相对论自治角动量投影壳模型及其应用
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摘要
根据原子核结构研究的需要，我们根据相对论平均场理论，发展了一个基于球形谐振子基可用于带有形变的原子核的自洽计算的相对论平均场计算程序，通过引入角动量投影方法在相对论平均场的基础上计算具有固定形变原子核的转动谱，这就是相对论自洽角动量投影壳模型(RECAPS)。RECAPS兼有相对论平均场自洽性好，预言能力强和投影壳模型计算组态空间小，物理信息直观的优点。
我们分别在本文的第二章、第三章论述了相对论平均场和角动量投影方法的原理以及RECAPS的具体实现方法，并简单介绍了RECAPS程序的结构和使用。在第四章，我们用RECAPS计算了幻数核包括~(18)O、-~(90)Zr、~(140)Ce和~(208)Pb，以及变形核~(20)Ne、~(176)Yb、~(168)Er、~(160)Gd、~(160)Dy等多个核素，把我们的计算、别人的计算以及实验做了进行比较，证明了我们的程序是可靠的。我们还估算了~(16)O、~(40)Ca、~(208)P单极巨共振能量，所得到的结果与实验符合很好。除了稳定核，我们还研究了Li丰中子同位素以及~(32)Ca和~(19)B的独特性质，分析了晕现象，并结合我们程序的特点给出一个晕的判断方法。另外，我们还计算并简单分析了114号和116号超重元素。在本文的第五章，我们利用RECAPS计算了~(176)Yb、~(168)Er、~(160)Gd、-~(160)Dy和~(165)Ho的基带转动谱以及电磁跃迁B(E2)。并就~(165)Ho的特殊情况论述了对单核子运动对平均场的反作用。
这些计算都表明，RECAPS是描述和预言原子核性质的便利手段，相对论自洽角动量投影壳模型将可能成为用来研究原子核结论领域中各种现象和问题的强有力工具。
原子核是量子体系，量子体系模拟的理想工具是量子计算机。我们在第六章中介绍了量子计算机，并且研究了量子搜索算法的相位匹配，全同二玻色子的纠缠刻画等问题。
Due to the requirement of nuclear physics studying for new tools, we have developed the relativistic consistent quangular-momentum projected shell model(RECAPS) by combining relativistic mean field theory in spherical harmonic basis, which can give a self-consistent calculation for deformed nuclei, and the angular momentum projection method, which can calculate the rotational energy levels of nuclei with constant deformation. It has both the advantages of the self-consistent calculation with relativistic mean field, which is self-consistent and can predict many ground state properties of nuclei(but not excited states), and angular momentum projection method, which can describe both ground and excited states with a small basis space(but not self-consistent). The new model is self-consistent in calculation, also can describe or predict the properties of both ground and excited rotational band.
The fundamentals and the way of imlementation of RECAPS are discuessed in chapter 2 and chapter 3. The Fortran code is described, too. The spherical nuclei 16O, 90Zr, 140Ce and 208Pb, and the deformed nuclei 20Ne, 176Yb, 168Er, 160Gd and 160Dy and some other nuclei are calculated by RECAPS in chapter 4 and the results are also compared with others' calculations and experiments, which suggested that the RECAPS is reliable. The giant monopole resonance in 16O, 40Ca and 208Pb are claculated. The numeric results agree with experiments well. Besides stable nuclei, the unstabel nuclei such as Li's isotopes with very neutron-rich and 32Ca and 19B's characters are studied, too. The halo phenomena is analized carefully and a new way by our model's speciality to tell if a nuclei has halo. Then super heavy element 114 and 116 are also calculated and studied. In chapter 5, the ground rotational energy levels and corresponding electromagnetic transitions for 176Yb, 168Er, 160Gd, 160Dy and 165Ho are calculated. 165Ho's ro
tating band, as an special case, is studied on the counteraction of single nucleon in the mean field.
The calculations show that RECAPS is indeed a good method in description and prediction for the properties of nuclei. RECAPS is a useful model and may be a powful tool to study phenomena and problems in nuclear research.
