Electric dipole polarizability in neutron-rich Sn isotopes as a probe of nuclear isovector properties

Z. Z. Li (李征征), Y. F. Niu (牛一斐), and W. H. Long (龙文辉)

Phys. Rev. C 103, 064301 – Published 3 June 2021

Abstract

The determination of nuclear symmetry energy and, in particular, its density dependence is a long-standing problem for the nuclear physics community. Previous studies have found that the product of electric dipole polarizability $α_{D}$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$ , the slope parameter of symmetry energy. However, the current uncertainty of $J$ hinders the precise constraint on $L$ . We investigate the correlations between electric dipole polarizability $α_{D}$ (or times symmetry energy at saturation density $J$ ) in Sn isotopes and the slope parameter of symmetry energy $L$ using the quasiparticle random-phase approximation based on the Skyrme Hartree-Fock-Bogoliubov model. A strong linear correlation between $α_{D}$ and $L$ is found in neutron-rich Sn isotopes where pygmy dipole resonance (PDR) gives a considerable contribution to $α_{D}$ , attributed to the pairing correlations playing important roles through PDR. This newly discovered linear correlation would help one to constrain $L$ and neutron-skin thickness $Δ R_{n} p$ stiffly if $α_{D}$ is measured with high resolution in neutron-rich nuclei. Additionally, a linear correlation between $α_{D} J$ in a nucleus around the $β$ -stability line and $α_{D}$ in a neutron-rich nucleus can be used to assess $α_{D}$ in neutron-rich nuclei.

Received 4 March 2021
Revised 25 April 2021
Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevC.103.064301

Physics Subject Headings (PhySH)

Nuclear structure & decays Photonuclear reactions Polarization phenomena Symmetry energy

90 ≤ A ≤ 149

Nuclear density functional theory

Nuclear Physics

Authors & Affiliations

Z. Z. Li (李征征), Y. F. Niu (牛一斐)^*, and W. H. Long (龙文辉)

School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China

^*niuyf@lzu.edu.cn

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Issue

Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
Plots for dipole polarizability $α_{D}$ against slope parameter of symmetry energy $L$ in Sn isotopes calculated by QRPA based on HFB with 24 Skyrme density functionals: SIII, SIV, SV, SVI (blue up triangles); SLy230a, SLy230b, SLy4, SLy5, SLy8 (red circles); SAMi, SAMi-J30, SAMi-J31, SAMi-J32, SAMi-J33 (green diamonds); SGI, SGII, SkM, SkM*, Ska (black squares); MSk1, MSk2, MSk7, BSk1, BSk2 (navy blue down triangles). A regression line (red solid line) is obtained by a least-square linear fit of the calculated $α_{D}$ as a function of $L$ . $r$ is Pearson coefficient and $k$ ( ${fm}^{3} / MeV$ ) is the slope of the regression line.
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Figure 2
The same as Fig. 1 but for ${}^{120, 140, 150, 160}{Sn}$ without the pairing correlations.
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Figure 3
The dipole polarizabilities as functions of mass number $A$ in even-even Sn isotopes calculated by QRPA (square line) and RPA (circle line) using Skyrme functional SLy4. The total dipole polarizabilities (red) and the contributions from PDR (blue) are shown, respectively.
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Figure 4
Plots for dipole polarizability contributed by PDR against slope parameter of symmetry energy in ${}^{134, 140, 150, 160}{Sn}$ isotopes calculated by QRPA based on HFB with 24 Skyrme density functionals: SIII, SIV, SV, SVI (blue up triangles); SLy230a, SLy230b, SLy4, SLy5, SLy8 (red circles); SAMi, SAMi-J30, SAMi-J31, SAMi-J32, SAMi-J33 (green diamonds); SGI, SGII, SkM, SkM*, Ska (black squares); MSk1, MSk2, MSk7, BSk1, BSk2 (navy blue down triangles). A linear fit is done for each nucleus (red solid line) with a corresponding Pearson coefficient $r$ .
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Figure 5
Plots for neutron-skin thickness $Δ R_{n} p$ against dipole polarizability $α_{D}$ in ${}^{150, 160}{Sn}$ calculated by QRPA based on HFB with 24 Skyrme density functionals: SIII, SIV, SV, SVI (blue up triangles); SLy230a, SLy230b, SLy4, SLy5, SLy8 (red circles); SAMi, SAMi-J30, SAMi-J31, SAMi-J32, SAMi-J33 (green diamonds); SGI, SGII, SkM, SkM*, Ska (black squares); MSk1, MSk2, MSk7, BSk1, BSk2 (navy blue down triangles). A regression line (red solid line) is obtained by a least-square linear fit of the calculated $Δ R_{n} p$ as a function of $α_{D}$ . $r$ is Pearson coefficient and $k$ ( ${fm}^{- 2}$ ) is the slope of regression line.
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Figure 6
The dipole polarizability $α_{D}$ (a) in ${}^{208}{Pb}$ and (b) in ${}^{160}{Sn}$ as a function of the dipole polarizability in ${}^{150}{Sn}$ . The dipole polarizability $α_{D}$ (c) in ${}^{208}{Pb}$ and (d) in ${}^{124}{Sn}$ times the symmetry energy at saturation density $J$ as a function of the dipole polarizability in ${}^{150}{Sn}$ . Calculations are done by QRPA based on HFB with 24 Skyrme density functionals: SIII, SIV, SV, SVI (blue up triangles); SLy230a, SLy230b, SLy4, SLy5, SLy8 (red circles); SAMi, SAMi-J30, SAMi-J31, SAMi-J32, SAMi-J33 (green diamonds); SGI, SGII, SkM, SkM*, Ska (black squares); MSk1, MSk2, MSk7, BSk1, BSk2 (navy blue down triangles). $r$ is the Pearson coefficient. Utilizing the experimental values of $α_{D}$ in ${}^{208}{Pb}$ [30, 34] and in ${}^{124}{Sn}$ [36], and assuming $J = 31.7 \pm 3.2$ MeV [2], the dipole polarizability of ${}^{150}{Sn}$ is predicted to be between 14.18 and 16.27 ${fm}^{3}$ .
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