{"id":"6533d00d-46ef-4ffe-9a63-edd970140a1c","arxiv_id":"hep-ph/0406218","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"A consolidated compilation of proton and neutron spin matrix elements from nine nuclear models, showing that the choice of model changes predicted spin-dependent WIMP scattering rates by factors of two to five.","lead":"This review collects, in thirteen tables, the proton and neutron spin expectation values that nine nuclear models predict for candidate dark matter target nuclei. Experimentalists use these numbers to turn a spin-dependent WIMP scattering rate into a neutralino-nucleus cross section.","discovery_kind":"review","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The tables' headline entries are not the ones the paper's own reliability criterion selects: models whose magnetic moment matches experiment only after quenching are listed unquenched, while §II argues against quenching the spin matrix element.","rationale":"I read the paper as a compilation review whose central claim is that the tabulated <Sp> and <Sn> determine the spin-dependent event rate and that model spread, not force choice, dominates the uncertainty. I first checked whether the tables are internally consistent, since a compilation lives or dies on that. They largely are: the ISPSM rows reproduce Eq. (19), and the quoted magnetic moments follow µ = gs<Sz> + gl<Lz> with <Lz> = J - <Sz> in the stretched state (27Al gives 4.793, 209Bi gives 2.63, 13C gives 0.638, 15N gives -0.264, all matching the tables). The formalism is also self-consistent: Eq. (6) follows from Eqs. (14) and (15), and Eq. (24) matches Eq. (15). I found no arithmetic or algebraic error. I also considered and rejected the objection that the claim 'the interaction is not the primary uncertainty' rests on only two realistic potentials: the numbers in Tables VIII–X show force-induced differences of roughly 0.01–0.06 in <Sn>, well below the 0.1–0.23 spread across alternate models for the same nuclei, so the claim survives on its own data. The load-bearing soft spot is instead the reliability ranking. The reader located the same region, the magnetic-moment benchmark, but framed it as the criterion being 'softer than the prose implies.' I think it is sharper than that: it is an inconsistency between the stated criterion and the tabulated headline entries, since the rows the tables foreground for 73Ge are precisely the ones that fail the paper's own test unless a quenching factor is applied, and the paper then argues against applying that factor to the spin matrix element. On the reader's two presentation gaps I agree they are real but minor; I would add that the single TFFS numbers in Tables VIII–XI are ambiguous between the <Sp> and <Sn> columns, which matters for 131Xe (-0.186) and 133Xe (-0.201) because the sign of <Sp> controls the interference term in Eq. (7). None of this rises to a load-bearing error, so CONDITIONAL remains the right verdict and I would not move it.","tokens_in":28326,"tokens_out":10429,"duration_ms":211448,"concrete_test":"For 73Ge, take the Ressell et al. large-space row of Table VI (<Sp>=0.011, <Sn>=0.468, µ=-1.239) and apply the isovector quenching factor 0.833 that Section II says brings µ to -0.879. Recompute Λ² and σ_SD(0) from Eq. (6) with representative ap and an, and compare against (a) the unquenched row and (b) the Dimitrov-Engel-Pittel hybrid row (0.030, 0.378). If the quenched Ressell value falls within about 10% of the hybrid value, the tables are effectively self-consistent once the paper's own criterion is applied and the concern dissolves. If it does not, the headline entries and the stated reliability rule are in conflict and the 'most reliable values' guidance needs restating.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The review's practical payload is the guidance that 'the most reliable values of <Sp(n)> are considered to be those of the approach which reproduces well the experimental value of the magnetic moment' (Summary and Conclusions). That criterion is applied inconsistently in the tables, and the inconsistency is load-bearing because it determines which number an experimentalist actually takes from Tables I–XIII. For 73Ge, Table VI lists 'SM (large), Ressell et al. [8]' with <Sp>=0.011, <Sn>=0.468 and µ=-1.239 µN against µ_exp=-0.879. The model does not reproduce µ unquenched; the paper itself states that agreement requires an isovector quenching factor of 0.833. Yet the unquenched row is the headline entry and the quenched row (0.009, 0.372) is presented as a variant. The hybrid calculation of Dimitrov, Engel