Nucleus-Nucleus Collision

Scientific Paper
Title	Nucleus-Nucleus Collision
Read in full	Link to paper
Author(s)	Ricardo L Carezani
Keywords	neutrino, special relativity, autodynamics
Published	1998
No. of pages	11

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Abstract

Part of the smaller Linear Momentum Transfer (LMT) found in Nucleus-Nucleus collision is explained by the application of autodynamics equations. The "missing mass" or "missing momentum" in RaE, 238U, muon decay and similar phenomena like anomalous mean pass, electron-electron and proton-proton annihilation, all have in common that the failure to explain the experimental values found is due to the application of special relativity equations. Autodynamics equations apply to these phenomena and explain precisely the results obtained experimentally. The momentum sum of all the products after compound nucleus fission has only a limited relation to the original projectile's momentum. In nucleus-nucleus collision, the "missing momentum" is inherent to the phenomenon itself. Looking at the experimental energies found causes a new idea to arise as proposed in this paper: a chain reaction.

Overview

Carezani applies his autodynamics to the long-standing puzzle of incomplete linear momentum transfer (LMT) in heavy-ion fusion-fission. When a projectile fuses with a target to form a compound nucleus that then fissions, the momentum carried away by the detected products routinely falls short of the projectile's momentum — often far short. The standard reading is that undetected neutral fragments and pre-equilibrium emission carry the balance. Carezani rejects that: the shortfall, he argues, is real, is present for both central and peripheral impacts, and arises because the products' momenta are being computed with the wrong kinematics.

His central methodological claim is a partition of physics into two regimes. Where a particle is given energy "from the external medium" — an accelerator field, a klystron, a chemical explosive — the special relativity expressions apply, and he accepts the Bertozzi experiment as confirming them. Where a particle receives its energy from decay, autodynamics applies instead, with kinetic energy E_c = m₀c²(1 − √(1 − β²)), mass m = m₀√(1 − β²) and momentum p = m₀√(1 − β²)v. Since compound-nucleus fission is a decay, the fragments' momenta are smaller than the relativistic values, and the "missing" momentum was never there. The same move, he says, disposes of the neutrino: the RaE (beta decay of ²¹⁰Bi) discrepancy that prompted Pauli's hypothesis — 1.16 MeV expected, 0.36 MeV found — is "explained perfectly" by the autodynamics kinetic energy, so no ghost particle is needed.

The argument

Two worked tables

Carezani constructs a model reaction: a mass-16 projectile with 315 MeV of kinetic energy forming a mass-254 compound nucleus, which fissions into two heavy fragments plus two boron, two beryllium, two alpha particles and six nucleons. Table I takes the fission symmetric (fragments of 101 mass units each); Table II makes it asymmetric (80 and 120). Each fragment's momentum is computed twice, relativistically (MR) and by autodynamics (MA), from the same assigned kinetic energies.

The result he emphasises is the difference in leverage. In the centre of mass the scalar momentum sums differ by only two per cent (SMA/SMR = 98.02 % in Table I), but in the laboratory the linear momentum transfer differs by twelve per cent — LMT_R = 3080, LMT_A = 2710 MeV/c, 88 % — because the transformation is dominated by the folding angle between the two heavy fragments, and small momentum changes move that angle. Table II, with a folding angle ten degrees wider, drops the autodynamics/relativity ratio to 78 % and the LMT to 42 % (relativistic) or 33 % (autodynamics) of the projectile momentum. He states the empirical regularity he is trying to capture: "There is an inverse ratio between the fission fragments' folding angle and the LMT. The larger the folding angle, the lower the LMT." He also notes that arranging LMT_A to equal the projectile momentum forces LMT_R to about 108 %, close to the maximum ~120 % occasionally reported.

The energy surplus and a proposed chain reaction

The paper's second theme is an energy balance that Carezani says nobody has commented on. In Table I the assigned fragment kinetic energies sum to E_T = 1600 MeV against a projectile kinetic energy of 315 MeV. Conceding that his assigned energies are probably too generous, he scales them: at half, the products carry 2.54 times the projectile energy; at a quarter, 1.27 times; and a "realistic" third gives 1.7 times. He checks the quarter case against measured fragment spectra and rejects it, because there is little carbon below 100 MeV, no boron below 50 MeV, and essentially no beryllium at 31 MeV.

