{"id":"925a436c-90df-42d0-bf04-0043f594643a","arxiv_id":"2501.04020","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The authors provide full (MC)RRPA atomic response functions for xenon and germanium for sub-GeV dark matter-electron scattering, and report a low-energy spin-dependent response distinct from the spin-independent one.","lead":"This paper computes new atomic response tables for dark matter scattering off electrons in xenon and germanium, using a relativistic many-body method and benchmarking them against photoabsorption data. The tables let experimental groups turn dark matter-electron recoil data into interaction limits, and suggest that spin-dependent and spin-independent interactions can be told apart at low energies.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The photoabsorption benchmark validates only charge multipoles at q ≈ T/c (≤ ~0.2 keV), not the axial multipoles or q up to 2.5 MeV that drive the DM rates and the SD/SI distinction; the central accuracy claim is therefore an extrapolation without direct external constraint.","rationale":"The paper is a real advance: (MC)RRPA treats relativistic, exchange, and correlation effects self-consistently; the photoabsorption benchmark is external and credible; and the released tables and codes are valuable. The reader's CONDITIONAL verdict matches my read. The load-bearing premise, as the reader identified, is that the photoabsorption benchmark — which tests only charge multipoles at q ≈ T/c ≤ 0.22 keV — justifies the accuracy of response functions at axial operators and at q up to 2.5 MeV. The internal comparisons (RRPA vs RFCA, Jmax ≤ 6 convergence) show consistency but cannot validate the absolute scale of the axial/high-q response. The SD/SI claim at T < 100 eV is especially exposed because that is the least benchmarked energy range. An independent many-body calculation at a modest set of (T, q) points would directly test the published tables; if the axial and high-q response functions agree, the central claims are substantially supported. Until such a check exists, CONDITIONAL is the appropriate verdict.","tokens_in":16480,"tokens_out":5784,"duration_ms":55557,"concrete_test":"Recompute the four xenon response functions with an independent relativistic many-body method (e.g., relativistic configuration interaction in a B-spline basis or a second RRPA implementation) at representative kinematically allowed points, for instance (T, q) = (50 eV, 0.1 MeV), (50 eV, 1 MeV), (500 eV, 1 MeV), (500 eV, 2.5 MeV), and compare R_C, R_L5, R_E5, R_M5 with the published tables. If any axial multipole or high-q entry differs by more than about 20%, the benchmarked accuracy does not extend to the DM-relevant regime, and the low-energy SD/SI distinction would need independent confirmation before being used for experiment.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central accuracy claim rests on the photoabsorption benchmark of Sec. II.B.1 (Fig. 1). Photons probe only the charge multipoles (M_J) at momentum transfer q = T/c; over the benchmarked range up to 30 keV, q never exceeds about 0.22 keV. The DM response functions used in Eqs. (4) and (5) are integrated over q up to 2.5 MeV and include axial multipoles L5, E5, M5 (Eqs. 2b-2d), which do not couple to real photons. The 5% photoabsorption agreement therefore provides no direct constraint on the axial response or on the q-dependence of any response where DM scattering actually occurs. The new SD/SI distinguishability claim (Figs. 7-8) depends precisely on the ratio of axial to charge response for T <~ 100 eV; this is also the region where the authors concede photoabsorption benchmarks are least reliable near edges and where the germanium atomic calculation is invalid below 80 eV. Internal checks (RFCA comparison, Jmax convergence) are useful but do not replace an external benchmark in the DM-relevant regime. The claims may well be correct, but their empirical support is narrower than the abstract suggests.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes atomic response functions for xenon and germanium using the (multiconfiguration) relativistic random phase approximation, for use in sub-GeV dark matter-electron scattering at leading order. It benchmarks the charge response against photoabsorption data, provides data tables and code, compares with earlier RFCA and other independent-particle approaches, and updates exclusion limits for several existing experiments. It also reports a low-energy (T<100 eV) difference between spin-dependent and spin-independent response functions, arguing that SD and SI interactions can be distinguished in unpolarized detectors.","tokens_in":16689,"tokens_out":6580,"duration_ms":65254,"significance":"If the results hold, the paper provides a comprehensive, many-body data set for two important direct-detection targets, with the practical advantage that the response functions are tabulated and the rate code is released. The (MC)RRPA method is ab initio and self-consistent, and the photoabsorption agreement is a genuine external test of the charge channel. However, the benchmark covers only the