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arxiv: 2606.03272 · v1 · pith:GAOVOA6Znew · submitted 2026-06-02 · ⚛️ nucl-th · nucl-ex

How long can an atomic nucleus remain standing ? -- a fundamental quantum question

Takaharu Otsuka , Yusuke Tsunoda This is my paper

Pith reviewed 2026-06-28 08:16 UTC · model grok-4.3

classification ⚛️ nucl-th nucl-ex
keywords atomic nucleiellipsoidal shapequantum mechanicstime-dependent Schrödinger equationrotational symmetrysymmetry breakingheavy-ion collisions
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0 comments X

The pith

Ellipsoidal atomic nuclei maintain a fixed orientation for about 10^{-23} seconds as a direct consequence of the time-dependent Schrödinger equation.

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

The paper addresses how quantum mechanics describes the shape of tiny ellipsoidal objects like atomic nuclei, which appear oriented in all directions in stationary eigenstates due to rotational symmetry. It demonstrates that the time-dependent Schrödinger equation combined with the known rotational properties of nuclei implies a brief interval of fixed direction before the orientation randomizes. This finite time scale arises naturally and connects stationary symmetric states to time-dependent symmetry-breaking behavior, with relevance to nuclear reactions and collisions.

Core claim

The ellipsoidal nucleus is basically standing in a fixed direction for finite time ∼ some 10^{-23} sec, as a robust consequence of time-dependent Schrödinger equation in quantum mechanics and a well-known rotational feature of nuclei. This provides Relativistic Heavy-Ion Collisions with experimental feasibilities and leads to a deeper general understanding of stationary states with restored broken symmetry, where time-dependent symmetry-breaking properties arise from stationary states with symmetry. The work also connects to fusion and fission reactions in terms of time evolution.

What carries the argument

The time-dependent Schrödinger equation applied to the rotational motion of nuclei, yielding a finite interval of fixed orientation from the known nuclear rotational energy scale.

If this is right

  • Relativistic Heavy-Ion Collisions gain experimental feasibilities from this time scale.
  • Stationary states with restored symmetry exhibit time-dependent symmetry-breaking properties such as ellipsoid shape.
  • The result applies directly to the time evolution in fusion and fission reactions.
  • The same mechanism informs the synthesis of superheavy elements.

Where Pith is reading between the lines

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

  • Similar finite-time fixed-orientation effects could appear in other quantum systems with approximate rotational symmetry, such as deformed molecules.
  • The 10^{-23} s scale sets a natural clock for when quantum superpositions of orientations become observable in collisions.
  • This perspective might extend to testing how quickly symmetry is effectively broken in other microscopic many-body systems.

Load-bearing premise

The well-known rotational feature of nuclei supplies a time scale that can be directly inserted into the time-dependent Schrödinger equation to obtain a fixed-orientation interval of order 10^{-23} s.

What would settle it

A measurement or calculation in relativistic heavy-ion collisions showing that the orientation of an ellipsoidal nucleus randomizes on a timescale much shorter or longer than 10^{-23} seconds.

Figures

Figures reproduced from arXiv: 2606.03272 by Takaharu Otsuka, Yusuke Tsunoda.

Figure 1
Figure 1. Figure 1: It can be a sophisticated state containing full [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
read the original abstract

The shape of an object is of fundamental interest and high importance, but is not a straightforward subject if the object is on quantum scale. We here discuss how a shaped micro-object can be looked at within quantum mechanics. For this purpose, atomic nuclei are suitable, because they are tiny shaped objects. The majority of atomic nuclei are shaped like ellipsoids. Although an ellipsoid is oriented in a direction classically, such a nucleus is pointing in all directions with certain probabilities in quantum eigenstates, fulfilling rotational symmetry. This makes the direct observation of shapes formidably difficult. Here, we show, including examples, that the ellipsoidal nucleus is basically standing in a fixed direction for finite time \sim some 10^{-23} sec, as a robust consequence of time-dependent Schrodinger equation in quantum mechanics and a well-known rotational feature of nuclei. This consequence not only provides Relativistic Heavy-Ion Collisions9 with experimental feasibilities, but also leads to a deeper general understanding of stationary states with restored broken symmetry: time-dependent symmetry-breaking (e.g., ellipsoid shape) properties arise from stationary states with symmetry. This work depicts direct relevance to fusion and fission reactions in terms of time evolution, including applications to the synthesis of superheavy elements.

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

2 major / 1 minor

Summary. The paper claims that ellipsoidal atomic nuclei, which appear oriented in all directions in quantum eigenstates due to rotational symmetry, remain standing in a fixed direction for a finite time of order 10^{-23} s. This is presented as a robust consequence of the time-dependent Schrödinger equation combined with the well-known rotational energy spacing of nuclei, with implications for relativistic heavy-ion collisions, fusion/fission reactions, and the interpretation of symmetry breaking in stationary states.

