Pith. sign in

REVIEW 5 major objections 4 minor 48 references

The paper claims that the leading finite-volume energy shift for a cluster–cluster bound state in a periodic box is multiplied by a purely geometric constant G_{A,C}—for fixed-spin–isospin nucleons, a product of binomials that equals 256 fo

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 23:12 UTC pith:IZYA377F

load-bearing objection Plausible and important if right, but the geometric-factor counting rests on an unproven equivalence and the 16O validation is too unstable to carry the load. the 5 major comments →

arxiv 2511.06726 v2 pith:IZYA377F submitted 2025-11-10 nucl-th

Jacobi Coordinates on Hyper-tori and Geometric Factors in the Volume Dependencies

Hang Yu This is my paper
classification nucl-th
keywords finite-volume energy shiftgeometric factorJacobi coordinatesperiodic boundary conditionsasymptotic normalization constantsnuclear clustershyper-torusvolume dependence
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard few-body formulas for how bound-state energies change with the size of the simulation volume are habitually applied to clusters by treating each cluster as a point-like particle. This paper shows that generalization misses a constant, state-independent factor: evaluated in the original A-nucleon configuration space, the finite-volume shift picks up a 'geometric factor' G_{A,C} that multiplies the two-cluster formula. For nuclei with fixed spin–isospin occupancies this factor is the product of four binomial coefficients counting the ways to choose which nucleons form the cluster; for 16O → 12C + α it is 256. The factor is a property of the many-body configuration space — the number of leading-order faces of the hypercube — not a multiplicity of physical channels, and it is not a directly measurable quantity. The paper argues it must be included when extracting asymptotic normalization constants (which set peripheral astrophysical reaction rates) from lattice and truncated-basis calculations, and it validates the factor in calculations on 4He, 20Ne and 16O.

Core claim

Central result, Eq. (28): in a periodic box of side L, a cluster–cluster bound state shifts by ΔE_L = G_{A,C} ΔE_{TB,L}, with ΔE_{TB,L} the point-like two-cluster shift (non-perturbative Coulomb included) and G_{A,C} a constant 'geometric factor'. For fixed spin–isospin nucleon degrees of freedom, G_{A,C} is a product of four binomials in the spin–isospin occupancies, e.g. 256 for 16O→12C+α. The factor is the count of leading-order faces of the many-body configuration hypercube surviving the surface-integral reduction, made computable by the paper's Jacobi-coordinates-on-a-hyper-torus construction. Numerical tests on 4He, 20Ne and 16O show extracted asymptotic normalization constants are wro

What carries the argument

The load-bearing object is the geometric factor G_{A,C} (Eq. 29): the number of leading-order boundary faces in the A-body overlap integral on a hyper-torus, equal for fixed spin–isospin nucleons to a product of four binomials. The derivation rides on two pieces: a surface-integral identity (v∇²u − u∇²v = ∇·(v∇u − u∇v)) that turns the volume overlap into boundary terms, and an iterative Jacobi-coordinate construction on the periodic lattice — shifting triangular regions of the fundamental cell by L — that aligns the box with cluster-internal and cluster-relative coordinates, preserves the integral, and removes the center-of-mass ambiguity. Counting shifts by multiples of L along the relative

Load-bearing premise

The central claim stands on the assumption that in the asymptotic region of the box boundary the A-nucleon wavefunction factorizes exactly into internal cluster wavefunctions times a two-cluster relative wavefunction, with all other breakup channels exponentially suppressed and well separated from the leading one (Eq. 23); if cluster internal structure is distorted near the boundary or subleading channels compete, the constant factor G_{A,C} cannot be factored out.

