pith. sign in

arxiv: 2607.00681 · v1 · pith:DEFMQK6Tnew · submitted 2026-07-01 · ⚛️ nucl-th · hep-lat

Elastic deuteron-deuteron scattering within Nuclear Lattice Effective Field Theory

Helen Meyer , Serdar Elhatisari , Ulf-G. Mei{\ss}ner This is my paper

Pith reviewed 2026-07-02 04:42 UTC · model grok-4.3

classification ⚛️ nucl-th hep-lat
keywords nuclear lattice effective field theorydeuteron-deuteron scatteringphase shiftseffective range expansionchiral interactionsadiabatic projection methodbig bang nucleosynthesis
0
0 comments X

The pith

Nuclear lattice calculation produces a deuteron-deuteron scattering length of 12.96 fm with stronger repulsion than earlier estimates.

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

The paper computes low-energy elastic deuteron-deuteron scattering in the spin-quintet channel by combining chiral nuclear forces at next-to-next-to-next-to-leading order with the adiabatic projection method on the lattice. Two stabilization techniques are applied to handle small eigenvalues that appear in the norm matrix of the radial cluster basis at large projection times. The methods produce consistent Coulomb-subtracted phase shifts, which are fitted to a Coulomb-modified effective-range expansion. The extracted scattering length is substantially larger than values from prior calculations, corresponding to stronger effective repulsion between the deuterons. This supplies the first lattice benchmark and prepares the ground for coupled-channel studies of reactions relevant to big-bang nucleosynthesis.

Core claim

The calculation yields Coulomb-subtracted phase shifts in the 5S2 channel that are more negative than those obtained in previous work. A Coulomb-modified effective-range analysis gives the values 5a_dd = (12.96 ± 0.26) fm and 5r_dd = (3.62 ± 0.79) fm. The two stabilization procedures, Tikhonov regularization and projection onto well-resolved norm eigenmodes, produce results consistent within statistical and numerical uncertainties.

What carries the argument

The adiabatic projection method applied to a radial cluster basis, stabilized by either Tikhonov regularization or projection onto well-resolved norm eigenmodes to control small eigenvalues at large Euclidean projection time.

If this is right

  • The phase shifts are more negative than those reported in earlier calculations.
  • The scattering length is substantially larger, indicating stronger effective repulsion in the 5S2 channel.
  • The results constitute the first nuclear-lattice benchmark for deuteron-deuteron scattering.
  • The framework supplies a basis for future coupled-channel calculations of deuteron-induced reactions.

Where Pith is reading between the lines

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

  • The benchmark values could be inserted into reaction networks to update predicted abundances of light elements formed in the early universe.
  • Applying the same stabilized projection method to other partial waves or three-body systems would test whether the observed repulsion pattern persists.
  • A direct comparison of the lattice phase shifts with measured low-energy cross sections would provide an external check on both the chiral forces and the stabilization techniques.

Load-bearing premise

The stabilization procedures remove numerical artifacts from small norm-matrix eigenvalues without biasing the extracted physical phase shifts.

What would settle it

An independent lattice or continuum calculation, or a direct experimental extraction, of the 5S2 deuteron-deuteron scattering length that lies outside 12.7 to 13.22 fm would falsify the central numerical result.

Figures

Figures reproduced from arXiv: 2607.00681 by Helen Meyer, Serdar Elhatisari, Ulf-G. Mei{\ss}ner.

Figure 1
Figure 1. Figure 1: Threshold energy of two non-interacting deuterons on the lattice as [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Coulomb-subtracted phase shift of the projected single-channel [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fitting the modified effective range expansion (ERE) to eq. (28). project by providing computing time on the GCS Supercom￾puters JUWELS and JUPITER at Jülich Supercomputing Cen￾tre (JSC) and the support of the project EXOTIC by the JSC by dedicated HPC time provided on the JURECA DC GPU par￾tition. Furthermore, the authors gratefully acknowledge the computing time provided on the high-performance computer … view at source ↗
read the original abstract