and Pittel [9], which reaches µ=-0.920 without an imposed factor, gives <Sn>=0.378, a roughly 20% reduction. Section II then argues the opposite direction: 'it is very doubtful that any extra quenching of the spin matrix elements (or equivalently the coupling constants a0 and a1) is desirable for these nuclei.' So the paper validates a model by a quantity that only agrees after quenching, and then declines to apply that same quenching to the quantity the tables report. A reader following the stated criterion literally would not select the rows the tables headline; a reader following the anti-quenching argument would not treat µ agreement as validation at all. The two positions cannot both be used to rank models. This is distinct from the meson-exchange-current caveat the paper already concedes (vector-current spin operators versus axial-vector), which it discusses openly; the unresolved issue is a consistency problem between the stated ranking rule and the tabulated entries, and it bears directly on the abstract's claim that these values 'allow a conclusion about the event rate.'","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"This is a review of the nuclear-structure input needed for spin-dependent (axial-vector) WIMP–nucleus scattering in the zero-momentum-transfer limit. The authors set out the formalism connecting the proton and neutron spin expectation values ⟨Sp⟩ and ⟨Sn⟩ to the spin-dependent cross section (Eqs. 2–15, and Appendix A), then compile, in Tables I–XIII, values of ⟨Sp⟩ and ⟨Sn⟩ obtained for nuclei across the periodic table within the independent single-particle shell model (ISPSM), the odd-group and extended odd-group models (OGM/EOGM), the interacting boson-fermion model (IBFM), the theory of finite Fermi systems (TFFS), the quasi Tamm-Dancoff approximation (QTDA), large-basis shell model calculations, and the hybrid symmetry-restored shell model of Dimitrov, Engel and Pittel. Section II narrates each model and its benchmarks, with particular attention to 29Si, 73Ge, 127I, 129Xe, 131Xe and 207Pb, and closes with a discussion, following Ressell and Dean, of the quenching problem and of why magnetic-moment agreement is an imperfect proxy for the axial-vector matrix element. The stated conclusion is that model-to-model spread, rather than the choice of residual interaction within a given model, dominates the theoretical uncertainty, and that the tabulated values permit an estimate of the spin-dependent event rate.","tokens_in":28646,"tokens_out":12898,"duration_ms":214566,"significance":"As a reference compilation the paper has clear value: to my knowledge it is the broadest single-table collection of ⟨Sp⟩ and ⟨Sn⟩ values assembled for this purpose, and it would save an experimentalist or phenomenologist a substantial literature search. The manuscript is also more careful than a bare table dump. The ISPSM magnetic-moment column is internally consistent with the free g-factors of Eq. (17) in every case I checked (e.g. 1H, 13C, 15N, 27Al, 51V, 183W, 209Bi), and the OGM rows reproduce Eq. (20) with the quoted experimental moments in the large majority of entries (e.g. 7Li, 19F, 27Al, 29Si, 73Ge, 121Sb, 131Xe, 137La). The authors explicitly flag the weakness of the magnetic-moment benchmark in Section II, noting that the magnetic-moment spin operators descend from the vector current and are strongly affected by meson-exchange currents whereas the WIMP matrix element descends from the axial-vector current and is not. That is an honest statement of a limitation that many compilations of this kind would have left implicit, and it is the right thing to have written. The paper does not ship code or machine-checked derivations, but the arithmetic cross-checks above are the (","major_comments":[{"comment":"The reliability criterion stated in the Summary and Conclusions — that 'the most reliable values of ⟨Sp(n)⟩ are considered to be those of the approach which reproduces well the experimental value of the magnetic moment' — is not applied consistently in how the tables present their entries, and this matters because the tables are the paper's deliverable. For 73Ge, Table VI headlines 'SM (large), Ressell et al. [8]' with ⟨Sp⟩=0.011, ⟨Sn⟩=0.468 and µ=−1.239 µN against µ_exp=−0.879 µN, while the text states that agreement requires an isovector quenching factor of 0.833; the quenched row (0.009, 0.372) is presented as a variant rather than as the row the stated criterion selects. Section II then argues the opposite direction, that 'it is very doubtful that any extra quenching of the spin matrix elements ... is desirable for these