arxiv: 2604.27605 · v1 · submitted 2026-04-30 · ⚛️ nucl-th · nucl-ex

Recognition: unknown

Probing Near-Threshold s-Wave Components in Heavy Nuclei via Coulomb-Assisted Neutron Transfer

Yuki Nakanishi , Junki Tanaka , Atsushi Tamii , Shimpei Endo

Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:41 UTC · model grok-4.3

classification ⚛️ nucl-th nucl-ex

keywords neutron transfers-wave componentsweakly bound statesCoulomb barrierDWBA calculationsheavy nucleiasymptotic wave functionsnear-threshold states

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The pith

Low-energy backward-angle (d,p) reactions can selectively probe the asymptotic tails of weakly bound s-wave neutrons near threshold in heavy nuclei.

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

The paper proposes using the (d,p) neutron-transfer reaction at low incident energies and backward angles to access weakly bound s-wave neutron components near the emission threshold in heavy nuclei. The Coulomb barrier localizes the reaction to the nuclear exterior, so the transition amplitude becomes sensitive to the extended asymptotic tail of the single-particle wave function. Finite-range DWBA calculations show that cross sections for weakly bound states vary only weakly with energy, whereas those for strongly bound states fall rapidly as energy decreases. Centrifugal barriers suppress contributions from l greater than or equal to 1 orbitals, giving the method selectivity for s-wave components. This approach therefore maps the strength distribution of near-threshold s-wave neutrons and the shape of their wave-function tails, quantities that are otherwise hard to isolate.

Core claim

At low incident energies and backward angles the (d,p) reaction is localized to the nuclear exterior by the Coulomb barrier, rendering the transition amplitude sensitive to the asymptotic part of the single-particle neutron wave function. Finite-range DWBA calculations demonstrate that this produces a weak energy dependence of the cross section for weakly bound s-wave states, a rapid decrease for strongly bound states, and strong suppression of l greater than or equal to 1 contributions by the centrifugal barrier, thereby providing a selective probe of the strength distribution and asymptotic structure of near-threshold s-wave components.

What carries the argument

Coulomb localization of the (d,p) transfer amplitude to the asymptotic tail of the neutron wave function at low energy and backward angles, with centrifugal suppression enforcing selectivity for s-wave orbitals.

If this is right

Cross sections for weakly bound s-wave states exhibit only weak dependence on incident energy.
Cross sections for strongly bound states decrease rapidly as incident energy is lowered.
Orbitals with angular momentum l of 1 or higher are suppressed by the centrifugal barrier.
The reaction provides a selective probe of the strength distribution of weakly bound s-wave components near threshold.
The method also gives access to the asymptotic structure of the corresponding wave functions.

Where Pith is reading between the lines

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

The same localization principle could be tested in other transfer reactions or lighter nuclei to check whether the selectivity holds beyond heavy systems.
High-resolution backward-angle data at several low energies on a single target would directly test the predicted weak energy dependence for known near-threshold states.
The extracted asymptotic amplitudes could constrain neutron-capture rates in astrophysical environments where s-wave components near threshold dominate.

Load-bearing premise

That the reaction at low energies and backward angles is localized enough to the nuclear exterior that interior contributions and higher-l admixtures remain negligible compared with the asymptotic s-wave tail.

What would settle it

A measurement in which the cross section for a known weakly bound s-wave state decreases rapidly with decreasing incident energy, or in which an l=1 state contributes comparably at backward angles, would falsify the claimed energy dependence and selectivity.

Figures

Figures reproduced from arXiv: 2604.27605 by Atsushi Tamii, Junki Tanaka, Shimpei Endo, Yuki Nakanishi.

**Figure 1.** Figure 1: (a) Density distributions for strongly and weakly view at source ↗

**Figure 2.** Figure 2: Angular distributions of differential cross sections for the (d, p) reaction at different incident energies and neutron separation energies. The upper panel shows the results at Ed = 40 MeV, while the lower panel corresponds to Ed = 5 MeV. The solid-red and dotted-blue curves correspond to transitions to weakly and strongly bound states, respectively. When the incident energy is reduced to 5 MeV, the cro… view at source ↗