We calculate low-energy deuteron-deuteron scattering in the spin-quintet $^{5}S_2$ channel using nuclear lattice effective field theory. The calculation combines chiral interactions at next-to-next-to-next-to-leading order, implemented through wavefunction matching, with the adiabatic projection method. Because the radial cluster basis develops small norm-matrix eigenvalues at large Euclidean projection time, we investigate two stabilization procedures: Tikhonov regularization and projection onto well-resolved norm eigenmodes. The two procedures yield consistent Coulomb-subtracted phase shifts within their statistical and numerical uncertainties. A Coulomb-modified effective-range analysis gives ${}^5a_{dd} = (12.96 \pm 0.26)\,\mathrm{fm}$ and ${}^5r_{dd} = (3.62 \pm 0.79)\,\mathrm{fm}$. The phase shifts are more negative, and the scattering length is substantially larger than in previous calculations, corresponding to a stronger effective repulsion in the $^{5}S_2$ channel. These results provide a first nuclear-lattice benchmark for deuteron-deuteron scattering and establish a basis for future coupled-channel calculations of the deuteron-induced reactions relevant to big-bang nucleosynthesis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript calculates low-energy elastic deuteron-deuteron scattering in the spin-quintet 5S2 channel within nuclear lattice effective field theory. It combines N3LO chiral interactions (implemented via wavefunction matching) with the adiabatic projection method on a radial cluster basis. Two stabilization procedures—Tikhonov regularization and projection onto well-resolved norm eigenmodes—are applied to handle small eigenvalues of the norm matrix at large Euclidean projection times. The procedures produce consistent Coulomb-subtracted phase shifts, from which a Coulomb-modified effective-range expansion yields 5a_dd = (12.96 ± 0.26) fm and 5r_dd = (3.62 ± 0.79) fm. These values indicate stronger effective repulsion than in prior calculations and are presented as the first nuclear-lattice benchmark for dd scattering.

Significance. If the central results hold, the work supplies the first lattice-EFT benchmark for deuteron-deuteron scattering parameters, directly relevant to big-bang nucleosynthesis reaction networks. Credit is due for the use of established N3LO interactions, the adiabatic projection framework, and the demonstration of internal consistency between two independent stabilization methods on the same observable.

major comments (1)
  1. [abstract / paragraph on radial cluster basis at large Euclidean projection time] Abstract / paragraph on radial cluster basis at large Euclidean projection time: the claim that the two stabilization procedures leave the physical phase shifts invariant rests on internal consistency within quoted uncertainties, but the manuscript provides no independent cross-check (e.g., application to a system with known exact results) that Tikhonov regularization or eigenmode projection preserves low-energy phase shifts without bias.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for recognizing the significance of providing the first nuclear-lattice benchmark for deuteron-deuteron scattering. We address the single major comment below.

read point-by-point responses

  1. Referee: Abstract / paragraph on radial cluster basis at large Euclidean projection time: the claim that the two stabilization procedures leave the physical phase shifts invariant rests on internal consistency within quoted uncertainties, but the manuscript provides no independent cross-check (e.g., application to a system with known exact results) that Tikhonov regularization or eigenmode projection preserves low-energy phase shifts without bias.

    Authors: We agree that an external benchmark on a system with known exact results would constitute the strongest possible validation. However, the two stabilization procedures (Tikhonov regularization and projection onto well-resolved norm eigenmodes) are mathematically distinct and were applied independently to the identical set of lattice data. Their agreement on the Coulomb-subtracted phase shifts within combined statistical and systematic uncertainties therefore functions as an internal cross-check against method-specific bias. Any residual bias would have to conspire to produce the same low-energy phase shifts in both approaches, which we regard as unlikely. We will revise the relevant paragraph and abstract to state this reasoning more explicitly and to note that a dedicated benchmark study on a simpler system remains a worthwhile direction for future work. revision: partial

Circularity Check

0 steps flagged

No circularity; scattering parameters are direct simulation outputs

full rationale

The derivation computes low-energy phase shifts and effective-range parameters via nuclear lattice EFT with N3LO interactions and the adiabatic projection method applied to the deuteron-deuteron system. The two stabilization procedures (Tikhonov regularization and eigenmode projection) are shown to produce internally consistent results within uncertainties, but the extracted 5a_dd and 5r_dd are outputs of the lattice calculation rather than quantities defined from or fitted to the target observables. No self-definitional steps, fitted-input predictions, or load-bearing self-citations that reduce the central claim to prior inputs by construction appear in the provided text. The work is a first benchmark application to a new channel and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of N3LO chiral EFT interactions (taken from prior literature) and on the correctness of the adiabatic projection and stabilization procedures for extracting phase shifts; no new free parameters are introduced in this work.