What would settle it

Directly compute the finite-volume shift for a simple two-cluster system (e.g., 16O → 12C+α) from the full many-body wavefunction in the periodic box and compare the ratio to G_{A,C}ΔE_{TB,L}; if the ratio deviates from the predicted 256 (or from the corresponding binomial product for another cluster partition) in the regime where the leading channel dominates, the geometric-factor derivation is wrong. Alternatively, use lattice data in the range L=12–16 fm, include G=256 in the two-channel fit, and check whether the extracted C_{16O,α} stays consistent with the independent pin-hole estimate ≈

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Whenever a few-body finite-volume formula is applied to a cluster channel, the extracted asymptotic normalization constant is off by the missing factor; for 16O the paper quotes C_{16O,α}=350(50) fm^{-1/2} with the factor, versus values differing by a factor of roughly 250 without it.
  • In single-particle/mean-field basis truncations (harmonic-oscillator-type), the analogous factor for an A−1–1 halo is the particle number A; including it recovers the expected 4He ANC from the numerical truncation data.
  • For 16O, the subleading α breakup channel (G=256) can dominate the leading proton channel (G=8) in the 6–12 fm region, so the volume dependence can change sign; fits that ignore this misidentify the leading channel.
  • For heavier systems the combinatorial factor grows explosively (e.g., about 2^54 ≈ e^{13} for 100Sn→α), so finite-volume corrections are much larger than naive few-body estimates suggest.
  • Scattering-region observables such as phase shifts are unaffected: the geometric factor cancels in the ratio that defines the quantization condition, so previous scattering-region formulations carry over.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper does not pursue it, but the same boundary-face counting should apply to any truncation in which a cluster emerges from a larger Hilbert space — harmonic-oscillator bases, no-core shell models, or single-particle-space many-body methods — so the geometric factor may be a general explanation for strong IR cutoff dependence in heavy nuclei.
  • An extension the paper leaves implicit: because G_{A,C} grows combinatorially while the exponential suppression depends on breakup momentum, multi-channel fits of finite-volume data should be weighted by G per channel; the 16O case, where the geometric factor flips the sign of the volume dependence, is the cleanest place to test this systematically.
  • A direct test of the Jacobi-lattice construction itself, independent of the volume formula, would be to compute the same cluster-relative observable on the original Cartesian lattice and on the Jacobi lattice; the paper's claim that the two integrals agree is asserted but not demonstrated numerically.
  • If G_{A,C} is as universal as claimed, the geometric factor should also appear in coupled-channel calculations that use quantization conditions near bound-state poles; the author notes scattering far from poles may need care, and checking that region is a natural next step.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper claims to derive a missing multiplicative 'geometric factor' G_{A,C} in the finite-volume energy shift for cluster-cluster bound states when the calculation is performed with nucleon degrees of freedom. The central result, Eq. (28), states that the energy shift is G_{A,C} times the two-body shift ΔE_{TB,L}, with G_{A,C} given by the product of binomials in Eq. (29) (e.g., G_{16O,α}=256). The derivation uses an iterative Jacobi-coordinate construction on a periodic lattice (Sec. III) to justify a surface-integral evaluation (Eqs. (26)-(27)). Numerical tests with IMSRG and NLEFT are presented for 4He, 20Ne, and 16O; the 16O case is argued to show the geometric factor amplifying a subleading α channel. The paper concludes that ignoring G leads to incorrect extracted ANCs.

Significance. If correct, the result would have immediate practical importance: existing finite-volume formulas applied to cluster channels in many-body calculations would be missing a potentially large constant factor, affecting any extraction of asymptotic normalization constants. The paper also offers a concrete, testable prediction (G factors for specific nuclei) and an explicit construction of Jacobi coordinates on hyper-tori, which could be a useful technical contribution. The numerical evidence for 20Ne and 16O, though preliminary and noisy, is suggestive. The central claim is falsifiable and the paper is transparent about the main assumptions, including the subleading-channel suppression in Eq. (23).