nuclei.' A reader applying the stated criterion literally would not choose the rows the tables headline, and a reader persuaded by the anti-quenching argument would not treat µ agreement as validation at all. The paper should resolve this explicitly, for example by marking in each table which row satisfies the stated criterion and which rows require an imposed quenching factor, and by saying plainly which number the authors recommend for each nucleus. As written, the guidance the review exists to provide is left ambiguous at exactly the nuclei (73Ge, 127I, 129Xe, 131Xe) where it is most needed.","section":"Section II and Tables VI, VIII–X","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Several single-value TFFS rows have ambiguous column placement, which defeats the purpose of a compilation table. In Table VIII the 123Te TFFS entry reads '0.21 —' with the number in the ⟨Sp⟩ column, but 123Te is an odd-neutron nucleus for which every other model gives ⟨Sp⟩≈0 and ⟨Sn⟩≈0.2, so 0.21 must be ⟨Sn⟩. The same problem appears in Table X for 131Xe, where the TFFS entry '−0.186 —' sits in the ⟨Sp⟩ column although the QTDA and shell-model entries place the neutron spin near −0.23 and the proton spin near −0.01 to −0.04. Table IX (125I) and Table XI (133Cs) have single TFFS numbers whose column assignment should be stated explicitly rather than left to alignment. Please place each value unambiguously in its column, or add a footnote giving the assignment for every partial row.","section":"Tables VIII–XI","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"A number of tabulated entries do not reproduce the formulas the paper itself supplies, and for a compilation these are load-bearing. In Table V the 55Mn OGM row gives ⟨Sp⟩=0.264 with µ_exp=3.453 µN; applying Eq. (20) with gsp−glp=4.586 gives (3.453−2.5)/4.586≈0.21, not 0.264. In Table VIII the 117Sn OGM row gives ⟨Sn⟩=0.126 with µ_exp=−1.001 µN; Eq. (20) gives 1.001/3.826≈0.26, a factor of two larger. In Table IV the 39K ISPSM row gives µ=0.324 µN while the 35Cl ISPSM row, which has the identical D3/2 single-particle configuration and identical ⟨Sp⟩=−0.3, gives µ=0.13 µN; the free-g-factor value for both is ≈0.12 µN. These look like transcription slips rather than physics errors, but they should be re-checked and corrected, and the authors may wish to state in the table captions that all OGM rows are generated from Eq. (20) so that readers can verify entries themselves.","section":"Tables IV, V, VI, VIII","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The text refers to 'lead 208Pb [3, 13]' but the calculation tabulated in Table XIII is for 207Pb; please make the isotope labels consistent between text and tables.","section":"Section I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'the spin-dependent interaction of the DM particles provides us with twice stronger constraints on the SUSY parameter space in comparison with the spin-independent interaction' is a strong and model-dependent statement resting on the self-citation [2]; it should be qualified as depending on the SUSY parameter region and on the target, or supported with a specific comparison.","section":"Section I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The IBFM discussion contains two statements that sit awkwardly together: that 'the ISPSM predictions are generally within 15% of their results for the nucleon spin matrix elements [15]', and that 'the spin-dependent WIMP-nucleus cross section associated with the IBFM spin matrix elements is always smaller than the ISPSM prediction but not more than a factor of 5 [15]'. A factor of 5 in cross section corresponds to a factor of about 2.2 in the amplitude, which is far outside 15%; please clarify whether the 15% refers to the unquenched IBFM and the factor of 5 to the quenched variant, and state which comparison is being made.","section":"Section II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The line 'with Λ = ⟨N|apSp+anSn|N⟩J = ap⟨Sp⟩J + an⟨Sn⟩J' appears to be missing a division by J; as printed it reads as multiplication, which is inconsistent with Eq. (14). Please correct the notation.","section":"Appendix A, below Eq. (24)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The 129Xe IBFM rows quote the experimental moment as (−0.778)exp in one row and (−0.788)exp in the next; one of these is a typo.","section":"Table X","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim in Section I that the long q-tail of the spin-dependent form factor 'allows detection of large nuclear recoil energy due to some nuclear structure effects' is stated without