Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The role of the surface energy in nuclear octupole excitations

Khlood Alharthi, Paul Stevenson

TL;DR

The paper investigates how the nuclear surface energy controls octupole vibrational modes in the doubly magic nucleus $^{208}$Pb using time-dependent density functional theory with Sky3d and a family of Skyrme SLy5sX interactions that vary the surface energy via $a_{surf}^{HF}$. Ground states are prepared by static HF, then an octupole boost $e^{i k r^3 Y_{30}}$ triggers real-time dynamics, from which the $3^-$ excitation energy $E_{3^-}$ is extracted through the Fourier transform of the time-dependent octupole moment. A strong positive linear correlation is found: $E_{3^-}=0.1506\,a_{surf}^{HF}+0.4812$, indicating that lower surface energy costs reduce the octupole energy, though the calculated values lie above the experimental $E_{3^-}$~2.614 MeV, highlighting systematic effects beyond surface energy. The result suggests that surface energy can be a constraint in Skyrme fits and that octupole excitations may provide a low-cost observable for tuning nuclear matter properties relevant to surface dynamics.

Abstract

Octupole excitations of atomic nuclei can be viewed as fluctuations around an equilibrium shape. These fluctuations in turn can be seen as probes of nuclear matter properties to the extent that the shape changes explore changes in compression, surface to volume ratio, or isospin overlap. In the present work we use a series of Skyrme interactions, which were fitted to provide a systematic range of surface energies, to explore the surface energy dependence of octupole excitations in $^{208}$Pb. We find a strong positive linear corelation between the surface energy of a Skyrme interaction and its prediction of the first $3^-$ octupole excitation energy.

The role of the surface energy in nuclear octupole excitations

TL;DR

The paper investigates how the nuclear surface energy controls octupole vibrational modes in the doubly magic nucleus Pb using time-dependent density functional theory with Sky3d and a family of Skyrme SLy5sX interactions that vary the surface energy via . Ground states are prepared by static HF, then an octupole boost triggers real-time dynamics, from which the excitation energy is extracted through the Fourier transform of the time-dependent octupole moment. A strong positive linear correlation is found: , indicating that lower surface energy costs reduce the octupole energy, though the calculated values lie above the experimental ~2.614 MeV, highlighting systematic effects beyond surface energy. The result suggests that surface energy can be a constraint in Skyrme fits and that octupole excitations may provide a low-cost observable for tuning nuclear matter properties relevant to surface dynamics.

Abstract

Octupole excitations of atomic nuclei can be viewed as fluctuations around an equilibrium shape. These fluctuations in turn can be seen as probes of nuclear matter properties to the extent that the shape changes explore changes in compression, surface to volume ratio, or isospin overlap. In the present work we use a series of Skyrme interactions, which were fitted to provide a systematic range of surface energies, to explore the surface energy dependence of octupole excitations in Pb. We find a strong positive linear corelation between the surface energy of a Skyrme interaction and its prediction of the first octupole excitation energy.
Paper Structure (4 sections, 5 equations, 2 figures, 1 table)

This paper contains 4 sections, 5 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results
  4. Discussion and Conclusion

Figures (2)

  • Figure 1: Correlation between the surface energy and the predicted octupole peak position for each Skyrme interaction in the SLy5s$X$ series.
  • Figure 2: Octupole strength in $^{208}$Pb for the forces SLy5s$X$ forces for $X=1..8$ in the region of the low-lying excited 3$^-$ state. Peak positions and strenghts are shown for all eight forces.