Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.20550

Prospects for modelling odd and odd-odd nuclei using energy density functionals

A. V. Afanasjev·B. Bally·M. Bender·J. Bonnard·J. Dobaczewski·M. Kortelainen·K. Nomura·S. Péru·N. Pillet·L. M. Robledo·R. Rodr\'ıguez-Guzmán·W. Ryssens·W. Younes
View original source ↗Read source document ↗Export metadata ↓

Abstract

About half of particle-bound nuclei have an odd number of nucleons. About one quarter more are odd-odd, meaning they have an odd number of neutrons and an odd number of protons. In this context, it is about time to shift the 70-odd-year focus of theories using nuclear energy density functionals (EDFs) away from the remaining one-quarter of even-even nuclei. This White Paper aims to present open, unresolved problems and promising research directions in nuclear EDFs that were discussed during the 2024 ESNT workshop in Saclay, France, on ``The microscopic modelling of odd-mass and odd-odd nuclei''.

Explore related subjects

nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. V. Afanasjev, B. Bally, M. Bender, J. Bonnard, J. Dobaczewski, M. Kortelainen, K. Nomura, S. Péru, N. Pillet, L. M. Robledo, R. Rodr\'ıguez-Guzmán, W. Ryssens, W. Younes. 2026-10-14. Prospects for modelling odd and odd-odd nuclei using energy density functionals. https://arxiv.org/abs/2610.20550

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Algebraic coefficients of fractional parentage for three particles in the oscillator Jacobi basis

We present a closed-form construction of the orbital coefficients of fractional parentage (CFP) of three identical particles in the translationally invariant harmonic oscillator (HO) Jacobi basis. These are usually obtained by numerically diagonalizing a permutation operator in every energy-angular-momentum block. We show this diagonalization is unnecessary. Dressing the class operator $P_{13} + P_{23}$ with the single unitary $W = H^1 Φ$ -- a fixed complexification followed by the HO bracket with mass parameter $d=1$ -- turns it into the label swap times an integer. Every CFP is then the single ket $|K_{i,s}\rangle = 2Q^s W^\dagger|i\rangle$ -- a 2-scaled, sign-decorated column of the $d=1$ bracket restricted to one $e_2$-parity of the labels -- whose norm, $1 + s\langle i | J | i \rangle$, is itself a single matrix element. The same $W$ carries label parity into swap symmetry, $W Q^s W^\dagger = R^s$, making the bookkeeping collapse. The eigenvalues are exact integers $\pm 2$ and $\pm 1$ labeling the $S(3)$ symmetry classes. The construction is uniform in $E$, $L$ and symmetry class, reducing CFP-specific work from $O(n^3)$ to $O(n^2)$ in block dimension. An eigensolver remains only inside the bracket engine supplying $H^1$, where all residual numerical error originates. We implement this on an SU(3)-basis bracket engine, checking all 1301 blocks up to $E=50$ (912 366 CFPs, largest block $2907 \times 2907$): the $S(3)$ class assignment is exact everywhere. The residual numerical error (entirely the bracket engine's) stays below $10^{-8}$ for $E \leq 35$, restoring to $\leq 10^{-22}$ via a quadruple-precision build beyond that. We further validate against independently generated antisymmetrization data of a production three-nucleon code, including the $^3$He ground-state energy.

nucl-th↗
arXiv2026

Inclusive breakup of three-body projectiles: A unified four-body framework for pair-detection and single-particle observables

Inclusive breakup measurements detect only part of a projectile while the remaining fragments interact with the target. For a projectile with three constituents, these measurements can probe correlations that are lost when the projectile is treated as two preformed clusters. I derive cross-section sum rules within the distorted-wave Born approximation for detecting either a pair or a single constituent, retaining the full three-body projectile wave function. For pair detection, the detected state is projected from this wave function. Comparing the resulting reaction source with its factorized limit tests, at the amplitude level, what the preformed-cluster approximation omits. For single-particle detection, both unobserved constituents can interact with the target, and their absorption includes a contribution mediated by target excitation that is absent from an independent-fragment description. The optical reduction recovers the Carlson-Frederico-Hussein absorption kernel [Phys. Lett. B \textbf{767}, 53 (2017)]; explicit coupling of the detected particle to target excitation adds further contributions. The ${}^6\mathrm{Li}=α+n+p$ example shows how neutron-proton states beyond the bound deuteron enter the reaction source. I give a route for calculating the single-particle spectrum using inelastic target transition form factors and three-body propagation.

nucl-th↗
arXiv2026

Binding energies in the $0^{-+}$ and $1^{--}$ fermion--antifermion channels from the ladder Bethe-Salpeter and Schrödinger equations

In this work, we calculate the binding energies of an equal-mass fermion--antifermion system in the $0^{-+}$ and $1^{--}$ channels from the ladder Bethe--Salpeter (BS) equation with scalar, pseudoscalar, and vector exchange. The results are compared with those of the Schrödinger equation with the corresponding leading static interaction in two regimes: pointlike massless exchange at weak coupling and finite-mass exchange with monopole form factors at stronger coupling. For the BS calculation, we use two independent numerical methods based on momentum-space integral equations and coordinate-space differential equations. The differential-equation method gives estimated relative binding-energy errors below $10^{-9}$ in both regimes. For massless vector exchange in Coulomb gauge, the numerical results are consistent with the uncrossed-ladder perturbative spectrum through the $O(mα^5)$ terms. The results for massless scalar exchange and vector exchange in Feynman gauge are consistent with the common Wick--Cutkosky expansion through order $mα^3$. For finite exchange masses, the differences from the leading static Schrödinger spectra at the same masses, couplings, and form factors depend strongly on the exchange and channel. Scalar exchange gives nearly degenerate channels with much weaker binding than the Schrödinger reference. In contrast, vector exchange with only the metric term retained gives stronger binding than the Schrödinger reference in $0^{-+}$ and weaker binding in $1^{--}$. Notably, retaining the full Proca numerator substantially increases the vector binding in both channels. Pseudoscalar exchange also supports bound states and favors $1^{--}$, although its leading static central interaction vanishes.

nucl-th↗