reference or demonstration; a citation or a one-sentence explanation would help.","section":"Section II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Given that the paper's stated purpose is to enable event-rate estimates, a short summary table or paragraph naming a recommended value of ⟨Sp⟩ and ⟨Sn⟩ (with an uncertainty band) for the nuclei of most experimental interest — 19F, 23Na, 29Si, 73Ge, 127I, 129Xe, 131Xe — would substantially increase the review's practical value.","section":"Summary and Conclusions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract states that the tabulated values 'allow a conclusion about the event rate', but the paper does not work through an example event rate or discuss the particle-physics side quantitatively; 'allow an estimate of the spin-dependent cross section, and hence of the event rate for a given SUSY model' would be more accurate.","section":"Abstract","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Several typographical errors should be corrected: 'niobium 93Nd' in Section I should be 93Nb; 'iodide 127I' should be 'iodine'; 'can be fobbed in Ref. [7]' should read 'found'; 'scattaring' in Section II should be 'scattering'; 'Gammov-Teller' should be 'Gamow-Teller'; 'neutralino-71Ge' should be 73Ge; 'Divari ar al.' in Table III should be 'Divari et al.'; 'IFBM' in Section II should be 'IBFM'; and the reference [32] author name 'Resler' should presumably be 'Ressell'.","section":"Typographical","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision"},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"This is a review, and it does the one thing a review in this niche should do: it puts every published calculation of ⟨Sp⟩ and ⟨Sn⟩ for dark matter target nuclei into one set of tables, from 1H through 209Bi, across nine nuclear models. If you work on spin-dependent direct detection you already know the pain of chasing these numbers through Ressell et al., Engel et al., Iachello et al., and the TFFS papers. Having them side by side, with the magnetic moments used as input marked in parentheses, is real value. The authors also did a small amount of original work: they converted the Ellis–Flores odd-group entries from λ²J(J+1) into ⟨Si⟩ and checked them, and they flag where models agree (39K, PT versus EOGM) and where they badly disagree (73Ge). That is honest bookkeeping, not a new result, and the abstract's claim [abstract:s2] that these values 'allow a conclusion about the event rate' is fair only in the sense that any tabulated nuclear input does. It changes no cross section and settles no physics question, which the paper does not pretend otherwise [abstract:s1]. The prose is candid about the main methodological weakness: the magnetic moment's spin operators come from the vector current and are hit by meson exchange currents, while the WIMP matrix element comes from the axial-vector current. They say so plainly, and that candor is a point in their favor. Where I'd push back is the ranking rule. The conclusions say the most reliable values are those from the approach that reproduces the measured magnetic moment, but Table VI headlines the unquenched Ressell et al. large-space 73Ge row at µ = −1.239 against µ_exp = −0.879, with the quenched variant demoted to a separate line, and §II then argues against quenching the spin matrix element at all. That is not a contradiction so much as a criterion applied loosely: µ agreement is a soft indicator, and the paper half-admits it. But a reader taking the stated rule literally would not pick the rows the tables headline, and the tables should say which rows are quenched and which are not. Two smaller things a referee should fix: several TFFS rows in Tables VIII–XI give a single number with no indication of which column it belongs to, and no entry carries an uncertainty. Neither breaks the compilation. This is a reference table for people doing spin-dependent direct detection or writing exclusion plots; it is not for anyone outside that community. It deserves a serious referee, mostly to tighten the table notes and the ranking language.","headline":"A genuinely useful 2004 compilation of spin matrix elements for spin-dependent WIMP scattering, with a soft ranking criterion and some table hygiene problems that a referee should clean up.","tokens_in":29425,"tokens_out":1121,"duration_ms":21861},"pith_extraction":{"msc":[],"pacs":["95.35.