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First Extraction of the Matter Radius of $^{132}$Sn via Proton Elastic Scattering at 200 MeV/Nucleon

Y. Hijikata, J. Zenihiro, S. Terashima, Y. Matsuda, H. Sakaguchi, P. Arthuis, T. Miyagi, S. Ota, H. Baba, S. Chebotaryov, M. Dozono, T. Furuno, T. Harada, C. Iwamoto, T. Kawabata, M. Kobayashi, A. J. Krasznahorkay, S. Leblond, T. Lokotko, Y. Maeda, S. Masuoka, M. Matsushita, S. Michimasa, E. Milman, T. Murakami, H. Nasu, J. Okamoto, S. Sakaguchi, M. Takaki, K. Taniue, H. Tokieda, M. Tsumura, O. Wieland, Y. Yamaguchi, Z. H. Yang, R. Yokoyama, T. Uesaka

TL;DR

This work reports the first extraction of the matter radius of $^{132}$Sn from proton elastic scattering at $196$–$210$ MeV/nucleon, spanning momentum transfers $0.80$–$2.1$ fm$^{-1}$. Using a medium-modified relativistic impulse approximation and densities constrained by the ISOLDE charge radius, the authors obtain a matter radius of $\langle r_m^2\rangle^{1/2}=4.758^{+0.023}_{-0.024}$ fm. When compared with ab initio IMSRG densities based on chiral NN+3N interactions, the Delta NNLO GO result provides the best agreement, but no theory simultaneously matches both the matter and charge radii, implying a small neutron skin and a relatively soft symmetry-energy EOS. The findings highlight the ongoing challenge of validating nuclear forces in heavy, neutron-rich systems and motivate further refinement of many-body calculations to exploit absolute radii as stringent tests of the nuclear interaction.

Abstract

The angular distribution of the differential cross sections for proton elastic scattering from $^{132}$Sn at 196-210 MeV/nucleon was successfully measured over a momentum transfer range of 0.80 to 2.1 fm$^{-1}$. Using a relativistic impulse approximation, the root-mean-square matter radius of $^{132}$Sn was extracted to be $4.758^{+0.023}_{-0.024}$ fm, which was compared with the state-of-the-art ab initio calculations. Combined with the charge radius measured at ISOLDE, there are no theoretical calculations consistent with both matter and charge radii within the experimental errors.

First Extraction of the Matter Radius of $^{132}$Sn via Proton Elastic Scattering at 200 MeV/Nucleon

TL;DR

This work reports the first extraction of the matter radius of Sn from proton elastic scattering at – MeV/nucleon, spanning momentum transfers – fm. Using a medium-modified relativistic impulse approximation and densities constrained by the ISOLDE charge radius, the authors obtain a matter radius of fm. When compared with ab initio IMSRG densities based on chiral NN+3N interactions, the Delta NNLO GO result provides the best agreement, but no theory simultaneously matches both the matter and charge radii, implying a small neutron skin and a relatively soft symmetry-energy EOS. The findings highlight the ongoing challenge of validating nuclear forces in heavy, neutron-rich systems and motivate further refinement of many-body calculations to exploit absolute radii as stringent tests of the nuclear interaction.

Abstract

The angular distribution of the differential cross sections for proton elastic scattering from Sn at 196-210 MeV/nucleon was successfully measured over a momentum transfer range of 0.80 to 2.1 fm. Using a relativistic impulse approximation, the root-mean-square matter radius of Sn was extracted to be fm, which was compared with the state-of-the-art ab initio calculations. Combined with the charge radius measured at ISOLDE, there are no theoretical calculations consistent with both matter and charge radii within the experimental errors.
Paper Structure (6 sections, 5 equations, 8 figures, 3 tables)

This paper contains 6 sections, 5 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Experiment
  3. Reaction framework
  4. Extraction of Matter Radius
  5. Comparison with theories
  6. Summary and Outlook

Figures (8)

  • Figure 1: Schematic view of the beamline, detectors, and materials.
  • Figure 2: Top view of the setup around the SHT. The figure in the upper left shows a side view of the RPS.
  • Figure 3: Correlations between the angle and energy for recoil protons. The energies are measured by the NaI(Tl) scintillators (top panel) and the TOF (bottom panel), respectively. The black and red lines show the kinematical correlations of the elastic scattering and inelastic scattering to the first excited state (4.04 MeV).
  • Figure 4: Excitation energy spectra for $^{132}$Sn(p,p) scattering. The recoil proton energies are measured by the NaI(Tl) scintillators (top panel) and the TOF (bottom panel), respectively.
  • Figure 5: Differential cross sections $\mathrm{d}\sigma/\mathrm{d}\Omega$ for elastic scattering from $^{132}$Sn at 196--210 MeV/nucleon. The circles show the experimental result. The solid lines are the predictions by the GDOP (green), the MH-model with the DH density (blue), the mm-RIA with DH density (black), and the mm-RIA with the best-fit density (red).
  • ...and 3 more figures