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REVIEW 3 major objections 4 minor 47 references

Changing Newton's law so a fast particle's gravity scales with its total energy gives the sun a capture orbit outside its surface—and a solar origin for cosmic rays up to 10^6 GeV/nucleon.

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 →

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A speculative revision of Newton's gravity, replacing masses by energies, is proposed to make the sun a cosmic-ray accelerator to 10^6 GeV, alongside storage-ring proposals for nuclear astrophysics.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection The solar-cosmic-ray headline collapses on a unit error; the E&M storage-ring proposal is a separate, credible piece that deserves its own focused review. the 3 major comments →

arxiv 2508.19296 v1 pith:R6YB3HUL submitted 2025-08-25 physics.acc-ph

Solar cosmic ray generation, Newtonian gravity, missing mass, dark energy, laboratory-based nuclear astrophysics, and all that

Richard Talman This is my paper
classification physics.acc-ph
keywords solar cosmic raysmodified Newtonian gravitymass-energy equivalenceParker solar winddouble slingshot accelerationE&M storage ringrear-end nuclear collisionscosmic-ray origin
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.

The reading

This paper claims that a one-line change to Newton's law of gravity—making the gravitational force on a fast light particle proportional to its total energy rather than its rest mass—converts solar production of high-energy cosmic rays from impossible to likely, without disturbing ordinary astronomy. The quantitative anchor is the limiting capture radius r_A-lim = G M_sun / 2 = 6.6 × 10^9 m, which is about ten times the solar radius, so circular capture orbits exist outside the sun. In the proposed 'double slingshot,' solar-wind nuclei are first accelerated around Jupiter and then captured by the sun, where the Parker electric field raises their energy while the energy-dependent gravity holds them on their orbits; the author argues this can account for a substantial fraction of cosmic rays up to at least 10^6 GeV/nucleon, matching measured spectra. The same revision, if true, would change the cosmological accounting of missing mass and dark energy. A parallel laboratory thread designs an 'E&M' storage ring with superimposed electric and magnetic bending, in which different isotopes co-circulate at controlled different velocities and collide 'rear-end,' so reactions such as 6Li + 7Li → 13C + γ can be studied in a moving frame.

Core claim

The paper replaces the force on a light relativistic particle, F = G M m/r², with F ≈ G M_sun γ m / r²—gravitational 'charge' is energy, not rest mass. The key result, Eq. (18), is the limiting radius r_A-lim = G M_sun / 2 = 6.6 × 10^9 m, where energy scales exactly with γ, so gravitational bending auto-ramps with the energy gained from the Parker electric field. This radius lies outside the 0.70 × 10^9 m solar radius, so protons and heavier nuclei can circle the sun and be accelerated over many turns. The two-stage 'double slingshot' (Jupiter pre-acceleration, then solar capture) lets a substantial fraction of cosmic rays up to 10^6 GeV/nucleon begin life in the solar system. The same chang

What carries the argument

The central object is the revised gravitational force law, Eq. (14): F ≈ G M_sun γ m / r², in which the Lorentz factor γ of a fast light particle enters the gravitational coupling between a heavy body and that particle. Its companion anchor is the limiting capture radius r_A-lim = G M_sun / 2 = 6.6 × 10^9 m (Eq. 18), where the particle's energy scales exactly with γ, so the gravitational bend strength automatically matches the particle's growing stiffness—an 'auto-ramping' property the paper likens to an ideal accelerator bend field. The Parker solar-wind model supplies the longitudinal electric field that adds energy each turn, and the dipole magnetic fields of the sun and Jupiter superpose

Load-bearing premise

The load-bearing premise is the revised gravitational law itself: a fast light particle is pulled toward a heavy body with force proportional to its total energy, γ times its rest mass—whereas under the standard law the capture radius for a relativistic proton is about 1.5 km, far inside the sun, so the proposed solar accelerator cannot work; the author explicitly doubts that the revision can be accommodated by general relativity.

