937 resultados para deformed odd-odd nucleus
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The high-spin level structure of Au-188 has been investigated via the Yb-173(F-19,4n gamma) reaction at beam energies of 86 and 90 MeV. The previously reported level scheme has been modified and extended significantly. A new I-pi = 20(+) state associated with pi h(11/2)(-1) circle times nu i(13/2)(-2)h(9/2)(-1) configuration and two new rotational bands, one of which is built on the pi h(9/2) circle times nu i(13/2) configuration, have been identified. The prolate-to-oblate shape transition through triaxial shape has been proposed to occur around Au-188 for the pi h(9/2) circle times nu i(13/2) bands in odd-odd Au isotopes. Evidence for pi h(11/2)(-1) circle times nu i(13/2)(-1) structure of nonaxial shape with gamma < -70 degrees has been obtained by comparison with total Routhian surface and cranked-shell-model calculations.
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Recent experiments have reached the neutron-rich Cr isotope with N = 40 and confirmed enhanced collectivity near this subshell. The current data focus on low-spin spectroscopy only, with little information on the states where high-j particles align their spins with the system rotation. By applying the projected shell model, we show that rotation alignment occurs in neutron-rich even-even Cr nuclei as early as spin 8 (h) over bar h and, owing to shell filling, the aligning particles differ in different isotopes. It is suggested that observation of irregularities in moments of inertia is a direct probe of the deformed single-particle scheme in this exotic mass region.
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Parity (P)-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in noncentral collisions. To study this effect, we investigate a three-particle mixed-harmonics azimuthal correlator which is a P-even observable, but directly sensitive to the charge-separation effect. We report measurements of this observable using the STAR detector in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62 GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators and discuss in detail possible contributions from other effects that are not related to P violation.
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Motivated by recent spectroscopy data from fission experiments, we apply the projected shell model to study systematically the structure of strongly deformed, neutron-rich, even-even Nd and Sm isotopes with neutron number from 94 to 100. We perform calculations for rotational bands up to spin I = 20 and analyze the band structure of low-lying states with quasiparticle excitations, with emphasis given to rotational bands based on various negative-parity two-quasiparticle (2-qp) isomers. Experimentally known isomers in these isotopes are described well. The calculations further predict proton 2-qp bands based on a 5(-) and a 7(-) isomer and neutron 2-qp bands based on a 4(-) and an 8(-) isomer. The properties for the yrast line are discussed, and quantities to test the predictions are suggested for future experiment.
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Properties for the ground state of C-9 are studied in the relativistic continuum Hartree-Bogoliubov theory with the NLSH, NLLN and TM2 effective interactions. Pairing correlations are taken into account by a density-dependent delta-force with the pairing strength for protons determined by fitting either to the experimental binding energy or to the odd-even mass difference from the five-point formula. The effects of pairing correlations on the formation of proton halo in the ground state of C-9 are examined. The halo structure is shown to be formed by the partially occupied valence proton levels p(3/2) and p(1/2).
Resumo:
通过重离子核反应116Cd(27Al,4n)与在束γ谱的实验技术,对A=130~140核区的奇A核139Pm的高自旋态进行了研究.根据γ-γ符合关系、γ射线的相对强度和各向异性度的测量结果,扩展并更新了139Pm的能级纲图.实验观测到基于πh11/2和πg7/2-[πh11/2]2(或者πd5/2-[πh11/2]2)组态的转动带,利用已有的理论计算结果对这些转动带进行了解释.同时还观测到三个具有很强M1跃迁、旋称劈裂很小的-I=1的带.通过简单分析和系统学比较,指认了它们的组态,发现它们具备磁转动带的特性,很可能是磁转动带.
