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Restoration of the natural $$E(1/2^+_1)-E(3/2^+_1)$$ energy splitting in odd-K isotopes towards $$N=40$$

Sun, Y. L.*; Obertelli, A.*; Doornenbal, P.*; Barbieri, C.*; 茶園 亮樹*; Duguet, T.*; Liu, H. N.*; Navr$'a$til, P.*; Nowacki, F.*; 緒方 一介*; et al.

Physics Letters B, 802, p.135215_1 - 135215_7, 2020/03

 被引用回数:1 パーセンタイル:25.8(Astronomy & Astrophysics)

カリウムは陽子数が19であるため、その$$1/2^+_1$$, $$3/2^+_1$$状態はそれぞれ陽子の$$s_{1/2}$$, $$d_{3/2}$$軌道の空孔状態によって支配されている。その中性子数を$$N=20$$から増やすとこの2つの準位のエネルギー差$$E(1/2^+_1)-E(3/2^+_1)$$は大きく変化することが知られており、中性子過剰核における殻進化と呼ばれる現象のプロトタイプとなっている。これまで$$E(1/2^+_1)-E(3/2^+_1)$$$$N=30$$まで知られていたが、この研究では、理化学研究所RIビームファクトリーにて、カルシウム同位体からの陽子ノックアウト反応によって$$^{51,53}$$Kの励起状態を生成し、そこからの脱励起ガンマ線を測定することによって、$$N=32, 34$$における$$E(1/2^+_1)-E(3/2^+_1)$$を測定することに成功した。歪曲波インパルス近似計算と実験で得られた断面積の比較から、$$1/2^+_1$$, $$3/2^+_1$$状態は空孔状態によって支配されていることを確かめた。$$E(1/2^+_1)-E(3/2^+_1)$$の値は$$N=28$$で最小となり、そこから中性子数を増やすとともに増大することがわかった。これは、中心力とテンソル力による殻進化描像にしたがった振る舞いである。


Ultralow thermal conductivity from transverse acoustic phonon suppression in distorted crystalline $$alpha$$-MgAgSb

Li, X.*; Liu, P.-F.*; Zhao, E.*; Zhang, Z.*; Guide, T.*; Le, M. D.*; Avdeev, M.*; 池田 一貴*; 大友 季哉*; 古府 麻衣子; et al.

Nature Communications (Internet), 11(1), p.942_1 - 942_9, 2020/02




Strong local moment antiferromagnetic spin fluctuations in V-doped LiFeAs

Xu, Z.*; Dai, G.*; Li, Y.*; Yin, Z.*; Rong, Y.*; Tian, L.*; Liu, P.*; Wang, H.*; Xing, L.*; Wei, Y.*; et al.

npj Quantum Materials (Internet), 5(1), p.11_1 - 11_7, 2020/02

 被引用回数:1 パーセンタイル:100(Materials Science, Multidisciplinary)

We use neutron scattering to study Vanadium (hole)-doped LiFe$$_{1-x}$$V$$_{x}$$As. In the undoped state, LiFeAs exhibits superconductivity at $$T_mathrm{c} = 18$$ K and transverse incommensurate spin excitations similar to electron overdoped iron pnictides. Upon Vanadium doping to form LiFe$$_{0.955}$$V$$_{0.045}$$, the transverse incommensurate spin excitations in LiFeAs transform into longitudinally elongated ones in a similar fashion to that of potassium (hole)-doped Ba$$_{0.7}$$K$$_{0.3}$$Fe$$_{2}$$As$$_{2}$$ but with dramatically enhanced magnetic scattering and elimination of superconductivity. This is different from the suppression of the overall magnetic excitations in hole-doped BaFe$$_{2}$$As$$_{2}$$ and the enhancement of superconductivity near optimal hole doping. These results are consistent with density function theory plus dynamic mean field theory calculations, suggesting that Vanadium doping in LiFeAs may induce an enlarged effective magnetic moment $$S_mathrm{eff}$$ with a spin crossover ground state arising from the inter-orbital scattering of itinerant electrons.


Shell evolution of $$N$$ = 40 isotones towards $$^{60}$$Ca; First spectroscopy of $$^{62}$$Ti

Cort$'e$s, M. L.*; Rodriguez, W.*; Doornenbal, P.*; Obertelli, A.*; Holt, J. D.*; Lenzi, S. M.*; Men$'e$ndez, J.*; Nowacki, F.*; 緒方 一介*; Poves, A.*; et al.

