Research on ground-state structure and neutron halo characteristics of <sup>29</sup>Ne using complex-momentum representation method

WANG Xinghao; LUO Yuxuan; LIU Quan

doi:10.7498/aps.74.20250768

Abstract

The neutron-rich nucleus ²⁹Ne, located in the $N = 20$ “island of inversion” challenges traditional shell-model predictions by exhibiting a ground-state valence neutron configuration primarily influenced by the $2{\mathrm{p}}_{3/2}$ orbital rather than the anticipated $1{\mathrm{f}}_{7/2}$ orbital. This study aims to reveal the mechanisms behind this shell inversion and explore the potential halo structure in ²⁹Ne, by using the interplay between weak binding, deformation, and low-$\ell$ orbital occupancy.The complex-momentum representation (CMR) method is used within a relativistic framework by integrating relativistic mean-field (RMF) theory with Woods-Saxon potentials to describe bound states, resonances, and continuum states. The model combines quadrupole deformation (β₂) to analyze single-particle energy evolution, orbital mixing, and radial density distribution. Key parameters are calibrated based on experimental data, including binding energy and neutron separation energy.The key results are presented below.1) Shell inversion: In the spherical limit ($\beta_2 = 0$), the $2{\mathrm{p}}_{1/2}$ and $2{\mathrm{p}}_{3/2}$ orbitals drop below the $1{\mathrm{f}}_{7/2}$ orbital, confirming the collapse of the $N = 20$ shell gap.2) Deformation-driven halo: For β₂ ≥ 0.58, the valence neutrons occupy 3/2[321] orbital (derived from 1f_7/2), but due to strong l-mixing, the p_3/2 component accounts for 68%. This orbital exhibits a diffuse radial density distribution, indicating a halo structure.3) Experimental consistency: The predicted ground-state spin-parity ($3/2^-$) and low separation energy (~1 MeV) align with measurements, supporting ²⁹Ne as a deformation-induced halo.From this study, some conclusions are obtained as shown below. The ²⁹Ne’s anomalous structure arises from the synergy of p-wave dominance and quadrupole deformation, which reduces centrifugal barriers and enhances spatial dispersion. The CMR method provides a unified description of bound and resonant states, offering new insights into the island of inversion and halo formation. Future work will include pairing correlations and experimental validation of density distributions.This work advances the understanding of exotic nuclear structures near drip lines and highlights the role of deformation in halo phenomena, which is of great significance for future experiments detecting neutron-rich nuclei.

Keywords:

island of inversion /
halo nucleus /
complex momentum representation method /
single particle energy level

Authors and contacts

1.
School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
2.
School of Electronic Information Engineering, Hefei Institute of Technology, Heifei 238076, China

Corresponding author: LIU Quan, quanliu@ahu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12475116) and the Leading Talent Team Project of Anhui Province, China (Grant No. Z010118169).

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References

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Cited By

图 1 复动量平面上$ \varOmega^\pi = 1/2^- $态在$ \beta_2 = 0.2 $时的单粒子谱图. 红色空心圆形、蓝色空心方形、绿色空心菱形和棕色空心三角分别代表从4条不同积分路径上分离出的共振态

Figure 1. Single-particle spectrum of $ \varOmega^\pi = 1/2^- $ states in the complex momentum plane at $ \beta_2 = 0.2 $. The red hollow circles, blue hollow squares, green hollow diamonds, and brown hollow triangles represent resonance states extracted from four different integration paths, respectively.

DownLoad: Full-Size Img PowerPoint

图 2 ²⁹Ne自旋宇称$ \varOmega^\pi = 1/2^\pm $, $ 3/2^\pm $, $ 5/2^\pm $, $ 7/2^\pm $, $ 9/2^\pm $的单粒子态在$ \beta_2 = -0.1 $, $ 0 $, $ 0.1 $, $ 0.2 $下的单粒子谱. 黑色空心圆和暗红色实线分别表示动量积分的连续域边界和积分轮廓线, 其他颜色符号表示计算得到的共振态

Figure 2. Single-particle spectra of $ ^{29} {\rm{Ne}}$ for spin-parity $ \varOmega^\pi = 1/2^\pm $, $ 3/2^\pm $, $ 5/2^\pm $, $ 7/2^\pm $, $ 9/2^\pm $ at $ \beta_2 = -0.1 $, 0, 0.1, 0.2. The black hollow circles and dark red solid lines denote the continuum boundaries and integration contours of momentum, respectively, while other colored symbols indicate calculated resonance states.