axioms (2)
  • domain assumption Chiral effective field theory at N3LO provides an accurate description of low-energy nuclear forces in the relevant channels
    The interactions are used as input without re-derivation in this paper.
  • domain assumption The adiabatic projection method combined with wavefunction matching can be applied to extract Coulomb-subtracted phase shifts from lattice wave functions
    This is the core extraction technique invoked in the abstract.

pith-pipeline@v0.9.1-grok · 5755 in / 1596 out tokens · 41356 ms · 2026-07-02T04:42:17.004546+00:00 · methodology

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

42 extracted references · 35 canonical work pages · 13 internal anchors

  1. [1]

    R. V . Wagoner, W. A. Fowler, F. Hoyle, On the Synthesis of elements at very high temperatures, Astrophys. J. 148 (1967) 3–49. doi:10.1086/149126

    work page doi:10.1086/149126 1967

  2. [2]

    R. H. Cyburt, B. D. Fields, K. A. Olive, T.- H. Yeh, Big Bang Nucleosynthesis: 2015, Rev. Mod. Phys. 88 (2016) 015004. arXiv:1505.01076, doi:10.1103/RevModPhys.88.015004

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.88.015004 2015

  3. [3]

    Pitrou, A

    C. Pitrou, A. Coc, J.-P. Uzan, E. Vangioni, Resolving con- clusions about the early Universe requires accurate nu- clear measurements, Nature Rev. Phys. 3 (4) (2021) 231–

    2021

  4. [4]

    arXiv:2104.11148, doi:10.1038/s42254-021-00294- 6

    work page doi:10.1038/s42254-021-00294-

  5. [5]

    Burns, T

    A.-K. Burns, T. M. P. Tait, M. Valli, PRyMordial: the first three minutes, within and beyond the standard model, Eur. Phys. J. C 84 (1) (2024) 86. arXiv:2307.07061, doi:10.1140/epjc/s10052-024-12442-0

    work page doi:10.1140/epjc/s10052-024-12442-0 2024

  6. [6]

    Y . Xu, S. Goriely, A. Jorissen, G. Chen, M. Arnould, Databases and tools for nuclear astrophysics applica- tions BRUSsels Nuclear LIBrary (BRUSLIB), Nuclear 6 Astrophysics Compilation of REactions II (NACRE II) and Nuclear NETwork GENerator (NETGEN), As- tron. Astrophys. 549 (2013) A106. arXiv:1212.0628, doi:10.1051/0004-6361/201220537

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201220537 2013

  7. [7]

    Pitrou, A

    C. Pitrou, A. Coc, J.-P. Uzan, E. Vangioni, Precision big bang nucleosynthesis with improved Helium-4 predic- tions, Phys. Rept. 754 (2018) 1–66. arXiv:1801.08023, doi:10.1016/j.physrep.2018.04.005

    work page doi:10.1016/j.physrep.2018.04.005 2018

  8. [8]

    T. A. Lähde, U.-G. Meißner, Nuclear Lattice Effective Field Theory: An introduction, V ol. 957, Springer, 2019. doi:10.1007/978-3-030-14189-9

    work page doi:10.1007/978-3-030-14189-9 2019

  9. [9]

    Meier, W

    W. Meier, W. Glöckle, Elastic scattering 2 H(d, d) 2 H below 360 keV, Nucl. Phys. A 255 (1975) 21–34. doi:10.1016/0375-9474(75)90144-X

    work page doi:10.1016/0375-9474(75)90144-x 1975

  10. [10]

    Wildermuth, W

    K. Wildermuth, W. McClure, Cluster Representa- tions of Nuclei, Springer Berlin, Heidelberg, 1966. doi:10.1007/BFb0045472

    work page doi:10.1007/bfb0045472 1966

  11. [11]

    Wildermuth, Y

    K. Wildermuth, Y . C. Tang, A Unified Theory of the Nucleus, Vieweg+Teubner Verlag, Wiesbaden, 1977. doi:10.1007/978-3-322-85255-7

    work page doi:10.1007/978-3-322-85255-7 1977

  12. [12]

    R. A. Malfliet, J. A. Tjon, Solution of the Faddeev equations for the triton problem using local two par- ticle interactions, Nucl. Phys. A 127 (1969) 161–168. doi:10.1016/0375-9474(69)90775-1

    work page doi:10.1016/0375-9474(69)90775-1 1969

  13. [13]

    I. N. Filikhin, S. L. Yakovlev, Microscopic calculation of low-energy deuteron-deuteron scattering on the basis of the cluster-reduction method, Phys. Atom. Nucl. 63 (2000). doi:10.1134/1.855624

    work page doi:10.1134/1.855624 2000

  14. [14]

