perturbation theory and a Lagrangian bias expansion, which models RSD, BAO and galaxy-lensing cross correlations within a consistent dynamical framework. As an example we present an analysis of clustering measured by the Baryon Oscillation Spectroscopic Survey in combination with CMB lensing measured by Planck. The post-reconstruction BAO strongly constrains the distance-redshift relation, the full-shape redshift-space clustering constrains the matter density and growth rate, and CMB lensing constrains the clustering amplitude. Using only the redshift space data we obtain Ω m = 0.303 ± 0.008, $H_0$ = 69.21 ± 0.78 and $σ_8$ = 0.743 ± 0.043. The addition of lensing information, even when restricted to the Northern Galactic Cap, improves constraints to Ω m = 0.303 ± 0.008, $H_0$ = 69.21 ± 0.77 and $σ_8$ = 0.707 ± 0.035, in tension with CMB and cosmic shear constraints. The combination of Ω m and $H_0$ are consistent with Planck, though their constraints derive mostly from redshift-space clustering. The low $σ_8$ value are driven by cross correlations with CMB lensing in the low redshift bin ($\textit{z}$ ≃ 0.38) and at large angular scales, which show a 20% deficit compared to expectations from galaxy clustering alone. We conduct several systematics tests on the data and find none that could fully explain these tensions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The impact of anisotropic redshift distributions on angular clustering

A leading way to constrain physical theories from cosmological observations is to test their predictions for the angular clustering statistics of matter tracers, a technique that is set to become ever more central with the next generation of large imaging surveys. Interpretation of this clustering requires knowledge of the projection kernel, or the redshift distribution of the sources, and the typical assumption is an isotropic redshift distribution for the objects. However, variations in the kernel are expected across the survey footprint due to photometric variations and residual observational systematic effects. Here, we develop the formalism for anisotropic projection and present several limiting cases that elucidate the key aspects. We quantify the impact of anisotropies in the redshift distribution on a general class of angular two-point statistics. In particular, we identify a mode-coupling effect that can add power to auto-correlations, including galaxy clustering and cosmic shear, and remove it from certain cross-correlations. If the projection anisotropy is primarily at large scales, the mode-coupling depends upon its variance as a function of redshift; furthermore, it is often of similar shape to the signal. In contrast, the cross-correlation of a field whose selection function is anisotropic with another one featuring no such variations — such as CMB lensing — is immune to these effects. We discuss explicitly several special cases of the general formalism including galaxy clustering, galaxy-galaxy lensing, cosmic shear and cross-correlations with CMB lensing, and publicly release a code to compute the biases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Extracting halo independent information from dark matter electron scattering data

Direct detection experiments and the interpretation of their results are sensitive to the velocity structure of the dark matter in our galactic halo. Here we extend the formalism that deals with such astrophysics-driven uncertainties, originally introduced in the context of dark-matter-nuclear scattering, to include dark-matter-electron scattering interactions. Using mock data, we demonstrate that the ability to determine the correct dark matter mass and velocity distribution is depleted for recoil spectra which only populate a few low-lying bins, such as models involving a light mediator. We also demonstrate how this formalism allows one to test the compatibility of existing experimental data sets (e.g. SENSEI and EDELWEISS), as well as make predictions for possible future experiments (e.g. GaAs-based detectors).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Light in the dark forest. Part I. An efficient optimal estimator for 3D Lyman-alpha forest power spectrum

The highly anisotropic nature of the Lyman-alpha (Lyα) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ( P 3D ). In this paper, we present the first fully optimal estimator for P 3D , which exactly deconvolves the survey window function and marginalizes contaminated modes that distort the power spectrum. Our approach adapts optimal estimator techniques developed for the 2D cosmic microwave background data to the 3D case. To achieve computational feasibility, we employ the conjugate gradient method and implement the P 3 M formalism to handle large-scale and small-scale operations separately and efficiently. We validate our estimator using Monte Carlo mocks and Gaussian simulations, demonstrating its accuracy and computational efficiency. We confirm that mode marginalization eliminates distortions arising from quasar continuum errors and delivers robust power spectrum estimation, though it also inflates errors at large scales. This first implementation works in the flat-sky case; we discuss the remaining steps needed to generalize it to the curved-sky case. This formalism offers a foundation for the Lyα forest P 3D measurements and a new path toward cosmological constraints from the Lyα forest data.