DownLoad: Full-Size Img PowerPoint

图 3 ²⁹Ne的单粒子能级随形变参数$ \beta_2 $的演化. 束缚能级(实线)和共振能级(虚线)用尼尔森标记$ \varOmega[Nn_z\varLambda] $标识, $ \beta_2 = 0 $处标有球形壳层标签

Figure 3. Evolution of single-particle energy levels in $ ^{29} {\rm{Ne}}$ as a function of deformation parameter $ \beta_2 $. Bound levels (solid lines) and resonance levels (dashed lines) are labeled with Nilsson notation $ \varOmega[Nn_z\varLambda] $, with spherical shell-model labels marked at $ \beta_2 = 0 $.

DownLoad: Full-Size Img PowerPoint

图 4 ²⁹Ne中$ 3/2[321] $单粒子态的主要球基组分占比随$ \beta_2 $的演化

Figure 4. Percentage contributions of major spherical components to the $ 3/2[321] $ single-particle state in $ ^{29} {\rm{Ne}}$ as a function of $ \beta_2 $.

DownLoad: Full-Size Img PowerPoint

图 5 $ \beta_2 = 0.6 $时, ²⁹Ne中$ 3/2[321] $轨道、$ 1/2[310] $轨道和$ 5/2[202] $轨道的径向密度分布

Figure 5. Radial density distributions of the $ 3/2[321] $, $ 1/2[310] $, and $ 5/2[202] $ orbitals in $ ^{29} {\rm{Ne}}$ at $ \beta_2 = 0.6 $.