Physics Letters B, 800, p.135071_1 - 135071_7, 2020/01

 被引用回数:2 パーセンタイル:25.8(Astronomy & Astrophysics)

ガンマ線分光による$$N$$=40同調体である$$^{62}$$Tiの分光学研究を$$^{63}$$V($$p$$,$$2p$$)$$^{62}$$TiをRIBFで行った。今回初めて測定された$$2_1^+ rightarrow 0_{rm gs}^+$$$$4_1^+ rightarrow 2_1^+$$の遷移はTiの基底状態が変形していることを示唆した。これらのエネルギーは近傍核の$$^{64}$$Crや$$^{66}$$Feと比較して大きく、したがって四重極集団運動が小さくなっていることが示唆される。今回の結果は大規模殻模型計算によって良く再現される一方、第一原理計算や平均場模型では今回の結果は再現されなかった。


Fine structure in the $$alpha$$ decay of $$^{223}$$U

Sun, M. D.*; Liu, Z.*; Huang, T. H.*; Zhang, W. Q.*; Andreyev, A. N.; Ding, B.*; Wang, J. G.*; Liu, X. Y.*; Lu, H. Y.*; Hou, D. S.*; et al.

Physics Letters B, 800, p.135096_1 - 135096_5, 2020/01

 被引用回数:1 パーセンタイル:25.8(Astronomy & Astrophysics)

Fine structure in the $$alpha$$ decay of $$^{223}$$U was observed in the fusion-evaporation reaction $$^{187}$$Re($$^{40}$$Ar,p3n) by using fast digital pulse processing technique. Two $$alpha$$-decay branches of $$^{223}$$U feeding the ground state and 244 keV excited state of $$^{219}$$Th were identified by establishing the decay chain $$^{223}$$U$$rightarrow$$$$^{219}$$Th$$rightarrow$$$$^{215}$$Ra$$rightarrow$$$$^{211}$$Rn. The $$alpha$$-particle energy for the ground-state to ground-state transition of $$^{223}$$U was determined to be 8993(17) keV, 213 keV higher than the previous value, the half-life was updated to be 62$$^{+14}_{-10} mu$$s. Evolution of nuclear structure for $$N$$=131 even-$$Z$$ isotones from Po to U was discussed in the frameworks of nuclear mass and reduced $$alpha$$-decay width, a weakening octupole deformation in the ground state of $$^{223}$$U relative to its lighter isotones $$^{219}$$Ra and $$^{211}$$Th was suggested.


Quasifree neutron knockout from $$^{54}$$Ca corroborates arising $$N=34$$ neutron magic number

Chen, S.*; Lee, J.*; Doornenbal, P.*; Obertelli, A.*; Barbieri, C.*; 茶園 亮樹*; Navr$'a$til, P.*; 緒方 一介*; 大塚 孝治*; Raimondi, F.*; et al.

Physical Review Letters, 123(14), p.142501_1 - 142501_7, 2019/10

 被引用回数:5 パーセンタイル:16.24(Physics, Multidisciplinary)

$$^{54}$$Caでは中性子魔法数34が現れると考えられているが、その直接的な実験的証拠を得るため、$$^{54}$$Caからの中性子ノックアウト反応$$^{54}$$Ca($$p,pn$$)$$^{53}$$Caによって生成される状態を理化学研究所のRI Beam Factoryによって調べた。基底状態および2.2MeVの励起状態が強く生成され、1.7MeVの励起状態の生成量は小さかった。$$^{53}$$Caの運動量分布から、基底状態および2.2MeVの励起状態は$$p$$軌道の中性子を叩き出して得られた状態であることが明らかになった。DWIA計算によって得られた分光学的因子から、$$^{54}$$Caは$$p$$軌道がほぼ完全に占有された閉殻構造を持つことが明らかになり、中性子魔法数34の出現が確実なものとなった。


Emergence of a complete heavy-quark spin symmetry multiplet; Seven molecular pentaquarks in light of the latest LHCb analysis

Liu, M.-Z.*; Pan, Y.-W.*; Peng, F.-Z.*; S$'a$nchez-S$'a$nchez, M.*; Geng, L.-S.*; 保坂 淳; Valderrama, M. P.*