Lyman alpha forest↗
DOE OSTI2026

Cosmological neutrino mass: a frequentist overview in light of DESI

We derive constraints on the neutrino mass using a variety of recent cosmological datasets, including DESI BAO, the full-shape analysis of the DESI matter power spectrum and the one-dimensional power spectrum of the Lyman-α forest (P1D) from eBOSS quasars as well as the cosmic microwave background (CMB). The constraints are obtained in the frequentist formalism by constructing profile likelihoods and applying the Feldman-Cousins prescription to compute confidence intervals. This method avoids potential prior and volume effects that may arise in a comparable Bayesian analysis. Parabolic fits to the profiles allow one to distinguish changes in the upper limits from variations in the constraining power σ of the different data combinations. We find that all profiles in the ΛCDM model are cut off by the ∑m ν ≥ 0 bound, meaning that the corresponding parabolas reach their minimum in the unphysical sector. The most stringent 95% C.L. upper limit is obtained by the combination of DESI DR2 BAO, Planck PR4 and CMB lensing at 53 meV, below the minimum of 59 meV set by the normal ordering. The corresponding constraining power σ is 43 meV, which highlights the importance of the cut-off by negative values in the determination of the upper limit. Extending ΛCDM to non-zero curvature and w 0 w a CDM relaxes the constraints past 59 meV again, but only w 0 w a CDM exhibits profiles with a minimum at a positive value. Additionally, we extend the formalism to constrain the lightest neutrino mass. For DESI DR2 BAO, Planck PR4 and CMB lensing, we find confidence limits at 20 and 19 meV for normal and inverted ordering, respectively. Using a combination of DESI DR1 full-shape, BBN and eBOSS Lyman-α P1D, we successfully constrain the neutrino mass independently of the CMB. This combination yields m l ≤ 97 and 98 meV in the normal and inverted orderings, and total neutrino mass ∑m ν ≤ 285 meV (95% C.L.). The addition of DESI full-shape or Lyman-α P1D to CMB and DESI BAO results in small but noticeable improvement of the constraining power of the data. Lyman-α free-streaming measurements especially improve the constraint. Since they are based on eBOSS data, this sets a promising precedent for upcoming DESI data.

Frequentist statistics↗
DOE OSTI2022

Mentoring in the USDA Forest Service: A Survey of Aquatic Professionals

Abstract Mentoring is suggested as an important strategy to promote workplace inclusivity and is shown to be positively associated with high employee morale, yet mentee needs and experiences may not be universal. To evaluate mentoring impacts from the perspective of USDA Forest Service employees, we conducted an online survey of 251 aquatic professionals, including managers and scientists. 70% of respondents had mentors, and mentorship status did not vary across demographic characteristics. Previous mentoring relationships were most frequently identified as “informal” rather than “formal”; female employees were more likely to desire formal mentoring. Mentored respondents found their work more challenging, fulfilling, and valuable than unmentored respondents. Mentees looked for mentors who could provide constructive feedback, speak candidly, use active listening skills, and who cared about their careers. Overall, respondents were satisfied with their mentors’ skills. Despite strong demand for mentoring, access to mentors among aquatic professionals appears low across all categories.

