* * * * 3 bold)
Student ID: (××× year × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × month × day × month × month × day × month × month × month × month × month × day × month × month × month × month × month ×
Instructor: (××× year × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × month × day × month × month × month × month × day × month × month × month × month × month ×
Major: (XX × YY × YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY × YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY× YY ×
Grade: (xx years × months × days × months × days × months × days × months × days × months × days × months × days × months × days × days × months × days × months × days × days × months × days × days × months × days × days × months × days × days × months × days × months × days × days × months × days × months × days × months × days × months × days ×
School: (××× year × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × day × month × month × day × month × month × day × month × month × day × month × month × day × month × month × month × day × month × month × month ×
4.2 Abstract: Abstract is a brief statement of the content of the paper, without comments and annotations, and should be stated in the third person. It should be independent and self-sufficient, that is, you can get the necessary information without reading the full text of the paper. The content of the paper should contain the same amount of main information as the paper, so that readers can determine whether it is necessary to read the full text, and it can also be used for secondary documents such as abstracts.
Generally, the purpose of research work, experimental research methods, results and final conclusions should be explained, with the focus on results and conclusions. In general, charts, tables and formulas are not needed. , symbols, terms and illegal units of measurement that are not commonly used.
The abstract page is placed behind the cover.
The Chinese abstract is generally about 300 words, with the 5th song style, and the abstract should contain key words.
English abstract is the English translation of Chinese abstract, and the English abstract page is placed after the Chinese abstract page. Those who apply for a degree must have it, and those who don't apply for a degree don't need an English abstract.
Keywords: keywords are words or terms selected from papers used for document indexing to express the information items of the full-text theme. Generally, 3 ~ 5 words should be selected as keywords for each paper. Keywords are separated by commas, and the last word is not punctuated. Ranked under the abstract of the same language, the text is prominent. If possible, try to use the standardized words provided by China Thesaurus and other glossaries.
4.3 Table of Contents Page: A table of contents page consists of serial numbers, names and page numbers of chapters, sections, articles, appendices and titles. Start a new page after the abstract page, and the chapters, sections and paragraphs are numbered 1. 1 respectively.
1. 1.2 and other numbers are marked in turn, and the directory page can be omitted.
5. Main body part
5. 1 format: the writing format of the main part begins with an introduction and ends with a conclusion. The main part must start on a new page.
5.2 serial number
Each chapter of graduation thesis should have a serial number, coded with Arabic numerals, and the hierarchical format is:
1×××× (bold No.3, center)
××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
1. 1××× (small three bold, left)
××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
1. 1. 1××× (bold No.4, left)
××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
example
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The phase transition between nucleus and strongly interacting matter establishes the concept of photon, blows the charge signal and guides people to explore the micro-world. Further research shows that the particles that make up the material world can be divided into hadrons and leptons, and the interactions between particles can be divided into four categories: gravitational interaction, electromagnetic interaction, weak interaction and strong interaction. Particles participating in strong interaction or systems with strong interaction are collectively called strong interaction substances (including hadron substances and quark substances) and their special forms-nuclei (systems composed of finite hadrons). The research on the phase structure and phase transition of nuclear and strong interaction system is very important for understanding the phase structure and phase transition of strong interaction system and the origin and evolution of the universe, and may become a test platform for statistical physics of finite systems. Therefore, in recent years, the study of the phase transition between nuclear and strong interaction systems is not only an important frontier topic in the fields of nuclear physics, astrophysics, cosmology and particle physics, but also attracts great attention in the fields of finite quantum many-body systems and statistical physics. This paper briefly introduces the research status of phase and phase transition in nuclear-strong interaction system.
Phase and phase transition of nucleus
2. Single particle motion and collective motion of1nucleus
The nucleus is a bound system composed of a limited number of hadrons, in which the nucleus (protons and neutrons) naturally has single particle motion. The shell model is established to successfully describe the corresponding properties of the nucleus. The experimental study of nuclear energy spectrum and electromagnetic transition shows that the nucleus also has integral motion, and the concept that the nucleus has collective motion modes such as shape, vibration and rotation is established. People usually describe the shape of the kernel according to the radius of the spherical harmonic function expansion, and the corresponding deformation is called extreme deformation (as shown in figure 1). There are many kinds of observed and predicted nuclear shapes, the most important one is quadrupole deformation, and the highest polar deformation observed in the experiment is 16 polar deformation. According to the viewpoint of shell model and collective model, magic number nuclei are mostly spherical, while those that deviate from the whole shell are deformed nuclei, which can be subdivided into long ellipsoid, flat ellipsoid, triaxial asymmetry, pear shape, banana shape and spindle shape. At the same time, the nucleus may also have the phenomenon of * * *(shape * * *).
Figure 1 is a schematic diagram of the shape of the polar deformation of the nucleus (taken from the literature, the shape phase transition of the ground state nucleus generally exists in all mass regions. The results show that even in the low excited state of the nucleus, there may be a phase transition between various shapes, and the mechanism of the phase transition from vibration to fixed-axis rotation in the low excited energy spectrum may be that with the increase of angular momentum, the vibration gradually weakens, the rotation gradually strengthens, and the critical point later becomes a good fixed-axis rotation. On the other hand, the study of nuclear phase transformation directly from the nuclear level has also made progress [36].
