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Electric dipole strength in $sd$-shell nuclei from small-angle proton scattering

R. W. Fearick, O. Le Noan, H. Matsubara, P. von Neumann-Cosel, K. Sieja, A. Tamii

TL;DR

This study probes the $E1$ dipole strength in light sd-shell nuclei by forward-angle inelastic proton scattering at 295 MeV, extracting $E1$ cross sections via a multipole decomposition and converting them to photoabsorption cross sections. It provides new data for $^{20}$Ne, $^{26}$Mg, and $^{36}$Ar, and tests both data-driven ANN predictions and large-scale configuration-interaction shell-model (CI-SM) calculations with a PSDPF interaction, including isovector $E1$ operators with effective charges. The CI-SM approach captures much of the observed fragmentation and gross cross-section features, but underestimates strength in several nuclei unless an implausible enhancement of the TRK sum rule is assumed, highlighting mass-dependent deficiencies and the need for refined modeling of strength, especially above 20 MeV. The results underscore the viability of CI-SM for predicting $E1$ strength in light nuclei and motivate its use in large-scale reaction networks for understanding ultrahigh-energy cosmic ray mass composition, as pursued in the PANDORA framework.

Abstract

The present work reports new total photoabsorption cross sections for the $N=Z$ nuclei in the $sd$-shell $^{20}$Ne, $^{24}$Mg, $^{28}$Si, $^{32}$S, $^{36}$Ar, and for $^{26}$Mg. The results are compared to predictions of a data-driven artificial neural network application and to configuration-interaction shell-model calculations covering the excitation energy region of the isovector giant dipole resonance. Double-differential cross sections of the $(p,p^\prime)$ reaction at 295 MeV have been measured between $0^\circ$ and $14^\circ$. The angular distributions of the $E1$ parts due to Coulomb excitation have been extracted with a multipole decomposition analysis for excitation energies 12 to 24 MeV and converted to equivalent photoabsorption cross sections with the virtual photon method. Reasonable agreement of the photoabsorption cross sections with previous experiments is found for $^{24}$Mg and $^{28}$Si, while the present results diverge for $^{32}$S. For the first time, data are presented for $^{20}$Ne, $^{26}$Mg and $^{36}$Ar. Configuration-interaction shell-model calculations provide an overall satisfactory description of the fragmented $E1$ strength distributions. The same holds for absolute cross sections except for $^{26}$Mg and $^{36}$Ar, where the experimental results significantly exceed the expected exhaustion of the Thomas-Reiche-Kuhn energy-weighted sum rule. Fot light nuclei, there is a larger model dependence compared to previous analyses in heavy nuclei, in particular for excitation energies above 20 MeV, due to the need to constrain the continuum background with additional assumptions. The overall success of the shell-model approach to describe the features of the experimental photoabsorption cross sections motivates its application in large-scale reaction network calculations aiming at an understanding of the mass composition of ultrahigh-energy cosmic rays.

Electric dipole strength in $sd$-shell nuclei from small-angle proton scattering

TL;DR

This study probes the dipole strength in light sd-shell nuclei by forward-angle inelastic proton scattering at 295 MeV, extracting cross sections via a multipole decomposition and converting them to photoabsorption cross sections. It provides new data for Ne, Mg, and Ar, and tests both data-driven ANN predictions and large-scale configuration-interaction shell-model (CI-SM) calculations with a PSDPF interaction, including isovector operators with effective charges. The CI-SM approach captures much of the observed fragmentation and gross cross-section features, but underestimates strength in several nuclei unless an implausible enhancement of the TRK sum rule is assumed, highlighting mass-dependent deficiencies and the need for refined modeling of strength, especially above 20 MeV. The results underscore the viability of CI-SM for predicting strength in light nuclei and motivate its use in large-scale reaction networks for understanding ultrahigh-energy cosmic ray mass composition, as pursued in the PANDORA framework.

Abstract

The present work reports new total photoabsorption cross sections for the nuclei in the -shell Ne, Mg, Si, S, Ar, and for Mg. The results are compared to predictions of a data-driven artificial neural network application and to configuration-interaction shell-model calculations covering the excitation energy region of the isovector giant dipole resonance. Double-differential cross sections of the reaction at 295 MeV have been measured between and . The angular distributions of the parts due to Coulomb excitation have been extracted with a multipole decomposition analysis for excitation energies 12 to 24 MeV and converted to equivalent photoabsorption cross sections with the virtual photon method. Reasonable agreement of the photoabsorption cross sections with previous experiments is found for Mg and Si, while the present results diverge for S. For the first time, data are presented for Ne, Mg and Ar. Configuration-interaction shell-model calculations provide an overall satisfactory description of the fragmented strength distributions. The same holds for absolute cross sections except for Mg and Ar, where the experimental results significantly exceed the expected exhaustion of the Thomas-Reiche-Kuhn energy-weighted sum rule. Fot light nuclei, there is a larger model dependence compared to previous analyses in heavy nuclei, in particular for excitation energies above 20 MeV, due to the need to constrain the continuum background with additional assumptions. The overall success of the shell-model approach to describe the features of the experimental photoabsorption cross sections motivates its application in large-scale reaction network calculations aiming at an understanding of the mass composition of ultrahigh-energy cosmic rays.
Paper Structure (12 sections, 7 equations, 6 figures, 2 tables)

This paper contains 12 sections, 7 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Experiment and data analysis
  3. Details of the experiment at RCNP
  4. Multipole decomposition analysis
  5. Extraction of electric dipole strength
  6. Results
  7. Comparison to previous work
  8. Comparison to ANN predictions
  9. Comparison to shell-model calculations
  10. Details of the shell-model approach
  11. Discussion
  12. Conclusions

Figures (6)

  • Figure 1: Differential cross sections for inelastic scattering of 295 MeV protons for various $sd$-shell nuclei in the energy region of the IVGDR. Spectra are shown for laboratory scattering angles of $0.40^\circ$, $1.74^\circ$, $2.38^\circ$, and $6.20^\circ$.
  • Figure 2: Comparison of $E1$ excitation cross section for an excitation energy of 18 MeV as calculated by DWUCK4 (blue) and from microscopic calculations for $^{40}$Ca (orange) and $^{48}$Ca, scaled to $^{40}$Ca kinematics (green).
  • Figure 3: Results of the multipole decomposition of the cross section for the spectra measured at a laboratory scattering angle of $0.4^\circ$. The blue region shows the contribution from $E1$, the orange region the contribution from $E2$, and the magenta region the contribution from quasifree scattering. $E3$ is negligible.
  • Figure 4: Photoabsorption cross sections obtained from the $E1$$(p,p^\prime)$ cross sections using the virtual photon method. The blue histograms show the data obtained in this experiment, while the points show previous results from the IAEA photon strength function database with the references given in the text.
  • Figure 5: Comparison of the present (histogram) and previous (data points) photoabsorption measurements for $^{20}$Ne, $^{24,26}$Mg, $^{28}$Si, $^{32}$S, and $^{36}$Ar with data-driven predictions of dipole strength functions based on ANN (red lines with shaded uncertainty band).
  • ...and 1 more figures