Resumo:
High-spin states in Pt-189 have been studied with the in-beam gamma-spectroscopy method via the Yb-176(O-18, 5n) reaction at beam energies of 88 MeV and 95 MeV. A new level scheme of Pt-189 has been established. Rotational bands based on the upsilon i(13/2)(-1), upsilon f(5/2)(p(3/2)) and upsilon i(13/2)(-2)upsilon f(p(3/2)) configurations, as well as several structures with irregular level spacings, have been observed. Properties of rotational bands have been analyzed in the framework of triaxial particle-rotor model. A gamma similar to -30 degrees triaxial shape and a near prolate shape have been proposed to the upsilon i(13/2)(-1) and uf(5/2)(p(3/2)) bands, respectively. Two Delta I=2 transition sequences with similar energies have been observed, and they have been proposed to be associated with the upsilon i(13/2)(-1)upsilon f(5/2)(p(3/2)) configuration. According to the relevant Nilsson orbitals, the bands built on the upsilon i(13/2)(-1)upsilon f(5/2)(p(3/2)) configuration could be interpreted as a pair of pseudo-spin partner.
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利用能量为164-180MeV的35Cl束流,通过重离子核反应149Sm(35Cl,5n) 研究了179Au的高自旋态能级结构。实验进行了γ射线的激发函数、X-γ和γ-γ-t符合测量。基于实验测量结果,首次建立了179Au的1/2[660](πi13/2)转动带。结合已有的实验数据,着重讨论了奇-A Au核中1/2[660](πi13/2) 转动带的形变和带头激发能随中子数的变化。用能量为140MeV的29Si束流轰击159Tb金属靶,布居了183Au核的高自旋态。实验中要求至少有3个高纯锗和2个BGO探测器同时点火,在此符合条件下,记录高纯锗探测器探测到的γ射线的能量和相对时间、BGO探测到的γ射线的总能量和多重性。通过对实验数据的分析,扩展并更新了183Au的能级纲图。首次建立了183Au的πi13/2转动带的能量非优先带。分析并讨论了缺中子奇-A Au中πh9/2转动带的能量非优先带和πf7/2转动带间的相互作用
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本论文介绍了原子核高自旋态研究的一般概况及有关核模型,描述了在束γ谱实验的原理与技术、数据分析与处理方法,然后着重分析和讨论了双奇核190Tl和146Tb高自旋能级结构的特性。 利用能量为175和167MeV的35Cl束流,通过反应160Gd(35Cl,5n)研究了双奇形变核190Tl的高自旋能级结构。实验进行了γ射线的激发函数和各向异度、X-γ和γ-γ-t符合测量,建立了由πh9/2νi13/2扁椭球转动带和一个具有单粒子激发特征的级联组成的190Tl能级纲图。确定地指定了190Tl的转动带自旋值,首次发现了190Tl πh9/2νi13/2扁椭球转动带的低自旋旋称反转。基于双奇核Tl能级结构的相似性,重新指定了双奇核192-200Tl πh9/2νi13/2扁椭球转动带能级自旋值,澄清了二十多年来国际上一直没有解决的自旋值指定问题且在这些扁椭形变核中均出现了低自旋旋称反转。考虑了p-n剩余相互作用的2-准粒子—转子模型定性地解释πh9/2νi13/2扁椭球转动带出现的低自旋旋称反转现象。 利用118Sn(32S ,1p3n)反应研究了双奇球形核146Tb的高自旋态,建立了激发能达8.39 MeV的能级纲图,其中包括新发现的41条γ射线和新建立的27个能级,并指定了新发现能级的自旋值和部分能级的组态。146Tb81的低位激发态是二准粒子态,高位的激发态是四准粒子态,或二准粒子与偶偶核芯低位激发态的耦合,更高位的能级则是六准粒子态,甚至八准粒子态。利用经验壳模型对部分全顺排组态的激发能进行了理论计算