major comments (5)
  1. [Sec. IV, Eqs. (23) and (29)] The derivation of the constant G as a binomial multiplicity is in tension with the factorization assumption in Eq. (23). Eq. (23) assumes that in the asymptotic region the wavefunction factors into ground-state cluster internal wavefunctions times a relative wavefunction, with subleading channels having well-separated κ*. However, Eq. (29) counts all binomial choices of which C nucleons form the cluster. For a closed-shell nucleus such as 16O, most of the 256 choices involve nucleons from different shells (e.g., p-shell rather than s-shell), producing internally excited cluster configurations with larger breakup momentum κ*. These contributions are exponentially suppressed relative to the ground-state configuration. Unless the paper proves that all binomial choices are degenerate in the leading exponential, G cannot be a single multiplicative constant; the sum in Eq. (22) would require a
  2. [Sec. III, Fig. 2] The Jacobi-lattice construction is described pictorially and asserted to preserve the integral and boundary conditions ('It is then not difficult to check...'), but this property is load-bearing: Eq. (24) replaces the Cartesian integration domain with the Jacobi box. The description of the iterative shift, including the 'additional offset' in the periodic boundary condition for r_i, is not formalized. A rigorous definition of the transformation, its Jacobian, and a proof that the surface integral in Eq. (27) is invariant under this change of coordinates is needed before Eq. (28) can be accepted.
  3. [Sec. IV, Eqs. (27)-(28)] The step from the surface integral in Eq. (27) to the closed-form result in Eq. (28) is not shown. In the two-body case, the factor 3 in Eq. (14) arises from a sum over the three spatial directions (or six faces) of the cubic box. The paper claims G has the same origin as that factor, but it is not demonstrated how the G face multiplicities combine with the d=3 factor without double counting, nor how the relative-coordinate boundary conditions on the Jacobi lattice (discussed at the end of Sec. III) are incorporated. The detailed evaluation of the surface integral should be supplied, at least in an appendix.
  4. [Sec. VI, Figs. 6 and 7] The numerical validation for the pivotal 16O case is unstable: fitting in the range 10-16 fm gives C_{16O,α}=350(50) fm^{-1/2}, while fitting the last four points (12-16 fm) gives 900(200) fm^{-1/2}, a factor of 2.6 difference. The paper attributes this to Monte Carlo statistics, but such sensitivity means the claim that G=256 is 'essential' for 16O is not robustly supported by the present data. A systematic study of fit-range dependence and an estimate of systematic uncertainty are needed before the numerical evidence can be considered confirmatory.
  5. [Sec. II, Eq. (15) and Sec. IV, Eq. (22)] The ansatz (15) is written for distinguishable particles, and the paper asserts that fermionic/bosonic statistics have no impact. However, the counting in Eq. (29) is specifically for identical nucleons with fixed spin and isospin. In a Slater determinant, the antisymmetrization introduces signs and permutations that can alter the sum over shifts in Eq. (22) (e.g., cancellations or additional combinatorial factors). The one-sentence caution after Eq. (28) does not address this. The derivation should either include the antisymmetrization explicitly or provide a formal argument for why the factor is unchanged.
minor comments (4)
  1. [Eq. (16)] In the second line of Eq. (16), the potential V(x) should likely carry a subscript j for consistency with the first line; a typographical issue.
  2. [Sec. VI, 4He analysis] The text states that without the 'A factor' the IMSRG extraction would need A times smaller corrections, but the connection between the single-particle factor A from Sec. II and the spin-isospin-fixed G of Eq. (29) is not explained. For 4He-N, Eq. (29) would give G=1 for a fixed nucleon species. Please clarify which factor is being used in which numerical analysis.
  3. [Eq. (21)] The set I={-1,0,1} is used, but later the text says n=0 is omitted; the notation is a little confusing. Also, the transition from 'Z^{d×A}' to 'I^{d×A}' assumes only nearest-image shifts contribute; this should be justified (it is standard but worth stating).
  4. [Sec. I, final paragraph] The statement that the geometric factor 'is not a measurable physical quantity' is somewhat at odds with the later claim that ignoring it leads to wrong ANCs. Since ANCs are physical, it would be clearer to say that G is a calculational artifact specific to the chosen degrees of freedom, not an observable itself.

