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Isotopic analysis of 295 MeV proton scattering off $^{204,206,208}$Pb for improvement of neutron densities and radii
Nuclear Theory · Submitted 1 Jun 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The isotopic neutron radius difference between $^{206}$Pb and $^{208}$Pb was obtained as $D(r_n)=-0.012$ fm with an acceptable range of $D(r_n)=-0.03 \sim -0.006$ fm.
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The abstract, sentence by sentence
A new method of reaction analysis for proton elastic scattering is proposed, combining systematic analyses of nuclear structure and reactions in a series of isotopes. This method is applied to $^{204}$Pb$(p,p)$, $^{206}$Pb$(p,p)$, and $^{208}$Pb$(p,p)$ at $E_p=295$ MeV to obtain improved neutron densities and radii from experimental cross section data. The reaction calculation is performed according to the relativistic impulse approximation using the modified Murdock and Horowitz model with density-dependent effective $NN$ interaction. Analysis of Pb isotopes is performed using theoretical densities given by the relativistic Hartree-Bogoliubov and nonrelativistic Skyrme Hartree-Fock-Bogoliubov calculations and the experimental density extracted from the $(p,p)$ data at 295 MeV. The isotopic ratios ($R(\sigma)$) of the $^{A}$Pb$(p,p)$-to-$^{206}$Pb$(p,p)$ cross sections are analyzed in connection with the isotopic differences ($D(\rho_n)$ and $D(r_n)$) in neutron densities $(\rho_n(r))$ and radii $(r_n)$ between $^A$Pb and $^{208}$Pb. A hole-model analysis is performed, assuming $^{204}$Pb and $^{206}$Pb as a $^{208}$Pb core and neutron holes to clarify the one-to-one correspondence between isotopic structure properties such as $D(\rho_n)$ and $D(r_n)$ and the isotopic cross-section ratio. By fitting $R(\sigma)$, the values of $D(\rho_n)$ and $D(r_n)$ are extracted from the experimental $(p,p)$ cross section data with less uncertainty of the structure and reaction models. The isotopic neutron radius difference between $^{206}$Pb and $^{208}$Pb was obtained as $D(r_n)=-0.012$ fm with an acceptable range of $D(r_n)=-0.03 \sim -0.006$ fm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A new method of reaction analysis for proton elastic scattering is proposed, combining systematic analyses of nuclear structure and reactions in a series of isotopes. | contribution 0.93 | 0.77 | 0.04 | asserted 1.00 |
| s1 | This method is applied to $^{204}$Pb$(p,p)$, $^{206}$Pb$(p,p)$, and $^{208}$Pb$(p,p)$ at $E_p=295$ MeV to obtain improved neutron densities and radii from experimental cross section data. | contribution 0.82 | 0.95 | 0.10 | asserted 1.00 |
| s2 | The reaction calculation is performed according to the relativistic impulse approximation using the modified Murdock and Horowitz model with density-dependent effective $NN$ interaction. | method 1.00 | 0.81 | 0.02 | asserted 1.00 |
| s3 | Analysis of Pb isotopes is performed using theoretical densities given by the relativistic Hartree-Bogoliubov and nonrelativistic Skyrme Hartree-Fock-Bogoliubov calculations and the experimental density extracted from the $(p,p)$ data at 295 MeV. | method 0.98 | 0.80 | 0.03 | asserted 0.98 |
| s4 | The isotopic ratios ($R(\sigma)$) of the $^{A}$Pb$(p,p)$-to-$^{206}$Pb$(p,p)$ cross sections are analyzed in connection with the isotopic differences ($D(\rho_n)$ and $D(r_n)$) in neutron densities $(\rho_n(r))$ and radii $(r_n)$ between $^A$Pb and $^{208}$Pb. | method 0.94 | 0.91 | 0.05 | asserted 0.98 |
| s5 | A hole-model analysis is performed, assuming $^{204}$Pb and $^{206}$Pb as a $^{208}$Pb core and neutron holes to clarify the one-to-one correspondence between isotopic structure properties such as $D(\rho_n)$ and $D(r_n)$ and the isotopic cross-section ratio. | method 0.96 | 0.93 | 0.04 | asserted 0.97 |
| s6 | By fitting $R(\sigma)$, the values of $D(\rho_n)$ and $D(r_n)$ are extracted from the experimental $(p,p)$ cross section data with less uncertainty of the structure and reaction models. | method 0.80 | 0.95 | 0.14 | asserted 1.00 |
| s7 | The isotopic neutron radius difference between $^{206}$Pb and $^{208}$Pb was obtained as $D(r_n)=-0.012$ fm with an acceptable range of $D(r_n)=-0.03 \sim -0.006$ fm. | result 1.00 | 0.95 | 0.72 | asserted 1.00 |
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The paper
Original abstract