Resumo:
能量为140 MeV的27Al束流轰击145Nd氧化靶,通过145Nd (27Al,4nγ)168Ta熔合蒸发反应对双奇核168Ta的高自旋态进行了实验研究。扩展了基于πh11/2(9/2-[514])νi13/2(5/2+[402])和πd5/2(5/2+[402])νi13/2(5/2+[642])准粒子组态下的转动带能级纲图。根据实验测量结果,对两转动带的准粒子顺排特征作了分析。通过B(M1)/B(E2)的理论与实验值比较以及168Ta相邻双奇核能级间隔系统性,进一步确定了两转动带的准粒子组态和能级的自旋宇称
Resumo:
利用能量为164-180MeV的35Cl束流,通过重离子核反应149Sm(35Cl,5n) 研究了179Au的高自旋态能级结构。实验进行了γ射线的激发函数、X-γ和γ-γ-t符合测量。基于实验测量结果,首次建立了179Au的1/2[660](πi13/2)转动带。结合已有的实验数据,着重讨论了奇-A Au核中1/2[660](πi13/2) 转动带的形变和带头激发能随中子数的变化。用能量为140MeV的29Si束流轰击159Tb金属靶,布居了183Au核的高自旋态。实验中要求至少有3个高纯锗和2个BGO探测器同时点火,在此符合条件下,记录高纯锗探测器探测到的γ射线的能量和相对时间、BGO探测到的γ射线的总能量和多重性。通过对实验数据的分析,扩展并更新了183Au的能级纲图。首次建立了183Au的πi13/2转动带的能量非优先带。分析并讨论了缺中子奇-A Au中πh9/2转动带的能量非优先带和πf7/2转动带间的相互作用
Resumo:
本论文介绍了原子核高自旋态研究的一般概况及有关核模型,描述了在束γ谱实验的原理与技术、数据分析与处理方法,然后着重分析和讨论了双奇核190Tl和146Tb高自旋能级结构的特性。 利用能量为175和167MeV的35Cl束流,通过反应160Gd(35Cl,5n)研究了双奇形变核190Tl的高自旋能级结构。实验进行了γ射线的激发函数和各向异度、X-γ和γ-γ-t符合测量,建立了由πh9/2νi13/2扁椭球转动带和一个具有单粒子激发特征的级联组成的190Tl能级纲图。确定地指定了190Tl的转动带自旋值,首次发现了190Tl πh9/2νi13/2扁椭球转动带的低自旋旋称反转。基于双奇核Tl能级结构的相似性,重新指定了双奇核192-200Tl πh9/2νi13/2扁椭球转动带能级自旋值,澄清了二十多年来国际上一直没有解决的自旋值指定问题且在这些扁椭形变核中均出现了低自旋旋称反转。考虑了p-n剩余相互作用的2-准粒子—转子模型定性地解释πh9/2νi13/2扁椭球转动带出现的低自旋旋称反转现象。 利用118Sn(32S ,1p3n)反应研究了双奇球形核146Tb的高自旋态,建立了激发能达8.39 MeV的能级纲图,其中包括新发现的41条γ射线和新建立的27个能级,并指定了新发现能级的自旋值和部分能级的组态。146Tb81的低位激发态是二准粒子态,高位的激发态是四准粒子态,或二准粒子与偶偶核芯低位激发态的耦合,更高位的能级则是六准粒子态,甚至八准粒子态。利用经验壳模型对部分全顺排组态的激发能进行了理论计算
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奇奇核作为研究准质子和准中子间相互作用的独特侯选核,近年来,人们给予了越来越多的关注。奇奇核高j组态带中观测到的低自旋旋称反转现象(Signature inversion)已成为原子核高自旋态领域中一个十分活跃的研究课题。近十年来,一系列基于二准粒子加转子模型框架的计算结果表明,奇奇核中这两个准粒子之间的相互作用与旋称反转现象的发生密切相关。相对于偶偶核和奇A核,奇奇核的能级结构更复杂一些,实验上对其高自旋态的研究比较困难,这主要体现在实验上所提供的许多奇奇核的能级纲图存在着一定程度的不确定性,例如能级的激发能位置、转动带的组态、自旋和宇称的指定,甚至在纲图结构、级联系列的核素归属等方面都有一些问题。其中,转动带能级自旋的指定直接关系到准粒子能量的劈裂属性(即正常劈裂还是反常劈裂、旋称反转发生在低自旋区还是高自旋区及旋称反转的发生位置等):自旋的奇偶性定错了,会导致本来是反转的旋称劈裂变成不反转的(反之亦然);自旋值定错了△I,会导致旋称反转的位置发生相应的漂移。由于实验上奇奇核转动带能级自旋指定的混乱局面,掩盖了旋称反转现象的客观规律,使得相关理论模型的计算结果得不到及时检验。基于激发能系统学分析方法、以顺排角动量相加性为判据,我们曾对A~160轻稀土区的πhl_(11/2)direct X vi_(13/2)转动带(17个核素)和A~130过渡区的πh_(11/2)direct XVh_(ll/2)转动带(20个核素)进行了系统研究,对其中20个核的自旋数据提出质疑、并提出了相应的修正方案,在此基础上总结了两核区旋称反转现象的系统规律。利用激发能系统学方法指定奇奇核转动带的能级自旋,主要遵循以下三点原则:①自旋奇偶性:根据推转壳模型的描述,当准粒子处于优惠态(Favored)时、较非优惠态(Unfavored)具有更大的顺排角动量。