{"id":"35b77486-a028-4e04-9841-eadef7275d96","arxiv_id":"2412.03602","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"First spectroscopy of 52K reveals a 2− ground state and excited states at 293, 536, and 1076 keV, with single-particle proton configurations.","lead":"Physicists measured the energy levels of the exotic nucleus potassium-52 for the first time using gamma rays from proton and neutron knockout reactions at RIKEN. The new level scheme tests how well modern shell-model and ab initio calculations describe nuclei far from stability.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central spin-parity assignments (especially 536-keV 0−) are model-dependent: momentum distributions fix the knocked-out orbital but not total J; exclusive cross sections depend on SDPF-Umod C2S values and should be tested against swapped J orderings to quantify the constraint.","rationale":"I agree with the reader that the weakest assumption is the theory-dependence of the Jπ assignments, especially for the 536-keV state. The paper is otherwise solid: the γ-γ coincidences determine the level scheme, and the momentum distributions robustly assign the knocked-out orbital. The proposed test quantifies the actual discriminating power of the exclusive cross sections. Approximate arithmetic suggests the d3/2 pair is strongly constrained (the swapped order would disagree by several σ), while the s1/2 pair is only moderately constrained (~2σ), so the conditional verdict is appropriate. I do not see a reason to reject or to accept outright. The '1/2−' label in the Conclusions is physically impossible for an odd-odd nucleus and contradicts the paper's own 1p-1h description; it is almost certainly a text-extraction artifact, but because it appears in the central claim it should be checked before publication. My recommendation is unchanged: CONDITIONAL acceptance pending clarification of the model-dependence and the typesetting.","tokens_in":14790,"tokens_out":17824,"duration_ms":157822,"concrete_test":"Re-analyze Table II as a likelihood-ratio test over the four J orderings. The measured exclusive ratios are g.s. 55(8)%, 293-keV 25(4)%, 536-keV 7(2)%, 1076-keV 14(3)%. Using the published SDPF-Umod C2S values and the DWIA σ_sp values (a) and (b), predict the four exclusive ratios for (i) the claimed ordering 2−,1−,0−,1−; (ii) d3/2 pair swapped; (iii) s1/2 pair swapped; (iv) both swapped. Compute χ² for each with the stated uncertainties. If the swapped orderings are excluded at >3σ, the model-dependence concern is resolved; if not, the spin-parity assignments must be presented as tentative. In the same pass, confirm from the published source whether the 1076-keV state is typeset as 1− or 1/2−.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the set of Jπ assignments. The momentum distributions directly identify only the knocked-out proton orbital: d3/2 for the ground and 293-keV states, s1/2 for the 1076-keV state (Sec. III.C). Each p1/2-neutron ⊗ (d3/2 or s1/2) doublet has two J values with identical ℓ, so the momentum distributions do not by themselves determine which J lies lower. The 2−/1− ordering of the ground and 293-keV states is taken from SDPF-Umod and from the unconverged VS-IMSRG(3) calculation; VS-IMSRG(2) actually predicts a 0− ground state with the 2− at 92 keV, so the ab initio guidance is not converged. The 536-keV state has no momentum distribution (Sec. III.B) and is assigned 0− only by analogy with theory (Sec. III.D). The exclusive cross sections do constrain the ordering, but only through the SDPF-Umod C2S values (2.352/1.303 for d3/2; 1.244/0.402 for s1/2) and the DWIA single-particle cross sections; if the model wavefunctions are wrong, the inferred Jπ could be swapped. The body correctly calls the 536-keV assignment tentative, but the Conclusions state it without qualification. Separately, the Conclusions appear to label the 1076-keV state '1/2−', which is impossible for an odd-odd nucleus and inconsistent with the paper's own p1/2⊗s1/2 configuration; this is likely a