Determination of the spin-dependent potentials with the multi-level algorithm

格式：pdf
大小：88.54 KB
文档页数：6

下载文档原格式

Isospin Dependence of the Spin-Orbit Force and Effective Nuclear Potentials

a r X i v :n u c l -t h /9410036v 1 20 O c t 1994Isospin Dependence of the Spin Orbit Force and Eﬀective Nuclear PotentialsM.M.SHARMA 1,LAZISSIS 2,J.K ¨ONIG 2,and P.RING 21Max Planck Institut f¨u r Astrophysik,Karl-Schwarzschildstrasse 1,D-85740Garching,Germany2Physik-Department der Technischen Universit¨a t M¨u nchen,D-85747Garching,Germany(Received 16October,1993)The isospin dependence of the spin-orbit potential is investigated for an eﬀective Skyrme-like energy functional suitable for density dependent Hartree-Fock calcula-tions.The magnitude of the isopin dependence is obtained from a ﬁt to experimental data on ﬁnite spherical nuclei.It is found to be close to that of relativistic Hartree models.Consequently,the anomalous kink in the isotope shifts of Pb nuclei is well reproduced.PACS numbers :21.60Cs,21.10.Dr,21.10.GvTypeset Using REVTEXThe Hartree-Fock approach based upon phenomenological density dependent forces[1–3] has proved to be very successful in the microscopic description of ground state properties of nuclear matter and ofﬁnite nuclei over the entire periodic table.In all these calculations the spin-orbit potential has been assumed to be isospin independent.Its only parameter, the strength,is usually adjusted to the experimental spin-orbit splitting in spherical nuclei like16O.The exchange term,however,causes for nuclei with neutron excess a strong isospin dependence of the correponding single-particle spin-orbitﬁeld.In recent years Relativistic Mean Field(RMF)theory[4]with nonlinear self-interactions between the mesons has gained considerable interest for the investigations of low-energy phenomena in nuclear structure.With only a few phenomenological parameters such the-ories are able to give a quantitative description of ground state properties of spherical and deformed nuclei[5,6]at and away from the stability line.In addition,excellent agreement with experimental data has been found recently also for collective excitations such as giant resonances[7]and for twin bands in rotating superdeformed nuclei[8].In many respects the relativistic mean-ﬁeld theory is regarded as similar to the density-dependent Hartree-Fock theory of the Skyrme type[9,10]Recently,however,detailed investigations of high precision data on nuclear charge radii in Pb isotopes[11,12]and of shell eﬀects at the neutron drip line[13,14]have shown considerable diﬀerences between the Skyrme approach and the relativistic meanﬁeld theory.In fact, density dependent Hartree-Fock calculations with Skyrme[11]or Gogny forces[15],which used so far antisymmetrized,isospin independent spin-orbit interactions,were not able to reproduce the kink in the isotope shifts of Pb nuclei(see Fig.1).On the other hand, this kink is obtained in the RMF theory without any new adjustment of parameters[12]. Another considerable diﬀerence has been found in theoretical investigation of shell eﬀects in very exotic Zr-isotopes near the neutron drip line:in conventional non-relativistic Skyrme calculations the shell gap at isotope122Zr with the magic neutron conﬁguration N=82is totally smeared out[13],whereas relativistic calculations using various parameter sets show at N=82a clear kink in the binding energy as a function of the neutron number[14].Thisdiﬀerence is caused by the diﬀerent spin-orbit splitting of