这样,通过对转动带中两signature分支系列的i_x大小的比较,可以辅助推断能级自旋的奇偶性;②顺排角动量相加性:在忽略p-n剩余相互作用条件下,奇奇核中总的顺排角动量近似等于相邻奇A核中相应组态带提取的准粒子顺排角动量之和。这样,利用i_x对自旋值比较敏感的特点,可以推断出能级自旋取值的大致范围;③激发能系统性分析:由于集体转动反映大量核子的集体行为,少数核子的改变不会对这种运动产生明显影响,利用转动惯量的组态相关特性,在一组同位素或同中子素系列链中,对应一定内禀结构的转动带,随着质子数或中子数的均匀递增,能级能量应表现光滑的变化趋势(即不发生突变)。这三个方面基于不同角度、相对独立地指定转动带自旋。其结论的统一、往往可以给出正确的自旋数据。然而,必须指出的是:系统学分析过程是一种经验方法,并不具有严格的理论基础,上述的自旋修正以及总结出的旋称反转规律,必须得到实验核谱学测量的支持。基于这一思想,针对两核区,我们分别选择情况较为阿典型的奇奇核~(158)Ho和~(124)Cs进行了集中的实验测量。本论文的主要研究目标就是要建立两核中晕带与低激发态或基态的联系,找出原纲图中错误自旋指定的原因所在,验证系统学结论的有效性,并用旋称反转的实验规律性对理论模型的系统计算结果进行检验。(一)奇奇核~(158)58Ho高自旋态的实验研究在原子能研究院的HI-13串列加速器上,通过~(152)Sm(~(11)B,5nγ)~(158)Ho融合蒸发反应(束流轰击能E_(lab)=60 MeV)、对目标核~(158)Ho的高自旋态进行布居。探测阵列由八个高纯锗探测器构成,为了提高低能射线的收集效率,使用了一个平面型高纯锗探测器。分别进行了激发函数曲线测量、γ-γ-t符合测量和剩余放射性测量。数据反演后,两重符合总记数~120x10~6。实验结果概括如下:1.建立了基态带,组态指定为:{πh_(11/2)[523]7/2-direct Xvh_(9/2)[521]3/2~-}K~π=5~+;2.建立了一个强度仅次于晕带的强耦合带结构(亚晕带:yrare band)。通过转动参数、跃迁几率、顺排角动量、带交叉频率等特征参量的分析,其组态指定为:{πg_(7/2)[404】7/2]~+ direct X vi_(3/2)[651]3/2~+}K~π=5~+。 尽管该带带头附近的结构还不完整,但观测到了带内几条能级退激、分别贯入到晕带和基态带,从而将晕带和亚晕带同基态联系起来,固定了晕带和亚晕带中能级的激发能位置,并通过对这些连接跃迁多极性的分析,指定了两个带中的能级自旋和宇称;3.晕带(πh_(11/2)direct X vi~(13/2))向高自旋端拓展了7条能级,最高自旋态达到26h,激发 能4.9MeV。肯定了原纲图中不确定的617kev跃迁的存在和放置,观测到了反转点(I_(inv.)≈16h),肯定了系统学研究对该核的自旋修正。基于本实验建立的连接关系,晕带中观测到的最低态(即70.8kev跃迁贯入能级)激发能为207.6kev,而对应该能级,原纲图中激发能为156.9kev。这意味着原能级纲图中,晕带向基态退激途径中漏掉了一个~5lkeV的"能隙"(Energy gap),自旋差|△I|=3。根据晕带与退激5-同质异能态的跃迁(156.9kev)的快符合关系,该"能隙"至少由两个跃迁构成。该结果否定了原纲图中对晕带带头处理的三种可能性(①70.8kev为连接跃迁,其退激的能级为带头;②70.8kev为带内跃迁,156.9kev、5-同质异能态为带头:⑨70.8kev为带内跃迁,156.9kev、5-同质异能态为带头,但带头附近仍存在尚未观测的跃迁)。不确切的连接关系是过去实验中无法正确指定晕带自旋的原因;4.建立了一个强耦合的转动带结构,其能级间距(跃迁E_γ)随角动量的增加均匀递增,组态指定为{πh_(11/2)[523]7/2~-direct Xvh_(11/2)[505]11/2~-}K~π=9~+;同时,观测到了另一高K激发态退激到该转动带。其内禀结构指定为:{πg_(7/2)[404]7/2~+direct Xvh_(11/2)[505]1 l/2~-}K~π=9~-;5.建立了基于156.9 kev(I~π=5~-、T_(1/2)=29 ns)同质异能态上的转动带,该带观测完整,具有较强耦合的结构特点。其内禀准粒子轨道指定为:{πh_(11/2)[523]_(7/2)~-direct X vd_(3/2)[402]3/2~+}K~π=5~-,与处于较低激发能(67.3 kev)的2~-态(T_(1/2)=27 min.)构成了一对GM伙伴态。否定了过去的实验中把该态指定为{πg_(7/2)~2+direct Xvh_(9/2)[521]3/2~-}K~π=2~-组态;6.观测到了一个基于65.5 kev激发态的转动带,通过理论模型预言的带头激发能及转动参数与实验值的比较、考虑到其较弱的布居强度和很低的顺排角动量、以及较强耦合的结构特点, 其组态指定为: {πd~(5/2)[402]5/2~direct X vh_(9/2)[521]3/2~-}K~π=4~-。这一结果肯定了过去放射性测量中对处于较高激发能(139.2 kev)、T_(1/2)=1.85 ns、I~π=1~-激发态的讨论,即二者构成了一对GM伙伴态;7.