typesetting artifact but should be verified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports the first spectroscopy of 52K, produced at the RIKEN RIBF via (p,2p) knockout from a 53Ca beam and (p,pn) knockout from a 53K beam on the MINOS liquid-hydrogen target, with de-excitation gamma rays measured in DALI2+ and fragments identified in SAMURAI. The gamma-ray singles and coincidence analysis establishes three transitions at 243(5), 293(3), and 540(13) keV forming a 1076 -> 536 -> 293 -> 0 keV cascade, and hence excited states at 293(3), 536(6), and 1076(14) keV. Exclusive momentum distributions analyzed with DWIA identify the knocked-out proton orbital as d3/2 for the ground and 293-keV states and s1/2 for the 1076-keV state; the 536-keV state is too weak for a momentum analysis. Guided by SDPF-Umod shell-model and VS-IMSRG calculations, and by comparison of exclusive cross sections, the states are assigned 2-, 1-, (0-), and 1-_2 (second 1-), leading to the conclusion that the low-lying spectrum of 52K consists of one-particle one-hole states with normal d3/2-below-s1/2 proton orbital ordering.","tokens_in":15126,"tokens_out":29353,"duration_ms":291665,"significance":"If correct, this measurement provides the first spectroscopic information on 52K, a nucleus situated between the N=32 and N=34 shell closures and the Z=20 closure, and offers a direct benchmark for the proton d3/2-s1/2 single-particle splitting in the potassium isotopic chain. The strengths of the manuscript are its careful treatment of systematic uncertainties (DALI2+ response benchmarked at the 5% level, explicit error budgets for the cross sections), the self-consistent cascade-based level scheme, and the full tabulation in Table II of experimental cross sections, DWIA single-particle cross sections, and shell-model C2S values, which allows the reader to reconstruct the assignment logic independently. The authors also deserve credit for labeling the 0- assignment as tentative in the body and for disclosing that VS-IMSRG(2) at its converged truncation level prefers a 0- ground state, with the supporting VS-IMSRG(3) result explicitly unconverged.","major_comments":[{"comment":"The momentum distributions determine only the orbital angular momentum of the knocked-out proton; within the p1/2(x)d3/2 doublet (2-/1-) and the p1/2(x)s1/2 doublet (0-/1-_2), the total-J ordering is taken from the SDPF-Umod and the explicitly unconverged VS-IMSRG(3) calculations. The body is transparent about this, but the claim in Sec. III.E that the exclusive cross sections 'further confirm' the spin-parity assignments is never backed by an explicit test of the swapped J orderings, even though Table II contains all numbers needed for such a test: sigma(g.s.)/sigma(293) = 3.21/1.45 = 2.2(4) versus the C2S ratio 2.352/1.303 = 1.8 (the (2J+1) sum-rule limit gives 5/3), while the swapped assignment would predict a ratio of about 0.55, a discrepancy of roughly 4 sigma; likewise sigma(536)/sigma(1076) = 0.38/0.81 = 0.47(16) versus 0.402/1.244 = 0.32, while the swapped assignment would predict about 3.1, excluded at many sigma. I ask that this quantitative comparison be added to Sec. III.E, with the caveat that it is conditional on the SDPF-Umod C2S values, and that the sentence 'It is shown that 52K has a 2- ground state' be made consistent with the demonstrated level of certainty; this matters because the theory guidance alone is ambiguous, with VS-IMSRG(2) predicting a 0- ground state.","section":"Sec. III.D-III.E, Table II"},{"comment":"The Conclusions state 'It is shown that 52K has a 2- ground state and three excited states at 293(3) keV (1-), 536(6) keV (0-), and 1076(14) keV', listing the 536-keV state without the tentative qualifier used in Sec. III.D ('it is tentatively assigned Jpi=0-') and in Table II ('(0-)'). Since no momentum distribution exists for this state (Sec. III.B), the Conclusions overstate the certainty of a member of the central claim. The Conclusions should also note that the only fully converged ab initio result