the single particle levels in these nuclei.Mass calculations within the Finite Range Droplet Model(FRDM)[16],which are based on an isospin dependent spin-orbit term carefully adjusted to experimental data,are in excellent agreement with the relativistic predictions.This gives us a hint,that one does not really need full relativistic calculations in order to understand these diﬀerences between conventional density dependent Hartree-Fock calcula-tions and RMF theory.A spin-orbit term with a properly chosen isospin dependence might represent the essential part of a relativistic calculation.In this letter,we therefore explore the isospin dependence of the spin-orbit term in non-relativistic Skyrme calculations and analyze the consequences of this on the nuclear properties.We start from the Skyrme type forceV(1,2)=t0(1+x0Pσ)δ(r1−r2)+t1(1+x1Pσ)(δ(r1−r2)k2+h.c.)+t2(1+x2Pσ)kδ(r1−r2)k(1)1+(p1−p2).In contrast to the conventional Skyrme ansatz,where the energy2functional contains a Hartree-and a Fock-contribution,we here neglect the exchange(Fock-)term for the spin-orbit potential in the last line of Eq.(1).Otherwise,the operator Pτwould be equivalent to+1for spin saturated systems.For the rest of the potential the Fock terms are included.The associated11parameters t i,x i(i=0...3),W0,x w andαof the Modiﬁed Skyrme Ansatz(MSkA)in Eq.(1)are determined by aﬁt to experimental data ofﬁnite spherical nuclei.The nuclear properties taken into consideration are the empirical binding energies and charge radii of the closed-shell nuclei16O,40Ca,90Zr,and208Pb.In order to take into account the variation in isospin we have also included Sn-isotopes116Sn, 124Sn,and the doubly closed nucleus132Sn as well as one of the lead isotopes214Pb.The resulting force and its parameters are presented in Table I.The spin-orbit term in the single-particleﬁeld derived from this force has the form Wτ(r)(p×σ)withWτ(r)=W1∇ρτ+,W2∇ρτ′=τ,(2)whereρτis the density for neutrons or protons(τ=n or p)and W1=W0(1+x w)/2, W2=W0/2.Conventional Skyrme calculations use a spin-orbit potential without isospin dependence and include the Fock term.This leads to x w=1and the relationship W1/W2= 2,which is nearly by a factor2diﬀerent from the value1.0005obtained within the modiﬁed Skyrme Ansatz MSkA(see Table I).It is interesting to note that theﬁt leads to a value of x w very close to zero,which corresponds to the one without the Fock term.In order to study the spin-orbit term in the RMF theory we start from the standard Lagrangian density[5]L=¯ψ(γ(i∂−gωω−gρ ρ τ−eA)−m−gσσ)ψ+14ΩµνΩµν+14RµνRµν+14FµνFµν(3)which contains nucleonsψwith mass m.σ-,ω-,ρ-mesons,the electromagneticﬁeld and nonlinear self-interactions U(σ)of theσ-ﬁeld,U(σ)=13g2σ3+1m2m∗2(C2σ+C2ω+C2ρ)∇ρτ+11W1=(C2σ+C2ω−C2ρ).(7)m2m∗2The r-dependence drops out in the ratio W1/W2which is1.13for the parameter set NL1[5] and1.10for the parameter set NL-SH[6].This is only slightly higher than the value1.0005 obtained in the Modiﬁed Skyrme Ansatz by theﬁt to the empirical data(see Table I).The absolute size of the spin-orbit term turns out to be r-dependent,which stems from the r-dependence of the eﬀective mass m∗(r).It can be approximated by m/m∗≈1+C2σ/m3ρ(r).A more careful consideration would therefore require an explicitly density dependent spin-orbit term.It has not been included in the present investigation.In Table II we show nuclear matter results obtained in the MSkA and compare it with the values from the conventional Skyrme force SkM∗.The saturation density is obtained asρ0=0.1531fm−3in MSkA.This is the same as the value obtained from an extensive ﬁt of the mass formula FRDM[16].The binding energy per particle E/A is16.006MeV, which is close to that of other Skyrme forces.The compression modulus K=319MeV is somewhat higher than that of the presently adopted Skyrme forces,but it is in good agreement with a recent analysis based upon the breathing mode energies[18].The third derivative e′′′=∂3(E/A)/∂ρ3has a value,which is close to that obtained in Ref.