Isoscalar giant resonances of <inline-formula><tex-math id="M1">\begin{document}$^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.png"/></alternatives></inline-formula> in relativistic approach

Wen Jing; Sun Shuai; Cao Li-Gang; Zhang Feng-Shou

doi:10.7498/aps.73.20231531

Abstract

The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play an important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon interaction and the hyperon-hyperon interaction have been mainly investigated experimentally by $\gamma$ spectroscopy of single-$\Lambda$ hypernuclei or double-$\Lambda$ hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. Most of these models focus mostly on the ground state properties of hypernuclei, and have given exciting results in producing the banding energy, the energy of single-particle levels, deformations, and other properties of hypernuclei. Only a few researches adopting Skyrme energy density functionals is devoted to the study of the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and use the methods to study the isoscalar collective excited state properties of double $\Lambda$ hypernuclei. First, the effect of $\Lambda$ hyperons on the single-particle energy of ¹⁶O and $^{18}_{\Lambda\Lambda}{\rm{O}}$ are discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon interaction, and hyperon-hyperon interaction. We find that it gives a larger attractive effect on the ${{\mathrm{s}}}_{1/2}$ state of proton and neutron, while gives a weaker attractive effect on the state around Fermi surface. The self-consistent relativistic random phase approximation is used to study the collectively excited state properties of hypernucleus $^{18}_{\Lambda\Lambda}{\rm{O}}$. The isoscalar giant monopole resonance and quadrupole resonance are calculated and analysed in detail, we pay more attention to the effect of the inclusion of $\Lambda$ hyperons on the properties of giant resonances. Comparing with the strength distributions of ¹⁶O, changes of response function of $^{18}_{\Lambda\Lambda}{\rm{O}}$ are evidently found both on the isoscalar giant monopole resonance and quadrupole resonance. It is shown that the difference comes mainly from the change of Hartree energy of particle-hole configuration and the contribution of the excitations of $\Lambda$ hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole resonance function and quadrupole response function in the low-energy region, and have almost no effect on the response functions in the high-energy region.

Keywords:

Authors and contacts

1.
Key Laboratory of Beam Technology of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
2.
Institute of Radiation Technology, Beijing Academy of Science and Technology, Beijing 100875, China
3.
Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China

Corresponding author: Cao Li-Gang, caolg@bnu.edu.cn ; Zhang Feng-Shou, fszhang@bnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12275025, 11975096, 12135004, 11635003, 11961141004) and the Fundamental Research Fund for the Central Universities, China (Grant No. 2020NTST06).

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References

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[52]	Vretenar D, Afanasjev A, Lalazissis G A, Ring P 2005 Phys. Rep. 409 101 Google Scholar
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[61]	Xu X D, Zhang S S, Signoracci A J, Smith M S, Li Z P 2015 Phys. Rev. C 92 024324 Google Scholar
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Cited By

图 1 中子、质子和超子的单粒子能级. 黑色实线为¹⁶O的单粒子能级, 红色虚线为$^{18}_{\Lambda\Lambda}{\rm{O}}$的核子和超子单粒子能级

Figure 1. Single-particle energies of neutrons, protons, and Lambda hyperons. Energy levels of ¹⁶O are denoted by black solid lines while those of $^{18}_{\Lambda\Lambda}{\rm{O}}$ are denoted by red dashed lines.

DownLoad: Full-Size Img PowerPoint

图 2 ¹⁶O和$^{18}_{\Lambda\Lambda}{\rm{O}}$同位旋标量巨单极共振响应函数　(a) Hartree响应函数; (b) RRPA响应函数

Figure 2. Response functions of isoscalar monopole resonance for ¹⁶O and $^{18}_{\Lambda\Lambda}{\rm{O}}$: (a) Hartree response; (b) RRPA response.

