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Relativistic mean-field model with density-dependent meson-nucleon couplings

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arXiv:nucl-th/0703039v1 13 Mar 20071Relativisticmean-fieldmodelwithdensity-dependentmeson-nucleoncouplings

KentaMinagawa,MasahiroKawabataandKoichiSaitoDepartmentofPhysics,FacultyofScienceandTechnology,TokyoUniversityofScience,Noda278-8510,Japan

Withintherelativisticmean-fieldapproach,weextendtheMiyazakimodel,wheretheNNσandNNωinteractionsaremodifiedtosuppressthecouplingsbetweenpositive-andnegative-energystatesofanucleoninmatter.Assumingappropriatedensity-dependenceofthemeson-nucleoncouplings,westudynuclearmatterandfinitenuclei.Themodelcanreproducetheobservedpropertiesof16Oand40Cawell.Wealsoexamineifthemodelisnatural.

Recently,therelativisticmean-fieldapproachwithdensity-dependentmeson-nucleoncouplingsdrawsmuchattention.1)ItisaneffectivemodelfortheDirac-Brueckner-Hartree-Fock(DBHF)theory,2)whichcanreproducethesaturationprop-ertyofnuclearmatterusingtheone-bosonexchangepotentialsextractedfromthenucleon-nucleonscatteringdata.IntheDBHFcalculation,therelativisticeffectprovidesastrongdensity-dependentrepulsion,whichisoriginatedfromthenucleon-antinucleonpairterm(Zgraph),anditisvitaltoobtainthenuclearsaturationproperty.Itshouldbenoticedthatanuclearmodelbasedonthequarksubstructureofanucleon,forexample,thequark-mesoncoupling(QMC)model,3)thequark-meanfield(QMF)model,4)alsogivesdensity-dependentmeson-nucleoncouplingsthroughthescalarfieldinanuclearmedium,namelythescalarpolarizability.3)Thus,itseemsquitenaturalthatthemeson-nucleoncouplingsdependonthenuclearenvironment.Aboutadecadeago,Miyazaki5)hasproposedaninteresting,relativisticmean-fieldmodelfornuclearmatter,inwhichtheNNσandNNωverticesaremodifiedtoreducethecouplingsbetweenpositive-andnegative-energystatesofthein-mediumnucleon(the+−couplings).Althoughthe+−couplingsplayanimportantroleintherelativisticnuclearmodelsincludingnucleon-nucleus(NA)scattering(withtherelativisticimpulseapproximation(RIA))atintermediateenergies,itisknownthattheeffectofthecouplingtonegativestatesistoostrongtoproducetheNAscatter-ingobservablesatlowenergies.6)TjonandWallacehaveremediedthisproblembydevelopingageneralizedRIA,inwhichthedifferent+−couplingsfromtheusualRIAareintroduced.6)ThevertexmodificationstudiedbyMiyazaki5)mayenableustoincludesuchvariationofthe+−couplingsattherelativisticmean-fieldlevel.Themodifiedverticesfinallyresultinthedensity-dependentNNσandNNωcouplings,whichcansimultaneouslyreproducethenuclearmatterpropertiesandtheDiracscalarandvectoropticalpotentialsgivenbytheDBHFcalculation.InthisLetter,wegeneralizetheMiyazakimodel,andstudynotonlythenuclearmatterpropertiesbutalsosingle-particleenergiesoffinitenuclei.Lastly,wediscussnaturalnessofthemodel.7)

typesetusingPTPTEX.cls󰀍Ver.0.9󰀎2WenowmodifytheverticesofNNσandNNωcouplingsusingtheenergyprojec-tionoperators,Λ±(p)=(±/p+M)/2M,wherepisthefour-momentumofanucleonandMisthemass.Sincethevertex,Γ(=Iorγµ),isexpressedby

Γ=Λ+(p′)ΓΛ+(p)+Λ−(p′)ΓΛ−(p)+Λ+(p′)ΓΛ−(p)+Λ−(p′)ΓΛ+(p),(1)itmaybepossibletovarythestrengthofthe+−couplings,introducingtwoparam-eters,0≤λ1,λ2≤1,as5)

Γ→λ1[Λ+(p′)ΓΛ+(p)+Λ−(p′)ΓΛ−(p)]+λ2[Λ+(p′)ΓΛ−(p)+Λ−(p′)ΓΛ+(p)],(2)=(λ1−λ2)/p′Γ/p+(λ1+λ2)ΓM2

ρ0

󰀁b

,(4)

whereρ0isthesaturationdensity,andeachλhastwoparameters,aandb.Notethat,inthelimitρv→0,ΓisidenticaltotheoriginalformEq.(1).Usingthevertex(3)andthemean-fieldapproximationforthemesonfields,theLagrangiandensityisgivenby5)