charge multipoles at momentum transfer q≈T/c, while the DM rate calculation uses the same response functions at q up to 2.5 MeV and includes axial operators that are not probed by real photons. The accuracy claim for DM scattering is therefore an extrapolation that needs to be stated more carefully.","major_comments":[{"comment":"The photoabsorption benchmark tests only the charge multipoles at q≈T/c, which for T≤30 keV is at most about 0.22 keV. The DM response functions used in Eqs. (4) and (5) are integrated over q up to 2.5 MeV and include the axial operators of Eqs. (2b)-(2d) that do not couple to real photons. The 5% photoabsorption agreement therefore provides no direct external constraint on the axial response or on the q-dependence of any response in the region where DM scattering occurs. The paper should state this limitation explicitly and discuss the degree to which the RMFA/RPA framework is expected to remain accurate at large q and for the spin-dependent operators, ideally with a quantitative estimate of the induced uncertainty on the differential rate.","section":"Sec. II.B.1, Fig. 1; Eqs. (4)-(5)"},{"comment":"The new claim that SD and SI interactions can be distinguished at T≲100 eV depends precisely on the ratio of axial to charge response at low energy and low momentum transfer. This is the same region where, as the paper notes, the photoabsorption benchmark is least reliable near the ionization edges and where the germanium atomic calculation is not valid below 80 eV. The authors should justify why the axial response is trustworthy in this regime, for example by decomposing the response into shell-wise contributions and by showing how the SD/SI ratio in Figs. 7-8 changes when the RPA correlation treatment is varied.","section":"Sec. IV, Figs. 7-8"},{"comment":"The high-momentum tail beyond 2.5 MeV is said to be extrapolated to the end point q_end=sqrt(2mA(T-Tmin)), but the extrapolation function is not specified and its error is not quantified. Since the differential rate in Eq. (4) integrates over this tail, please describe the extrapolation method and show its contribution to the rate for representative (T,q) values.","section":"Sec. II.B.2"}],"minor_comments":[{"comment":"The phrase 'energies less than 1 GeV is' should be 'energies less than 1 GeV are'.","section":"Abstract"},{"comment":"The data tables and code are hosted on a webpage; for long-term accessibility, consider depositing them in a permanent repository (e.g., Zenodo) and citing the DOI.","section":"Sec. III.B"},{"comment":"Please confirm that the sum over J for the L5 response starts at J=0 while the E5 and M5 sums start at J=1, given the definitions in Eqs. (2b)-(2d); if this is intentional, a brief note would help the reader.","section":"Sec. II, Eq. (5b)"},{"comment":"The paper mentions an erratum for the earlier RFCA result in Ref. [20]; it would be helpful to state explicitly that the present SD results supersede those of Ref. [20] on the points where they differ.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid computational contribution with a useful data release. The main weakness is that the central accuracy claim for DM-electron scattering is not directly supported by the external benchmark: photoabsorption tests only the charge channel at near-zero momentum transfer, while the DM rate calculation relies on the same response functions at q up to 2.5 MeV and on spin-dependent operators that are not probed by real photons. This is a load-bearing issue, but it is fixable by a more careful statement of the validity range and by additional internal consistency checks or comparisons with independent finite-q calculations. I do not see a reason to reject, but the authors should temper the abstract and the SD/SI distinguishability claim accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a careful look, but the headline claim needs to be read with its limits. The genuinely new part is the full (MC)RRPA response tables for xenon and germanium, data and code included, with correlation and axial operators that earlier RFCA-based papers didn't have. The photoabsorption benchmark is a real check on the charge channel, and the agreement within ~5% over 30 keV is credible evidence for that channel. They are open about the germanium threshold at 80 eV because solid-state effects matter below that, and they flag a coding mistake in their own previous SD work — that is honest.\n\nThe soft spot is exactly what the stress-test note says: the benchmark tests charge multipoles at q = T/c, so effectively zero momentum transfer on the DM scale. The axial multipoles that drive the SD response do not couple to real photons at all, and the q range used in the DM integrals goes up to 2.5 MeV. So the 5% accuracy claim does not directly support the axial response or the high-q behavior. The internal comparisons with RFCA and Jmax convergence are useful but don't replace an external check in the region that matters. The low-energy SD/SI distinction is a plausible and well-illustrated result, but it rests on the unbenchmarked axial response at T below ~100 eV — exactly where they say correlation is strongest. No uncertainties are propagated anywhere, so one cannot tell whether the SD/SI ratio difference is significant or a few-percent artifact.