Forestry↗
DOE OSTI2020

A line-binned treatment of opacities for the spectra and light curves from neutron star mergers

ABSTRACT The electromagnetic observations of GW170817 were able to dramatically increase our understanding of neutron star mergers beyond what we learned from gravitational waves alone. These observations provided insight on all aspects of the merger from the nature of the gamma-ray burst to the characteristics of the ejected material. The ejecta of neutron star mergers are expected to produce such electromagnetic transients, called kilonovae or macronovae. Characteristics of the ejecta include large velocity gradients, relative to supernovae, and the presence of heavy r-process elements, which pose significant challenges to the accurate calculation of radiative opacities and radiation transport. For example, these opacities include a dense forest of bound–bound features arising from near-neutral lanthanide and actinide elements. Here we investigate the use of fine-structure, line-binned opacities that preserve the integral of the opacity over frequency. Advantages of this area-preserving approach over the traditional expansion–opacity formalism include the ability to pre-calculate opacity tables that are independent of the type of hydrodynamic expansion and thus eliminate the computational expense of calculating opacities within radiation-transport simulations. Tabular opacities are generated for all 14 lanthanides as well as a representative actinide element, uranium. We demonstrate that spectral simulations produced with the line-binned opacities agree well with results produced with the more accurate continuous Monte Carlo Sobolev approach, as well as with the commonly used expansion–opacity formalism. The agreement between the line-binned and expansion–opacity results is explained as arising from the similarity in their opacities in the limit of low optical depth, where radiation transport is important in the ejecta. Additional investigations illustrate the convergence of opacity with respect to the number of included lines, and elucidate sensitivities to different atomic physics approximations, such as fully and semirelativistic approaches.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure

ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Price, M. A.↗
DOE OSTI2025

Dark matter substructure or source model systematics? A case study of cluster lens Abell S1063

Mapping the small-scale structure of the universe through gravitational lensing is a promising tool for probing the particle nature of dark matter. Curved Arc Basis (CAB) has been proposed as a local lensing formalism in galaxy clusters, with the potential to detect low-mass dark matter substructure. In this work, we analyse the cluster lens Abell S1063 in search of dark matter substructure with the CAB formalism, using multiband imaging data from James Webb Space Telescope ( JWST ). We use two different source modelling methods: shapelets and pixel-based source reconstruction based on Delaunay triangulation. We find that source modelling systematics from shapelets result in a disagreement between CAB parameters measured from different filters. Source modelling with Delaunay significantly alleviates this systematic, as seen in the improvement in agreement across filters. We also find that inadequate complexity in source modelling can result in convincing spurious detections of dark matter substructure from strong gravitational lenses, as seen by our $\Delta \text{BIC} > 20$ measurement of a $M \sim 10^{10}$ ${\rm M}_{\odot }$ subhalo with shapelets, a spurious detection that is not reproduced with Delaunay source modelling. We demonstrate that multiband analysis with different JWST filters is key for disentangling source and lens model systematics from dark matter substructure detections.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Auxiliary field Quantum Monte Carlo for dilute neutrons on the lattice

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. In conclusion, we perform initial calculations for a range of nuclear systems from two- to few-body neutron systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Elastic and resonance structures of the nucleon from the hadronic tensor in lattice QCD: Implications for neutrino-nucleon scattering and hadron physics

We compute the Euclidean hadronic tensor from charge density operators and extract elastic and resonance structures by employing exponential fits to the four-point function correlator, as well as a Bayesian reconstruction inverse algorithm to obtain the corresponding spectral density for qualitative comparison. We present the determination of the nucleon’s Sachs electric form factor using the hadronic tensor formalism and verify that it is consistent with that from the conventional three-point function calculation. Beyond the elastic peak, we observe a structure located approximately 0.5–0.7 GeV above the nucleon mass in the Bayesian reconstruction. This structure is interpreted as a mixture of the Roper resonance [𝑁⁡(1440)], and states with both positive and negative parities in this mass region, as well as multihadron states. Assuming the observed structure is dominated by 𝐽 𝑃 = 1/2 ± states, we extract the transition electric form factor 𝐺$^*_𝐸$⁡(𝑄 2 ) and the corresponding longitudinal helicity amplitude 𝑆 1/2 ⁡(𝑄 2 ), and compare them with those determined from the CLAS experimental data of nucleon-to-Roper transition. Although fitting to the four-point correlation function or using the inverse algorithm does not resolve individual resonances, it nevertheless enables the determination of total inclusive lepton–nucleon scattering cross sections in appropriate energy bins. This lattice QCD calculation presents the first major step toward studying the inclusive 𝑁 → 𝑋 contributions within the hadronic tensor formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Typical medium cluster approach for multibranch phonon localization