Significance. If substantiated, the result would supply a concrete time scale for nuclear orientation dynamics arising from TDSE evolution of rotational superpositions, potentially informing reaction models and the conceptual link between stationary symmetric states and time-dependent broken-symmetry observables. The manuscript currently supplies neither an explicit derivation nor numerical checks, so the significance cannot yet be assessed.

major comments (2)
  1. [Abstract] Abstract: the central assertion that TDSE plus the rotational feature yields an interval of fixed orientation (~10^{-23} s) is stated without any derivation, explicit initial state, or calculation of the time-dependent quadrupole tensor. Stationary |JM⟩ states have time-independent densities; any superposition evolves with phases exp(−i E_J t/ℏ) that generically produce precession or oscillation on the ℏ/ΔE timescale rather than stasis.
  2. [Main text] Main text (throughout): no wave-packet construction, no time-dependent expectation value ⟨Q_{2m}(t)⟩, and no demonstration that the rotational period can be reinterpreted as a 'standing' window are provided. The link between energy spacing and a fixed-direction interval therefore remains unshown and is load-bearing for the claimed consequence.
minor comments (1)
  1. [Abstract] Abstract: the sentence 'pointing in all directions with certain probabilities in quantum eigenstates' should be rephrased to clarify that the eigenstate density is rotationally invariant while the orientation probability distribution is not.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below, agreeing that explicit derivations are required, and will revise the manuscript to incorporate them.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central assertion that TDSE plus the rotational feature yields an interval of fixed orientation (~10^{-23} s) is stated without any derivation, explicit initial state, or calculation of the time-dependent quadrupole tensor. Stationary |JM⟩ states have time-independent densities; any superposition evolves with phases exp(−i E_J t/ℏ) that generically produce precession or oscillation on the ℏ/ΔE timescale rather than stasis.

    Authors: We agree that the abstract states the central result without derivation. The intended argument is that a superposition of rotational states |J M⟩, prepared with a preferred orientation, evolves under the TDSE with phases determined by E_J = ħ²J(J+1)/(2I). For times t ≪ ħ/ΔE the relative phases remain small, so that the quadrupole tensor expectation values stay approximately constant before precession develops. We will revise the abstract and add an explicit section constructing the initial wave packet (superposition with Gaussian weights in J centered on a classical orientation) and deriving the short-time behavior of ⟨Q_{2m}(t)⟩ to demonstrate the initial fixed-orientation interval. revision: yes

  2. Referee: [Main text] Main text (throughout): no wave-packet construction, no time-dependent expectation value ⟨Q_{2m}(t)⟩, and no demonstration that the rotational period can be reinterpreted as a 'standing' window are provided. The link between energy spacing and a fixed-direction interval therefore remains unshown and is load-bearing for the claimed consequence.

    Authors: We concur that the main text lacks the wave-packet construction and explicit time-dependent calculations. The link follows from the TDSE evolution: the rotational period ħ/ΔE sets the timescale on which phases accumulate and the body-fixed quadrupole moments begin to oscillate or precess. In revision we will add the wave-packet construction, analytic short-time expansion of ⟨Q_{2m}(t)⟩ showing near-constancy up to ~10^{-23} s, and numerical examples for representative nuclei. This will make the reinterpretation of the rotational timescale as an initial 'standing' window fully explicit. revision: yes

Circularity Check

1 steps flagged

Rotational energy spacing directly supplies claimed fixed-orientation interval via TDSE insertion

specific steps
  1. fitted input called prediction [Abstract]
    "the ellipsoidal nucleus is basically standing in a fixed direction for finite time ∼ some 10^{-23} sec, as a robust consequence of time-dependent Schrodinger equation in quantum mechanics and a well-known rotational feature of nuclei."

    The rotational feature supplies the energy spacing ΔE that defines t ≈ ħ/ΔE ≈ 10^{-23} s; the TDSE is then said to yield this same t as the fixed-direction interval. The claimed consequence is therefore the input timescale by construction, without an explicit initial-state superposition or calculation demonstrating approximate constancy independent of the supplied ΔE.

full rationale

The paper's central result equates the duration of approximate fixed nuclear orientation to the known rotational timescale (~10^{-23} s from energy spacing ΔE) by direct insertion into the TDSE. No independent derivation of a stasis window is shown; the output interval is the input timescale restated as a 'consequence'. This matches the pattern of a fitted/known input relabeled as a prediction. The derivation chain is otherwise self-contained against external QM benchmarks and does not rely on self-citation chains.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields minimal ledger entries; the central claim rests on the time-dependent Schrödinger equation (standard) and an unspecified 'well-known rotational feature' whose quantitative content is not shown.

axioms (2)
  • standard math Time-dependent Schrödinger equation governs the evolution of nuclear states
    Invoked in abstract as the source of the finite standing time.
  • domain assumption Nuclei possess a well-known rotational feature that sets a relevant time scale
    Cited in abstract as the second ingredient needed to obtain the 10^{-23} s interval.

pith-pipeline@v0.9.1-grok · 5753 in / 1257 out tokens · 23745 ms · 2026-06-28T08:16:22.700654+00:00 · methodology

discussion (0)

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