\n\nI would not call the paper circular: the response functions are ab initio and the benchmark is external. The reliance on their own earlier RFCA work is lineage, not circularity. The central accuracy claim is overstated in the abstract, though — 'benchmarked with ~5% errors' should really say 'benchmarked for the charge channel at low momentum transfer.'\n\nSend it to a referee. A referee can push on the axial response and the SD/SI claim, and the shipped data/code will let others check the pipeline. If the authors can provide an independent check of the axial channel, this becomes a very useful resource. As is, it is a solid computational data paper with one genuinely new observation that needs stronger support.","headline":"Solid data paper with real new response tables, but the accuracy claim is over-broad: the photoabsorption benchmark doesn't test the axial or high-q response that the new SD/SI result depends on.","tokens_in":17296,"tokens_out":2389,"would_cite":true,"duration_ms":20290,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper supplies complete many-body atomic response tables for xenon and germanium dark-matter searches and shows that spin-dependent and spin-independent interactions can be told apart at low recoil energies.","keywords":["dark matter","sub-GeV dark matter","dark matter-electron scattering","atomic response functions","relativistic random phase approximation","xenon","germanium","spin-dependent interaction"],"falsifier":"Compute the axial response functions for xenon at $T<100$ eV with an independent correlated method; if the SD/SI differential-rate ratio returns to 3 in that range, the paper's central distinction claim fails.","tokens_in":16250,"feed_emoji":"⚛️","tokens_out":8057,"duration_ms":71004,"temperature":0.7,"pith_summary":"This paper aims to supply the atomic physics input needed to interpret sub-GeV dark matter-electron scattering in xenon and germanium detectors. Using the (multiconfiguration) relativistic random phase approximation, which treats relativity, exchange, and electron correlation in one self-consistent framework, it computes four response functions over the energy and momentum range relevant to dark matter masses up to about 1 GeV. The results are benchmarked against photoabsorption measurements from threshold to 30 keV and agree within about 5% away from ionization edges. A central finding is that below about 100 eV the spin-dependent response is no longer a constant multiple of the spin-independent one, so the two interaction types could in principle be separated in unpolarized detectors. If the calculation is reliable, the response tables provide a reusable many-body input for future direct-detection limits.","feed_headline":"Xenon and germanium atomic response tables sharpen dark-matter limits","feed_subtitle":"Correlated relativistic calculations separate spin-dependent from spin-independent electron signals below 100 eV.","key_machinery":"The central object is the (multiconfiguration) relativistic random phase approximation, a self-consistent many-body method that solves for the ground state with Dirac-Fock or MCDF and for ionized final states with RRPA or MCRRPA, so exchange and electron-electron correlation are included together with relativity. For each momentum transfer $q$ and multipole $J$, it evaluates the reduced matrix elements of four transition operators — charge, axial longitudinal, axial transverse electric, and axial transverse magnetic — whose squared moduli define the response functions $R_C$, $R_{L5}$, $R_{E5}$, and $R_{M5}$ entering the dark-matter differential cross section. The method carries the argument because it is the only ingredient in the rate calculation that needs expensive atomic physics; once tabulated, the response functions are the reusable input for any dark-matter mass, velocity distribution, or coupling.","core_discovery":"The atomic response of xenon (above 12.2 eV) and germanium (above 80 eV) to dark matter-electron interactions is governed by four multipole response functions, and the paper computes them with (MC)RRPA, including all subshells except the inert 1s electrons of xenon and all electrons of germanium. The resulting photoabsorption cross sections match experimental data within roughly 5% from threshold to 30 keV. The key qualitative claim is that the spin-dependent response functions deviate substantially from the spin-independent ones at low energy transfer, breaking the factor-of-3 scaling that holds for nonrelativistic independent-particle atoms; this makes spin-dependent versus spin-independent dark matter-electron interactions distinguishable in unpolarized detector media at low recoil energies.","pith_inferences":["The tabulated response functions could be reused directly for other low-energy electron-recoil processes, such as neutrino-electron scattering or absorption of dark photons, because those processes share the same atomic transition amplitudes.","A natural next test