[18].The asymmetry energy J is close to the empirical value of33MeV.The eﬀective mass m∗is in good agreement with that of SkM∗.In Table III we show binding energies and charge radii obtained in the MSkA for a number of spherical nuclei and compare them with those from SkM∗.A comparison with the empirical values shows,that the binding energies obtained with MSkA have improved over those of SkM∗.The slightly reduced charge radii in MSkA seem to be connected with a slightly higher binding energy,which improves the results for the lighter Pb-isotopes.In general the charge radii are improved including that of16O.In Fig.1we show the isotope shifts of Pb nuclei for the Modiﬁed Skyrme Ansatz MSkA together with experimental data and results of conventional Skyrme calculations.For MSkAwe observe a clear kink at the double magic nucleus208Pb,whereas the conventional Skyrme force SkM∗with an isospin independent spin-orbit term gives an almost straight line.For the lighter isotopes both theories give excellent agreement,on the heavier side MSkA comes closer to the experimental isotope shifts.It may be recalled,that the RMF theory[12]is successful in reproducing the full size of this kink.MSkA uses a density independent spin-orbit force.In contrast the spin-orbit term derived from the RMF theory(see Eq.5)is implicitly density dependent through the density dependence of the eﬀective mass m∗(r).A density dependence of the spin-orbit term in Skyrme theory might improve the charge radii of the heavier Pb-isotopes.In Fig.2we present binding energies of Zr-nuclei about the neutron drip line as a function of the mass number.It is observed that in agreement with earlier investigations [13]within the conventional Skyrme theory shell eﬀects about the closed shell nucleus122Zr are weakened considerably.In contrast,RMF-calculations exhibit strong shell eﬀects in the drip line region.It has been surmised in Ref.[14]that this is caused by the diﬀerences in the spin-orbit terms in the two approaches.It is gratifying to see that introduction of an isospin dependent(not antisymmetrized)spin-orbit term in Skyrme theory leads to stronger shell eﬀects.This is also in agreement with the predictions of the FRDM[16],where also an isospin dependent spin-orbit term is used.A more quantitative analysis shows that the ratio W1/W2in FRDM is close to1.06for the Pb-nuclei and1.09for122Zr.Summarizing,we conclude that the isospin dependence of the spin-orbit term has an essential inﬂuence on the details of anomalous isotope shifts of Pb-nuclei.A new Modiﬁed Skyrme Ansatz has been proposed,and the isospin dependence of the spin-orbit strength has been determined.The magnitude of this isospin dependence x w is in agreement with the deductions from the relativistic mean-ﬁeld theory.A reasonably good agreement with the experimental data on the binding energies and charge radii has been obtained.The kink in the isotope shifts of Pb-nuclei has been obtained in the modiﬁed Skyrme ansatz.However, the agreement with the empirical isotope shifts for heavy Pb-nuclei is not so good as in the RMF theory.This calls for further investigations including a density dependence of thespin-orbit term.Finally a remark about the isospin dependence of the spin-orbit term:our investigations lead to the interesting result,that the parameter x w in the Eq.