+d","12.60.Jv","14.80.Ly"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The rate at which a dark matter particle would spin-scatter off a nucleus reduces to two numbers per isotope — the proton and neutron spin averages — and a review of every nuclear model that computes them shows those numbers disagree by up到","keywords":["spin-dependent dark matter scattering","neutralino-nucleus scattering","nuclear spin matrix elements","odd-group model","nuclear shell model","interacting boson-fermion model","direct detection event rate","magnetic moment quenching"],"falsifier":"Find an isotope where a model that reproduces the measured magnetic moment gives a demonstrably wrong axial-vector spin matrix element — for instance, an ab initio or large-basis calculation for $^{73}$Ge or $^{131}$Xe that matches $μ$ yet lands outside the tabulated $⟨S_n⟩$ range, or a measured Gamow-Teller strength that contradicts the spin value the magnetic moment implies. That would break the ranking the tables rest on.","tokens_in":29627,"feed_emoji":"⚛️","tokens_out":3051,"duration_ms":51250,"temperature":0.7,"pith_summary":"A weakly interacting massive particle that couples to nuclear spin scatters off a nucleus at a rate set, at zero momentum transfer, by a single combination of two quantities: the average proton spin $⟨S_p⟩$ and average neutron spin $⟨S_n⟩$ inside that nucleus. The paper's purpose is to gather, in one place, every published calculation of those two numbers across the periodic table, and to ask how much the answer depends on which nuclear model you trust. The authors argue that the spread between different models — the independent single-particle shell model, the odd-group model built from measured magnetic moments, large-basis shell-model diagonalizations, the interacting boson-fermion model, finite-Fermi-systems theory, the quasi Tamm-Dancoff approximation — is the dominant theoretical uncertainty, larger than the difference between two different realistic nucleon-nucleon forces inside the same model. If that is right, then any spin-dependent dark matter limit quoted from a single nuclear model is really a point inside a band, and the band's width is a nuclear-structure question rather than a particle-physics one. The practical payoff is a lookup table: pick a target nucleus, read off $⟨S_p⟩$ and $⟨S_n⟩$, and the spin-dependent event rate follows once the neutralino couplings are fixed.","feed_headline":"Dark matter's spin signal reduces to two numbers per nucleus","feed_subtitle":"Nuclear models disagree by factors of a few on the proton and neutron spin that set the scattering rate.","key_machinery":"The load-bearing object is the zero-momentum-transfer spin structure function, which the authors write as $S_{SD}(0) = (2J+1)Λ^2/(π J(J+1))$ with $Λ = a_p⟨S_p⟩ + a_n⟨S_n⟩$, where $a_p$ and $a_n$ carry the particle-physics couplings and $⟨S_p⟩$, $⟨S_n⟩$ carry all the nuclear physics. Everything else in the review is in service of that factorization: because the nuclear and particle sides separate cleanly at $q=0$, the nuclear side can be compiled once and reused for any WIMP model. The second piece of machinery is the benchmark used to rank the models — the nuclear magnetic moment, $μ = ⟨g_s^n S_n + g_l^n L_n + g_s^p S_p + g_l^p L_p⟩$, which is built from the same spin operators, so a model that reproduces the measured $μ$ is taken as more credible. The third is the odd-group model's inversion of that relation, $⟨S_p⟩ = (μ - J)/4.586$ and $⟨S_n⟩ = -μ/3.826$, which converts a measured magnetic moment directly into a spin average.","core_discovery":"The paper's central claim is that the spin-dependent neutralino-nucleus cross section at zero momentum transfer, $S_{SD}(0) = (2J+1)/(4π) |(a_0+a_1)⟨S_p⟩ + (a_0-a_1)⟨S_n⟩|^2$ in the isospin language the authors use, is determined by two nuclear matrix elements that can be tabulated, and that a complete table of them now exists. The authors assemble the proton and neutron spin expectation values calculated within essentially every nuclear model applied to the problem and lay them side by side for nuclei from $^1$H through $^{209}$Bi. The review's substantive conclusion is a ranking: the phenomenological single-particle shell model overestimates the spin content almost everywhere and is inadequate; the odd-group model, which extracts the spin from the measured magnetic moment, is a clear improvement and agrees well with shell-model work for light nuclei but degrades as configuration mixing grows; and for open-shell medium-heavy and heavy nuclei the models of choice are the interacting boson-fermion model, finite-Fermi-systems theory, and the quasi Tamm-Dancoff approximation. The authors also report a specific and consequential comparison: for $^{127}$I, Ressell and Dean's shell-model calculation raises the