建立了基于{πh_(11/2)[523]7/2~-direct X v_(7/2)[523]5/2~-}K~π=6~+激发态的强耦合转动带结构,其带头激发能为450.1 kev,与I~π=1~+、激发能为146.9 kev的同质异能态构成了一对GM伙伴态;8.在过去的放射性衰变测量中,提供了三个2~+激发态(激发能分别为117.7 kev、74.95 kev和316 kev)。其中两个2~+态(117.7和74.95 kev)同时指定具有{πh_(11/2)[523↑]7/2~-direct X vh_(9/2)[521↓]3/2~-}K~π=2~+组态。这里,我们指定1 17.7 kev的2~+激发态为{πg_(7/2)[404↓]7/2~+ direct X vi_(l3/2)[651↓]3/2~+}K~π=2+组态,即与本实验建立的亚晕带内禀激发态构成了一对GM伙伴态,而74.95 kev的2~+激发态指定为 {πh_(11/2)[523↑]7/2~-direct X vh_(9/2)[521↓]3/2~-}K~π=2~+组态,即与基态构成了一对GM伙伴态。基于本实验中K~π=9~+激发态的观测及其转动带的建立,我们指定激发能为3 1 6 kev的2~+激发态具有{πh_(11/2)[523↓]7/2~-direct X vh_(11/2)[505个]1 1/2~-}K~π=2~+组态,即这两个态构成了一对GM伙伴态;9.通过本实验、提供了~(158)Ho中各能态的跃迁强度和跃迁几率等数据。概括起来,奇奇核~(158)Ho的能级纲图大大完善了。综合本实验观测到的高自旋转动带结构和放射性测量中的部分激发态信息,我们可以整理出10对GM伙伴态,并提供了四个分别对应自旋平行和反平行耦合的GM能量漂移(GM Shift),即:{πh_(ll/2)[523]7/2~-direct Xvh_(9/2)[521]3/2~-}K~π=5~+、2~+,EGM=101.4 kev;{πh_(11/2)[523] 7/2~-direct X vd_(3/2)[402]3/2~+}K~π=5~-、2~-,E_(GM)=64.1 kev;{πd_(5/2)[402]5/2~+direct X vh_(9/2)[521]3/2~-}K~π =4~-、1~-,E_(GM)=113.3 kev;{πh_(11/2)[523]7/2~-direct Xvf_(7/2)[523]5/2~-}K~π=6~+、1~+,EGM=255.7 keV。(二)奇奇核~(124)Cs高自旋态的实验研究在原子能院的HI-13串列加速器上,利用~(116)Sn(~(11)B,3nγ)~(124)Cs融合蒸发反应(束流轰击能E_(lab.)=45 MeV),对奇奇核~(124)Cs的高自旋态进行了布居。探测阵列由10个高纯锗探测器和一个小平面探测器组成。数据反演后,总的两重符合事件数达到160x10~6。实验结果概括如下:1.高自旋转动带的信息更丰富了:建立了三个新的转动带结构,其中两个耦合带、一个退耦带,组态分别为:{πh_(11/2)[550]1/2~- direct X vhd_(5/2)[413]5/2~+}K~π=3~-、{πg_(7/2)[413]5/2~+direct X vg_(7/2)[402】5/2~+}K~π=5~+以及{πh_(11/2)[550]1/2~- direct X vd_(3/2)[400]l/2~+}K~π=1~-;2.低激发态的信息更丰富了:观测到了20多条新的低激发态跃迁,增加了10多个新的低激发态;3.转动带之间以及转动带与低激发态间耦合的信息大大丰富了:在过去的研究中观测到了三个彼此孤立、悬空的转动带结构,这里指定它们的组态为:{πh_(11/2) [550]1/2~-direct X vh_(11/2)[523]7/2~-}K~π=4~+(晕 带) ; {πh_(11/2)[550]1/2~- (direct X)vg_(7/2)[402]5/2~+}K~π=3~-(亚晕带:布居强度仅次于晕带);{πh_(11/2)[550]1/2~-(direct X)vs_(1/2)[411]1/2~+}K~π=1~-(双退耦结构)。其中,亚晕带(yrare band)通过至少三个独立的退激路径与低激发态联系起来;同时,建立了晕带与亚晕带间的多条连接关系。其它转动带分别与晕带和亚晕带联系起来,从而,在奇奇核~(124)Cs中,转动带的"悬空"不再存在,限定了各转动带中能级的激发能位援,并通过这些连接跃迁多极性的分析,分别指定了各能态的自旋和宇称。4.基于本实验建立的连接关系,晕带的最低态(124kev射线贯入能级)的激发能为618.9kev,该能量值比过去研究中的同一能级高出11.7kev。这表明原能级纲图中晕带的退激途径漏掉了一个11.7kev的"能隙"(根据Weisskopf估计,该能隙很可能由两个偶极跃迁构成)。该"能隙"的漏观测,正是导致过去实验中无法正确指定晕带自旋的原因所在;