L=¯ψ(/ˆp−M)ψ−12m2ωω2+gσ

2M2[(λv1−λv2)(¯ψ/←−ˆp)γ0(/ˆpψ)+(λv1+λv2)M2¯ψγ0ψ]ω,(5)whereσandωarerespectivelythemean-fieldvaluesoftheσandωmesons,andλs(v)i(i=1,2)istheparameterforthescalar(vector)vertex.ThemesonmassandtheNNσ(ω)couplingconstantinvacuumarerespectivelydenotedbymσ(ω)andgσ(ω).FollowingtheprescriptionexplainedinRef.5),wecanconstructaneffectiveLagrangiandensity,inwhichtheeffectofvariationofthe+−couplingsinmatterisincluded,

Leff=¯ψ(/ˆp−γ0Uv−M∗)ψ−12m2ωω2,(6)

wheretheeffectivenucleonmass,M∗,andtheDiracscalar,Us,andvector,Uv,potentialsinmatteraredefinedas

M−M∗=g∗σσ=−Us,Uv=g∗ωω,(7)3withtheeffectivecouplingconstantsg∗σ=1

2[(λv1+λv2)−(λv1−λv2)(m∗2−v2)]gω,(9)m∗=M∗/Mandv=Uv/M.Notethat,whenλs1=λv2=1,theeffectivecoupling

constantscoincidewiththoseintheMiyazakimodel.Theenergypernucleon,W,forsymmetricnuclearmatteristhenwrittenby

W=34M∗ρsCsˆρ󰀃1−m∗

Cvˆρ󰀃v

a3sbsˆρ(1−m∗),Cv=4cρv

−2(λv1−λv2)m∗v,(14)

bv=λs1+λs2−(λs1−λs2)(m∗2−2m∗+v2)+2(λs1−λs2)(1−m∗)vρs

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量子力学第二版(周世勋)

量子力学第二版(周世勋)


2µ
2µ
= qBnη = nB ⋅ qη
2µ
2µ
= nBNB ,
其中， M B
=
qη 2µ
是玻尔磁子，这样，发现量子化的能量也是等间隔的，而且
具体到本题，有
∆E = BM B
根据动能与温度的关系式
∆E = 10 × 9 × 10−24 J = 9 × 10−23 J
E = 3 kT 2
以及
1k ⋅ K = 10−3 eV = 1.6 × 10−22 J
∂ ∂r
(1 eikr ) − r
1 eikr r
∂ ∂r
(1 r
e
−ikr
ρ )]r0
=
iη [1 (− 2m r
1 r2
+ ik 1) − 1 (− rr
1 r2
−
ik
1 r
)]ρr0
可见，
ρ J2
=
−
ηk mr 2
ρr0
=
−
ηk mr 3
ρr
与rρ反向。表示向内(即向原点) 传播的球面波。
补充：设ψ (x) = eikx ，粒子的位置几率分布如何？这个波函数能否归一化？
1．3 氦原子的动能是 E = 3 kT （k 为玻耳兹曼常数），求 T=1K 时，氦原子的德布罗意波 2
长。
解 根据
2
PDF 文件使用 "pdfFactory Pro" 试用版本创建
知本题的氦原子的动能为
1k ⋅ K = 10−3 eV ，
E = 3 kT = 3 k ⋅ K = 1.5 ×10−3 eV , 22
解 关于两个光子转化为正负电子对的动力学过程，如两个光子以怎样的概率转化为正 负电子对的问题，严格来说，需要用到相对性量子场论的知识去计算，修正当涉及到这个过 程的运动学方面，如能量守恒，动量守恒等，我们不需要用那么高深的知识去计算，具休到 本题，两个光子能量相等，因此当对心碰撞时，转化为正风电子对反需的能量最小，因而所 对应的波长也就最长，而且，有
用基础量子力学解释氢原子

用基础量子力学解释氢原子

用基础量子力学解释氢原子四川师范大学本科毕业论文用基本量子力学解释氢原子——量子力学与氢原子的相遇相知相交学生姓名黄兰院系名称物理与电子工程学院专业名称物理学班级2008级 2 班学号2008070219指导教师侯邦品四川师范大学教务处二○一二年五月用基本量子力学解释氢原子本科生：黄兰指导老师：侯邦品内容摘要：主要从以下几个方面来运用基本量子力学解释氢原子。