DownLoad: Full-Size Img PowerPoint

[1]	Haxel O, Jensen J H D, Suess H E 1949 Phys. Rev. 75 1766
[2]	Mayer M G 1949 Phys. Rev. 75 1969 Google Scholar
[3]	丁斌刚, 张大立, 鲁定辉 2009 物理学报 58 865 Google Scholar Ding B G, Zhang D L, Lu D H 2009 Acta Phys. Sin. 58 865 Google Scholar
[4]	孙帅, 安荣, 祁淼, 曹李刚, 张丰收 2025 物理学报 74 032101 Google Scholar Sun S, An R, Qi M, Cao L G, Zhang F S 2025 Acta Phys. Sin. 74 032101 Google Scholar
[5]	Poves A, Retamosa J 1987 Phys. Lett. B 184 311 Google Scholar
[6]	Tripathi V, Tabor S L, Mantica P F, et al. 2007 Phys. Rev. C 76 021301(R Google Scholar
[7]	Brown B A 2001 Prog. Part. Nucl. Phys. 47 517 Google Scholar
[8]	Otsuka T, Honma M, Mizusaki T, Shimizu N, Utsuno Y 2001 Prog. Part. Nucl. Phys. 47 319 Google Scholar
[9]	Liu H N, Lee J, Doornenbal P, et al. 2017 Phys. Lett. B 767 58 Google Scholar
[10]	Zhi Q J, Zhang X P 2009 Nucl. Phys. Rev. 26 275
[11]	Warturbon E K, Becker J A, Brown B A 1990 Phys. Rev. C 41 1147 Google Scholar
[12]	Moiseyev N, Corcoran C 1979 Phys. Rev. A 20 814 Google Scholar
[13]	刘建业, 郭文军, 邢永忠, 李希国, 左维 2006 物理学报 55 1068 Google Scholar Liu J Y, Guo W J, Xing Y Z, Li X G, Zuo W 2006 Acta Phys. Sin. 55 1068 Google Scholar
[14]	Tanihata I, Hamagaki H, Hashimoto O, et al. 1985 Phys. Rev. Lett. 55 2676 Google Scholar
[15]	Sagawa H 1992 Phys. Lett. B 286 7 Google Scholar
[16]	Meng J, Ring P 1996 Phys. Rev. Lett. 77 3963 Google Scholar
[17]	Pöschl W, Vretenar D, Lalazissis G A, Ring P 1997 Phys. Rev. Lett. 79 3841 Google Scholar
[18]	Meng J, Ring P 1998 Phys. Rev. Lett. 80 460 Google Scholar
[19]	林承键, 张焕乔, 刘祖华, 吴岳伟, 杨峰, 阮明 2003 物理学报 52 823 Google Scholar Lin C J, Zhang H Q, Liu Z H, Wu Y W, Yang F, Ruan M 2003 Acta Phys. Sin. 52 823 Google Scholar
[20]	Zhang H F, Gao Y, Wang N, Li J Q, Zhao E G, Royer G 2012 Phys. Rev. C 85 014325 Google Scholar
[21]	Zhou S G, Meng J, Ring P, Zhao E G 2010 Phys. Rev. C 82 011301(R Google Scholar
[22]	Hamamoto I 2010 Phys. Rev. C 81 021304(R Google Scholar
[23]	Tian Y J, Liu Q, Heng T H, Guo J Y 2017 Phys. Rev. C 95 064329 Google Scholar
[24]	李楚良, 段宜武, 黄笃之 1994 物理学报 43 14 Google Scholar Li C L, Duan Y W, Huang D Z 1994 Acta Phys. Sin. 43 14 Google Scholar
[25]	任中洲, 徐躬耦 1991 物理学报 40 1229 Google Scholar Ren Z Z, Xu G O 1991 Acta Phys. Sin. 40 1229 Google Scholar
[26]	Kubota Y, Corsi A, Authelet G, et al. 2020 Phys. Rev. Lett. 125 252501 Google Scholar
[27]	Tanihata I, Savajols H, Kanungo R 2013 Prog. Part. Nucl. Phys. 68 215 Google Scholar
[28]	Meng J, Zhou S G 2015 J. Phys. G: Nucl. Part. Phys. 42 093101 Google Scholar
[29]	Nakamura T, Kobayashi N, Kondo Y, et al. 2014 Phys. Rev. Lett. 112 142501 Google Scholar
[30]	Hong J, Bertulani C A, Kruppa A T 2017 Phys. Rev. C 96 064603 Google Scholar
[31]	Kobayashi N, Nakamura T, Kondo Y, et al. 2016 Phys. Rev. C 93 014613 Google Scholar
[32]	Li J G, Michel N, Li H H, Zuo W 2022 Phys. Lett. B 832 137225 Google Scholar
[33]	Wigner E P, Eisenbud L 1947 Phys. Rev. 72 29 Google Scholar
[34]	Hale G M, Brown R E, Jarmie N 1987 Phys. Rev. Lett. 59 763 Google Scholar
[35]	Taylor J R 1972 Scattering Theory: The Quantum Theory on Nonrelativistic Collisions (New York: Wiley) pp38–55
[36]	Cao L J, Ma Z Y 2002 Phys. Rev. C 66 024311 Google Scholar
[37]	Humblet J, Filippone B W, Koonin S E 1991 Phys. Rev. C 44 2530 Google Scholar
[38]	Masui H, Aoyama S, Myo T, Katō K, Ikeda K 2000 Nucl. Phys. A 673 207 Google Scholar
[39]	Lu B N, Zhao E G, Zhou S G 2012 Phys. Rev. Lett. 109 072501 Google Scholar
[40]	Lu B N, Zhao E G, Zhou S G 2013 Phys. Rev. C 88 024323 Google Scholar