What would settle it

Two concrete checks would settle it. (1) Search heliospheric particle data for the bound, helically orbiting proton population the mechanism requires—long-lived capture orbits between one and ten solar radii with energies ramping over many turns; spacecraft observations instead show a radially outflowing solar wind with no gravitationally bound relativistic component. (2) Measure the gravitational deflection of relativistic particles as a function of Lorentz factor: general relativity predicts deflection nearly independent of γ at leading order, while the revised law predicts deflection propor

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

If this is right

  • If the revised law is right, a substantial fraction of cosmic rays up to at least 10^6 GeV/nucleon can be produced inside the solar system, and the measured flux would be an incoherent mixture of a solar-system class and a non-solar class that current detectors cannot separate by source.
  • The revision would leave ordinary astronomy and low-energy physics untouched—slow or heavy bodies have E ≈ m—so all well-understood gravitational processes survive; the effect appears only for relativistic light particles near a massive body.
  • Energy-coupling gravity would alter the interpretation of missing mass and dark energy, because the gravitational contribution of relativistic matter would be systematically underestimated in the standard cosmological accounting.
  • The proposed E&M storage ring would let two different isotopes co-circulate at different velocities with a fixed, phase-locked crossing pattern, enabling rear-end nuclear collisions in a moving frame—for instance 6Li + 7Li → 13C + γ—with spin control and weak-interaction channels not accessible in fixed-target experiments.

Where Pith is reading between the lines

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

  • My inference: the cleanest discriminator is a γ-dependence test. General relativity predicts gravitational deflection of a relativistic particle that is essentially independent of its Lorentz factor at leading order, while the revised law predicts deflection growing ∝ γ; the author notes that no experiment has ever been motivated to look for such an effect, so a deflection measurement at two parti
  • My inference: the paper's ceiling of 10^6 GeV/nucleon (about 1 PeV) sits essentially at the observed 'knee' of the cosmic-ray spectrum. If the solar mechanism is correct, the knee would reflect solar-system acceleration limits—set by the Parker field strength and the roughly 10-year run imposed by the 22-year magnetic cycle—rather than Galactic propagation, a distinction testable through compositi
  • My inference: the argument generalizes to every magnetized, windy star, so the double-slingshot efficiency implied by solar-system production could be extrapolated over the galaxy's stellar population to predict a diffuse galactic cosmic-ray budget; comparing that budget with observed fluxes would give an independent check of the claimed efficiency.
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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

3 major / 4 minor

Summary. The paper argues that replacing masses by total energies in Newton's law, Eq. (14), allows the Sun to capture and accelerate protons to energies of at least 10^6 GeV/nucleon within the solar system. The key quantitative anchor is Eq. (18), r_A-lim = G M_sun/2 = 6.6e9 m, which the paper compares with the solar radius 0.6957e9 m. A "double slingshot" mechanism is then proposed, involving pre-acceleration at Jupiter and capture around the Sun. A large fraction of the manuscript is devoted to accelerator physics: co-circulating E&M storage rings, rear-end nuclear collisions, kinematic tables, and a proposed lattice design for experiments such as 6Li + 7Li -> 13C + gamma.

Significance. If the modified gravitational law were correct, the paper would have broad implications for cosmic-ray origin, missing mass, and dark energy. The storage-ring material contains detailed kinematic tables and design considerations for co-moving beams, which may be of technical interest. However, the central astrophysical claim rests on an unsupported, ad hoc modification of Newtonian gravity and on a capture-radius calculation that is dimensionally inconsistent. The numerical agreement claimed between r_A-lim and r_sun is an artifact of unit mishandling, so the proposed solar cosmic-ray mechanism is not established.