3 phase transition of strongly interacting substances
3. Liquid-gas phase transition of1nucleus
As early as 1930s, people put forward Fermi gas model and droplet model of nuclear structure according to the properties of nuclear observed by experiments. This shows that under some conditions, the nucleus is liquid, or some of its properties are liquid; On the other hand, nuclei appear in the gas phase. At this level, the so-called "liquid phase" and "gas phase" are only phenomenological expressions of the different properties of the nucleus, and they don't care about the evolution between the two phases at all.
In the mid-1990s, with the deepening of the research on intermediate and high energy nuclear collisions, people studied the relationship between the temperature of the system formed by nuclear collisions and the excitation energy of the nucleus. The first result [37] reported by GSI in Germany, as shown in Figure 3, is obviously the same as the relationship between temperature and average energy of a single particle in liquid phase, gas phase and their phase transitions, thus indicating that a liquid-gas phase transition has taken place. Because the phase transition is usually studied from thermodynamic function and equation of state, the liquid-gas phase transition of nucleus naturally becomes a breakthrough in studying the equation of state of nuclear matter, and then studying the state and evolution of nuclear celestial bodies. Therefore, nuclear physicists in international laboratories such as Brookhaven National Laboratory, Lawrence National Laboratory, Michigan State University, Texas College of Agricultural Machinery, Dubna in Russia, GSI in Germany, GANIL and LNS Saclay in France, del Sud National Laboratory in Italy have systematically studied the relationship between the temperature of the system formed by intermediate and high energy nuclei and the single event excitation energy. The methods of heat capacity, high fragmentation, collective expansion, finite size and Fisher's Law scale [38 ~ 4 1], nuclear Boltzmann equation [42], finite system fermion-molecular dynamics [43] and total antisymmetric molecular dynamics [44] have been developed theoretically, and these systems are studied by penetration theory [45]. The results show that these studies need to be further studied, especially the order parameters of phase transition, isospin correlation, critical temperature of phase transition and its influence on the structure and evolution of nuclear celestial bodies.
Fig. 3 Relationship between temperature and mononucleon energy of the system formed by nuclear collision (from reference [37])
Fig. 3 the relationship between the temperature of the system formed by nuclear-nuclear collision and the energy of a single nuclear (quoted from references). [37]) 3.2 Phase transition of strongly interacting substances.
Strongly interacting matter is a general term for hadron matter composed of hadrons (including baryons and mesons) and quark matter composed of quarks and gluons. Therefore, studying the composition, properties, phase structure and phase transition of strongly interacting substances is an important subject of equal concern in nuclear physics, particle physics, astrophysics and cosmology.
We already know that hadron is made up of quarks and gluons. It can be compared to a pocket in which quarks and gluons are bound. The pocket constant provided by the difference between the interaction between quarks and gluons in the pocket and the action in a strongly interacting vacuum is usually used to describe the strength of binding. With the increase of the temperature of hadron material system, the energy of hadron irregular motion and the energy of quarks and gluons in it will increase, and the pressure will also increase. The increase of system density will also cause the increase of pressure. When the vacuum pressure of the system can't balance the pressure inside the hadron, the hadron will disappear, and quarks and gluons will become quarks, that is, phase changes can occur. Quark matter formed by the release of confinement may exist in plasma state, thus forming quark gluon plasma (QGP). On the other hand, the basic theory describing the strong interaction is Quantum Chromodynamics (QCD), which has the property of asymptotic freedom (the above phase transition is the result and expression of asymptotic freedom) and zero-mass fermions (quarks, etc.). ) There is equivalence between the left hand and the right hand, which is called chiral symmetry. However, the real hadron world is in the low energy region, quarks are confined, have mass and have no chiral symmetry. However, after the confinement phase transition, the chiral symmetry may recover, resulting in chiral recovery phase transition. Furthermore, we know that phonons can provide weak attraction between electrons due to the interaction of electroacoustic interaction, thus forming electron Cooper pairs and superconductivity; Quarks can also form quark-Cooper pairs because the special interaction paths between quarks are inherently attractive. Because quarks have three colors, three colors are mixed or one color is opposite to it to form colorless hadrons, but the pair formed by two quarks is colored, so the condensed state formed by quark-Cooper pairs is called colored superconducting state [46]. According to the color and taste structure of quark-Cooper pairs in the color superconducting state, the color superconducting state has many phases (sometimes referred to as color superconducting phases for short), such as two-color superconducting and color-taste-locked color superconducting. Current research shows that the phase diagram of strongly interacting substances is shown in Figure 4.
Fig. 4 The phase diagram of strongly interacting substances (taken from Molly) is interested in nuclear physics, particle physics, astrophysics, cosmology, statistical physics and other fields. Much significant progress has been made. However, both specific problems and research methods need further study.
Key words: nucleus, strongly interacting matter, phase and phase transition.