Physical Review Letters, 122(24), p.242001_1 - 242001_5, 2019/06

 被引用回数:58 パーセンタイル:0.23(Physics, Multidisciplinary)

A recent analysis by the LHCb Collaboration suggests the existence of three narrow pentaquarklike states-the $$P_c$$(4312), $$P_c$$(4440), and $$P_c$$(4457)-instead of just one in the previous analysis [the $$P_c$$(4450)]. The closeness of the $$P_c$$(4312) to the $$bar{D}^{*}Sigma_c$$ threshold and the $$P_c$$(4440) and $$P_c$$(4457) to the $$bar{D}^{*}Sigma_c$$ threshold suggests a molecular interpretation of these resonances. We show that these three pentaquarklike resonances can be naturally accommodated in a contact-range effective field theory description that incorporates heavy-quark spin symmetry. This description leads to the prediction of all the seven possible $$S$$-wave heavy antimeson-baryon molecules [that is, there should be four additional molecular pentaquarks in addition to the $$P_c$$(4312), $$P_c$$(4440), and $$P_c$$(4457)], providing the first example of a heavy-quark spin symmetry molecular multiplet that is complete. If this is confirmed, it will not only give us an impressive example of the application of heavy-quark symmetries and effective field theories in hadron physics, it will also uncover a clear and powerful ordering principle for the molecular spectrum, reminiscent of the SU(3)-flavor multiplets to which the light hadron spectrum conforms.


Evaluation and modelling report of Task 9A based on comparisons and analyses of predictive modelling results for the REPRO WPDE experiments; Task 9 of SKB Task Force GWFTS - Increasing the realism in solute transport modelling based on the field experiments REPRO and LTDE-SD

Soler, J. M.*; Neretnieks, I.*; Moreno, L.*; Liu, L.*; Meng, S.*; Svensson, U.*; Trinchero, P.*; Iraola, A.*; Ebrahimi, H.*; Molinero, J.*; et al.

SKB R-17-10, 153 Pages, 2019/01



Dirac surface state-modulated spin dynamics in a ferrimagnetic insulator at room temperature

Tang, C.*; Song, Q.*; Chang, C.-Z.*; Xu, Y.*; 大沼 悠一; 松尾 衛*; Liu, Y.*; Yuan, W.*; Yao, Y.*; Moodera, J. S.*; et al.

Science Advances (Internet), 4(6), p.eaas8660_1 - eaas8660_6, 2018/06

 被引用回数:6 パーセンタイル:28.4(Multidisciplinary Sciences)

This work demonstrates markedly modified spin dynamics of magnetic insulator (MI) by the spin momentum-locked Dirac surface states of the adjacent topological insulator (TI). As the Bi concentration $$x$$ is systematically tuned in 5-nm-thick (Bi$$_{x}$$Sb$$_{1-x}$$)$$_{2}$$Te$$_{3}$$ TI films, the weight of the surface relative to bulk states peaks at $$x$$ = 0.32 when the chemical potential approaches the Dirac point. At this concentration, the Gilbert damping constant of the precessing magnetization in 10-nm-thick Y$$_{3}$$Fe$$_{5}$$O$$_{12}$$ MI films in the MI/TI heterostructures is enhanced by an order of magnitude, the largest among all concentrations. In addition, the MI acquires additional strong magnetic anisotropy that favors the in-plane orientation with similar Bi concentration dependence. These extraordinary effects of the Dirac surface states distinguish TI from other materials such as heavy metals in modulating spin dynamics of the neighboring magnetic layer.


Quantitative characterization of the nanoscale local lattice strain induced by Sr dopants in La$$_{1.92}$$Sr$$_{0.08}$$CuO$$_{4}$$

Lin, J. Q.*; Liu, X.*; Blackburn, E.*; 脇本 秀一; Ding, H.*; Islam, Z.*; Sinha, S. K.*

Physical Review Letters, 120(19), p.197001_1 - 197001_6, 2018/05

 被引用回数:0 パーセンタイル:100(Physics, Multidisciplinary)



CIELO collaboration summary results; International evaluations of neutron reactions on uranium, plutonium, iron, oxygen and hydrogen

Chadwick, M. B.*; Capote, R.*; Trkov, A.*; Herman, M. W.*; Brown, D. A.*; Hale, G. M.*; Kahler, A. C.*; Talou, P.*; Plompen, A. J.*; Schillebeeckx, P.*; et al.