A new method of reaction analysis for proton elastic scattering is proposed, combining systematic analyses of nuclear structure and reactions in a series of isotopes. This method is applied to $^{204}$Pb$(p,p)$, $^{206}$Pb$(p,p)$, and $^{208}$Pb$(p,p)$ at $E_p=295$ MeV to obtain improved neutron densities and radii from experimental cross section data. The reaction calculation is performed according to the relativistic impulse approximation using the modified Murdock and Horowitz model with density-dependent effective $NN$ interaction. Analysis of Pb isotopes is performed using theoretical densities given by the relativistic Hartree-Bogoliubov and nonrelativistic Skyrme Hartree-Fock-Bogoliubov calculations and the experimental density extracted from the $(p,p)$ data at 295 MeV. The isotopic ratios ($R(\sigma)$) of the $^{A}$Pb$(p,p)$-to-$^{206}$Pb$(p,p)$ cross sections are analyzed in connection with the isotopic differences ($D(\rho_n)$ and $D(r_n)$) in neutron densities $(\rho_n(r))$ and radii $(r_n)$ between $^A$Pb and $^{208}$Pb. A hole-model analysis is performed, assuming $^{204}$Pb and $^{206}$Pb as a $^{208}$Pb core and neutron holes to clarify the one-to-one correspondence between isotopic structure properties such as $D(\rho_n)$ and $D(r_n)$ and the isotopic cross-section ratio. By fitting $R(\sigma)$, the values of $D(\rho_n)$ and $D(r_n)$ are extracted from the experimental $(p,p)$ cross section data with less uncertainty of the structure and reaction models. The isotopic neutron radius difference between $^{206}$Pb and $^{208}$Pb was obtained as $D(r_n)=-0.012$ fm with an acceptable range of $D(r_n)=-0.03 \sim -0.006$ fm.
Human review
References
How the literature uses it
3 arXiv papers cite this in 10 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 2 papers
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The nucleon–nucleus potentials were obtained by folding the vector and scalar densities of target nuclei obtained by the structure calculations as described in my previous papers [ref] .
Deformation effects on the surface neutron densities of stable S and Ni isotopes probed by proton elastic scattering via isotopic analysis · Calculations of proton elastic scattering reactions · 0.85
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Using the theoretical densities, the Sn$(p,p)$ reactions were calculated with the RIA+ddMH model in the same way as in a previous study [ref] .
Neutron $3s_{1/2}$ occupation change across the stable tin isotopes investigated using isotopic analysis of proton scattering at 295 MeV · Introduction · 0.87
What it cites · 13 sentences without a confident label
Uses the method or tool of 3 papers
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The theoretical densities of Pb isotopes, which are used as inputs for nucleon-nucleus folding potentials in Pb$(p,p)$ calculations, are obtained via the RHB and SHFB calculations of spherical nuclei using the computational codes named DIRHB [ref] and HFBRAD [ref] , respectively.
DIRHB -- a relativistic self-consistent mean-field framework for atomic nuclei · Target densities · 1.00
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The theoretical densities of Pb isotopes, which are used as inputs for nucleon-nucleus folding potentials in Pb$(p,p)$ calculations, are obtained via the RHB and SHFB calculations of spherical nuclei using the computational codes named DIRHB [ref] and HFBRAD [ref] , respectively.
Coordinate-space solution of the Skyrme-Hartree-Fock-Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.0) · Target densities · 1.00
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For the former, the DD-ME2 [ref] and DD-PC1 [ref] interactions are used; in this paper, these are simply denoted by me2 and pc1, respectively.
Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies · Target densities · 0.95
Cites as support 1 paper
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However, the $r_n$ values of the Pb isotopes determined by the $(p,p)$ data still contain significant experimental errors, mainly because of the large uncertainty of the extracted neutron density in the internal region, to which proton scattering at several hundreds of MeV is insensitive [ref] .
Insensitivity of the elastic proton-nucleus reaction to the neutron radius of 208Pb · Introduction · 0.96
Cites as background 1 paper
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For electron elastic scattering, an isotopic analysis of the cross sections has been performed to discuss the isotopic difference in the charge radius [ref] ; however, its application is limited.
Theoretical study of elastic electron scattering off stable and exotic nuclei · Introduction · 0.81
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