(1)is close to zero.This leads practically to an isospin independent single-particle spin-orbitﬁeld in Eq.(2).This is in agreement with relativistic calculations,where the entire isospin-dependence of the spin-orbit ﬁeld is caused by the parameter Cρin Eq.(5),which is in fact rather small.In contrast the two-body spin-orbit potiential in conventional Skyrme theory is isospin independent.The exchange term,however,causes a strong isospin dependence in the corresponding single-particle spin-orbitﬁeld.On the other hand,in the RMF theory the spin-orbitﬁeld has its origin in Lorentz covariance.There is no contribution from a two-body spin-orbit potential and an exchange term is therefore excluded.One of the authors(G.A.L)acknowledges support from the E.U.,HCM program,con-tract:EG/ERB CHBICT-930651,This work is also supported in part by the Bundesmin-isterium f¨u r Forschung und Technologie under the project06TM733.REFERENCES1 D.Vautherin and D.M.Brink,Phys.Rev.C5,626(1972).2P.Quentin and H.Flocard,Ann.Rev.Nucl.Sci.28,523(1978).3J.Decharge and D.Gogny,Phys.Rev.C21,1568(1980).4 B.D.Serot and J.D.Walecka,Adv.Nucl.Phys.16,1(1986)5Y.K.Gambhir,P.Ring,and A.Thimet,Ann.Phys.(NY)198,132(1990)6M.M.Sharma,M.A.Nagarajan and P.Ring,Phys.Lett.B312,377(1993)7 D.Vretenar,H.Berghammer,and P.Ring,Nucl.Phys.A,in print.8J.K¨o nig and P.Ring,Phys.Rev.Lett.71,3079(1993).9M.Thies.Phys.Lett.B166,23(1986).10P.-G.Reinhard,Rep.Prog.Phys.52,439(1989).11N.Tajima,P.Bonche,H.Flocard,P.-H.Heenen and M.S.Weiss,Nucl.Phys.A551, 434(1993)12M.M.Sharma,lazissis,and P.Ring,Phys.Lett.B317,9(1993).13J.Dobaczewski et al,,Phys.Rev.Lett.72,981(1994).14M.M.Sharma,lazissis,W.Hillebrandt,and P.Ring,Phys.Rev.Lett.72,1431 (1994).15J.L.Egido,private communication.16P.M¨o ller,J.R.Nix,W.D.Myers,and W.J.Swiatecki,At.Data Nucl.Data Tables(to be published).17J.K¨o nig,to be published18M.M.Sharma,The compressibility of nuclear matter revisited:the third derivative ofEOS from breathing mode,Daresbury preprint DL/NUC/P323T(December1991). 19 E.W.Otten,in Treatise on Heavy-Ion Science,edited by D.A.Bromley(Plenum,NewYork,1989)Vol7,p.517.FIGURESFIG.1.Isotopic shifts in the charge radii of Pb isotopes normalized to the nucleus208Pb as a function of the mass number A in the Modiﬁed Skyrme Ansatz(MSkA)as compared to the Skyrme force SkM∗and the empirical data.FIG.2.Binding energy of Zr isotopes at neutron drip line in the MSkA and SkM∗calculation.TABLESTABLE I.Parameters of the interaction in the modiﬁed Skyrme Ansatz(MSkA).t0=−1200.074(MeV fm3)x0=0.187 t1=396.302(MeV fm5)x1=0.018 t2=−105.579(MeV fm5)x2=−0.059 t3=10631.527(MeV fm3+3α)x3=0.046 W0=316.38(MeV fm5)x w=0.0005α=0.7557TABLE II.Nuclear matter properties obtained in the modiﬁed Skyrme Ansatz(MSkA).MSkA SkM∗TABLE III.The binding energies and charge radii obtained with the Modiﬁed Skyrme Ansatz (MSkA)in the Hartree-Fock approximation as compared with the normal Skyrme force SkM*and the empirical values.Binding Energies(MeV)Charge Radii(fm) Nuclei expt.MSkA SkM*expt.MSkA SkM*This figure "fig1-1.png" is available in "png" format from: /ps/nucl-th/9410036v1This figure "fig1-2.png" is available in "png" format from: /ps/nucl-th/9410036v1。