Nuclear Data Sheets, 148, p.189 - 213, 2018/02

 被引用回数:20 パーセンタイル:3.34(Physics, Nuclear)

CIELO国際協力では、原子力施設の臨界性に大きな影響を与える重要核種($$^{235}$$U, $$^{238}$$U, $$^{239}$$Pu, $$^{56}$$Fe, $$^{16}$$O, $$^{1}$$H)の中性子断面積データの精度を改善し、これまで矛盾していると考えられた点を解消することを目的として研究が行われた。多くの研究機関が参加したこのパイロットプロジェクトは、IAEAの支援も受けて、OECD/NEAの評価国際協力ワーキングパーティ(WPEC)のSubgroup 40として組織された。本CIELOプロジェクトは、新たな実験研究や理論研究を行う動機付けとなり、測定データを正確に反映し臨界性の積分テストに優れた新たな一連の評価済みライブラリとして結実した。本報告書は、これまでの研究成果と、本国際協力の次の段階の計画概要をまとめたものである。


Atomically dispersed Pt on the surface of Ni particles; Synthesis and catalytic function in hydrogen generation from aqueous ammonia-borane

Li, Z.*; He, T.*; 松村 大樹; Miao, S.*; Wu, A.*; Liu, L.*; Wu, G.*; Chen, P.*

ACS Catalysis, 7(10), p.6762 - 6769, 2017/10

 被引用回数:67 パーセンタイル:4.26(Chemistry, Physical)

We report herein that the single-atom alloy (SAA) made of atomically dispersed Pt on the surface of Ni particles (Pt is surrounded by Ni atoms) exhibits improved catalytic activity on the hydrolytic dehydrogenation of ammonia-borane, a promising hydrogen storage method for onboard applications. Specifically, an addition of 160 ppm of Pt leads to ca. 3-fold activity improvement in comparison to that of pristine Ni/CNT catalyst. The turnover frequency based on the isolated Pt is 12000 mol$$_{rm{H}2}$$ mol$$_{rm{Pt}}$$$$^{-1}$$ min$$^{-1}$$, which is about 21 times the value of the best Pt-based catalyst ever reported. Our simulation results indicate that the high activity achieved stems from the synergistic effect between Pt and Ni, where the negatively charged Pt (Pt$$^{delta -}$$) and positively charged Ni (Ni$$^{delta +}$$) in the Pt-Ni alloy are prone to interact with H and OH of H$$_{2}$$O molecules, respectively, leading to an energetically favorable reaction pathway.


The $$^{95}$$Zr($$n, gamma$$)$$^{96}$$Zr cross section from the surrogate ratio method and its effect on $$s$$-process nucleosynthesis

Yan, S. Q.*; Li, Z. H.*; Wang, Y. B.*; 西尾 勝久; Lugaro, M.*; Karakas, A. I.*; 牧井 宏之; Mohr, P.*; Su, J.*; Li, Y. J.*; et al.

Astrophysical Journal, 848(2), p.98_1 - 98_8, 2017/10

 被引用回数:0 パーセンタイル:100(Astronomy & Astrophysics)

The $$^{95}$$Zr($$n, gamma$$)$$^{96}$$Zr reaction cross section is crucial in the modelling of $$s$$-process nucleosynthesis in asymptotic giant branch stars because it controls the operation of the branching point at the unstable $$^{95}$$Zr and the subsequent production of $$^{96}$$Zr. We have carried out the measurement of the $$^{90}$$Zr($$^{18}$$O,$$^{16}$$O) and $$^{94}$$Zr($$^{18}$$O,$$^{16}$$O) reactions and obtained the $$gamma$$-decay probability ratio of $$^{92}$$Zr$$^{*}$$ and $$^{96}$$Zr$$^{*}$$ to determine the $$^{95}$$Zr($$n, gamma$$)$$^{96}$$Zr reaction cross sections with the surrogate ratio method. We tested our deduced maxwellian-averaged cross section in stellar models with masses between 2 and 6 $$M_{odot}$$ and metallicities 0.014 and 0.03. The largest changes - up 80 % variations in $$^{96}$$Zr - are seen in the models of 3-4 $$M_{odot}$$, where the $$^{22}$$Ne neutron source is mildly activated. The new rate can still provide a match to data from meteoritic stardust silicon carbide grains, provided the maximum mass of the parent stars is below 4 $$M_{odot}$$, for a metallicity of 0.03.