DownLoad: Full-Size Img PowerPoint

图 3 ¹⁶O和$^{18}_{\Lambda\Lambda}{\rm{O}}$的同位旋标量巨四极共振响应函数　(a) Hartree响应函数; (b) RRPA响应函数

Figure 3. Response functions of isoscalar quadrupole resonance for ¹⁶O and $^{18}_{\Lambda\Lambda}{\rm{O}}$: (a) Hartree response; (b) RRPA response.

DownLoad: Full-Size Img PowerPoint

表 1 TM1参数, 核子以及介子质量的单位为MeV

Table 1. Parameter sets TM1, and the masses of nucleons and mesons are given in MeV

	M	m_σ	m_ω	m_ρ	m_σ	m_ω	m_ρ	g₂/fm^–1	g₃	c₃
TM1	938.0	511.2	783.0	770.0	10.029	12.614	4.632	–7.233	0.618	71.307

DownLoad: CSV

表 2 使用相对论平均场模型计算得到的$^{16}$O和$^{18}_{\Lambda\Lambda}$O中质子、中子的单粒子能级($\varepsilon$), $\Delta \varepsilon$表示普通核与超核之间的相应能级差 (单位为MeV)

Table 2. Single-particle energies of neutrons and protons in $^{16}$O and $^{18}_{\Lambda\Lambda}$O, the results are obtained by using the RMF model. $\Delta \varepsilon$ is the difference of corresponding level in normal nucleus and hypernucleus (unit in MeV).

		p			n
	$ \varepsilon $($^{16}{\rm O}$)	$ \varepsilon ({}^{18}_{\Lambda\Lambda}{\rm O})$)	$\Delta \varepsilon$	$ \varepsilon ({}^{16}{\rm O}$)	$ \varepsilon ({}^{18}_{\Lambda\Lambda}{\rm O}$)	$\Delta \varepsilon$
${\rm{1 s}}_{1/2}$	–36.55	–38.12	1.57	–40.72	–42.29	1.57
${\rm{1 p}}_{3/2}$	–17.75	–19.07	1.32	–21.66	–22.97	1.31
${\rm{1 p}}_{1/2}$	–12.14	–12.70	0.56	–15.99	–16.53	0.54
${\rm{1 d}}_{5/2}$	–1.20	–2.23	1.03	–4.67	–5.74	1.07
${\rm{2 s}}_{1/2}$	0.70	0.35	0.35	–2.12	–2.56	0.44