六边形堆砌的莫比乌斯图的Wiener指标

· 62·
河南科技大学学报：自然科学版
2012图7
H3 ， 5
（ Ⅰ）边界上有 2 k + 1 个 3 度点，任取一个点 v，按照图 8a 所示的两条虚线以及中间线，把顶点分成 3 部分以及单个顶点 w ，然后分别计算各部分的顶点到 v 的距离之和，去掉其中重复的计算即得［ 2 × 2 （ 1 + 2 + 3 + … + （ k + 1 ））－ 1］ + ［ 2 （ 1 + 2 + 3 + … + （ k + 1 ））－ 1］－（ 2 + 1 + 2 ） + 4 = 4 × （ k + 1）（ k + 2）（ k + 1）（ k + 2） +2 × － 3 = 3（ k + 1）（ k + 2）－ 3。 2 2
所以当 k ≥ 3 时， 2k + 1 W （ H3 ，［ 3 （ k + 1 ）（ k + 2 ）－ 3 + 3 （ k + 1 ）（ k + 2 ） + 3 + 2 （ k + 1 ）（ k + 2 ） + k（ k + 1）］ = 2k +1 ） = 2 2k + 1 2k + 1 ［ 8 （ k + 1 ）（ k + 2 ） + k（ k + 1）］ = ［（ k + 1 ）（ 9 k + 16 ）］。 2 2 证毕。参考文献：
六边形堆砌的莫比乌斯图的 Wiener 指标

Spin dependent structure function g

2
q k P
1
q k1 kg p
1
p
1
k1 P
k
1
p kg
p
1
a
b
Fig.
3: The diagrams, which determine the contribution to g2(x) of Compton amplitude with di erent number of partons in the initial and nal nucleon wave functions.
2 Quark-parton interpretation of g2(x)
We start from the standart de nition of the hadronic tensor:
4
M W = X(2 ) hp; sjJ jX ihX jJ jp; si (P + q ? P ) = X 4
q p1 P p2 p
3
p1
L =1 z
Fig.
L z =0
1: The naive parton model diagram of deep inelastic scattering. The arrows denote nucleon and guarks helicities for helicity- ip amplitude which determine structure function g2 (x)
Spin dependent structure function g (x) in quark-parton model. Possible interpretation and numerical estimates

Spin pumping by a field-driven domain wall

(1)
and contains, to lowest order in spatial derivatives of the magnetization direction, two contributions due the presence of electric current.
where σ↑ and σ↓ denote the conductivities of the majority and minority electrons, respectively, and ρs is their density diﬀerence. (The elementary charge is denoted by |e|.) The second term in Eq. (1) due to the current is the dissipative spin transfer torque39 that is proportional to β 19,20,21 . Both this parameter, and the Gilbert damping parameter αG , have their microscopic origin in processes in the hamiltonian that break conservation of spin, such as spin-orbit interactions. It turns out that the phenomenology of current-driven domain-wall motion depends crucially on the value of the ratio β/αG . For example, for β = 0 the domain wall is intrinsically pinned18 , meaning that there is a critical current even in the absence of inhomogeneities. For β/αG = 1 on the other hand, the domain wall moves with velocity vs . Although theoretical studies indicate that generically β = αG 26,27,28,30 , it is not well-understood what the relative importance of spin-dependent disorder and spin-orbit eﬀects in the bandstructure is, and a precise theoretical prediction of β/αG for a speciﬁc material has not been attempted yet. Moreover, the determination of the ratio β/αG from experiments on currentdriven domain wall motion has turned out to be hard because of extrinsic pinning of the domain and nonzerotemperature29,38 eﬀects. In this paper we present the theory of the current pumped by a ﬁeld-driven domain wall for the situation that spin is not conserved. In particular, we show that a ﬁeld-driven domain wall in a metallic ferromagnet generates a charge current that depends strongly on the ratio β/αG . This charge current arises from the fact that a time-dependent magnetization generates a spin current, similar to the spin-pumping mechanism proposed

光子自旋霍尔效应的弱测量理论及应用研究

摘要近年来，类似于电子系统中的自旋霍尔效应，一种新型的物理现象-光子自旋霍尔效应引起了人们的广泛兴趣。

光子自旋霍尔效应是指当一束空间受限的线偏振光在两种不同介质的界面处发生反射与折射时，自旋手性相反的光子沿垂直于折射率梯度的两个相反方向移动，从而导致入射光束分裂成两束左旋与右旋圆偏振光并分居入射面的两侧。