Shell evolution beyond $$Z$$=28 and $$N$$=50; Spectroscopy of $$^{81,82,83,84}$$Zn

Shand, C. M.*; Podoly$'a$k, Zs.*; G$'o$rska, M.*; Doornenbal, P.*; Obertelli, A.*; Nowacki, F.*; Otsuka, T.*; Sieja, K.*; Tostevin, J. A.*; Tsunoda, T.*; et al.

Physics Letters B, 773, p.492 - 497, 2017/10

 被引用回数:13 パーセンタイル:12.29(Astronomy & Astrophysics)

Low-lying states in neutron-rich $$^{81,82.83.84}$$Zn nuclei were measured for the first time via in-beam $$gamma$$-ray spectroscopy at RIKEN. These include the 4$$_1^+$$ to 2$$_1^+$$ in $$^{82}$$Zn and the 2$$_1^+$$ to 0$$_1^+$$ and 4$$_1^+$$ to 2$$_1^+$$ in $$^{84}$$Zn. The reduced E($$2^+$$) energies and increased E(4$$^+$$)/E(2$$^+$$) ratios at $$N$$=52,54 compared to $$^{80}$$Zn attest that the magicity is confined just on the neutron number $$N$$=50 only. The levels observed in $$^{84}$$Zn suggest the onset of deformation towards heavier Zn isotopes. The data were compared to state-of-the-art shell model calculations.


Inter-comparison of Dose Distributions Calculated by FLUKA, GEANT4, MCNP, and PHITS for Proton Therapy

Yang, Z.-Y.*; Tsai, P.-E.; Lee, S.-C.*; Liu, Y.-C.*; Chen, C.-C.*; 佐藤 達彦; Sheu, R.-J.*

EPJ Web of Conferences, 153, p.04011_1 - 04011_8, 2017/09

 被引用回数:5 パーセンタイル:1.34

広く普及している4つの放射線挙動解析コードGEANT4, FLUKA, MCNPX及びPHITSについて、ペンシルビーム照射条件により陽子治療計画への適用性を検証した。最初の条件として、水ファントムへの単色陽子照射を仮定し、各コードによる深度線量曲線の積分値(IDDCs)を比較した。2つ目のケースとして、エネルギーが分布する陽子ビーム照射に関するIDDCsを検証した。これらの結果は、米国ニュージャージのProCure陽子治療センターにおける実験結果と比較した。実測値に対する各コードによる結果は一定でなく、ファントム中の浅い領域やBraggピーク付近で線量の計算値で差が生じることを確認した。この他、3つ目ケースとして、拡大ブラッグピーク(SOBP)の調査を進めている。


Observation of magnetoelastic effects in a quasi-one-dimensional spiral magnet

Wang, C.*; Daiwei, Y.*; Liu, X.*; Chen, R.*; Du, X.*; Hu, B.*; Wang, L.*; 飯田 一樹*; 蒲沢 和也*; 脇本 秀一; et al.

Physical Review B, 96(8), p.085111_1 - 085111_5, 2017/08


 被引用回数:3 パーセンタイル:69.64(Materials Science, Multidisciplinary)

This paper presents a systematic study of spin and lattice dynamics in the quasi-one-dimensional spiral magnet CuBr$$_2$$, using Raman scattering in conjunction with infrared and neutron spectroscopy. Along with the development of spin correlations upon cooling, we observe a rich set of broad Raman bands at energies that correspond to phonon-dispersion energies near the one-dimensional magnetic wave vector. The low-energy bands further exhibit a distinct intensity maximum at the spiral magnetic ordering temperature.


Shape evolution in neutron-rich krypton isotopes beyond N=60; First spectroscopy of $$^{98,100}$$Kr

Flavigny, F.*; Doornenbal, P.*; Obertelli, A.*; Delaroche, J.-P.*; Girod, M.*; Libert, J.*; Rodriguez, T. R.*; Authelet, G.*; 馬場 秀忠*; Calvet, D.*; et al.