DownLoad: CSV

[1]	Danysz M, Pniewski J 1953 Lond. Edinb. Dublin Philos. Mag. 44 348 Google Scholar
[2]	Ma Y G 2013 J. Phys.: Conf. Ser. 420 012036 Google Scholar
[3]	Brinkmann K T, Gianotti P, Lehmann I 2006 Nucl. Phys. News 16 15 Google Scholar
[4]	Tamura H 2012 Prog. Theor. Exp. Phys. 2012 02B012
[5]	Yang J C, Xia J W, Xiao G Q, Xu H S, Zhao H W, Zhou X H, Ma X W, He Y, Ma L Z, Gao D Q, Meng J, Xu Z, Mao R S, Zhang W, Wang Y Y, Sun L T, Yuan Y J, Yuan P, Zhan W L, Shi J, Chai W P, Yin D Y, Li P, Li J, Mao L J, Zhang J Q, Sheng L N 2013 Nucl. Instrum. Methods Phys. Res., Sect. B 317 263 Google Scholar
[6]	Feng Z Q 2020 Phys. Rev. C 101 064601 Google Scholar
[7]	Feng Z Q 2020 Phys. Rev. C 101 014605 Google Scholar
[8]	Kohri H, Ajimura S, Hayakawa H, Kishimoto T, Matsuoka K, Minami S, Miyake, Mori T, Morikubo K, Saji E, Sakaguchi A, Shimizu Y, Sumihama M 2002 Phys. Rev. C 65 034607 Google Scholar
[9]	Rayet M 1981 Nucl. Phys. A 367 381 Google Scholar
[10]	Zhou X R, Schulze H J, Sagawa H, Wu C X, Zhao E G 2007 Phys. Rev. C 76 034312 Google Scholar
[11]	Yamamoto Y, Hiyama E, Rijken T 2010 Nucl. Phys. A 835 350 Google Scholar
[12]	Ma Z Y, Speth J, Krewald S, Chen B Q, Reuber A 1996 Nucl. Phys. A 608 305 Google Scholar
[13]	Xu R L, Wu C, Ren Z Z 2012 J. Phys. G: Nucl. Part. Phys. 39 085107 Google Scholar
[14]	Rong Y T, Tu Z H, Zhou S G 2021 Phys. Rev. C 104 054321 Google Scholar
[15]	Haidenbauer J, Meiβner U G, Nogga A 2020 Eur. Phys. J. A 56 91 Google Scholar
[16]	Nemura H, Akaishi Y, Suzuki Y 2002 Phys. Rev. Lett. 89 142504 Google Scholar
[17]	Hiyama E, Yamada T 2009 Prog. Part. Nucl. Phys. 63 339 Google Scholar
[18]	Isaka M, Yamamoto Y, Motoba T 2020 Phys. Rev. C 101 024301 Google Scholar
[19]	Wang Y N, Shen H 2010 Phys. Rev. C 81 025801 Google Scholar
[20]	Vidaña I, Polls A, Ramos A, Schulze H J 2001 Phys. Rev. C 64 044301 Google Scholar
[21]	Tan Y H, Zhong X H, Cai C H, Ning P Z 2004 Phys. Rev. C 70 054306 Google Scholar
[22]	Sun T T, Lu W L, Zhang S S 2017 Phys. Rev. C 96 044312 Google Scholar
[23]	Lu B N, Hiyama E, Sagawa H, Zhou S G 2014 Phys. Rev. C 89 044307 Google Scholar
[24]	Lu B N, Zhao E G, Zhou S G 2011 Phys. Rev. C 84 014328 Google Scholar
[25]	Song C Y, Yao J M, Meng J 2009 Chin. Phys. Lett. 26 122102 Google Scholar
[26]	Lu H F, Meng J, Zhang S Q, Zhou S G 2003 Eur. Phys. J. A 17 19 Google Scholar
[27]	Yao J M, Li Z P, Hagino K, Win M T, Zhang Y, Meng J 2011 Nucl. Phys. A 868-869 12 Google Scholar
[28]	Li A, Hiyama E, Zhou X R, Sagawa H 2013 Phys. Rev. C 87 014333 Google Scholar
[29]	Zhang Y, Sagawa H, Hiyama E 2021 Phys. Rev. C 103 034321 Google Scholar
[30]	Chen C F, Chen Q B, Zhou X R, Cheng Y Y, Cui J W, Schulze H J 2022 Chin. Phys. C 46 064109 Google Scholar
[31]	Mei H, Hagino K, Yao J M 2016 Phys. Rev. C 93 011301(R Google Scholar
[32]	Gaitanos T, Lenske H 2014 Phys. Lett. B 737 256 Google Scholar
[33]	Cheng H G, Feng Z Q 2022 Phys. Lett. B 824 136849 Google Scholar
[34]	Ring P, Ma Z Y, Van Giai N, Vretenar D, Wandelt A, Cao L G 2001 Nucl. Phys. A 694 249 Google Scholar
[35]	Ma Z Y, Wandelt A, Van Giai N, Vretenar D, Ring P, Cao L G 2002 Nucl. Phys. A 703 222 Google Scholar
[36]	Paar N, Ring R, Nikšić T, Vretenar D 2003 Phys. Rev. C 67 034312 Google Scholar