光子自旋霍尔效应与电子自旋霍尔效应具有类比的特性：其中自旋电子的角色由自旋光子扮演, 而外场的角色则由介质折射率梯度扮演。

自旋-轨道相互作用是产生光子自旋霍尔效应的根本原因，它表现为光的偏振与光束的传播轨迹之间的相互影响。

以往的研究大部分都局限于不同物理系统中光子自旋霍尔效应相关的理论计算与实验观测，而有关其应用方面的研究却鲜有报道。

值得关注的是，光自旋霍尔效应是一种灵敏的物理效应，它对于物理系统中结构参数的变化非常敏感。

因此，光子自旋霍尔效应在精密测量领域具有潜在的应用价值。

但是，光子自旋霍尔效应又是一种十分弱小的现象，它所产生的自旋位移值只有约几十纳米，一般的测量仪器都无法对它进行直接探测。

弱测量技术的出现为解决这一问题提供了可能。

弱测量是指在一般量子测量的过程中引入前选择与后选择的状态，当前选择态与后选择态接近正交时，测量结果可以得到显著放大。

因此，可以利用弱测量技术对不同物理系统中的光子自旋霍尔效应进行有效探测。

基于以上认识，本文对基于光子自旋霍尔效应弱测量理论进行了系统的研究，并在其应用研究方面开展了有特色的工作，取得了如下几项研究成果：（1）在光波波段，光子自旋霍尔效应非常的弱且相应的自旋位移值仅为几十纳米。

因此在以往的光子隧穿实验中，已有的实验仪器无法对其进行直接响应。

该工作通过构建一种势垒模型,利用弱测量技术首次观测到了光子隧穿中自旋霍尔效应。

实验证明光子隧穿效应不再是一个二维过程，而是一个三维的过程。

同时还发现，光子自旋霍尔效应所产生的自旋位移值甚至大于势垒的宽度。

研究结果不仅为光子隧穿效应的研究提供了新的思路，而且也为研制基于自旋的新型光电子器件提供了可能。

Spin-coating method, determination method for spin

专利名称：Spin-coating method, determination methodfor spin-coating condition and mask blank发明人：Hideo Kobayashi,Takao Higuchi申请号：US10405505申请日：20030403公开号：US07195845B2公开日：20070327专利内容由知识产权出版社提供专利附图：摘要：A spin-coating method according to the present invention includes a uniforming step of rotating a substrate at a predetermined main rotation speed for a predetermined main rotation time so as to primarily make a resist film thickness uniform, and asubsequent drying step of rotating the substrate at a predetermined drying rotation speed for a predetermined drying rotation time so as to primarily dry the uniform resist film. In the present invention, a contour map, for example, of film thickness uniformity within an effective region (critical area) shown in FIG. A is determined (generated), and resist-coating is performed by selecting a condition within the optimum region in this contour map in which the film thickness uniformity (within an effective region) can be the maximum, or within the region in which the film thickness uniformity (within an effective region) can be high enough for a desirably specified.申请人：Hideo Kobayashi,Takao Higuchi地址：Tokyo JP,Tokyo JP国籍：JP,JP代理机构：Sughrue Mion, PLLC更多信息请下载全文后查看。