    S. L. Yakovlev, I. N. Filikhin, Calculations of scatter- ing lengths in four nucleon system on the basis of clus- ter reduction method for Yakubovsky equations (1 1997). arXiv:nucl-th/9701020

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  15. [15]

    H. M. Hofmann, G. M. Hale, Microscopic calcula- tion of the He-4 system, Nucl. Phys. A 613 (1997) 69–106. arXiv:nucl-th/9608046, doi:10.1016/S0375- 9474(96)00418-6

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0375- 1997

  16. [16]

    Kellermann, H

    H. Kellermann, H. M. Hofmann, C. Elster, Gaussian Pa- rameterization of a Meson TheoreticalNNPotential for Microscopic Nuclear Structure Calculations, Acta Phys. Austriaca 7 (1989) 31–53

    1989

  17. [17]

    H. M. Hofmann, G. M. Hale, He-4 can experiments serve as a database for determining the three-nucleon force?, Phys. Rev. C 77 (2008) 044002. arXiv:nucl-th/0512065, doi:10.1103/PhysRevC.77.044002

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.77.044002 2008

  18. [18]

    R. B. Wiringa, V . G. J. Stoks, R. Schiavilla, An Accu- rate nucleon-nucleon potential with charge independence breaking, Phys. Rev. C 51 (1995) 38–51. arXiv:nucl- th/9408016, doi:10.1103/PhysRevC.51.38

    work page doi:10.1103/physrevc.51.38 1995

  19. [19]

    B. S. Pudliner, V . R. Pandharipande, J. Carlson, S. C. Pieper, R. B. Wiringa, Quantum Monte Carlo calculations of nuclei with A<=7, Phys. Rev. C 56 (1997) 1720–1750. arXiv:nucl-th/9705009, doi:10.1103/PhysRevC.56.1720

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.56.1720 1997

  20. [20]

    J. F. Carew, Deuteron-deuteron elastic and three- and four- body breakup scattering using the Faddeev-Yakubovskii equations, Phys. Rev. C 103 (1) (2021) 014002. doi:10.1103/PhysRevC.103.014002

    work page doi:10.1103/physrevc.103.014002 2021

  21. [21]

    J. F. Carew, Variational bounds in n-particle scatter- ing using the faddeev–yakubovskii equations: Deuteron- deuteron s=2 scattering, Few-Body Systems 55 (2014) 171–190. doi:10.1007/s00601-014-0844-0

    work page doi:10.1007/s00601-014-0844-0 2014

  22. [22]

    Modern Theory of Nuclear Forces

    E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Modern Theory of Nuclear Forces, Rev. Mod. Phys. 81 (2009) 1773–1825. arXiv:0811.1338, doi:10.1103/RevModPhys.81.1773

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.81.1773 2009

  23. [23]

    Elhatisari, et al., Wavefunction matching for solv- ing quantum many-body problems, Nature 630 (8015) (2024) 59–63

    S. Elhatisari, et al., Wavefunction matching for solv- ing quantum many-body problems, Nature 630 (8015) (2024) 59–63. arXiv:2210.17488, doi:10.1038/s41586- 024-07422-z

    work page doi:10.1038/s41586- 2024

  24. [24]

    Hildenbrand, S

    F. Hildenbrand, S. Elhatisari, U.-G. Meißner, H. Meyer, Z. Ren, A. Herten, M. Bode, Lattice Calculation of the Sn Isotopes near the Proton Dripline, Phys. Rev. Lett. 136 (6) (2026) 062501. arXiv:2509.08579, doi:10.1103/n7nt- s64t

    work page doi:10.1103/n7nt- 2026

  25. [25]

    Z. Ren, S. Elhatisari, U.-G. Meißner, Ab Initio Study of the Radii of Oxygen Isotopes, Phys. Rev. Lett. 135 (15) (2025) 152502. arXiv:2506.02597, doi:10.1103/y6s2- 43ym

    work page doi:10.1103/y6s2- 2025

  26. [26]

    Ab initio alpha-alpha scattering

    S. Elhatisari, D. Lee, G. Rupak, E. Epelbaum, H. Krebs, T. A. Lähde, T. Luu, U.-G. Meißner, Ab initio alpha-alpha scattering, Nature 528 (2015) 111. arXiv:1506.03513, doi:10.1038/nature16067

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/nature16067 2015

  27. [27]