[37]	Niu Z M, Niu Y F, Liang H Z, Long W H, Meng J 2017 Phys. Rev. C 95 044301 Google Scholar
[38]	Wang Z H, Naito T, Liang H Z, Long W H 2020 Phys. Rev. C 101 064306 Google Scholar
[39]	Cao L G, Ma Z Y 2004 Mod. Phys. Lett. A 19 2845 Google Scholar
[40]	Kružić G, Oishi T, Vale D, Paar N 2020 Phys. Rev. C 102 044315 Google Scholar
[41]	Chang S Y, Wang Z H, Niu Y F, Long W H 2022 Phys. Rev. C 105 034330 Google Scholar
[42]	Yang D, Cao L G, Tian Y, Ma Z Y 2010 Phys. Rev. C 82 054305 Google Scholar
[43]	Roca-Maza X, Cao L G, Colo G, Sagawa H 2016 Phys. Rev. C 94 044313 Google Scholar
[44]	Cao L G, Roca-Maza X, Colo G, Sagawa H 2015 Phys. Rev. C 92 034308 Google Scholar
[45]	Colo G, Cao L G, Giai N V, Capelli L 2013 Comput. Phys. Commun. 184 142 Google Scholar
[46]	Cao L G, Sagawa H, Colo G 2011 Phys. Rev. C 83 034324 Google Scholar
[47]	Wen P W, Cao L G, Margueron J, Sagawa H 2014 Phys. Rev. C 89 044311 Google Scholar
[48]	Minato F, Hagino K 2012 Phys. Rev. C 85 024316 Google Scholar
[49]	Lü H, Zhang S S, Zhang Z H, Wu Y Q, Liu J, Cao L G 2018 Chin. Phys. Lett. 35 062102 Google Scholar
[50]	Serot B D, Walecka J D 1986 Advances in Nuclear Physics (Vol. 16) (New York-London: Plenum Press) pp77–105
[51]	Meng J, Toki H, Zhou S G, Zhang S Q, Long W H, Geng L S 2006 Prog. Part. Nucl. Phys. 57 470 Google Scholar
[52]	Vretenar D, Afanasjev A, Lalazissis G A, Ring P 2005 Phys. Rep. 409 101 Google Scholar
[53]	Geng L S, Toki H, Meng J 2005 Prog. Theor. Phys. 113 785 Google Scholar
[54]	Xia X W, Lim Y, Zhao P W, Liang H Z, Qu X Y, Chen Y, Liu H, Zhang L F, Zhang S Q, Kim Y, Meng J 2018 At. Data Nucl. Data Tables 121–122 1
[55]	Cao L G, Ma Z Y 2004 Eur. Phys. J. A 22 189 Google Scholar
[56]	An R, Jiang X, Cao L G, Zhang F S 2022 Phys. Rev. C 105 014325 Google Scholar
[57]	An R, Dong X X, Cao L G, Zhang F S 2023 Commun. Theor. Phys. 75 035301 Google Scholar
[58]	An R, Sun S, Cao L G, Zhang F S 2023 Nucl. Sci. Tech. 34 119 Google Scholar
[59]	Zhong S Y, Zhang S S, Sun X X, Smith M S 2022 Sci. China Phys. Mech. Astron. 65 262011 Google Scholar
[60]	Zhang S S, Sun B H, Zhou S G 2007 Chin. Phys. Lett. 24 1199 Google Scholar
[61]	Xu X D, Zhang S S, Signoracci A J, Smith M S, Li Z P 2015 Phys. Rev. C 92 024324 Google Scholar
[62]	Zhang Y, Luo Y X, Liu Q, Guo J Y 2023 Phys. Lett. B 838 137716 Google Scholar
[63]	Ma Z Y, Giai N V, Toki H, L’Huillier M 1997 Phys. Rev. C 55 2385 Google Scholar
[64]	Sugahara Y, Toki H 1994 Nucl. Phys. A 579 557 Google Scholar
[65]	Shen H, Yang F, Toki H 2006 Prog. Theor. Phys. 115 325 Google Scholar

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Isoscalar giant resonances of $^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$ in relativistic approach

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Corresponding author: Cao Li-Gang, caolg@bnu.edu.cn ; Zhang Feng-Shou, fszhang@bnu.edu.cn

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Isoscalar giant resonances of $^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$ in relativistic approach

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Corresponding author: Cao Li-Gang, caolg@bnu.edu.cn ; Zhang Feng-Shou, fszhang@bnu.edu.cn

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