Spin Current in Spin-Orbit Coupling Systems

which describes conventional semiconductors such as Si, Ge, GaAs and InSb. The geometrical structure of the eﬀect is such that for an electric ﬁeld applied on the z direction, a y -polarized spin current will ﬂow in the x direction. The electric ﬁeld induced spin current can be summarized by the following formula
PACS numbers: 72.10.-d, 72.15.Gd, 73.50.Jt
Spintronics aims to manipulate spins of particles. As such, an essential step in the ﬁeld is the generation of a reliable spin current. The injection of spin polarized electron current from a ferromangetic metal is not favorable because polarization is lost at the interface due to the conductance mismatch [1, 2]. Injections from ferromagnetic semiconductors into nonmagnetic semiconductors have been successfully developed in recent several years [3, 4, 5]. The theory of spin transport in the forementioned cases depends on the detailed mechanism of spin relaxation, where spin transport generally is a dissipative process. Recently, Murakami, Nagaosa and Zhang[6] have discovered a dissipationless and topological spin Hall current in the hole doped semiconductors with strong spin orbit coupling. These authors studied the eﬀective Luttinger Hamiltonian [12] HL = 5 1 [(γ1 + γ2 )P 2 − 2γ2 (P · S )2 ]. 2m 2 (1)

In order the spin dependence conduction component

专利名称：In order the spin dependence conduction component and the electronic parts and themagnetic part null发明人：猪俣浩一郎,斉藤好昭,岸達也申请号：JP1998039343申请日：19980220公开号：JP3556457B2公开日：20040818专利内容由知识产权出版社提供摘要：PROBLEM TO BE SOLVED: To provide a spin-dependent transmission element, which is capable of obtaining an extremely large magnetic resistance change rate at a room temperature and which has an amplification function. SOLUTION: A ferromagnetic layer 3 mode of more than one layer, electrode layers 1 and 5 mode of more than two layers, where at least one layer is constituted of a ferromagnetic body and dielectric layers (tunnel layers) 2 and 4 which are stacked and arranged between the ferromagnetic layer 3 and the electrode layers 1 and 5, and the multiple tunnel junctions of more than double junctions are provided. In a spin-dipendent transmission element, a discrete energy level is formed for the ferromagnetic layer 3, and an electrode for controlling the energy level is provided. The multiple tunnel junction is formed via a granular magnetic layer having ferromagnetic fine particles distributed in a dielectric matrix is formed, and the discrete energy level based on electrostatic energy in formed in the discrete energy level.申请人：株式会社東芝地址：東京都港区芝浦一丁目１番１号国籍：JP代理人：須山佐一更多信息请下载全文后查看。

