原子核巨共振是指基态原子核受到外场激发后,核内核子发生集体运动的现象。其中原子核巨四级共振作为巨共振中最重要的激发模式之一,是人们探究核物质状态方程特征参量和介质中核子–核子相互作用特性的有效工具。因此,针对产生原子核...原子核巨共振是指基态原子核受到外场激发后,核内核子发生集体运动的现象。其中原子核巨四级共振作为巨共振中最重要的激发模式之一,是人们探究核物质状态方程特征参量和介质中核子–核子相互作用特性的有效工具。因此,针对产生原子核巨四级共振的激发模式开展自洽的理论推导,对于核物质性质的研究具有重要意义。球谐函数通常被用来描述量子力学中粒子在有心力场(如氢原子)中的运动状态,是提取原子核巨共振中激发算符和激发模式公式的重要工具。然而,在之前原子核巨四级共振的相关理论工作中,人们通常利用一个经验方程来开展相应的研究。本论文从量子力学中的球谐函数出发,推导了原子核巨四级共振的激发算法和激发模式的形式,为原子核物理中巨共振现象的理论研究提供了一种新的方法,更为本科物理教学中的拓展部分提供了新的素材。在大学物理课堂中引入相关的科研工作,不仅可以引导学生的认知从课本内容过渡到前沿研究,更可以培养学生的科学思维和批判性思维,以达到科教融合的目的。Nuclear giant resonance refers to the collective motion phenomenon in the nucleus after the ground-state nucleus is excited by an external field. As one of the most important excitation modes in giant resonance, the nuclear giant quadruple resonance is an effective tool to explore the characteristic parameters in the equation of the state of nuclear matter and properties of in-medium nucleon-nucleon interaction. Therefore, it is of great significance to study the properties of nuclear matter to carry out the self-consistent theoretical derivation about the excitation mode of generating the nuclear giant quadruple resonance. Spherical harmonics are commonly used in quantum mechanics to describe the motion state of particles in a centered force field (such as hydrogen atoms), and serve as important methods to extract the formulas for excitation operators and modes within the nuclear giant resonance. However, previous theoretical work on the nuclear giant quadruple resonance often relied on an empirical equation for corresponding research. In this paper, we derive the excitation operator and the corresponding excitation modes for the nuclear giant quadrupole resonance using the spherical harmonic function in quantum mechanics. This approach offers a novel method for theoretical research on the giant resonance phenomenon in nuclear physics and provides new material for the expansion section of undergraduate physics curricula. Incorporating related scientific research into college physics classrooms not only helps guide students in transitioning from textbook content to frontier research but also fosters their scientific thinking and critical thinking, thereby achieving the integration of science and education.展开更多
By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that...By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.展开更多
文摘原子核巨共振是指基态原子核受到外场激发后,核内核子发生集体运动的现象。其中原子核巨四级共振作为巨共振中最重要的激发模式之一,是人们探究核物质状态方程特征参量和介质中核子–核子相互作用特性的有效工具。因此,针对产生原子核巨四级共振的激发模式开展自洽的理论推导,对于核物质性质的研究具有重要意义。球谐函数通常被用来描述量子力学中粒子在有心力场(如氢原子)中的运动状态,是提取原子核巨共振中激发算符和激发模式公式的重要工具。然而,在之前原子核巨四级共振的相关理论工作中,人们通常利用一个经验方程来开展相应的研究。本论文从量子力学中的球谐函数出发,推导了原子核巨四级共振的激发算法和激发模式的形式,为原子核物理中巨共振现象的理论研究提供了一种新的方法,更为本科物理教学中的拓展部分提供了新的素材。在大学物理课堂中引入相关的科研工作,不仅可以引导学生的认知从课本内容过渡到前沿研究,更可以培养学生的科学思维和批判性思维,以达到科教融合的目的。Nuclear giant resonance refers to the collective motion phenomenon in the nucleus after the ground-state nucleus is excited by an external field. As one of the most important excitation modes in giant resonance, the nuclear giant quadruple resonance is an effective tool to explore the characteristic parameters in the equation of the state of nuclear matter and properties of in-medium nucleon-nucleon interaction. Therefore, it is of great significance to study the properties of nuclear matter to carry out the self-consistent theoretical derivation about the excitation mode of generating the nuclear giant quadruple resonance. Spherical harmonics are commonly used in quantum mechanics to describe the motion state of particles in a centered force field (such as hydrogen atoms), and serve as important methods to extract the formulas for excitation operators and modes within the nuclear giant resonance. However, previous theoretical work on the nuclear giant quadruple resonance often relied on an empirical equation for corresponding research. In this paper, we derive the excitation operator and the corresponding excitation modes for the nuclear giant quadrupole resonance using the spherical harmonic function in quantum mechanics. This approach offers a novel method for theoretical research on the giant resonance phenomenon in nuclear physics and provides new material for the expansion section of undergraduate physics curricula. Incorporating related scientific research into college physics classrooms not only helps guide students in transitioning from textbook content to frontier research but also fosters their scientific thinking and critical thinking, thereby achieving the integration of science and education.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060 and the Natural Science Foundation of Shandong Provirice of China under Grant No. Y2004A09
文摘By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.