major comments (3)
  1. [Section 8, Eqs. (17)-(18), and Recapitulation Eqs. (41)-(42)] The quantitative anchor is dimensionally inconsistent. With SI units restored, G M_sun/2 = 6.6e19 m^3/s^2; converting to a length requires division by c^2, giving about 7.4e2 m (0.74 km), not 6.6e9 m. Equivalently, using KE_A = (gamma_A - 1) m_A c^2 in Eq. (17) gives r_A-lim = (G M_sun / 2c^2) gamma_A/(gamma_A - 1), which approaches 0.74 km for gamma_A >> 1. This is five orders of magnitude smaller than the solar radius, not ten times larger. The claimed capture orbits outside the Sun and the 'double slingshot' mechanism therefore do not follow from Eq. (18).
  2. [Section 8, Eq. (14)] The modified gravitational force law F = G E1 E2 / r^2 is introduced as a postulate, with no derivation. The text itself states 'I doubt that this is possible' concerning consistency with general relativity. Every subsequent capture and acceleration result is a direct consequence of the gamma factor in this assumed law. Under standard rest-mass coupling, the capture radius for a relativistic proton is G M_sun / c^2 ~ 1.5 km, far inside the Sun, so the proposed mechanism fails unless Eq. (14) is independently established. The paper supplies no equivalence-principle test, no ultrarelativistic gravitational-deflection prediction, and no other falsifiable consequence of the modified law.
  3. [Section 8, 'Double slingshot' and 'Improving the performance'] The paper gives no quantitative flux, spectrum, or arrival-direction prediction. The mechanism is described as 'semi-quantitative', and the expected energy distribution is left as 'As a guess, one hopes/expects...'. This prevents any observational discrimination between solar and galactic cosmic-ray origin. In addition, the static longitudinal electric-field line-integral objection is dismissed with 'Perhaps, or even probably' (bullet 2) that the 22-year solar cycle overcomes it; no model or calculation demonstrates that net acceleration survives the cycle.
minor comments (4)
  1. [Section 8, Eq. (14)] The symbol r is introduced as 'the radius of the sun' in the sentence after Eq. (14), but is then used as a general radial coordinate. This obscures the derivation and should be fixed.
  2. [Appendix A] Typos: 'Coles-Notes' should be 'CliffsNotes'; 'read read' appears in the text. A careful proofreading pass is needed throughout.
  3. [References] Reference [8] is listed twice for the same book; reference [16] is used for two different sources; reference [42] has no author. Several bibliographic entries are incomplete.
  4. [Section 8, Eq. (16)] Equation (16) identifies KE_A with gamma_A m_A v_A^2/2, which is not the relativistic kinetic energy (gamma_A - 1)m_A c^2 used elsewhere in the paper. This inconsistency should be resolved or the derivation revised.

Circularity Check

3 steps flagged

The headline solar-capture result is computed from the modified gravitational law that was itself adopted to make solar cosmic rays possible; the 'prediction' restates the input.

specific steps
  1. fitted input called prediction [Section 8, Eq. (14)]
    "Fp = G E1E2/r2 ≈ G m1γpmp/r2 , (14) ... I am forced to revise Newton ’s gravitational law in this new way in order to explain how most of the cosmic rays observed in nature, at least up to 106 GeV/nucleus for example, can have been produced within the solar system."

    The modified force law is introduced specifically so that relativistic protons feel a γ-enhanced gravitational force and can be captured by the Sun. The subsequent cosmic-ray energies are then presented as consequences of that law, but they are the motivation for the law, not independent predictions. No external data, equivalence-principle test, or parameter-free constraint is used to fix Eq. (14); the solar-capture conclusion is built into the chosen input.

  2. self definitional [Section 8, Eqs. (16)-(18); Section 12, Eqs. (41)-(42)]
    "rA−lim = G Msun 2 = 6.6 × 109 m. (18) ... The most persuasive theoretical indication that this replacement of mass by energy may be physically correct comes in the comparison of Eq. (18) and Eq. (19)."

    Eq. (18) is just the limiting radius obtained by inserting E≈γm into the assumed force law and setting the kinetic-energy factor to 1. Comparing that computed radius with the observed solar radius is offered as evidence for the force law, but the comparison is a consistency check with no independent predictive content: the force law was chosen so that capture at solar-system scales would be possible. The 'prediction' is the definition of the model, not a test of it.

  3. other [Section 8, Eqs. (17)-(18)]
    "Following Eq.(58) in Appendix B, the final factor in Eq. (17) has been set equal to 1."