[41]	Li Z P, Meng J, Zhang Y, Zhou S G, Savushkin L N 2010 Phys. Rev. C 81 034311 Google Scholar
[42]	Tanaka N, Suzuki Y, Varga K 1997 Phys. Rev. C 56 562 Google Scholar
[43]	Zhang S S, Smith M S, Arbanas G, Kozub R L 2012 Phys. Rev. C 86 032802(R Google Scholar
[44]	Zhang S S, Smith M S, Kang Z S, Zhao J 2014 Phys. Lett. B 730 30 Google Scholar
[45]	Xu X D, Zhang S S, Signoracci A J, Smith M S, Li Z P 2015 Phys. Rev. C 92 024324 Google Scholar
[46]	Hazi A U, Taylor H S 1970 Phys. Rev. A 1 1109 Google Scholar
[47]	Mandelshtam V A, Ravuri T R, Taylor H S 1993 Phys. Rev. Lett. 70 1932 Google Scholar
[48]	Mandelshtam V A, Taylor H S, Rayboy V, Moiseyev N 1994 Phys. Rev. A 50 2764 Google Scholar
[49]	Zhang L, Zhou S G, Meng J, Zhao E G 2008 Phys. Rev. C 77 014312 Google Scholar
[50]	杨威, 丁士缘, 孙保元 2024 物理学报 73 062102 Google Scholar Yang W, Ding S Y, Sun B Y 2024 Acta Phys. Sin. 73 062102 Google Scholar
[51]	Matsuo M 2001 Nucl. Phys. A 696 371 Google Scholar
[52]	Sun T T, Zhang S Q, Zhang Y, Hu J N, Meng J 2014 Phys. Rev. C 90 054321 Google Scholar
[53]	Sun T T, Qian L, Chen C, Ring P, Li Z P 2020 Phys. Rev. C 101 014321 Google Scholar
[54]	Chen C, Li Z P, Li Y X, Sun T T 2020 Chin. Phys. C 44 084105 Google Scholar
[55]	Odsuren M, Kikuchi Y, Myo T, Khuukhenkhuu G, Masui H, Katō K 2017 Phys. Rev. C 95 064305
[56]	Myo T, Kikuchi Y, Masui H, Katō K 2014 Prog. Part. Nucl. Phys. 79 1 Google Scholar
[57]	Guo J Y, Fang X Z, Jiao P, Wang J, Yao B M 2010 Phys. Rev. C 82 034318 Google Scholar
[58]	刘野, 陈寿万, 郭建友 2012 物理学报 61 112101 Google Scholar Liu Y, Chen S W, Guo J Y 2012 Acta Phys. Sin. 61 112101 Google Scholar
[59]	Li N, Shi M, Guo J Y, Niu Z M, Liang H Z 2016 Phys. Rev. Lett. 117 062502 Google Scholar
[60]	Fang Z, Shi M, Guo J Y, Niu Z M, Liang H Z, Zhang S S 2017 Phys. Rev. C 95 024311
[61]	Guo J Y, Liu Q, Niu Z M, Heng T H, Wang Z Y, Shi M, Cao X N 2018 Nucl. Phys. Rev. 35 401
[62]	Dai H M, Cao X N, Liu Q, et al. 2020 Nucl. Phys. Rev. 37 574
[63]	Luo Y X, Fossez K, Liu Q, Guo J Y 2021 Phys. Rev. C 104 014307
[64]	Wei Y M, Liu Q 2023 Nucl. Phys. Rev. 40 188
[65]	Alberto P, Fiolhais M, Malheiro M, Delfino A, Chiapparini M 2001 Phys. Rev. Lett. 86 5015 Google Scholar
[66]	Alberto P, Fiolhais M, Malheiro M, Delfino A, Chiapparini M 2002 Phys. Rev. C 65 034307 Google Scholar
[67]	Lalazissis G A, König J, Ring P 1997 Phys. Rev. C 55 540 Google Scholar
[68]	王晓伟, 郭建友 2019 物理学报 68 092101 Google Scholar Wang X W, Guo J Y 2019 Acta Phys. Sin. 68 092101 Google Scholar
[69]	Ragnarsson I, Nilsson S G, Sheline R K 1978 Phys. Rep. 45 1 Google Scholar
[70]	Butler P. A., Nazarewicz W 1996 Rev. Mod. Phys. 68 349 Google Scholar
[71]	Luo Y X, Liu Q, Guo J Y 2023 Phys. Rev. C 108 024320 Google Scholar
[72]	Cao X N, Ding K M, Shi M, Liu Q, Guo J Y 2020 Phys. Rev. C 102 044313 Google Scholar
[73]	Ding K M, Shi M, Guo J Y, Niu Z M, Liang H Z 2018 Phys. Rev. C 98 014316 Google Scholar
[74]	孟杰 1993 物理学报 42 368 Google Scholar Meng J 1993 Acta Phys. Sin. 42 368 Google Scholar
[75]	Sun T T, Liu Z X, Qian L, Wang B, Zhang W 2019 Phys. Rev. C 99 054316 Google Scholar

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Research on ground-state structure and neutron halo characteristics of ²⁹Ne using complex-momentum representation method

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Research on ground-state structure and neutron halo characteristics of 29Ne using complex-momentum representation method

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Research on ground-state structure and neutron halo characteristics of ²⁹Ne using complex-momentum representation method