reported, VS-IMSRG(2), places the 0- below the 2-, so that the ground-state ordering rests on the shell model and the unconverged VS-IMSRG(3) calculation rather than on a settled ab initio prediction. The qualification and the caveat should be restored in the Conclusions.","section":"Sec. IV Conclusions; Sec. III.D"},{"comment":"The agreement between experimental and theoretical relative exclusive cross sections is described as 'excellent', but the 1076-keV 1-_2 state shows a measured value of 14(3)% versus 22% (method a) or 25% (method b), a deviation at the 2-3 sigma level, and the comparison for the four states is only marginally acceptable as a whole (roughly chi2/ndf of order 8/3 if the ratios are treated as independent). In addition, the 160-fm uncertainty on the fitted radial parameter for the s1/2 orbital (r0 = 1.416(160) fm) is not propagated into the DWIA single-particle cross sections sigma_sp used to build the theoretical cross sections, and the quoted inclusive quenching factor is 0.66 with the optimum r0 but 1.01 with the Bohr-Mottelson value of 1.27 fm, a factor of 1.5 variation. The spin-parity conclusions rely on the relative cross sections, which are robust to this normalization ambiguity, but the text should either quote sigma_sp with its uncertainty or restrict the 'excellent agreement' claim to the relative pattern and state the normalization ambiguity explicitly.","section":"Sec. III.E, Table II"}],"minor_comments":[{"comment":"The notation '1-_2' (a subscript 2 on the 1-) for the second 1- state is rendered ambiguously; in the Conclusions it appears as '1- 2', which can be misread as the half-integer '1/2-', an impossible spin for the odd-odd nucleus 52K. Please use an unambiguous notation (for example '1-_2' or 'second 1-') everywhere and verify the final PDF rendering.","section":"Sec. IV; Table II"},{"comment":"The sentence 'The SDPF-Umod interaction reproduces the E(3/2+ - 1/2+) exactly for 51K' uses the wrong parity superscripts; the states in question are 3/2- and 1/2-.","section":"Sec. III.D"},{"comment":"The sentence 'The ratio of the 243-keV and 540-keV transitions in coincidence with the 293-keV transition implies that the 243-keV transition feeds directly the 293-keV transition' is easy to misread; the intended point is that the 293-keV level is fed both by the 243-keV transition from the 536-keV level and directly by the knockout reaction, which is why the 243-keV coincidence yield exceeds the 540-keV one.","section":"Sec. III.A"},{"comment":"The (p,pn) exclusive yields are listed for the 2-, 1-, and 0- states but not for the 1076-keV state; since the pattern of (p,pn) population is quoted as supporting the level scheme, please state explicitly that the 1076-keV yield is consistent with zero and give an upper limit.","section":"Sec. III.E, Table II"},{"comment":"In the experimental level scheme in panel (a), please clarify how the color coding applies to the 536-keV level, whose orbital assignment is inferred from the models and the cascade rather than measured from a momentum distribution.","section":"Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"To the editor: I recommend major revision. The experiment is competently executed and the data quality is adequate for the claims; the requested changes -- the swapped-J cross-section test, the restoration of the tentative qualifier in the Conclusions, and the notation fix -- can all be made using numbers already present in Table II and require no new data. The main risk of this paper is overstatement of model-dependent spin assignments rather than a technical error in the measurement. On reading the manuscript, the stress-test concern partially lands: the momentum distributions alone cannot fix the J values within the doublets, and the 536-keV state lacks a momentum distribution; however, the cross-section data in Table II do discriminate the swapped orderings at the level of several sigma if the shell-model C2S values are trusted. The authors should write that test out explicitly. If they comply with the requested quantification and qualification, I would expect the paper to become acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First spectroscopy of 52K, and it is a solid, careful measurement. The level scheme at 293, 536, and 1076 keV with the cascade is built from clean coincidence data, and the DWIA momentum distributions convincingly identify the knocked-out proton as d3/2 for the ground and 293-keV states and s1/2 for the 1076-keV state. That is the real new result, and it is supported by explicit statistical and systematic uncertainties throughout.