投影壳模型对丰中子核及原子核同核异能态的结构研究
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摘要
由于近年来放射性核束及γ探测装置在原子核实验上的应用,使人们探素极端条件下的原子核结构成为可能。同时,对核天体物理的研究也首先必须揭示丰中子、丰质子区的不稳定原子核的性质。受此驱动,我们采用投影壳模型研究了当前核物理的前沿课题之一:丰中子核结构与同核异能态结构。
投影壳模型从形变Nilsson单粒子态出发,通过BCS方法来处理对力,这样就形成了一个Nilsson+BCS的形变准粒子基。然后将角动量投影应用到该准粒子形变基上,最终得到一个投影的准粒子形变基。在此投影基下对角化哈密顿量得到系统的能量和本征函数。投影壳模型适合于包括偶偶核、奇质量核及奇奇核在内的形变原子核结构计算,具有组态空间小、运行速度快和适用范围广等优点。
本论文的理论研究紧密结合当前国际上核物理实验的研究热点。我们对A = 60和160质量区的丰中子原子核进行了直到高自旋(I = 20 )的计算。在A = 60质量区,我们对丰中子核Cr与Fe从中子数N = 30到44的同位素进行了研究。讨论集中在晕谱、转动惯量和电磁性质(B(E2), g-factor)上,通过在计算中引入中子g9/2轨道,我们成功地解释了晕谱和B(E2)的反常现象,揭示了N≈40同位素核的晕态附近软的特性并预言了66,68Fe中存在低能量的高K同核异能带。对于奇质量Cr核,我们主要探讨了9/2+同核异能态及其相应的转动带的本质,研究表明9/2+同核异能态具有长椭球形变,主要成分为K = 1/2[440]Nilsson轨道。对于A = 160质量区,我们对大形变丰中子偶偶核Nd和Sm从中子数N = 94到100的同位素以及奇质量核的一个代表159Sm进行了系统的研究。我们给出了所研究核的基带和边带能级,并讨论了其中负宇称2准粒子同核异能态及基于其上的转动带结构,还预言了一些质子2准粒子和中子2准粒子同核异能带。同时也预言了159Sm中的两个基于中子1准粒子的新转动带。
投影壳模型对上述两个丰中子核区原子核的系统计算尚属首次,计算近乎完美的再现实验数据,表明了投影壳模型对于描述不稳定核区的适用性,从而极大地推广了投影壳模型在核结构理论研究中的应用范围。
Due to the recent application of radioactive ion beam and advancedγdetectingdevice in nuclear experiments, it becomes possible to study the structure of nuclei un-der extreme conditions. Furthermore, to study Nuclear Astrophysics which is one ofthe current frontier topics in nuclear physics, one must reveal the property of unsta-ble nuclei in the neutron-rich and proton-rich regions. Motivated by these, we applythe projected shell model (PSM) to study some neutron-rich nuclei and the relevantnuclear isomer structure.
The PSM begins with deformed Nilsson single-particle states, and the pairingcorrelations are incorporated into these states by a BCS calculation. Thus the Nilsson-BCS calculation defines a deformed quasiparticle (qp) basis on which the PSM isbased. Then angular-momentum projection is carried out on those multi-qp states toform a projected basis. Finally a two-body shell model Hamiltonian is diagonalized inthis projected space, from which we get the eigenvalues and wave functions. The PSMhas some advantages such as the use of a small configuration space, fast computationprocess, and wide application domain. It can be applied to most deformed nucleiincluding even-even, odd-mass, and odd-odd nuclei.
The theoretical studies in this thesis have a close connection with the current nu-clear physical experiments. We perform PSM calculations for neutron-rich nuclei inthe mass A = 60 and 160 region up to high spins (I = 20 ). In the A = 60 massregion, we study systematically the structure of Cr and Fe isotopes with neutron num-ber from 30 to 44. Discussions focus on the character of the yrast spectra, momentsof inertia, and electromagnetic properties (B(E2), g-factor). By including the neutrong9/2 orbital in our calculation, we successfully interpret the irregularities found in theyrast spectra and B(E2) values. Our study reveals a soft property near the ground state of N≈40 isotopes and predicts low-lying high-K isomeric band in 66,68Fe. For theodd-mass neutron-rich Cr, the nature of the 9/2+ isomeric state and the associated ro-tational band are interpreted to have a main component of the K = 1/2[440] Nilssonstate with prolate deformation. In the A = 160 mass region, the strongly-deformedneutron-rich, even–even Nd and Sm isotopes with neutron number from 94 to 100 andthe odd-mass 159Sm (as a representative example for the odd-mass isotopes) are stud-ied. We present the ground band and side band energies for each isotope studied inthis mass region. The emphasis is given to rotational bands based on various negative-parity 2-qp isomers. Our calculations further predict several proton 2-qp and neutron2-qp isomeric bands. Meantime, new bands in 159Sm based on neutron 1-qp are alsopredicted.