is to compute the SD/SI ratio for argon or other detector targets to see whether the low-energy breakdown of the factor-3 scaling is generic or specific to xenon and germanium's outer-shell structure.","If the SD/SI separation survives, experiments with single-electron sensitivity could search for a spectral-shape distortion rather than a total-rate excess, which would require event-by-event energy reconstruction and would be much more robust against background uncertainties."],"forward_implications":["The tabulated response functions cover the full $(T,q)$ plane for sub-GeV dark matter: xenon from 12.2 eV, germanium from 80 eV, up to $T \\approx 5$ keV and $q$ up to 2.5 MeV.","For $T > 300$ eV the correlated (MC)RRPA rates agree with the simpler frozen-core approximation within about 20%, but below 300 eV the difference can be much larger, so independent-particle calculations should not be trusted at low recoil energies.","The spin-dependent and spin-independent differential rates do not scale by the constant factor 3 across the whole spectrum; below about 100 eV the ratio moves well away from 3, giving SD and SI interactions different low-energy spectral shapes.","Updated 90% confidence exclusion limits using published liquid-xenon data shift: low-threshold data become more constraining with the correlated response, while high-threshold data become slightly less so."],"supporting_citations":[{"why":"Supplies the multichannel RRPA equations used to compute xenon transition amplitudes.","marker":"[28]"},{"why":"Supplies the multiconfiguration RRPA generalization used for germanium's open-shell ground state.","marker":"[29]"},{"why":"Compiled photoabsorption cross-section data used to benchmark (MC)RRPA from threshold to 30 keV.","marker":"[41]"},{"why":"Provides precision xenon photoionization measurements in the benchmark comparison.","marker":"[42]"},{"why":"Provides xenon photoabsorption cross sections at 2.1-6.0 keV used as a high-energy benchmark.","marker":"[44]"},{"why":"Earlier frozen-core response and constraints from the same group, the baseline for evaluating correlation effects.","marker":"[10]"},{"why":"Earlier treatment of spin-dependent dark matter-electron interactions that this work extends and corrects.","marker":"[20]"},{"why":"Independent local-exchange-approximation calculation compared in the event-number spectra.","marker":"[26]"},{"why":"Independent-particle xenon response calculation used for comparison.","marker":"[6]"},{"why":"Prior MCRRPA germanium photoionization calculation whose results the germanium benchmark reproduces.","marker":"[50]"}],"fun_headline_variants":["Relativistic response functions distinguish DM spin modes in Xe and Ge","Sub-100 eV atomic response separates spin-dependent and independent DM","New response tables sharpen sub-GeV dark matter searches in Xe and Ge","Atomic response splits SD from SI for dark matter-electron scattering","Many-body calculations reveal spin contrast in low-energy DM hits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that (MC)RRPA transition amplitudes remain accurate at momentum transfers up to 2.5 MeV and for the axial (spin-dependent) multipole operators, although the photoabsorption benchmark only validates the charge operator at the much smaller momenta $q \\sim T/c$ of photon absorption.","fun_headline_variants_meta":{"raw":{"variants":["Relativistic response functions distinguish DM spin modes in Xe and Ge","Sub-100 eV atomic response separates spin-dependent and independent DM","New response tables sharpen sub-GeV dark matter searches in Xe and Ge","Atomic response splits SD from SI for dark matter-electron scattering","Many-body calculations reveal spin contrast in low-energy DM hits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000665,"raw_usage":{"total_tokens":3016,"prompt_tokens":907,"completion_tokens":2109,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":523,"completion_tokens_details":{"reasoning_tokens":2020}},"tokens_in":523,"tokens_out":2109,"duration_ms":12988,"temperature":1.0,"reasoning_tokens":2020,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:23:21.401066+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the axial response functions for xenon at $T<100$ eV with an independent correlated method; if the SD/SI differential-rate ratio returns to 3 in that range, the paper's central distinction claim fails.","supporting_citations":[{"cited_title":"Fuelling the search for light dark matter-electron scattering with spherical proportional counters","cited_arxiv_id":"2110.02985","evidence_quote":"Supplies the multichannel RRPA equations used to compute xenon transition amplitudes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides precision xenon photoionization measurements in the benchmark comparison."},{"cited_title":"Samson and W","cited_arxiv_id":null,"evidence_quote":"Provides xenon photoabsorption cross sections at 2.1-6.0 keV used as a high-energy benchmark."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior MCRRPA germanium photoionization calculation whose results the germanium benchmark reproduces."}],"review_version":1}