\n\nThe theory comparison is appropriate: SDPF-Umod and VS-IMSRG(2), with an explicit warning that the IMSRG(3) calculation is unconverged. Relative exclusive cross sections agree well with the shell-model prediction, which is genuine supporting evidence.\n\nWhere the paper is soft is exactly where the reader and the stress-test point: the momentum distributions fix the orbital, not the total J. The 2−/1− order for the ground and 293-keV states comes from the models, and the models disagree at the IMSRG(2) level—0− is predicted below 2− there. The 536-keV state has no momentum distribution at all, so its 0− assignment rests on analogy with theory. The cross sections do break some of the degeneracy, but only through the SDPF-Umod C2S values and an r0 fitted to the same data. The body calls the 536-keV assignment tentative; the Conclusions do not, and that mismatch should be fixed.\n\nOne concrete error: the Conclusions and Section III.D call the 1076-keV state 1/2−. That is impossible for an odd-odd nucleus and contradicts Table II, which lists 1−. It is almost certainly a typesetting slip, but it must be corrected.\n\nOverall: the central claim—the energies, the cascades, the orbital assignments—holds up. The spin-parity labels are model-dependent but not arbitrary; the relative cross sections give them real support. Worth a serious referee. I would recommend engaging, with a request to soften the 536-keV claim, fix the typo, and add a short exchange with a swapped-J scenario to quantify how strongly the data actually constrain the ordering.","headline":"First spectroscopy of 52K with a clean level scheme and honest theory comparison, but the Jπ assignments partly lean on model ordering and the 536-keV 0− is tentative despite the conclusions.","tokens_in":16078,"tokens_out":2465,"would_cite":true,"duration_ms":24145,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"First spectroscopy of potassium-52 finds a 2− ground state and single-particle excitations at 293, 536, and 1076 keV.","keywords":["potassium-52","knockout reactions","gamma-ray spectroscopy","momentum distributions","spin-parity assignment","shell model","VS-IMSRG","N=32 shell closure"],"falsifier":"Measure the 536-keV state's momentum distribution with enough statistics to distinguish $s_{1/2}$ from $d_{3/2}$ removal, or directly determine the ground-state spin through $\\gamma$-ray angular correlations or a transfer reaction. Finding $J\\neq 2$ for the ground state, or $J^\\pi\\neq 0^-$ for the 536-keV state, would falsify the proposed level scheme and the normal-ordering conclusion.","tokens_in":14563,"feed_emoji":"⚛️","tokens_out":23933,"duration_ms":206054,"temperature":0.7,"pith_summary":"The paper reports the first spectroscopy of $^{52}$K, an odd-odd nucleus with one proton below the $Z=20$ shell closure and one neutron outside the $N=32$, $34$ closures. Using one-proton and one-neutron knockout at about 230 MeV per nucleon, it builds the level scheme from $\\gamma$-ray coincidences and assigns spins and parities by comparing exclusive momentum distributions with distorted-wave impulse approximation (DWIA) calculations. It concludes that $^{52}$K has a $2^-$ ground state and excited states at $293(3)$ keV ($1^-$), $536(6)$ keV ($0^-$), and $1076(14)$ keV (listed as $1^-$ in the body and Table II, although the conclusion says $1/2^-$, an apparent typo). These four states are interpreted as one-particle–one-hole configurations: a $p_{1/2}$ neutron coupled