He then repeats the exercise on published data (Fatyga et al., 1985): a 40 MeV proton, folding angle 176.6°, p_|| = 230 MeV/c, two fragments of 119 mass units — from which he obtains 135.6 MeV of fragment kinetic energy, and 123.81 MeV for the 175.9°, 265 MeV/c case. Asking "where do the fission residue energies come from?", he answers that part comes from the projectile and "the complementary part must be provided by compound nucleus mass decay". From this he draws the paper's most striking suggestion: if each fusion-fission event releases more energy than the projectile brought, "it should be possible to produce a chain reaction using an inexpensive element like Pb mixed with other inexpensive elements". A conversation with Hans Kautzky of Fermilab is reported as suggesting a second application — bombarding nuclear waste to transmute it.

The Addendum

Unusually, Carezani prints the referee's reports in full. The reviewer objects that momentum conservation "is one of the most thoroughly tested laws in physics", suggests he instead posit an unknown process absorbing the discrepancy, and lists two further "unpalatable" commitments: rejection of the neutrino, and the claim that the charge of the electron decreases with velocity. In a second report the reviewer nonetheless recommends publication — "the article is not blatantly 'crackpot' and it does not have any readily demonstrable errors in development" — while noting that Carezani "has actually not provided a physical basis for using these 'autodynamics' formulas".

Carezani replies that he needs no extra process, that more than two hundred experiments show the discrepancy, and that his charge-variation claim applies only to particles in decay, not to the electron emitted in beta decay, which is "a formal electron" with its full charge. He also offers a unification: writing E_c = M(1 − √(1 − β²)), one recovers autodynamics when M = m₀c² and special relativity when M = m₀c² + E_c.

Assessment

The tables were checked line by line, and Carezani's arithmetic is very largely correct. Taking 931.494 MeV per mass unit, the relativistic momenta reproduce exactly: for the 101-unit fragment at 225 MeV, √(T² + 2Tm₀c²) = 6510.5 against his 6510; the 80- and 120-unit fragments of Table II give 5463.3 and 6689.7 against 5463 and 6689. The autodynamics column is equally sound: setting s = 1 − T/m₀c² and p = m₀c·s·√(1 − s²) returns 6487.2, 1878.7, 1420.8, 751.5, 296.7 and 307.7 for the fragment, boron, beryllium, alpha and nucleon rows against his 6487, 1878, 1420, 751, 296 and 307. The energy and mass sums (1600 MeV and 254 units in Table I; 1770 and 252 in Table II) add up, and the percentages 98.02, 88, 78, 42 and 33 all follow from the printed figures. The folding-angle reconstruction is right too: 230 MeV/c across a 176.6° folding angle gives two fragments of 3876 MeV/c each and a kinetic energy of 135.6 MeV, exactly as stated, and the 175.9° case gives 123.8 MeV. The Addendum's identity is also a genuine identity — E_c = (m₀c² + E_c)(1 − s) rearranges algebraically to E_c = m₀c²(1/s − 1), the relativistic formula. Carezani computes carefully, and the referee was right that there are no demonstrable errors of development.

The problems lie elsewhere, and they are severe.

Autodynamics caps momentum at half m₀c. With p = m₀c·β√(1 − β²), the momentum rises, peaks at β = 1/√2 with p = 0.5m₀c, and then falls back to zero as β → 1. The kinetic energy is capped at m₀c². Nothing in nature obeys this: LEP accelerated electrons to about 100 GeV, two hundred thousand times the electron rest energy, and their momenta were measured by magnetic rigidity, not inferred. Carezani's escape is that such particles receive external energy so relativity applies to them — but the escape is not available for decay products, and decay products routinely exceed the cap. The muons produced in pion decay in a beam line, the ~50 GeV muons from cosmic-ray pion decay whose survival at sea level is the classic time-dilation measurement, and the multi-TeV decay products reconstructed in collider detectors all have momenta far above 0.5m₀c. In practice a beam is bent by a known field and its radius measured; the momentum so obtained is a direct observable, and it does not saturate.