    Eq. (17) contains the factor γ_A m_A / KE_A. Setting this factor to 1 is not a consequence of Eq. (58), which is the non-relativistic approximation E≈E0+mv^2/2; for a relativistic proton the factor is not 1 in the same units. This algebraic choice removes the energy dependence that would otherwise determine the numerical radius, so the claimed 6.6×10^9 m result is effectively inserted by hand rather than derived.

full rationale

The paper contains two distinct projects. The storage-ring sections (Sections 9-11) are concrete accelerator-physics designs and are not circular: they use standard Lorentz-force optics and are checked against internal kinematic consistency. The headline claim, however, is the solar cosmic-ray mechanism, and that claim is circular in the central sense. Eq. (14) is an ad hoc replacement of rest mass by total energy in Newton's law, explicitly adopted 'in order to explain' solar production of cosmic rays up to 10^6 GeV/nucleon. The key quantitative anchor, r_A-lim = G M_sun/2, is then derived from that same equation and exhibited as 'the most persuasive theoretical indication' that the mass-to-energy replacement is correct. That is comparing the model's own assumption with an observed radius, not testing the assumption. The step from Eq. (17) to Eq. (18) further sets the kinetic-energy factor to 1 without justification, making the numerical result an even more direct construction. Thus the central derivation reduces by construction to its input: the gamma factor in the input law produces the gamma factor in the capture condition, and the capture radius is presented as validation. The paper's own admission that it is 'forced' to revise the law and its doubt about compatibility with general relativity reinforce that the premise is not independently established. Score 8: the headline result is forced by definition, while the non-cosmic-ray accelerator material remains independent.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 1 invented entities

The central claim rests on an ad hoc modification of Newton's law plus a set of domain assumptions about the Parker wind and a closed solar system. The only quantitative anchor, the capture radius, is derived from the modified law and its printed value is suspect. The storage-ring design parameters are numerous but do not support the gravity claim.

free parameters (6)
  • Energy coupling factor gamma2 in modified Newton law
    The revised law F = G E1 E2 / r^2 is an unmeasured postulate; the gamma factor is the mechanism that makes solar capture possible.
  • Injection energy E_inj = 10 MeV
    Chosen arbitrarily for the solar accelerator start-up to ensure significant beam current; Fermi used 200 MeV.
  • Capture radius r_A-lim = 6.6 x 10^9 m
    Used as the key result to compare with the solar radius; the value as printed does not match standard G M_sun / c^2 and appears selected to lie near 10 R_sun.
  • Planetary magnetic moment fit beta* = spans roughly three orders of magnitude
    Empirical factor in Eq (10) adjusted per body; mentioned in support of the magnetic-rotational scaling, not central.
  • PTR electric field exponent mnom = 0.32349
    Tuned to place horizontal and vertical tunes on the difference resonance for the storage ring design.
  • Electric bending fudge factor = 1.1
    Applied in Table 1 to coarsely adjust collision point centering; a design tuning parameter.
axioms (7)
  • ad hoc to paper Gravitational force between a heavy body and a light relativistic particle is F = G E1 E2 / r^2 approx G M_sun gamma m / r^2 (Eq 14).
    No derivation is given; the paper states the author is 'forced to revise' Newton's law to explain solar cosmic rays and doubts its compatibility with general relativity.
  • domain assumption The Parker solar wind provides a longitudinal electric field that accelerates captured ions.
    The paper treats the solar wind as a DC arc discharge tube and relies on the Parker spiral electric field; the line integral constraint is acknowledged and hand-waved via the 22-year solar cycle.
  • domain assumption The solar system is treated as a closed and isolated system for cosmic ray accounting.
    The author declares this policy to avoid explaining non-solar cosmic rays; it limits the claim to a subset of observations.
  • standard math KE_A approx gamma_A m_A in the ultrarelativistic limit, used to derive r_A-lim.
    Standard limit, but its combination with circular orbits gives a radius inside the sun for ordinary gravity, so the modified law carries the entire result.
  • standard math Cary-Brizard guiding-center adiabatic theory applies to ions in the solar wind.
    Background theory in Appendix A used for helical orbits and centrifugal potential energy.
  • domain assumption Solar isotope abundance ratios can be read as evidence for solar-system cosmic ray production.
    The paper reinterprets 'cosmic ray' abundances as solar without a quantitative model linking the two.
  • ad hoc to paper The 22-year solar magnetic cycle overcomes the impossibility of a static longitudinal electric field line integral.
    The author writes 'perhaps, or even probably' this resolves the constraint; no calculation is supplied.
invented entities (1)
  • Energy-weighted gravitational coupling for light particles no independent evidence
    purpose: Make the sun able to capture and accelerate protons to about 10^6 GeV and explain solar-origin cosmic rays.
    No external handle is provided; the apparent evidence is the capture radius derived from the law itself, and that radius's numerical value is questionable.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Solar cosmic ray generation, Newtonian gravity, missing mass, dark energy, laboratory-based nuclear astrophysics, and all that." pith.science (2026). https://pith.science/paper/R6YB3HUL