Circularity Check

0 steps flagged

No circular reduction: G_{A,C} is computed via periodic-image counting and tested against external ANC estimates; prior self-authored inputs are stated assumptions, not reconstructed outputs.

full rationale

The derivation is not circular. The geometric factor G_{A,C} is not a fitted parameter; it is computed from the periodized many-body ansatz by grouping periodic-image shifts into cluster labels and counting multiplicities (Sec. IV, Eqs. 21–29: “We count multiplicity of label C and call it G_{A,C}”). The two-body baseline Eq. (14) and the image-sum ansatz are adopted from prior derivations [11,19]; those are stated assumptions/prior results, not quantities reconstructed from the paper’s own target. The central validation is external: extracted ANCs with G included are compared with independent pin-hole estimates [44] (C_{16O,α}=350(50) vs 380(80) fm^{-1/2}), and “without this factor we would have … apparently wrong” — a falsifiable check, not a tautology. The factorization of the asymptotic wavefunction into cluster internal parts times relative motion in Eq. (23) is an explicit approximation, and the paper itself acknowledges subleading breakup channels κ* and fits a two-channel form in Eq. (30); whether the binomial count overcounts excited internal configurations is a correctness/validity concern, not a circular reduction of the claimed result to its input. The manuscript’s own caveats — e.g., “extreme sensitivity to the range of data selected” for 16O (Fig. 7) and the note that the factor is “an artifact when we choose the degrees of freedom” — are limitations, but they do not turn the derivation into a self-referential loop.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The derivation is largely self-contained beyond the prior two-body formula of [11] and König-Lee [19]; no new physical entities are introduced. The main load-bearing axioms are the image-sum ansatz and the asymptotic cluster factorization. The only fitted quantities appear in the numerical validation, not in the derivation.

free parameters (1)
  • Asymptotic normalization constants C_0 in numerical fits = C_{4He,N}=6.7(2), C_{20Ne,α}=4.2(2)e3, C_{16O,α}=350(50) fm^-1/2 (range-dependent; 900(200) for last four points)
    These are fit outputs used to validate G_{A,C}, not parameters of the derivation. The central claim does not depend on their precise values, but the numerical evidence does; the 16O value is sensitive to the chosen fit range (Fig. 7).
axioms (5)
  • domain assumption Finite-volume wavefunction is approximated by sum over periodic images: A_{L,0}(x)=Σ_n A(x+nL)
    Eq. (17); standard Lüscher-style ansatz, not derived.
  • domain assumption In the asymptotic region the wavefunction factorizes as A_{A-C}(x) A_C(r) ψ(R_0), with subleading breakup channels κ* well separated and exponentially suppressed.
    Eq. (23) and following sentence; load-bearing for reducing the overlap integral to the two-body surface term.
  • domain assumption The iterative Jacobi-lattice shift of hypercube regions preserves the integral, the volume, and the periodic boundary conditions.
    Sec. III, Fig. 2; asserted pictorially ('It is then not difficult to check'), not proven formally.
  • domain assumption Mean-field/independent-particle description of the reference state, V=Σ_i V(r_i), with distinguishable particles; statistics claimed not to affect the factor.
    Sec. II, Eqs. (3)-(6); used to derive the A factor in the Dirichlet case and motivate the cluster counting.
  • standard math Divergence theorem/surface-integral transformation u∇²v = v∇²u + ∇·(v∇u-u∇v)
    Eq. (25), details in Refs. [11,37]; standard vector calculus.

pith-pipeline@v1.3.0-alltime-deepseek · 13218 in / 15675 out tokens · 157934 ms · 2026-08-03T23:12:31.924599+00:00 · methodology