**Figure 3.** Figure 3: Incident-energy dependence of the (d, p) reaction cross section at 180◦ . The solid-red and dotted-blue curves correspond to transitions to weakly and strongly bound states, respectively. 3. Incident-energy dependence of the reaction cross sections We next examine how the sensitivity to the asymptotic wave function manifests itself in the incident-energy dependence of the cross section view at source ↗

read the original abstract

We propose a method to probe weakly bound s-wave neutron components near the neutron emission threshold in heavy nuclei using Coulomb-assisted neutron transfer reactions. Weakly bound s-wave neutrons have large asymptotic amplitudes, which are difficult to access directly with conventional methods. This work focuses on the $(d,p)$ reaction at low incident energies and backward angles, where the reaction is localized in the nuclear exterior due to the Coulomb barrier. Under these conditions, the transition amplitude becomes sensitive to the asymptotic part of the single-particle wave function. Finite-range DWBA calculations show that the cross section for weakly bound states exhibits a weak dependence on incident energy, while that for strongly bound states decreases rapidly with decreasing energy. Contributions from orbitals with $l \geq 1$ are suppressed by the centrifugal barrier, resulting in selectivity for s-wave components. This method provides a probe of the strength distribution of weakly bound s-wave components near threshold and the asymptotic structure of their wave functions.

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.

Desk Editor's Note private letter to a colleague

This paper proposes low-energy backward-angle (d,p) kinematics to selectively probe asymptotic s-wave tails in heavy nuclei, but the DWBA evidence for clean exterior localization is thin on explicit checks.

read the letter

The main takeaway is that the authors suggest using low incident energies and backward angles in deuteron stripping on heavy targets to isolate weakly bound s-wave neutron components near threshold. The Coulomb barrier is meant to push the reaction into the nuclear exterior where the asymptotic tail dominates, while centrifugal barriers suppress l greater than or equal to 1 contributions. Finite-range DWBA runs are said to confirm that cross sections for weakly bound s-states stay relatively flat with decreasing energy, unlike strongly bound states that drop rapidly, giving a handle on the strength distribution of those tails. That combination of kinematics for near-threshold s-selectivity is not standard in the literature they cite, so the proposal adds a concrete experimental signature worth considering. The motivation for accessing asymptotic wave functions is laid out clearly and ties to relevant applications like astrophysical rates. The calculations follow conventional reaction theory without obvious internal contradictions. The soft spot is the localization claim itself. The abstract states that the DWBA demonstrates negligible interior and higher-l pieces, yet the description lacks radial integrand plots, zero-range versus finite-range comparisons, or partial-wave breakdowns that would show the interior contribution is truly under a few percent for the chosen potentials and deuteron wave function. If those contributions leak in more than assumed, the claimed selectivity weakens. This is for nuclear reaction and structure groups working on weakly bound or neutron-rich systems. Readers who model or measure transfer reactions could pick up the proposed energy and angle dependence as a test. It deserves peer review because the idea is specific, the framework is standard, and experts can check the missing details or suggest data comparisons. Send it to referees familiar with DWBA for heavy nuclei.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a method to probe weakly bound s-wave neutron components near the neutron emission threshold in heavy nuclei via the (d,p) reaction at low incident energies and backward angles. The central claim is that the Coulomb barrier localizes the reaction to the nuclear exterior, rendering the transition amplitude sensitive to the asymptotic tail of the single-particle wave function. Finite-range DWBA calculations are invoked to show that the cross section for weakly bound s-wave states has weak incident-energy dependence, while strongly bound states decrease rapidly with decreasing energy, and that l ≥ 1 contributions are suppressed by the centrifugal barrier, yielding s-wave selectivity. The method is positioned as a probe of near-threshold strength distributions and asymptotic wave-function structure.

Significance. If the localization and resulting selectivity are confirmed, the proposal could provide a useful new experimental handle on the asymptotic normalization and strength of near-threshold s-wave components in heavy nuclei, complementing existing transfer and breakup techniques. Credit is due for employing finite-range DWBA rather than zero-range approximations, which is the appropriate level of reaction theory for assessing asymptotic sensitivity. The approach has no free parameters introduced by the authors themselves and rests on standard optical-model inputs, which is a methodological strength. However, the overall significance remains provisional until the key numerical evidence for exterior dominance is supplied.

major comments (2)

[DWBA calculations] The central claim rests on the assertion (Abstract) that finite-range DWBA calculations demonstrate localization to the nuclear exterior with negligible interior and l ≥ 1 contributions. No radial integrand plots, partial-wave decompositions, or quantitative interior/exterior contribution percentages are reported for the chosen optical potentials and deuteron wave function. This verification is load-bearing; without it the claimed energy dependence and l-selectivity cannot be evaluated.
The weakest assumption—that the (d,p) reaction at low E and backward angles is localized by the Coulomb barrier so that the transition amplitude is dominated by the asymptotic tail (r ≫ R_nucleus)—is stated but not numerically demonstrated. Explicit comparisons (e.g., full vs. truncated radial integrals or zero-range vs. finite-range results) are required to substantiate that interior contributions remain below a few percent across the relevant binding energies.