@misc{pith2026250819296,
  author       = {Pith},
  title        = {Pith review of: Solar cosmic ray generation, Newtonian gravity, missing mass, dark energy, laboratory-based nuclear astrophysics, and all that},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R6YB3HUL}},
  note         = {Machine review of arXiv:2508.19296}
}
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abstract

Begun as part of a promotion of accelerator-based nuclear astrophysics, research toward this goal has shifted to cosmic ray production within the solar system. This has been motivated by the high quality of data collected recently by programs such as the International Space Station (ISS), by the fundamental importance of the topic, and by the unsatisfactory state of our understanding of the actual source of cosmic rays. A ``minor'' change in the Newtonian gravitational formulation converts solar production of high energy cosmic rays from ``impossible'' to ``likely'', without much disrupting the vast existent domain of well understood astronomical gravitational processes. This change enables the sun to ``capture'' protons of energy so high that they would, otherwise, escape the solar system. This change in Newton's gravitational formula would disrupt current cosmological understanding of missing mass and dark energy. With this changed understanding of gravity, it has been quite easy to produce a semi-quantitative understanding of the solar origin of cosmic rays up to energies at least as great as $10^6$\,GeV/nucleon that have by now been detected and measured so persuasively. A ``Double Slingshot'' mechanism is proposed according to which at least a substantial fraction of all cosmic rays could have begun their life within the solar system. Accelerator-based nuclear astrophysics is promoted, beginning with the functioning of an ``{\rm E}\&{\rm M}'' storage ring for laboratory-based study of processes such as ${\rm 6LI} + {\rm 7Li} \rightarrow {\rm 13C} + \gamma$. Especially to be emphasized are experiments made possible by ''rear-end collisions'' between nuclear isotopes of two different types traveling simultaneously at different velocities in the same direction in the same storage ring. This amounts to ``studying nuclear physics in a moving frame of reference''.

Figures

Figures reproduced from arXiv: 2508.19296 by Richard Talman.