The phenomenon of Anderson localization in various disordered media has sustained significant interest over many decades. Specifically, the Anderson localization of phonons has been viewed as a potential mechanism for creating fascinating thermal transport properties in materials. However, despite extensive work, the influence of the vector nature of phonons on the Anderson localization transition has not been well explored. Here, to achieve such an understanding, we extend a recently developed phonon dynamical cluster approximation (DCA) and its typical medium variant (TMDCA) to investigate spectra and localization of multibranch phonons in the presence of pure mass disorder. We validate the new formalism against several limiting cases and exact diagonalization results. A comparison of results for the single-branch versus multibranch case shows that the vector nature of the phonons does not significantly affect the Anderson transition of phonons. The developed multibranch TMDCA formalism can be employed for studying phonon localization in real materials.

Mondal, Wasim Raja [Middle Tennessee State Univ., ↗
DOE OSTI2025

Pulse and Polarization Structures in Axion-Converted X-Rays from Pulsars

Neutron stars (NSs) with their strong magnetic fields and hot dense cores could be powerful probes of axions, a classic benchmark of feebly coupled new particles, through abundant production of axions with the axion-nucleon coupling and subsequent conversion into x-rays due to the axion-photon coupling. In this Letter, we point out that the pulsation structures in both the intensity and polarization of x-rays from NSs could provide us additional information about axions and their couplings. We develop new analytical formalisms of pulsation-polarization structure applicable to a wide range of NSs in the axion scenario and argue that they hold in complicated astrophysical environments. As a case study, we apply our formalism to a representative X-ray Dim Isolated Neutron Star, RX J1856.6-3754, with an unexpected hard x-ray excess which might be axion induced. We show with an updated fit that the axion explanation is compatible with both the intensity and pulsation data available, and combining the pulsation data does not shift the posterior by more than 1⁢𝜎. Yet, the preferred parameter space is close to being excluded by other astrophysical constraints. With a 75% reduction of the uncertainties in the pulsation data, we could potentially draw a definite conclusion on the axion-induced x-rays at more than 3⁢𝜎 level.

Axions↗
DOE OSTI2025

Microscopic scattering approach to in-gap states: Cr adatoms on superconducting 𝛽−Bi 2 ⁢Pd

We develop a microscopic scattering formalism to describe Yu-Shiba-Rusinov (YSR) states due to a single Cr adatom on the Bi-terminated surface of 𝛽−Bi 2 ⁢Pd, by combining ab initio Wannier functions with a real-space Green's function approach in the Bogoliubov–de Gennes formalism. Our framework reproduces key scanning tunneling spectroscopy features, including a single particle-hole asymmetric YSR peak and isotropic 𝑑⁢𝐼/𝑑⁢𝑉 maps around the impurity. Decomposing the YSR states reveals contributions from four nearly degenerate 𝐶 4⁢𝑣 representations, with energy broadening masking their individual signatures. Spin-orbit coupling induces partial spin polarization, while the spatial asymmetry between particle and hole components arises from Cr 𝑑−Bi 𝑝 hybridization. These results highlight the importance of realistic band structures and microscopic modeling for interpreting STM data and provide a foundation for studying impurity chains hosting topological excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors

Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.

Approximation methods for many-body systems↗