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High-order isospin-dependent surface tension contribution to the fourth-order symmetry energy of finite nuclei

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Title: High-order isospin-dependent surface tension contribution to the fourth-order symmetry energy of finite nuclei
Authors: Cai, Bao-Jun, Wang, Rui, Zhang, Zhen, Chen, Lie-Wen
Source: Phys. Rev. C 106, 044319 (2022)
Publication Year: 2022
Collection: Astrophysics
Nuclear Experiment
Nuclear Theory
Subject Terms: Nuclear Theory, Astrophysics - High Energy Astrophysical Phenomena, Nuclear Experiment
More Details: The relation between the fourth-order symmetry energy $E_{\rm{sym,4}}(\rho_0)$ of nuclear matter at saturation density $\rho_0$ and its counterpart $a_{\rm{sym,4}}(A)$ of finite nuclei in a semiempirical nuclear mass formula is revisited by considering the high-order isospin-dependent surface tension contribution to the latter. We derive the full expression of $a_{\rm{sym,4}}(A)$, which includes explicitly the high-order isospin-dependent surface tension effects, and find that the value of $E_{\rm{sym,4}}(\rho_0)$ cannot be extracted from the measured $a_{\rm{sym,4}}(A)$ before the high-order surface tension is well constrained. Our results imply that a large $a_{\rm{sym,4}}(A)$ value of several MeVs obtained from analyzing nuclear masses can nicely agree with the empirical constraint of $E_{\rm{sym,4}}(\rho_0)\lesssim 2$ MeV from mean-field models and does not necessarily lead to a large $E_{\rm{sym,4}}(\rho_0)$ value of $\approx 20$ MeV obtained previously without considering the high-order surface tension. Furthermore, we also give the expression for the sixth-order symmetry energy $a_{\rm{sym,6}}(A)$ of finite nuclei, which involves more nuclear matter bulk parameters and the higher-order isospin-dependent surface tension.
Comment: 7 pages, 2 figures. Minor corrections. Published version in PRC
Document Type: Working Paper
DOI: 10.1103/PhysRevC.106.044319
Access URL: http://arxiv.org/abs/2208.10438
Accession Number: edsarx.2208.10438
Database: arXiv
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  Data: High-order isospin-dependent surface tension contribution to the fourth-order symmetry energy of finite nuclei
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  Data: <searchLink fieldCode="AR" term="%22Cai%2C+Bao-Jun%22">Cai, Bao-Jun</searchLink><br /><searchLink fieldCode="AR" term="%22Wang%2C+Rui%22">Wang, Rui</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Zhen%22">Zhang, Zhen</searchLink><br /><searchLink fieldCode="AR" term="%22Chen%2C+Lie-Wen%22">Chen, Lie-Wen</searchLink>
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  Data: Phys. Rev. C 106, 044319 (2022)
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  Label: Publication Year
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  Data: 2022
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  Data: Astrophysics<br />Nuclear Experiment<br />Nuclear Theory
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– Name: Abstract
  Label: Description
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  Data: The relation between the fourth-order symmetry energy $E_{\rm{sym,4}}(\rho_0)$ of nuclear matter at saturation density $\rho_0$ and its counterpart $a_{\rm{sym,4}}(A)$ of finite nuclei in a semiempirical nuclear mass formula is revisited by considering the high-order isospin-dependent surface tension contribution to the latter. We derive the full expression of $a_{\rm{sym,4}}(A)$, which includes explicitly the high-order isospin-dependent surface tension effects, and find that the value of $E_{\rm{sym,4}}(\rho_0)$ cannot be extracted from the measured $a_{\rm{sym,4}}(A)$ before the high-order surface tension is well constrained. Our results imply that a large $a_{\rm{sym,4}}(A)$ value of several MeVs obtained from analyzing nuclear masses can nicely agree with the empirical constraint of $E_{\rm{sym,4}}(\rho_0)\lesssim 2$ MeV from mean-field models and does not necessarily lead to a large $E_{\rm{sym,4}}(\rho_0)$ value of $\approx 20$ MeV obtained previously without considering the high-order surface tension. Furthermore, we also give the expression for the sixth-order symmetry energy $a_{\rm{sym,6}}(A)$ of finite nuclei, which involves more nuclear matter bulk parameters and the higher-order isospin-dependent surface tension.<br />Comment: 7 pages, 2 figures. Minor corrections. Published version in PRC
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