The energy surplus violates the mass balance it appeals to. Carezani asks the right question — where does the extra energy come from? — and gives the right kind of answer, the compound nucleus's mass. But that quantity is measured and bounded. For his own Table I reaction, a mass-254 compound nucleus splitting into two 101-unit fragments plus two ¹⁰B, two ⁹Be, two alphas and six free nucleons, the binding-energy difference is about 170 MeV (fission Q-values in this region are near 200 MeV, and stripping six nucleons free costs roughly 8 MeV each). Adding the 315 MeV projectile gives about 490 MeV available in total. His table assigns 1600 MeV to the products — over three times the budget. Even the "realistic" third of that, 533 MeV, exceeds it. Only the quarter-scale version, 400 MeV, fits, and it is the one he rejects on spectroscopic grounds. The proposed lead-based chain reaction therefore rests on an energy surplus that his own reaction cannot supply; it is not a new nuclear regime but a failure to close the mass-energy books.

Two internal inconsistencies in the same passage. He reports 135.6 MeV as "3.8 times bigger than the bombarding proton's" 40 MeV; the ratio of his own numbers is 3.39. And he says that "in the last case the energy is less than the projectile's", but his own value there is 123.81 MeV against a 40 MeV proton — three times larger, not smaller. Separately, in Table I the projectile is assigned an autodynamics momentum of 3016 MeV/c, but applying his own formula to a 16-unit projectile of 315 MeV gives 2983.6; the 3016 appears to have been carried across from the compound-nucleus row to force lab momentum conservation. Since PLMTA (89.86 %) is 2710/3016, that percentage inherits the discrepancy.

The RaE argument compares a spectrum endpoint with a spectrum mean. The 1.16 MeV figure is the endpoint of the ²¹⁰Bi beta spectrum; the 0.36 MeV figure is the average energy per disintegration measured calorimetrically by Ellis and Wooster in 1927. They are not two determinations of one quantity, and the gap between them is not a computational error. The observation the neutrino was introduced to explain is the continuity of the spectrum — electrons emerge with every energy from zero to the endpoint — and no modification of the kinematic relation between one electron's speed and its energy can produce a continuous distribution from a two-body decay of nuclei with sharp masses. Autodynamics assigns a single energy where experiment sees a distribution. The neutrino has since been detected directly, in the Reines-Cowan reactor experiment of 1956 and in every solar and reactor experiment since, and its flavour oscillations were measured at Super-Kamiokande and SNO.

Charge invariance is measured. The reviewer flagged the velocity-dependent electron charge, and Carezani restricts it to decaying particles. But charge invariance under boosts is tested to extraordinary precision by the electrical neutrality of atoms and molecules — the electrons in a heavy atom move at appreciable fractions of c while the nucleus does not — with limits on any residual charge of order 10⁻²¹ of the electron charge.

Finally, the reviewer's deeper point stands unanswered in this paper. The autodynamics expressions are not derived here from any principle; they are a functional form found to fit, as the reviewer observed. Carezani's reply — that all phenomena are ultimately decay, so the two-regime rule is not ad hoc — is difficult to hold alongside his own concession that the accelerator and the cannon ball obey relativity. The line between "energy from the external medium" and "energy from decay" is drawn case by case, and it is that line, not the formulae, that does the explanatory work. The paper's real merit is elsewhere: the observation that incomplete momentum transfer correlates inversely with the fission folding angle is a genuine and testable regularity in the data he cites, and his closing recommendation — that existing experiments be re-analysed to compare the two kinematics on concurrent fission residues — is a fair and cheap test to propose.

See also

• Ricardo L Carezani
• Autodynamics
• Neutrino
• Special Relativity
• Nucleus
• Wolfgang Pauli
• Electric Charge
• Muon
• Mass