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基于相对论平均场理论(RMF), 采用TM1以及有效超子−核子和超子−超子相互作用, 首先研究了16O和
$^{18}_{\Lambda\Lambda}{\rm{O}}$ 的单粒子能级受超子的影响情况, 发现超子的加入使得核子能级能量降低. 其次基于相对论无规位相近似方法(RRPA), 自洽地计算了16O和$^{18}_{\Lambda\Lambda}{\rm{O}}$ 同位旋标量巨单极和四极共振态. 发现相比于16O各巨共振的响应函数, 超核的响应函数会发生改变. 研究表明: 这种改变主要来自于超子的加入导致的核子单粒子能级的改变, 以及超子粒子−空穴组态跃迁的贡献, 而超子−超子剩余相互作用对单极和四极共振在低能区的响应函数的影响比较小, 特别对高能区的响应函数基本没有影响.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.[1] Danysz M, Pniewski J 1953 Lond. Edinb. Dublin Philos. Mag. 44 348
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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
Fig. 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.
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
Fig. 2. Response functions of isoscalar monopole resonance for 16O and $^{18}_{\Lambda\Lambda}{\rm{O}}$: (a) Hartree response; (b) RRPA response.
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
Fig. 3. Response functions of isoscalar quadrupole resonance for 16O and $^{18}_{\Lambda\Lambda}{\rm{O}}$: (a) Hartree response; (b) RRPA response.
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 mσ mω mρ mσ mω mρ 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 
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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
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[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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