0 comments
read the original abstract

We derive the volume dependence of bound states from a cluster-cluster picture with nucleon degrees of freedom. A constant factor called the ``geometric factor'' appears in the generalization from point-like particles to clusters. We show that this factor becomes explicit and correct when the underlying overlap integral is evaluated directly in the original many-body space. We achieve this by constructing Jacobi coordinates on the lattice under the periodic boundary. The derivation requires only the interaction \textit{between} the clusters to be short-ranged, with the non-perturbative Coulomb force included. The factor emerges as a geometric property of the many-body configuration space rather than a multiplicity of physical channels. We validate our derivation using many-body calculations; in particular, we find this factor to be essential in extracting asymptotic normalization constants from lattice calculations of the 16O ground state.

Figures

Figures reproduced from arXiv: 2511.06726 by Hang Yu.

Figure 1
Figure 1. Figure 1: Iterative coordinate transformation. x r x ( ) 0 r( ) 0 r( ) 0 r [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Coordinate transformation at the i-th iteration. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Truncation dependence in IMSRG calculations. We [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Geometric factors in NLEFT calculations on [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Volume dependence in NLEFT calculations on [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Geometric factors in NLEFT calculations on [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

48 extracted references · 28 linked inside Pith

  1. [1]

    L¨ uscher, Volume dependence of the energy spectrum in massive quantum field theories - I

    M. L¨ uscher, Volume dependence of the energy spectrum in massive quantum field theories - I. Stable particle states, Comm. Math. Phys.104, 177 (1986)

    1986

  2. [2]

    surface-integral

    lim L→∞ AL,0(r) =A(r), 3.A L,0(r) =A L(r) +O(exp(−2κL)). We note that this arrangement can be extended to both bosonic and fermionic particles, and will not change our conclusion. The first condition guarantees the hard wall boundary condition, the second condition fixes the level we want to look at whenL→ ∞. The last condition ensures the desired level o...

  3. [3]

    where theκhere is determined by the dominant break-up channel

    lim L→∞ AL,0(x) =A(x), 3.A L,0(x) =A L(x) +O(exp(−κL)). where theκhere is determined by the dominant break-up channel. The Third condition can be shown in a similar manner as Eq. (8). We applyH L to our ansatz and find HLAL(x) =E ∞AL(x) +η(x).(18) and η(x)∝ ′X n∈Zd×A Z Bd×A dxV(x)A(x+nL),(19) with now the center of mass can be fixed at the origin, lo- cal...

  4. [4]

    L¨ uscher, Volume dependence of the energy spectrum in massive quantum field theories - II

    M. L¨ uscher, Volume dependence of the energy spectrum in massive quantum field theories - II. Scattering states, Comm. Math. Phys.105, 153 (1986)

    1986

  5. [5]

    Luscher, Two particle states on a torus and their re- lation to the scattering matrix, Nucl

    M. Luscher, Two particle states on a torus and their re- lation to the scattering matrix, Nucl. Phys. B354, 531 (1991)

    1991

  6. [6]

    L¨ uscher, Signatures of unstable particles in finite vol- ume, Nuclear Physics B364, 237 (1991)

    M. L¨ uscher, Signatures of unstable particles in finite vol- ume, Nuclear Physics B364, 237 (1991)

    1991

  7. [7]

    R. A. Briceno, Z. Davoudi, T. C. Luu, and M. J. Sav- age, Two-Baryon Systems with Twisted Boundary Con- ditions, Phys. Rev. D89, 074509 (2014), arXiv:1311.7686 [hep-lat]

    Pith/arXiv arXiv 2014

  8. [8]

    S. Bour, S. Koenig, D. Lee, H. W. Hammer, and U.- G. Meissner, Topological phases for bound states mov- ing in a finite volume, Phys. Rev. D84, 091503 (2011), arXiv:1107.1272 [nucl-th]