    N. Li, S. Elhatisari, E. Epelbaum, D. Lee, B.-N. Lu, U.-G. Meißner, Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to- leading order, Phys. Rev. C 98 (4) (2018) 044002. arXiv:1806.07994, doi:10.1103/PhysRevC.98.044002

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.98.044002 2018

  28. [28]

    Elhatisari, T

    S. Elhatisari, T. A. Lähde, D. Lee, U.-G. Meißner, T. V onk, Alpha-alpha scattering in the Multi- verse, JHEP 02 (2022) 001. arXiv:2112.09409, doi:10.1007/JHEP02(2022)001

    work page doi:10.1007/jhep02(2022)001 2022

  29. [29]

    Elhatisari, F

    S. Elhatisari, F. Hildenbrand, U.-G. Meißner, Ab ini- tio lattice study of neutron–alpha scattering with chi- ral forces at N3LO, J. Phys. G 52 (12) (2025) 125102. arXiv:2507.08495, doi:10.1088/1361-6471/ae2145

    work page doi:10.1088/1361-6471/ae2145 2025

  30. [30]

    H. Tong, S. Elhatisari, U.-G. Meißner, Ab initio calcula- tion of hyper-neutron matter, Sci. Bull. 70 (2025) 825–

    2025

  31. [31]

    arXiv:2405.01887, doi:10.1016/j.scib.2025.01.008. 7

    work page doi:10.1016/j.scib.2025.01.008 2025

  32. [32]

    Arrington, N

    D. Lee, Lattice Effective Field Theory Simulations of Nuclei, Ann. Rev. Nucl. Part. Sci. 75 (1) (2025) 109–128. arXiv:2501.03303, doi:10.1146/annurev-nucl- 101918-023343

    work page doi:10.1146/annurev-nucl- 2025

  33. [33]

    Ab initio $\alpha$-$\alpha$ scattering with high-fidelity chiral interactions

    A. Sarkar, S. Elhatisari, T. A. Lähde, U.-G. Meißner, Ab initioα-αscattering with high-fidelity chiral interactions (6 2026). arXiv:2606.28987

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  34. [34]

    M. Pine, D. Lee, G. Rupak, Adiabatic projection method for scattering and reactions on the lattice, Eur. Phys. J. A 49 (2013) 151. arXiv:1309.2616, doi:10.1140/epja/i2013- 13151-3

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epja/i2013- 2013

  35. [35]

    Nucleon-deuteron scattering using the adiabatic projection method

    S. Elhatisari, D. Lee, U.-G. Meißner, G. Rupak, Nucleon- deuteron scattering using the adiabatic projection method, Eur. Phys. J. A 52 (6) (2016) 174. arXiv:1603.02333, doi:10.1140/epja/i2016-16174-2

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epja/i2016-16174-2 2016

  36. [36]

    Elhatisari, Adiabatic projection method with Euclidean time subspace projection, Eur

    S. Elhatisari, Adiabatic projection method with Euclidean time subspace projection, Eur. Phys. J. A 55 (8) (2019)

    2019

  37. [37]

    arXiv:1906.01046, doi:10.1140/epja/i2019-12844-9

    work page doi:10.1140/epja/i2019-12844-9 1906

  38. [38]

    A. N. Tikhonov, V . Y . Arsenin, Solutions of Ill-Posed Problems, V . H. Winston & Sons, Washington, DC, 1977, distributed by Halsted Press, New York

    1977

  39. [39]

    D. E. Hilt, D. W. Seegrist, U. S. F. Service, P. Northeast- ern Forest Experiment Station (Radnor, Ridge, a computer program for calculating ridge regression estimates, V ol. no.236, Upper Darby, Pa, Dept. of Agriculture, Forest Ser- vice, Northeastern Forest Experiment Station, 1977

    1977

  40. [40]

    P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Prob- lems, Society for Industrial and Applied Mathematics,

  41. [41]

    doi:10.1137/1.9780898719697

    work page doi:10.1137/1.9780898719697

  42. [42]

    B.-N. Lu, T. A. Lähde, D. Lee, U.-G. Meißner, Precise determination of lattice phase shifts and mixing angles, Phys. Lett. B 760 (2016) 309–313. arXiv:1506.05652, doi:10.1016/j.physletb.2016.06.081. 8 Appendix A. Euclidean time extrapolation of phase shift results For each individual momentum point we calculate the phase shift as described in section 2.3 ...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2016.06.081 2016