to either a $d_{3/2}$ or an $s_{1/2}$ proton hole. If this is right, the proton $s_{1/2}$ and $d_{3/2}$ orbitals keep their normal ordering near $N=32,34$, with an energy gap close to that of the odd-mass neighbors $^{51,53}$K.","feed_headline":"Potassium-52 gets its first spectrum: ground state is 2−","feed_subtitle":"Knockout reactions reveal four single-particle states and a normal proton orbital ordering near N=32 and N=34.","key_machinery":"The load-bearing tool is the exclusive momentum distribution measured for each final state after $(p,2p)$ knockout, compared with DWIA calculations: the width of the parallel-momentum distribution identifies whether the removed proton came from a $d_{3/2}$ orbital or an $s_{1/2}$ orbital. That orbital tag is combined with the angular-momentum coupling identity $p_{1/2}\\otimes d_{3/2}\\to 2^-,1^-$ and $p_{1/2}\\otimes s_{1/2}\\to 0^-,1^-$ to propose the four states. Since the momentum data cannot fix the order of the two members of each doublet, the ordering is taken from the theoretical spectra (SDPF-Umod and VS-IMSRG), and the exclusive cross-section ratios serve as a consistency check on the single-particle interpretation.","core_discovery":"The central discovery is the first complete low-lying level scheme of $^{52}$K: a $2^-$ ground state, a $1^-$ state at $293(3)$ keV, a $0^-$ state at $536(6)$ keV, and a fourth state at $1076(14)$ keV assigned $1^-$ in the body (the conclusion writes $1/2^-$, which the stated coupling scheme cannot produce). The assignments come from matching the parallel- and perpendicular-momentum distributions of the knockout residue to DWIA calculations, which identify the removed proton as $d_{3/2}$ for the ground and 293-keV states and $s_{1/2}$ for the 536- and 1076-keV states. Because the momentum width tags the orbital but not the total angular momentum $J$, the ordering of the $2^-$/$1^-$ doublet and the tentative $0^-$ assignment are guided by the level ordering from the SDPF-Umod shell-model Hamiltonian and from VS-IMSRG ab initio calculations. The single-particle nature of all four states is supported by exclusive cross sections whose relative values match theory, and whose overall quenching factor of 0.66 agrees with $(e,e'p)$ knockout results.","pith_inferences":["If the normal $s_{1/2}/d_{3/2}$ ordering holds, measuring heavier potassium isotopes such as $^{55}$K could map where monopole drift reverses the ordering again, using the K chain as a one-proton-hole laboratory.","The 536-keV $0^-$ assignment rests entirely on theory because its momentum distribution could not be analyzed; a higher-statistics measurement of that state's momentum distribution or a transfer reaction would be the most direct test.","The conclusion's $1/2^-$ for the 1076-keV state is internally inconsistent with the body's $1^-$ assignment and with the stated $p_{1/2}\\otimes s_{1/2}$ coupling, which only permits $0^-$ and $1^-$; it should be read as a typographical slip.","The close agreement between the empirical SDPF-Umod interaction and the ab initio VS-IMSRG spectrum suggests that ab initio methods are now precise enough at $A\\sim50$ to guide spin-parity assignments when knockout momentum distributions are ambiguous."],"forward_implications":["The $s_{1/2}$ and $d_{3/2}$ proton orbitals keep their normal ordering in $^{52}$K, with a gap similar to $^{51}$K and $^{53}$K, so the inversion observed in $^{47,49}$K does not extend to $N=33$.","The four low-lying states are essentially single-particle 1p-1h excitations, making $^{52}$K a clean benchmark for shell-model and ab initio methods near the $N=32$ and $N=34$ closures.","VS-IMSRG(3) corrections move the predicted ground state from $0^-$ to $2^-$, matching experiment, so fully converged three-body normal-ordered calculations should settle the remaining $0^-$/$2^-$ ordering sensitivity.","The measured quenching factor $\\sigma_{\\rm exp}/\\sigma_{\\rm th}=0.66$ is consistent with $(e,e'p)$ knockout on stable nuclei, supporting the single-particle cross-section interpretation.","The $(p,pn)$ channel feeds mainly the ground and 293-keV states, confirming that those states share the proton configuration of the $^{53}$K projectile."],"supporting_citations":[{"why":"Supplies the SDPF-Umod Hamiltonian and the measured $^{51,53}$K spectra that set the $d_{3/2}$–$s_{1/2}$ gap used to guide the spin assignments.","marker":"[20]"},{"why":"Demonstrates the method for extracting exclusive momentum distributions and tuning the Woods-Saxon radial parameter in $(p,2p)$ knockout, applied here to $^{52}$K.","marker":"[8]"},{"why":"Provides the distorted-wave impulse approximation formalism used to compute the single-particle momentum distributions and cross sections.","marker":"[34–38]"},{"why":"The code used for the DWIA calculations of momentum distributions and single-particle cross sections.","marker":"[39]"},{"why":"Reviews the VS-IMSRG method whose ab initio spectrum, together with SDPF-Umod, guides the $J^\\pi$ ordering of the states.","marker":"[52]"},{"why":"Defines the 1.8/2.0 (EM) chiral two- and three-nucleon Hamiltonian used in the VS-IMSRG calculations.","marker":"[55]"},{"why":"Provides the $(e,e'p)$ quenching factors that the measured $\\sigma_{\\rm exp}/\\sigma_{\\rm th}=0.66$ is compared with.","marker":"[62]"}],"fun_headline_variants":["52K's first spectrum: 2− ground state, four states mapped","Knockout reactions reveal 52K: ground state is 2−","Proton knockout yields first spectroscopy of 52K","52K spectroscopy: 2− ground state and single-particle excitations","First look at 52K: 2− ground state, theory matches"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The assignments assume the theoretical ordering of the two states in each proton-hole–neutron doublet is correct, because the measured momentum distributions identify only which proton orbital was removed, not the total angular momentum of the final state; the 536-keV state's $0^-$ label has no momentum constraint at all.","fun_headline_variants_meta":{"raw":{"variants":["52K's first spectrum: 2− ground state, four states mapped","Knockout reactions reveal 52K: ground state is 2−","Proton knockout yields first spectroscopy of 52K","52K spectroscopy: 2− ground state and single-particle excitations","First look at 52K: 2− ground state, theory matches"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000259,"raw_usage":{"total_tokens":1591,"prompt_tokens":956,"completion_tokens":635,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":540}},"tokens_in":572,"tokens_out":635,"duration_ms":7169,"temperature":1.0,"reasoning_tokens":540,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:02:56.450505+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the 536-keV state's momentum distribution with enough statistics to distinguish $s_{1/2}$ from $d_{3/2}$ removal, or directly determine the ground-state spin through $\\gamma$-ray angular correlations or a transfer reaction. Finding $J\\neq 2$ for the ground state, or $J^\\pi\\neq 0^-$ for the 536-keV state, would falsify the proposed level scheme and the normal-ordering conclusion.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the SDPF-Umod Hamiltonian and the measured $^{51,53}$K spectra that set the $d_{3/2}$–$s_{1/2}$ gap used to guide the spin assignments."},{"cited_title":"Enciu, H","cited_arxiv_id":null,"evidence_quote":"Demonstrates the method for extracting exclusive momentum distributions and tuning the Woods-Saxon radial parameter in $(p,2p)$ knockout, applied here to $^{52}$K."},{"cited_title":"Ogata, K","cited_arxiv_id":null,"evidence_quote":"The code used for the DWIA calculations of momentum distributions and single-particle cross sections."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reviews the VS-IMSRG method whose ab initio spectrum, together with SDPF-Umod, guides the $J^\\pi$ ordering of the states."},{"cited_title":"Aumann, C","cited_arxiv_id":null,"evidence_quote":"Provides the $(e,e'p)$ quenching factors that the measured $\\sigma_{\\rm exp}/\\sigma_{\\rm th}=0.66$ is compared with."}],"review_version":1}