Nuclei are quantum systems. Quantum computer is a perfect tool to simulate such systems. Quantum computer is described in chapter 6. The phase matching in the quantum searching algorithm is studied. The description of entanglement in identical two-particle systems is discussed, too.
我们分别在本文的第二章、第三章论述了相对论平均场和角动量投影方法的原理以及RECAPS的具体实现方法，并简单介绍了RECAPS程序的结构和使用。在第四章，我们用RECAPS计算了幻数核包括~(18)O、-~(90)Zr、~(140)Ce和~(208)Pb，以及变形核~(20)Ne、~(176)Yb、~(168)Er、~(160)Gd、~(160)Dy等多个核素，把我们的计算、别人的计算以及实验做了进行比较，证明了我们的程序是可靠的。我们还估算了~(16)O、~(40)Ca、~(208)P单极巨共振能量，所得到的结果与实验符合很好。除了稳定核，我们还研究了Li丰中子同位素以及~(32)Ca和~(19)B的独特性质，分析了晕现象，并结合我们程序的特点给出一个晕的判断方法。另外，我们还计算并简单分析了114号和116号超重元素。在本文的第五章，我们利用RECAPS计算了~(176)Yb、~(168)Er、~(160)Gd、-~(160)Dy和~(165)Ho的基带转动谱以及电磁跃迁B(E2)。并就~(165)Ho的特殊情况论述了对单核子运动对平均场的反作用。
这些计算都表明，RECAPS是描述和预言原子核性质的便利手段，相对论自洽角动量投影壳模型将可能成为用来研究原子核结论领域中各种现象和问题的强有力工具。
原子核是量子体系，量子体系模拟的理想工具是量子计算机。我们在第六章中介绍了量子计算机，并且研究了量子搜索算法的相位匹配，全同二玻色子的纠缠刻画等问题。
Due to the requirement of nuclear physics studying for new tools, we have developed the relativistic consistent quangular-momentum projected shell model(RECAPS) by combining relativistic mean field theory in spherical harmonic basis, which can give a self-consistent calculation for deformed nuclei, and the angular momentum projection method, which can calculate the rotational energy levels of nuclei with constant deformation. It has both the advantages of the self-consistent calculation with relativistic mean field, which is self-consistent and can predict many ground state properties of nuclei(but not excited states), and angular momentum projection method, which can describe both ground and excited states with a small basis space(but not self-consistent). The new model is self-consistent in calculation, also can describe or predict the properties of both ground and excited rotational band.
The fundamentals and the way of imlementation of RECAPS are discuessed in chapter 2 and chapter 3. The Fortran code is described, too. The spherical nuclei 16O, 90Zr, 140Ce and 208Pb, and the deformed nuclei 20Ne, 176Yb, 168Er, 160Gd and 160Dy and some other nuclei are calculated by RECAPS in chapter 4 and the results are also compared with others' calculations and experiments, which suggested that the RECAPS is reliable. The giant monopole resonance in 16O, 40Ca and 208Pb are claculated. The numeric results agree with experiments well. Besides stable nuclei, the unstabel nuclei such as Li's isotopes with very neutron-rich and 32Ca and 19B's characters are studied, too. The halo phenomena is analized carefully and a new way by our model's speciality to tell if a nuclei has halo. Then super heavy element 114 and 116 are also calculated and studied. In chapter 5, the ground rotational energy levels and corresponding electromagnetic transitions for 176Yb, 168Er, 160Gd, 160Dy and 165Ho are calculated. 165Ho's ro
tating band, as an special case, is studied on the counteraction of single nucleon in the mean field.
The calculations show that RECAPS is indeed a good method in description and prediction for the properties of nuclei. RECAPS is a useful model and may be a powful tool to study phenomena and problems in nuclear research.
Nuclei are quantum systems. Quantum computer is a perfect tool to simulate such systems. Quantum computer is described in chapter 6. The phase matching in the quantum searching algorithm is studied. The description of entanglement in identical two-particle systems is discussed, too.
引文
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