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The structural evolution of an ice-quenched high-density polyethylene (HDPE) subjected to uniaxial tensile deformation at elevated temperatures was examined as a function of the imposed strains by means of combined synchrotron small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) techniques. The data show that when stretching an isotropic sample with the spherulitic structure, intralamellar slipping of crystalline blocks was activated at small deformations, followed by a stress-induced fragmentation and recrystallization process yielding lamellar crystallites with their normal parallel to the stretching direction. Stretching of an isothermally crystallized HDPE sample at 120 degrees C exhibited changes of the SAXS diagram with strain similar to that observed for quenched HDPE elongated at room temperature, implying that the thermal stability of the crystal blocks composing the lamellae is only dependent on the crystallization temperature.
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The structural evolution of high-density polyethylene subjected to uniaxial tensile deformation was investigated as a function of strain and after annealing at different temperatures using a scanning synchrotron small-angle X-ray scattering (SAXS) technique. The results confirm that in the course of tensile deformation intralamellar block slips were activated at small deformations followed by a stress-induced fragmentation and recrystallization process yielding thinner lamellae with their normal parallel to the stretching direction. The original sheared lamellae underwent severe internal deformation so that they were even less stable than the newly developed thinner lamellae. Accordingly, annealing results in a melting of the original crystallites even at moderate strains where the stress-induced fragmentation and recrystallization just sets in and generates a distinctly different form of lamellar stacks aligned along the drawing direction. It was found that the lamellae newly formed during stretching at moderate strains remain stable at lower temperature. Only at a very high annealing temperature of 120 degrees C can they be melted, leading to an isotropic distribution of the lamellar structure.