The systemic calculations for these nuclei are carried out for the first time in PSM.A nearly perfect agreement between the PSM calculations and experiment indicatesthat the PSM is suitable for description of unstable nuclei, which extends greatly theapplication domain of the PSM in the nuclear structure study.
投影壳模型从形变Nilsson单粒子态出发,通过BCS方法来处理对力,这样就形成了一个Nilsson+BCS的形变准粒子基。然后将角动量投影应用到该准粒子形变基上,最终得到一个投影的准粒子形变基。在此投影基下对角化哈密顿量得到系统的能量和本征函数。投影壳模型适合于包括偶偶核、奇质量核及奇奇核在内的形变原子核结构计算,具有组态空间小、运行速度快和适用范围广等优点。
本论文的理论研究紧密结合当前国际上核物理实验的研究热点。我们对A = 60和160质量区的丰中子原子核进行了直到高自旋(I = 20 )的计算。在A = 60质量区,我们对丰中子核Cr与Fe从中子数N = 30到44的同位素进行了研究。讨论集中在晕谱、转动惯量和电磁性质(B(E2), g-factor)上,通过在计算中引入中子g9/2轨道,我们成功地解释了晕谱和B(E2)的反常现象,揭示了N≈40同位素核的晕态附近软的特性并预言了66,68Fe中存在低能量的高K同核异能带。对于奇质量Cr核,我们主要探讨了9/2+同核异能态及其相应的转动带的本质,研究表明9/2+同核异能态具有长椭球形变,主要成分为K = 1/2[440]Nilsson轨道。对于A = 160质量区,我们对大形变丰中子偶偶核Nd和Sm从中子数N = 94到100的同位素以及奇质量核的一个代表159Sm进行了系统的研究。我们给出了所研究核的基带和边带能级,并讨论了其中负宇称2准粒子同核异能态及基于其上的转动带结构,还预言了一些质子2准粒子和中子2准粒子同核异能带。同时也预言了159Sm中的两个基于中子1准粒子的新转动带。
投影壳模型对上述两个丰中子核区原子核的系统计算尚属首次,计算近乎完美的再现实验数据,表明了投影壳模型对于描述不稳定核区的适用性,从而极大地推广了投影壳模型在核结构理论研究中的应用范围。
Due to the recent application of radioactive ion beam and advancedγdetectingdevice in nuclear experiments, it becomes possible to study the structure of nuclei un-der extreme conditions. Furthermore, to study Nuclear Astrophysics which is one ofthe current frontier topics in nuclear physics, one must reveal the property of unsta-ble nuclei in the neutron-rich and proton-rich regions. Motivated by these, we applythe projected shell model (PSM) to study some neutron-rich nuclei and the relevantnuclear isomer structure.
The PSM begins with deformed Nilsson single-particle states, and the pairingcorrelations are incorporated into these states by a BCS calculation. Thus the Nilsson-BCS calculation defines a deformed quasiparticle (qp) basis on which the PSM isbased. Then angular-momentum projection is carried out on those multi-qp states toform a projected basis. Finally a two-body shell model Hamiltonian is diagonalized inthis projected space, from which we get the eigenvalues and wave functions. The PSMhas some advantages such as the use of a small configuration space, fast computationprocess, and wide application domain. It can be applied to most deformed nucleiincluding even-even, odd-mass, and odd-odd nuclei.
The theoretical studies in this thesis have a close connection with the current nu-clear physical experiments. We perform PSM calculations for neutron-rich nuclei inthe mass A = 60 and 160 region up to high spins (I = 20 ). In the A = 60 massregion, we study systematically the structure of Cr and Fe isotopes with neutron num-ber from 30 to 44. Discussions focus on the character of the yrast spectra, momentsof inertia, and electromagnetic properties (B(E2), g-factor). By including the neutrong9/2 orbital in our calculation, we successfully interpret the irregularities found in theyrast spectra and B(E2) values. Our study reveals a soft property near the ground state of N≈40 isotopes and predicts low-lying high-K isomeric band in 66,68Fe. For theodd-mass neutron-rich Cr, the nature of the 9/2+ isomeric state and the associated ro-tational band are interpreted to have a main component of the K = 1/2[440] Nilssonstate with prolate deformation. In the A = 160 mass region, the strongly-deformedneutron-rich, even–even Nd and Sm isotopes with neutron number from 94 to 100 andthe odd-mass 159Sm (as a representative example for the odd-mass isotopes) are stud-ied. We present the ground band and side band energies for each isotope studied inthis mass region. The emphasis is given to rotational bands based on various negative-parity 2-qp isomers. Our calculations further predict several proton 2-qp and neutron2-qp isomeric bands. Meantime, new bands in 159Sm based on neutron 1-qp are alsopredicted.
The systemic calculations for these nuclei are carried out for the first time in PSM.A nearly perfect agreement between the PSM calculations and experiment indicatesthat the PSM is suitable for description of unstable nuclei, which extends greatly theapplication domain of the PSM in the nuclear structure study.
引文
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