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arxiv: 2607.01190 · v1 · pith:CMDTW2MVnew · submitted 2026-07-01 · ⚛️ nucl-th

Semi-regularised three-body pseudopotential for mean-field and beyond-mean-field calculations

Valentin Guillon , Michael Bender , Karim Bennaceur , Philippe Da Costa This is my paper

Pith reviewed 2026-07-02 04:28 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords three-body pseudopotentialnuclear energy density functionalmean-field calculationsbeyond-mean-field calculationsparticle-hole channelparticle-particle channelinfinite nuclear matterspherically symmetric systems
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The pith

A local leading-order semi-regularised three-body pseudopotential produces consistent contributions to the nuclear energy density functional in both particle-hole and particle-particle channels.

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

The paper derives the most general form of a local leading-order semi-regularised three-body pseudopotential. This form is constructed to generate contributions to the nuclear energy density functional in the particle-hole and particle-particle channels. The goal is to enable its use in mean-field and beyond-mean-field calculations without introducing ambiguities or mathematical difficulties. Analytical expressions for properties of infinite nuclear matter are derived from the resulting EDF, along with the explicit structure of the EDF and mean fields for spherically symmetric systems. A sympathetic reader would care because current nuclear EDF approaches often face inconsistencies when extending calculations beyond the mean-field level.

Core claim

We derive the most general form of a local leading-order semi-regularised three-body pseudopotential. This particular form of pseudopotential is developed with the aim of generating contributions to the nuclear energy density functional (EDF) in both the particle-hole and particle-particle channels and, hence, to be usable in mean-field and beyond-mean-field calculations without ambiguities or mathematical difficulties. Once the EDF is obtained, analytical expressions of commonly considered properties of infinite nuclear matter are provided. Finally, the structure of the EDF and the associated mean fields are given for spherically-symmetric systems.

What carries the argument

The semi-regularised three-body pseudopotential, a local leading-order interaction form that produces EDF contributions in both the particle-hole and particle-particle channels without requiring extra regularization parameters.

If this is right

  • The pseudopotential contributes to the EDF simultaneously in the particle-hole and particle-particle channels.
  • Analytical expressions become available for standard properties of infinite nuclear matter.
  • Explicit mean-field equations can be written down for spherically symmetric systems.
  • The same interaction can be used without change of form in both mean-field and beyond-mean-field frameworks.

Where Pith is reading between the lines

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

  • The same construction might be extended to deformed nuclei by relaxing the spherical symmetry assumption while keeping the local leading-order form.
  • If the EDF terms remain free of ambiguities, pairing correlations treated at the beyond-mean-field level could become more stable across different nuclei.
  • The approach could be tested by comparing predicted saturation properties of nuclear matter against existing Skyrme or Gogny parametrizations that lack a consistent three-body term.

Load-bearing premise

A local leading-order three-body pseudopotential can be constructed in semi-regularised form such that it produces unambiguous EDF contributions in both channels without additional regularization parameters or breaking mathematical consistency.

What would settle it

An explicit calculation in infinite nuclear matter that applies the derived pseudopotential to a beyond-mean-field method and produces either mathematical ambiguities in the EDF or requires additional regularization parameters to remain consistent.

read the original abstract

We derive the most general form of a local leading-order semi-regularised three-body pseudopotential. This particular form of pseudopotential is developed with the aim of generating contributions to the nuclear energy density functional (EDF) in both the particle-hole and particle-particle channels and, hence, to be usable in mean-field and beyond-mean-field calculations without ambiguities or mathematical difficulties. Once the EDF is obtained, analytical expressions of commonly considered properties of infinite nuclear matter are provided. Finally, the structure of the EDF and the associated mean fields are given for spherically-symmetric systems.

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

0 major / 2 minor

Summary. The manuscript derives the most general form of a local leading-order semi-regularised three-body pseudopotential. This form is constructed to generate unambiguous contributions to the nuclear energy density functional (EDF) in both the particle-hole and particle-particle channels, enabling use in mean-field and beyond-mean-field calculations. Analytical expressions are provided for properties of infinite nuclear matter, and the structure of the EDF together with the associated mean fields is given for spherically symmetric systems.

Significance. If the claimed derivation holds, the result supplies a technically consistent route to include three-body terms in EDFs without channel-specific ambiguities or extra regularization parameters. The explicit infinite-matter expressions and spherical mean-field forms constitute reproducible, falsifiable content that can be directly implemented or tested in existing nuclear-structure codes.

minor comments (2)
  1. A short paragraph contrasting the new semi-regularised form with previously published three-body pseudopotentials (e.g., those of Refs. [X] and [Y]) would clarify the precise advance in avoiding mathematical difficulties.
  2. Notation for the regularization cutoff and the spin-isospin operators should be introduced once in a dedicated subsection before the general derivation to improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending acceptance. We are pleased that the derivation of the semi-regularised three-body pseudopotential and the provided expressions for infinite matter and spherical systems were found to be clear and reproducible.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim is a mathematical derivation of the most general local leading-order semi-regularised three-body pseudopotential that produces unambiguous EDF contributions in both channels. No quoted step reduces a result to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames an empirical pattern. The derivation is presented as a direct construction from the requirements of locality, leading order, and semi-regularisation, with subsequent analytic expressions for infinite matter and spherical mean fields following from that form. Absent any load-bearing reduction to prior fitted quantities or self-referential definitions in the provided abstract and summary, the chain is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the semi-regularisation procedure itself may implicitly introduce regularization choices but none are stated.

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discussion (0)

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Reference graph

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