    Pith/arXiv arXiv 2011

  9. [9]

    Bubna, H.-W

    R. Bubna, H.-W. Hammer, F. M¨ uller, J.-Y. Pang, A. Rusetsky, and J.-J. Wu, L¨ uscher equation with long- range forces, JHEP05, 168, arXiv:2402.12985 [hep-lat]

    Pith/arXiv arXiv

  10. [10]

    S. R. Beane and M. J. Savage, Two-Particle Elastic Scat- tering in a Finite Volume Including QED, Phys. Rev. D 90, 074511 (2014), arXiv:1407.4846 [hep-lat]

    Pith/arXiv arXiv 2014

  11. [11]

    Guo and V

    P. Guo and V. Gasparian, Charged particles interaction in both a finite volume and a uniform magnetic field, Phys. Rev. D103, 094520 (2021)

    2021

  12. [12]

    Guo, Coulomb corrections to two-particle interactions in artificial traps, Phys

    P. Guo, Coulomb corrections to two-particle interactions in artificial traps, Phys. Rev. C103, 064611 (2021)

    2021

  13. [13]

    H. Yu, S. K¨ onig, and D. Lee, Charged-Particle Bound States in Periodic Boxes, Phys. Rev. Lett.131, 212502 (2023), arXiv:2212.14379 [nucl-th]

    Pith/arXiv arXiv 2023

  14. [14]

    Polejaeva and A

    K. Polejaeva and A. Rusetsky, Three particles in a finite volume, Eur. Phys. J. A48, 67 (2012), arXiv:1203.1241 [hep-lat]

    Pith/arXiv arXiv 2012

  15. [15]

    R. A. Briceno and Z. Davoudi, Three-particle scattering amplitudes from a finite volume formalism, Phys. Rev. D 10 87, 094507 (2013), arXiv:1212.3398 [hep-lat]

    Pith/arXiv arXiv 2013

  16. [16]

    Mai and M

    M. Mai and M. D¨ oring, Three-body Unitarity in the Finite Volume, Eur. Phys. J. A53, 240 (2017), arXiv:1709.08222 [hep-lat]

    Pith/arXiv arXiv 2017

  17. [17]

    D¨ oring, H.-W

    M. D¨ oring, H.-W. Hammer, M. Mai, J.-Y. Pang, A. Rusetsky, and J. Wu, Three-body spectrum in a fi- nite volume: the role of cubic symmetry, Phys. Rev. D 97, 114508 (2018), arXiv:1802.03362 [hep-lat]

    Pith/arXiv arXiv 2018

  18. [18]

    Hammer, J.-Y

    H.-W. Hammer, J.-Y. Pang, and A. Rusetsky, Three- particle quantization condition in a finite volume: 2. gen- eral formalism and the analysis of data, Journal of High Energy Physics2017, 115 (2017)

    2017

  19. [19]

    Meißner, G

    U.-G. Meißner, G. R ´ ıos, and A. Rusetsky, Spectrum of three-body bound states in a finite volume, Phys. Rev. Lett.114, 091602 (2015), [Erratum: Phys. Rev. Lett.117 069902 (2016)], arXiv:1412.4969 [hep-lat]

    Pith/arXiv arXiv 2015

  20. [20]

    R. A. Brice˜ no, M. T. Hansen, S. R. Sharpe, and A. P. Szczepaniak, Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite- volume formalism, Phys. Rev. D100, 054508 (2019), arXiv:1905.11188 [hep-lat]

    Pith/arXiv arXiv 2019

  21. [21]

    K¨ onig and D

    S. K¨ onig and D. Lee, Volume Dependence of N- Body Bound States, Phys. Lett. B779, 9 (2018), arXiv:1701.00279 [hep-lat]

    Pith/arXiv arXiv 2018

  22. [22]

