Mon·Aug 26, 2024Monday·August 26, 2024

1. 01*

   Refining the isovector component of the Woods-Saxon potential

   L. Xayavong🇰🇷 · Y. Lim🇰🇷 · N. A. Smirnova🇫🇷 · G. Nam🇰🇷

   We investigate the isovector component in the phenomenological mean field model of nuclei. Lane's isospin dependence, initially proposed for the nuclear optical potential, is reexamined within the context of bound states using the Woods-Saxon potential. We demonstrate that the original parametrization can be reexpressed in terms of parameters associated with the compound nucleus, enhancing its suitability for bound states. Comparisons with the conventional symmetry term are performed to assess how well each approach fits experimental data on single-particle/hole energies and reproduces charge-radius systematics. Our results indicate that Lane's formula provides better accuracy compared with the traditional approach to the nuclear potential. Additionally, we find that the isovector component of the nuclear potential favors a surface-peaked form factor, especially one described by the first derivative of the Fermi like function divided by the radial coordinate. This consideration is crucial for open-shell nuclei where Woods-Saxon eigenfunctions serve as a realistic basis for other many-body methods. Our findings also enable discrimination among various shell-model calculations of the isospin-symmetry breaking correction to superallowed $0^{+}\to 0^{+}$ nuclear $\beta$ decays [I.~S. Towner and J.~C. Hardy, Phys. Rev. C {\bf 77}, 025501 (2008)]. This disparity currently constitutes the main source of theoretical uncertainty in subsequent tests of the standard model.

   ↳ nucl-thnucl-ex0 citations
2. 02*

   Statistical uncertainty quantification for multireference covariant density functional theory

   X. Zhang🇨🇳 · C. C. Wang🇨🇳 · C. R. Ding🇨🇳 · J. M. Yao🇨🇳

   We present a theoretical framework to quantify statistical uncertainties in covariant density functional theory (CDFT) for both nuclear matter and finite nuclei, based on a relativistic point-coupling energy density functional (EDF). By sampling approximately one million parameter sets, with nine parameters varied around their values in the PC-PK1 functional, we construct a probability density function for nuclear matter properties. Incorporating empirical values of nuclear matter at saturation density and those of predictions from chiral nuclear forces, and measured $B(E2)$ values of finite nuclei, we infer posterior distributions for the model parameters within a Bayesian framework. These posterior distributions are then propagated to the low-lying states of finite nuclei using the newly developed subspace-projected (SP)-CDFT approach, in which the wave functions of target EDF parameter sets are expanded in a subspace spanned by low-lying states obtained from a set of training parameterizations. We find that the observables of low-lying states in deformed nuclei ${}^{150}$Nd and ${}^{150}$Sm are well reproduced once statistical uncertainties are taken into account. In contrast, those of near spherical nuclei ${}^{136}$Xe and ${}^{136}$Ba remain difficult to describe within the present framework, a limitation that is expected to be alleviated by extending the model space to include quasiparticle excitations.

   ↳ nucl-thnucl-exChinese Physics C, 2026·8 citations
3. 03*

   Spatial imaging of polarized deuterons at the Electron-Ion Collider

   Heikki Mäntysaari🇫🇮 · Farid Salazar🇺🇸 · Björn Schenke🇺🇸 · Chun Shen🇺🇸 · Wenbin Zhao🇺🇸

   We study diffractive vector meson production at small-$x$ in the collision of electrons and polarized deuterons $e+d^{\uparrow }$. We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-$x$ observables studied in this work will be accessible at the future Electron-Ion Collider.

   ↳ nucl-thhep-phnucl-exPLB(2024)·8 citations
4. 04*

   Vertex correction to nuclear matrix elements of double-$\beta$ decays

   Jun Terasaki🇨🇿

   The predicted neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay is the crucial phenomenon to prove the existence of the Majorana neutrino, which gives a foundation to leptogenesis to explain the matter prevalence of the universe. The nuclear matrix element (NME) of $0\nu \beta \beta$ decay is an important theoretical quantity to determine the effective neutrino mass and help the detector design for the next generation of the $0\nu \beta \beta$ decay search. Reliable calculation of this NME is a long-standing problem because of the diversity of the predicted values of the NME. The main reason for this difficulty is that the effective strength of the Gamow-Teller transition operator $g_A$ for this decay is unknown. I will show the lowest-order vertex corrections for the $0\nu \beta \beta$ and the $2\nu \beta \beta$ NME of ${}^{136}$Xe in the framework of the hybrid application of the quantum field theory to the leptons and the Rayleigh-Schrödinger perturbation to the nucleus. The unperturbed nuclear states are obtained by the quasiparticle random-phase approximation. These corrections reduce the $0\nu \beta \beta$ NME by 30%. The effective $g_A$ referring to this reduced NME is also obtained, and it is shown for the first time that the effective $g_A$ for the $0\nu \beta \beta$ NME is not quite different from that for the $2\nu \beta \beta$ NME; the difference is only 10%. This indicates the possibility that the phenomenological effective $g_A$ to reproduce the experimental half-life of the $2\nu \beta \beta$ decay can be approximately used for the calculation of the $0\nu \beta \beta$ NME.

   ↳ nucl-thhep-phnucl-exPoS(2025)·0 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.