1、氢原子的能级和能量本征函数。

首先介绍在量子力学中的波函数，再利用薛定谔方程来导出氢原子的能量本征函数，最后再分析它的物理含义。

2、氢原子的四个量子数的物理意义。

解释它们其与氢原子的能级的关系。

3、径向波函数和角度波函数。

主要是得出径向波函数和角度波函数同时给出它的物理意义。

4、简并性破除与量子激光。

氢原子的内部结构中电子在原子中受到的磁场的作用所产生的正常塞曼效应和反常塞曼效应，以及可能引起的电子跃迁。

5、氢原子的Stark效应。

氢原子在外场的作用下表现的Stark 效应，这部分将作简单的介绍。

关键词：量子量子力学氢原子 stark效应Schr?dinger方程Using quantum mechanics to explain the physical phenomena in hydrogen atomsAbstract:we shall use quantum mechanics to explain the physicalphenomena in the hydrogen atoms as follows: 1, the energy eigenfunctions for hydrogen are obtained after introducing the wave function in quantum mechanics . 2 , physical significance of the four quantum numbers in the hydrogen atoms.Here we shall focus on the hydrogen atom electron spin and its physical meaning of the four quantum numbers . 3, the radial wave function and the angle wave function . Coming to the radial wave function and the angle of the wave function at the same time we will get its physical significance. 4, the degeneracy is broken by magnetic fields. The normal and the anomalous Zeeman effect induced by magnetic field are introduced. 5, Finally, the the Stark effect in the hydrogen atomis briefly introduced.Key Words:Quantum Quantum mechanics Hydrogen atoms stark effect Schr?dinger equation目录引言 (4)1氢原子的能级和能量本征函数 (6)1.1波函数与Shr?dinger方程 (6)1.1.1波函数 (6)1.1.2波函数的归一化 (6)1.2 Shr?dinger方程 (7)1.2.1不含时Shr?dinger方程 (7)1.2.2 Shr?dinger方程的一般形式 (7)1.3中心力场中角动量守恒与径向方程 (7)1.4氢原子的能级与本征函数波函数 (8)2氢原子四个量子数 (11)2.1氢原子的定态薛定谔方程 (11)2.2 三个量子数 (12)2.3电子的自旋与第四量子数 (15)2.3.1斯特恩--盖拉赫实验(1921年) (15)3径向波函数和角度波函数 (17)3.1径向几率分布 (17)3.2电子的几率密度随角度的变化 (19)4氢原子四个量子数 ................................................................ 错误！未定义书签。

Search for a new state of matter – the Quark-Gluon Plasma一个物质–夸克胶子等离子体的新状态搜索 43

Search for a new state of matter – the Quark-Gluon Plasma一个物质–夸克胶子等离子体的新状态搜索 43

-- Fragmentation
-- multi-parton dynamics (recombination or coalescence or …)
-- Hydrodynamics (constituent quarks ? parton dynamics from gluons to constituent quarks? )
Nucleus-Nucleus Collisions and Volcanic Eruption
Volcanic high pT -- Strombolian eruption
Volcanic mediate pT – Spatter (clumps)
6
Volcanic low pT – Bulk matter flows
Evidence for Multi-parton Dynamics in Hadronization of Bulk Partonic Matter at RHIC
Huan Zhong Huang (黄焕中) Department of Physics and Astronomy
University of California Los Angeles
Rafelski+Danos, Molnar+Voloshin …..) Quark Recombination – (R.J. Fries et al, R. Hwa et al)
13
Constituent Quark Scaling
Constituent (n) Quark Scaling -- Meson n=2 and Baryon n=3 grouping
p td d td p N y d 2 1 π p td dtd p N 1 y i 12ic vo s ψ R () i)1( 0
格点量子色动力学进展.pptx

格点量子色动力学进展.pptx


The fDs puzzle?
Experimental results
Comparison
Independent determination of Vcs
More comparisons…
Is is a puzzle?
只有HPQCD的结果偏离最严重 Vcs需要单独确定 目前还不是很严重的问题…
理论方面的探讨
相关的唯象理论工作
Shallow bound state of two D mesons (S.L. Zhu et al, ) PRD77,034003 Tetra-quark resonance above threshold (X.-H Liu et al, PRD77, 094005) Threshold enhancement (J.L. Rosner, ) PRD76,114002
The Berlin wall & lattice QCD c o s t
m m
z
a
z 4, 7
Berlin wall crushing…
More physical…
Pion mass 700MeV below 300MeV where cPT starts to work…
Matrix elements
B_K 的计算 B ˆB KKBK K((8 0|/Q 3 ))L fSK s (L 232M )|(K K 2)0,2/Q 9L 1S L 2(s(43s)d()L)(sJd3)L
Renormalization dilemma
Continuum perturbation done in the MS-bar Naive Dimensional Regularization scheme (MS-bar NDR-scheme)