    Busch, B.-G

    T. Busch, B.-G. Englert, K. Rza˙ zewski, and M. Wilkens, Two Cold Atoms in a Harmonic Trap, Found. Phys.28, 549 (1998)

    1998

  23. [23]

    T. Luu, M. J. Savage, A. Schwenk, and J. P. Vary, Nucleon-Nucleon Scattering in a Harmonic Potential, Phys. Rev. C82, 034003 (2010), arXiv:1006.0427 [nucl- th]

    Pith/arXiv arXiv 2010

  24. [24]

    Zhang and R

    X. Zhang and R. J. Furnstahl, Fast emulation of quantum three-body scattering, Phys. Rev. C105, 064004 (2022)

    2022

  25. [25]

    R. J. Furnstahl, S. N. More, and T. Papenbrock, System- atic expansion for infrared oscillator basis extrapolations, Phys. Rev. C89, 044301 (2014)

    2014

  26. [26]

    S. N. More, A. Ekstr¨ om, R. J. Furnstahl, G. Hagen, and T. Papenbrock, Universal properties of infrared oscillator basis extrapolations, Phys. Rev. C87, 044326 (2013)

    2013

  27. [27]

    R. J. Furnstahl, G. Hagen, T. Papenbrock, and K. A. Wendt, Infrared extrapolations for atomic nuclei, J. Phys. G: Nucl. Part. Phys.42, 034032 (2015)

    2015

  28. [28]

    Borsanyiet al.(BMW), Ab initio calculation of the neutron-proton mass difference, Science347, 1452 (2015), arXiv:1406.4088 [hep-lat]

    S. Borsanyiet al.(BMW), Ab initio calculation of the neutron-proton mass difference, Science347, 1452 (2015), arXiv:1406.4088 [hep-lat]

    Pith/arXiv arXiv 2015

  29. [29]

    Elhatisari, F

    S. Elhatisari, F. Hildenbrand, and U.-G. Meißner, Ab initio lattice study of neutron-alpha scattering with chiral forces at N3LO (2025), arXiv:2507.08495 [nucl-th]

    Pith/arXiv arXiv 2025

  30. [30]

    Miyagi, X

    T. Miyagi, X. Cao, R. Seutin, S. Bacca, R. F. Gar- cia Ruiz, K. Hebeler, J. D. Holt, and A. Schwenk, Im- pact of Two-Body Currents on Magnetic Dipole Mo- ments of Nuclei, Phys. Rev. Lett.132, 232503 (2024), arXiv:2311.14383 [nucl-th]

    Pith/arXiv arXiv 2024

  31. [31]

    R. J. deBoeret al., The 12C(α,γ)16O reaction and its implications for stellar helium burning, Rev. Mod. Phys. 89, 035007 (2017), arXiv:1709.03144 [nucl-ex]

    Pith/arXiv arXiv 2017

  32. [32]

    Freer, H

    M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, and U.-G. Meißner, Microscopic Clustering in Light Nuclei, Rev. Mod. Phys.90, 035004 (2018), arXiv:1705.06192 [nucl-th]

    Pith/arXiv arXiv 2018

  33. [33]

    Hergert, A Guided Tour ofab initioNuclear Many-Body Theory, Front

    H. Hergert, A Guided Tour ofab initioNuclear Many-Body Theory, Front. in Phys.8, 379 (2020), arXiv:2008.05061 [nucl-th]

    Pith/arXiv arXiv 2020

  34. [34]

    Hagen, T

    G. Hagen, T. Papenbrock, M. Hjorth-Jensen, and D. J. Dean, Coupled-cluster computations of atomic nuclei, Rept. Prog. Phys.77, 096302 (2014), arXiv:1312.7872 [nucl-th]

    Pith/arXiv arXiv 2014

  35. [35]

    B. R. Barrett, P. Navratil, and J. P. Vary, Ab initio no core shell model, Prog. Part. Nucl. Phys.69, 131 (2013)

    2013

  36. [36]