minor comments (2)

A figure or table quantifying the cross-section energy dependence for representative weakly bound s-wave, strongly bound, and l=1 cases would make the selectivity claims concrete and allow readers to judge the magnitude of the reported weak vs. rapid dependence.
The abstract and title introduce 'Coulomb-assisted neutron transfer' without referencing prior literature on low-energy transfer or Coulomb-barrier localization effects; adding one or two key citations would clarify the novelty relative to existing work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review, which correctly identifies the need for explicit numerical support of the localization and selectivity claims. We agree that these verifications are essential and will incorporate the requested analyses in the revised manuscript.

read point-by-point responses

Referee: [DWBA calculations] The central claim rests on the assertion (Abstract) that finite-range DWBA calculations demonstrate localization to the nuclear exterior with negligible interior and l ≥ 1 contributions. No radial integrand plots, partial-wave decompositions, or quantitative interior/exterior contribution percentages are reported for the chosen optical potentials and deuteron wave function. This verification is load-bearing; without it the claimed energy dependence and l-selectivity cannot be evaluated.

Authors: We agree that the manuscript would benefit from explicit verification. In the revised version we will add radial integrand plots for representative binding energies and angular momenta at the proposed low energies and backward angles. These will be accompanied by partial-wave decompositions and quantitative breakdowns (interior versus exterior contributions obtained by truncating the radial integral at the nuclear radius plus a few fm). The new figures will demonstrate that, for weakly bound s-wave states, the integrand is overwhelmingly exterior while interior and l ≥ 1 contributions remain small, thereby supporting the reported energy dependence and selectivity. revision: yes
Referee: [—] The weakest assumption—that the (d,p) reaction at low E and backward angles is localized by the Coulomb barrier so that the transition amplitude is dominated by the asymptotic tail (r ≫ R_nucleus)—is stated but not numerically demonstrated. Explicit comparisons (e.g., full vs. truncated radial integrals or zero-range vs. finite-range results) are required to substantiate that interior contributions remain below a few percent across the relevant binding energies.

Authors: We acknowledge that direct numerical evidence for the dominance of the asymptotic tail was not supplied. The revised manuscript will include explicit comparisons of full versus truncated radial integrals (truncation at r = R_nucleus + 3 fm) for the same optical potentials and deuteron wave function used in the original calculations. These will show that, for weakly bound s-wave states, the truncated cross section differs by only a few percent from the full result, while the difference is substantially larger for strongly bound states. We will also present finite-range versus zero-range comparisons to illustrate the enhanced asymptotic sensitivity of the finite-range treatment under the proposed kinematics. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper proposes using low-energy backward-angle (d,p) reactions to probe asymptotic s-wave neutron components, with the central support coming from finite-range DWBA calculations that exhibit weak energy dependence for weakly bound states and rapid suppression for strongly bound or higher-l states. These results are presented as outcomes of applying established DWBA formalism under the stated kinematic conditions rather than as predictions derived from the paper's own fitted parameters or self-referential definitions. No equations, self-citations, or ansatzes are quoted that would reduce the selectivity claim to an input by construction. The localization due to the Coulomb barrier is invoked as a standard feature of the reaction mechanism, not as a result that loops back to the paper's inputs. The derivation chain is therefore self-contained against external benchmarks in nuclear reaction theory.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on established assumptions from nuclear reaction theory without introducing new free parameters or postulated entities. The proposal depends on the validity of standard DWBA and barrier-localization assumptions in the context of heavy nuclei.

axioms (3)

domain assumption Distorted-wave Born approximation (DWBA) is valid for describing the (d,p) reaction under the proposed low-energy, backward-angle conditions.
The paper relies on finite-range DWBA calculations to demonstrate the selectivity and energy dependence.
domain assumption The Coulomb barrier localizes the reaction to the nuclear exterior at low incident energies and backward angles.
This is the key assumption enabling sensitivity to the asymptotic wave function.
domain assumption Centrifugal barrier suppresses contributions from l ≥ 1 orbitals.
Invoked to explain the resulting s-wave selectivity.

pith-pipeline@v0.9.0 · 5474 in / 1723 out tokens · 92394 ms · 2026-05-07T06:41:35.186677+00:00 · methodology

discussion (0)

Reference graph

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