spin-dependent sensitivity by roughly a factor of twenty over what had previously been assumed, which reshapes how much of a sodium-iodide detector's spin response comes from iodine rather than sodium.","pith_inferences":["If the model spread really dominates over the choice of nucleon-nucleon force, then a spin-dependent limit quoted from one nuclear model should be published with the envelope over models attached, in the same way scalar limits carry a form-factor uncertainty band.","The magnetic-moment benchmark is a proxy, not a calibration: an independent handle such as measured Gamow-Teller strength or polarized electron scattering on the same isotope would test whether magnetic-moment agreement actually transfers to the axial-vector matrix element.","For $^{73}$Ge the two most comprehensive calculations disagree by roughly a factor of two in $⟨S_n⟩$, so any germanium-based spin-dependent limit inherits that factor as a theory error rather than a statistical one.","The tables are indifferent to whether the WIMP is a neutralino, since the same axial-vector matrix elements govern any Majorana WIMP coupling to spin, so the compilation outlives the specific supersymmetric motivation."],"forward_implications":["Spin-dependent dark matter exclusion limits can be recomputed for any target in the tables by substituting the tabulated $⟨S_p⟩$ and $⟨S_n⟩$ into the cross-section formula, without redoing the nuclear calculation.","Because $^{19}$F combines an unquenched spin matrix element with isospin channels that add coherently, it is identified as the most favorable target for light spin-coupled dark matter.","Iodine's spin-dependent sensitivity is roughly twenty times higher than earlier estimates, so a sodium-iodide detector's spin response is still dominated by sodium but by a smaller margin than previously believed.","For neutralino masses above a few tens of GeV and medium-to-heavy targets, the zero-momentum approximation fails and the finite-momentum-transfer structure functions $S_{00}$, $S_{11}$, $S_{01}$ must be used instead."],"supporting_citations":[{"why":"Large-basis shell-model calculation of $^{29}$Si and $^{73}$Ge spin matrix elements and form factors; supplies the germanium values that later work is measured against.","marker":"[8]"},{"why":"Shell-model calculation for $A≈127$ nuclei, source of the iodine and xenon spin values and of the factor-of-twenty sensitivity revision.","marker":"[6]"},{"why":"Odd-group and extended odd-group model, the magnetic-moment-based estimates used as the phenomenological baseline throughout the tables.","marker":"[29]"},{"why":"Hybrid symmetry-restored variational calculation for $^{73}$Ge, giving the competing neutron spin value that disagrees with the shell-model result.","marker":"[9]"},{"why":"Interacting boson-fermion model calculation of spin matrix elements for heavy targets, one of the three methods recommended for open-shell heavy nuclei.","marker":"[15]"},{"why":"Finite-Fermi-systems calculation of spin averages and of their quenching in the nuclear medium, used as the second recommended heavy-nucleus method.","marker":"[30]"},{"why":"Shell-model and perturbation-theory calculation for $^{27}$Al and $^{39}$K, and the source of the meson-exchange-current caveat about magnetic moments.","marker":"[7]"},{"why":"Quasi Tamm-Dancoff calculation of the $^{131}$Xe spin structure and its momentum dependence, supplying the $⟨S_p⟩=-0.041$, $⟨S_n⟩=-0.236$ values.","marker":"[12]"},{"why":"Independent single-particle shell model estimates, the naive baseline that the review shows systematically overestimates the spin content.","marker":"[28]"},{"why":"Shell-model calculation with Cohen-Kurath and Reid interactions, providing the light-nucleus comparison points that validate the extended odd-group model.","marker":"[14]"}],"fun_headline_variants":["Two nuclear spins set the spin-dependent dark matter rate","Nuclear spin table ranks models for dark matter scattering","Iodine's spin response rises twentyfold in shell-model recheck","Single-particle shell model overstates nuclear spin content","Odd-group model beats single-particle shell model for light nuclei"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The review ranks nuclear models by whether they reproduce the measured nuclear magnetic moment, but the magnetic moment's spin terms come from the vector current and are strongly renormalized by meson exchange, while the dark-matter matrix element comes from the axial-vector current and is not — so agreement on the magnetic moment does not by itself certify the tabulated spin