    K¨ onig, Efficient few-body calculations in finite volume, J

    S. K¨ onig, Efficient few-body calculations in finite volume, J. Phys. Conf. Ser.2453, 012025 (2023), arXiv:2211.00395 [nucl-th]

    Pith/arXiv arXiv 2023

  37. [37]

    Rothman, B

    M. Rothman, B. Johnson-Toth, G. Hagen, M. Heinz, and T. Papenbrock, NuLattice: Ab initio computations of atomic nuclei on lattices (2025), arXiv:2509.08771 [nucl- th]

    arXiv 2025

  38. [38]

    K¨ onig, Few-Body Bound States and Resonances in Fi- nite Volume, Few-Body Syst.61, 20 (2020)

    S. K¨ onig, Few-Body Bound States and Resonances in Fi- nite Volume, Few-Body Syst.61, 20 (2020)

    2020

  39. [39]

    H. Yu, N. Yapa, and S. K¨ onig, Complex scaling in finite volume, Phys. Rev. C109, 014316 (2024), arXiv:2309.03196 [nucl-th]

    Pith/arXiv arXiv 2024

  40. [40]

    Niu and B.-N

    Z.-W. Niu and B.-N. Lu, Sign-Problem-Free Nuclear Quantum Monte Carlo (2025), arXiv:2506.12874 [nucl- th]

    arXiv 2025

  41. [41]

    Ekstr¨ om, G

    A. Ekstr¨ om, G. Hagen, T. D. Morris, T. Papenbrock, and P. D. Schwartz, ∆ isobars and nuclear saturation, Phys. Rev. C97, 024332 (2018), arXiv:1707.09028 [nucl-th]

    Pith/arXiv arXiv 2018

  42. [42]

    Miyagi, NuHamil : A numerical code to generate nu- clear two- and three-body matrix elements from chiral effective field theory, Eur

    T. Miyagi, NuHamil : A numerical code to generate nu- clear two- and three-body matrix elements from chiral effective field theory, Eur. Phys. J. A59, 150 (2023), arXiv:2302.07962 [nucl-th]

    Pith/arXiv arXiv 2023

  43. [43]

    Lee, Lattice simulations for few- and many-body systems, Prog

    D. Lee, Lattice simulations for few- and many-body systems, Prog. Part. Nucl. Phys.63, 117 (2009), arXiv:0804.3501 [nucl-th]

    Pith/arXiv arXiv 2009

  44. [44]

    T. A. L¨ ahde and U.-G. Meißner,Nuclear Lattice Effective Field Theory: An introduction, Vol. 957 (Springer, 2019)

    2019

  45. [45]

    B.-N. Lu, N. Li, S. Elhatisari, D. Lee, E. Epelbaum, and U.-G. Meißner, Essential elements for nuclear bind- ing, Phys. Lett. B797, 134863 (2019), arXiv:1812.10928 [nucl-th]

    Pith/arXiv arXiv 2019

  46. [46]

    Harriset al., Quantifying alpha clustering in the ground states of 16-O and 20-Ne (2025), arXiv:2507.17059 [nucl-ex]

    E. Harriset al., Quantifying alpha clustering in the ground states of 16-O and 20-Ne (2025), arXiv:2507.17059 [nucl-ex]

    Pith/arXiv arXiv 2025

  47. [47]

    K¨ onig, D

    S. K¨ onig, D. Lee, and H.-W. Hammer, Volume Depen- dence of Bound States with Angular Momentum, Phys. Rev. Lett.107, 112001 (2011)

    2011

  48. [48]

    Elhatisariet al., Wavefunction matching for solving quantum many-body problems, Nature630, 59 (2024), arXiv:2210.17488 [nucl-th]

    S. Elhatisariet al., Wavefunction matching for solving quantum many-body problems, Nature630, 59 (2024), arXiv:2210.17488 [nucl-th]

    Pith/arXiv arXiv 2024