Figure 1
Figure 1. Figure 1: Parameters not defined in the original table caption are [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top: Copied from Owens and Forsythe[5], as follows: “A sketch of the steady￾state solar magnetic field in the ecliptic plane. Close to the sun, in a spatial region approximately bounding the solar corona, the magnetic field dominates the plasma flow and undergoes significant non-radial (or super-radial) expansion with height. At the source surface , typically taken to be a few solar-radii, the pressure-dri… view at source ↗
Figure 3
Figure 3. Figure 3: Counter-traveling helical orbits of a single nuclear isotope and a single electron [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The Coulomb repulsion between positive nuclear isotopes is represented by [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The two figures on this page are explained and referenced in the text. The [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Matched with the lower plot of Figure 5, and including the original caption, [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Figure (copied from Wiens)[14]) exhibiting solar wind fractional isotope ratios. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mass, orbit periods, P, and magnetic moments, M of the planets. Copied from [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Clipped from a figure in the Rolfs and Rodney “Cauldrons” book, this figure [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Mass density within the sun, plotted as a function of radius, copied from [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Planetary parameters, copied from Biemond[19]. Angular velocity Ω, magnetic [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Log-log-plot copied from the same Biemond paper as Figure 11. [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Top left: Magnetic dipole field pattern. Top right: Perspective view of dipole field pattern. 16 field lines are shown (actually +1, including the straight line from observer’s view point). Bottom: 2025 image shows magnetic fields radiating from the sun’s poles. Courtesy of NASA’s Goddard Space Flight Center. Superimposed is the outline of the aperture of the sun as a particle accelerator. Interpolated on… view at source ↗
Figure 14
Figure 14. Figure 14: Copied from a Yang et al.[21] article, this figure shows typical magnetic fields [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Jupiter magnetic field contours, copied from reference [24]. [PITH_FULL_IMAGE:figures/full_fig_p036_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Time Lag comparisons, 1950-2020, of sunspot number (SSN), open solar flux [PITH_FULL_IMAGE:figures/full_fig_p037_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Artist’s conception of two stage “Double-Slingshot” solar system production [PITH_FULL_IMAGE:figures/full_fig_p038_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Views of selections of particles falling in toward the sun. [PITH_FULL_IMAGE:figures/full_fig_p039_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Stable RF buckets for different velocity ratio beams. [PITH_FULL_IMAGE:figures/full_fig_p042_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Left: Lattice layout for PTR, the proposed nuclear transmutation storage ring. “Compromise quadrupoles” are shown inset. The circumference has been taken to be 102.5 m, but the entire lattice can be scaled, e.g. to reduce peak field requirements. Right: Perspective sector mock-up of one PTR sector. Cos θ-dipoles surround the beam tube, within which are the capacitor plate electrodes. The superimposed coil… view at source ↗
Figure 22
Figure 22. Figure 22: For increased luminosity this ring has two round beam, low beta intersection [PITH_FULL_IMAGE:figures/full_fig_p042_22.png] view at source ↗
Figure 21
Figure 21. Figure 21: Refined PTR tuning, with quad strengths and [PITH_FULL_IMAGE:figures/full_fig_p043_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Beta-squeezed round beam collider schematic. The (seemingly quadrupole [PITH_FULL_IMAGE:figures/full_fig_p044_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Experimental observation of the resonant production of an N=3 example of [PITH_FULL_IMAGE:figures/full_fig_p048_23.png] view at source ↗
Figure 25
Figure 25. Figure 25: Figure showing a table provided by D. Raparia,[44] of side-by-side low [PITH_FULL_IMAGE:figures/full_fig_p050_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Figure copied from Wikipedia, showing, on the left, the theoretically calculated [PITH_FULL_IMAGE:figures/full_fig_p051_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Screenshot of MAPLE worksheet evaluating the roots of the quartic equation [PITH_FULL_IMAGE:figures/full_fig_p052_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Graphs of final state angular and kinetic energy as functions of center of [PITH_FULL_IMAGE:figures/full_fig_p054_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Graphs of kinetic energy as functions of center of mass angle for the process [PITH_FULL_IMAGE:figures/full_fig_p055_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: . Two-body jet scattering representation of the ( [PITH_FULL_IMAGE:figures/full_fig_p057_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Left: Plot of lab polar angles vs CM polar angles, for the final state of the reaction e − +h → t+ν. Both incident beams are at (0,0) in this plot. Notice that, viewed in the laboratory, the produced tritium nuclei are reasonably well collimated, while the (invisible) scattered neutrinos are more or less isotropic. Right: Plot of final state kinetic energies vs CM polar angles, for e − + 3He → triton + ν … view at source ↗
Figure 32
Figure 32. Figure 32: The equation shown, AB+DE=CE, when expressed in terms of [PITH_FULL_IMAGE:figures/full_fig_p070_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: RHIC report by Dehan Trbojevic explaining mass corrections associated with [PITH_FULL_IMAGE:figures/full_fig_p072_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: RHIC report by Dehan Trbojevic explaining mass corrections associated with [PITH_FULL_IMAGE:figures/full_fig_p073_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Wagoner et al. 1974 formulas. Q-values in MeV are shown on the right. Temperature Tg is defined in their Appendix A, Eq. (A15); valid at very high temperature (Tg > 10). 74 [PITH_FULL_IMAGE:figures/full_fig_p074_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Wagoner et al. 1974 formulas, continued. [PITH_FULL_IMAGE:figures/full_fig_p075_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Dolgov and Zeldovich 1981 synthesis of Wagoner et al. 1974 production rate [PITH_FULL_IMAGE:figures/full_fig_p076_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Astronomical terms and constants copied from www.astro.princeton.edu. [PITH_FULL_IMAGE:figures/full_fig_p078_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: Astronomical terms and constants copied from www.astro.princeton.edu. [PITH_FULL_IMAGE:figures/full_fig_p079_39.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.