averages.","fun_headline_variants_meta":{"raw":{"variants":["Two nuclear spins set the spin-dependent dark matter rate","Nuclear spin table ranks models for dark matter scattering","Iodine's spin response rises twentyfold in shell-model recheck","Single-particle shell model overstates nuclear spin content","Odd-group model beats single-particle shell model for light nuclei"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1365,"prompt_tokens":914,"completion_tokens":451,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":385}},"tokens_in":914,"tokens_out":451,"duration_ms":7722,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":385,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-13T08:40:32.876294+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"pipeline_version":"pith-pipeline@v1.5.0-archive-selfhost","input_kind":null,"input_chars":null,"input_total_chars":null,"passes_missing":null,"published_standing":null,"published_confidence":null,"objection_audit":null,"run_record":null,"basis":{"kind":"not_recorded","source":null,"chars_given":null,"chars_total":null},"receipt":null,"falsifier":"Find an isotope where a model that reproduces the measured magnetic moment gives a demonstrably wrong axial-vector spin matrix element — for instance, an ab initio or large-basis calculation for $^{73}$Ge or $^{131}$Xe that matches $μ$ yet lands outside the tabulated $⟨S_n⟩$ range, or a measured Gamow-Teller strength that contradicts the spin value the magnetic moment implies. That would break the ranking the tables rest on.","supporting_citations":[{"cited_title":"Nuclear shell model calculations of neutralino - nucleus cross-sections for Si-29 and Ge-73","cited_arxiv_id":null,"evidence_quote":"Large-basis shell-model calculation of $^{29}$Si and $^{73}$Ge spin matrix elements and form factors; supplies the germanium values that later work is measured against."},{"cited_title":"Spin-Dependent Neutralino-Nucleus Scattering for $A \\sim 127$ Nuclei","cited_arxiv_id":"hep-ph/9702290","evidence_quote":"Shell-model calculation for $A≈127$ nuclei, source of the iodine and xenon spin values and of the factor-of-twenty sensitivity revision."},{"cited_title":"Spin dependent cross-sections o f weakly interacting massive particles on nuclei","cited_arxiv_id":null,"evidence_quote":"Odd-group and extended odd-group model, the magnetic-moment-based estimates used as the phenomenological baseline throughout the tables."},{"cited_title":"Scatttering of Weakly Interacting Massive Particles from Ge73","cited_arxiv_id":"hep-ph/9408246","evidence_quote":"Hybrid symmetry-restored variational calculation for $^{73}$Ge, giving the competing neutron spin value that disagrees with the shell-model result."},{"cited_title":"Spin dependent scattering of weakly interacting massive particles in heavy nuclei","cited_arxiv_id":null,"evidence_quote":"Interacting boson-fermion model calculation of spin matrix elements for heavy targets, one of the three methods recommended for open-shell heavy nuclei."},{"cited_title":"Quenc hing of the spin dependent scattering of weakly interacting massive particles on heavy nuclei","cited_arxiv_id":null,"evidence_quote":"Finite-Fermi-systems calculation of spin averages and of their quenching in the nuclear medium, used as the second recommended heavy-nucleus method."},{"cited_title":"Response of Mica to Weakly Interacting Massive Particles","cited_arxiv_id":"hep-ph/9504322","evidence_quote":"Shell-model and perturbation-theory calculation for $^{27}$Al and $^{39}$K, and the source of the meson-exchange-current caveat about magnetic moments."},{"cited_title":"Nuclear form-factors for the scattering of w eakly interacting massive particles","cited_arxiv_id":null,"evidence_quote":"Quasi Tamm-Dancoff calculation of the $^{131}$Xe spin structure and its momentum dependence, supplying the $⟨S_p⟩=-0.041$, $⟨S_n⟩=-0.236$ values."},{"cited_title":"Realistic predictions for the detection of supersymmetric dark matter","cited_arxiv_id":null,"evidence_quote":"Independent single-particle shell model estimates, the naive baseline that the review shows systematically overestimates the spin content."},{"cited_title":"Nuclear structure corr ections to estimates of the spin dependent WIMP nucleus cross-section","cited_arxiv_id":null,"evidence_quote":"Shell-model calculation with Cohen-Kurath and Reid interactions, providing the light-nucleus comparison points that validate the extended odd-group model."}],"lane_accuracy":{"status":"not yet measured","lane":{"model":"selfhosted/deepseek-v4.1-flash","input_kind":null},"url":"https://pith.science/accuracy"},"review_version":1}