Physical Review Letters, 118(24), p.242501_1 - 242501_6, 2017/06

 被引用回数:21 パーセンタイル:10.34(Physics, Multidisciplinary)

The first $$gamma$$-ray spectroscopy of very neutron rich $$^{98,100}$$Kr isotopes was carried out at the RIBF at RIKEN Nishina center. Excited states in these isotopes were populated via (p,2p) reactions using radioactive $$^{99,101}$$Rb beams accelerated to 220 MeV/nucleon. The new data show a significant increase in deformation beyond N=60, as well as competing configurations (shape-coexistence) at low energy. The data were compared with beyond-mean-field calculations which predict level energies in good agreement with observation, and suggest oblate-prolate shape coexistence.


$$gamma$$ decay of unbound neutron-hole states in $$^{133}$$Sn

Vaquero, V.*; Jungclaus, A.*; Doornenbal, P.*; Wimmer, K.*; Gargano, A.*; Tostevin, J. A.*; Chen, S.*; N$'a$cher, E.*; Sahin, E.*; 志賀 慶明*; et al.

Physical Review Letters, 118(20), p.202502_1 - 202502_5, 2017/05

 被引用回数:13 パーセンタイル:17.71(Physics, Multidisciplinary)

Excited states in $$^{133}$$Sn were populated following one-neutron knockout reaction from an unstable $$^{134}$$Sn beam at the RIBF laboratory in RIKEN. In addition to the already known $$gamma$$ rays, additional $$gamma$$ strength was observed for the first time in the excitation-energy range 3.5-5.5 MeV. Since the neutron separation energy of $$^{133}$$Sn is low, this observation provides direct evidence for the radioactive decay of neutron-unbound states in this nucleus. The ability of $$gamma$$ decay to compete with neutron emission was attributed to a mismatch between the wave functions of the initial and final states in the neutron emission case. These findings suggest that in the region south-east of $$^{132}$$Sn, nuclear structure effects play a significant role in the decay of unbound states, which are instead usually ignored in the evaluation of neutron-emission probabilities in astrophysical simulations.


Low-lying structure and shape evolution in neutron-rich Se isotopes

Chen, S.*; Doornenbal, P.*; Obertelli, A.*; Rodriguez, T. R.*; Authelet, G.*; 馬場 秀忠*; Calvet, D.*; Ch$^a$teau, F.*; Corsi, A.*; Delbart, A.*; et al.

Physical Review C, 95(4), p.041302_1 - 041302_6, 2017/04

 被引用回数:15 パーセンタイル:9.29(Physics, Nuclear)

Neutron-rich isotopes of selenium, $$^{88,90,92,94}$$Se, where studied via in beam $$gamma$$-ray spectroscopy after nucleon removal reactions at RIBF in RIKEN. The low-energy excitations of these nuclei were investigated using $$gamma$$-$$gamma$$ coincidences, and the first and second excited 2$$^+$$ states were found at remarkably low energies. The analysis and comparison with self-consistent beyond-mean field calculations suggest that both shape coexistence and triaxiality are needed to describe these isotopes.


Intruder configurations in the ground state of $$^{30}$$Ne

Liu, H. N.*; Lee, J.*; Doornenbal, P.*; Scheit, H.*; 武内 聡*; 青井 考*; Li, K. A.*; 松下 昌史*; Steppenbeck, D.*; Wang, H.*; et al.

Physics Letters B, 767, p.58 - 62, 2017/04


 被引用回数:9 パーセンタイル:20.74(Astronomy & Astrophysics)

理化学研究所のRIBFにて、中性子過剰核$$^{30}$$Neビームを生成し、それを用いた$$^{12}$$C($$^{30}$$Ne, $$^{29}$$Ne+$$gamma$$)$$X$$陽子ノックアウト反応にて$$^{29}$$Neの励起状態を調べた。また、運動量分布も調べることにより、生成された状態のスピン・パリティを推定した。得られた励起準位の構造は、中性子数20が魔法数であると仮定したものとは大きく異なり、この原子核で侵入者配位(殻ギャップを超えて励起した状態)が基底状態および低励起状態が支配的となっていることがわかった。$$sd$$殻と$$pf$$殻の下半分の軌道を取り入れた大規模殻模型計算はこうした準位構造の性質自体は再現するものの、より定量的な一致を得るには$$pf$$殻を完全に取り入れた計算が必要であることがわかった。

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