二剂量法测定乳链菌肽效价及其C_运算程序_辛宇

第34卷第1期河北工业大学学报2005年2月V ol.34No.1JOURNAL OF HEBEI UNIVERSITY OF TECHNOLOGY February2005文章编号：1007-2373(2005)01-0080-05二剂量法测定乳链菌肽效价及其运算程序辛宇1，吴兆亮1，于广和2（1.河北工业大学生物工程系，天津300130；2.康益生物技术有限公司，天津301801）摘要：准确测定乳链菌肽效价是发酵法工业化生产乳链菌肽很重要的环节．效价检测过程中影响因素很多，其中标准品和样品所产生差异的一些因素对测定有很大的影响．本文利用二剂量法检测乳链菌肽效价，检测过程中只需研究样品溶液和标准品溶液对检测造成的影响，排除了其它影响因素；确定了效价计算的C++运算程序，避免了通过标准曲线法计算效价产生的误差．大幅度提高了测定乳链菌肽效价的准确性．关键词：乳链菌肽；效价；琼脂扩散法；二剂量法；运算程序中图分类号：TQ465.6文献标识码：ATwo Dosage Technique for Nisin Determination and the C++Program for Data CalculationXIN Yu1，WU Zhao-liang1，YU Guang-he2(1.School of Chemical Engineering and Technology,Hebei University of Technology,Tianjin300130,China;2.Kangyi CO.LTD.of Biological Technique,Tianjin301801,China)Abstract:The conditions of agar diffusion technique determining nisin potency were studied.It is very important to de-termine nisin potency for the fermentation industrialization of nisin.There are many impressing factors in the determiningcourse.For two dosage technique,only the differents of product and sample have efficient effects on nisin potency.Inthis way,the determination of nisin potency was simplified.A computer program was designed to calculate the data ob-tained.This program directly makes use of formula of two dosage technique to calculate potency.Key words:nisin；potency；agar diffusion technique；two dosage technique；program for data calculation０引言乳链菌肽（Nisin）是一种由34个氨基酸组成的多肽细菌素，由乳酸乳球菌乳酸亚种的某些菌株产生．Nisin是目前世界上唯一允许使用于食品防腐的抗生素．乳链菌肽效价的测定方法，最早是1934年Cox G.A.等人建议采用的四基兰还原法，后来又发明了许多液体检测法，如：延迟期法（美兰定量模型法）、比浊法[1]、试管稀释法[2]等，但这些方法操作繁琐，条件不易控制，检测结果不够稳定．目前用于检测食品中Nisin含量的最常用方法是琼脂扩散法，它是Tramer等人1964年建立起来的[3]．其原理是利用琼脂表面检测菌的生长显示出抑菌效果，为消除干扰因素的影响，常使Nisin标准液与未知样品在同一平板上扩散，并由它们的抑菌圈直径及标准液效价换算出未知液的效价．目前效价计算普遍采用标准曲线法[4]，但由于不同的检测平板之间存在较大差异，即使是同一批检测平板之间也存在差异，使用同一条标准曲线会对检测结果产生很大影响．因此考虑直接利用二剂量法公式[5]计算效价，并以计算机程序处理结果．此外标准曲线法要求所有检测平板高度一致，而实际操作中很难做到一致，因为影响检测的因素很多，如检测菌种类、检测培养基组成、检测平板的扩散系数、细菌吸附情况、最低抑菌浓度、pH等[6]，而且这些因素彼此又相互影响．如果采用二剂量法，平板制备的影响因收稿日期：2004-09-09作者简介：辛宇（1979-），男（汉族），硕士生．81辛宇，等：二剂量法测定乳链菌肽效价及其C++运算程序第1期素就可以忽略，只有对标准品和样品产生差异的一些因素才能对测定结果影响较大，但目前这方面的报道还没有．本文针对二剂量法的主要影响因素和应用此方法计算效价进行了研究．１材料与方法１．１材料检测菌种：藤黄八叠球菌，由天津康益生物技术有限公司提供．Nisin 标准品：Sigma 公司生产．检测培养基：胰蛋白胨0.8%，葡萄糖0.5%，Na 2HPO 40.2%，酵母粉0.25%，Nacl 0.5%，琼脂粉1.6%．１．２方法1.2.1分装和灭菌将检测培养基加热煮沸溶化，冷却至50℃，调pH 值至6.8分装于50mL 三角瓶，每瓶加量26mL ，8~10磅115℃灭菌20min ，置冰箱保存备用．1.2.2检测菌悬液制备检测菌接种于生长培养基斜面，30℃培养24h ，加入生理盐水2mL 使斜面上的菌苔洗脱下来，并呈均匀的菌悬液备用．取检测菌原液10020混匀，待冷却至50℃（此温度水浴控制）．将备用菌悬液（6mL ）全部倒入其中，单方向水平摇匀（不可产生气泡），迅速倾入水平放置的无菌平皿内，待其凝固后，置冰箱保存备用．1.2.4标准液制备用万分之一天平准确称取10mg Nisin 标准品，用5mL 刻度吸管取0.02mol/L HCl 溶液5mL 溶解标准品，检测时用0.02mol/L HCl 溶液分别将此溶液稀释成300倍和600倍．1.2.5打孔与加样用一无菌、直径7mm 中空打孔器在平板上打出8个孔洞．打孔时，打孔器与培养表面呈垂直角度，孔间距不得小于20mm ，且孔与孔间距相等．用无菌眼科摄子轻轻挑出琼脂柱，弃去．用微量加样器，分别加入等量标准品和被测样品不同倍数的稀释液，使孔洞充满，但不可外溢．盖上平皿盖，水平移至培养箱于37℃培养20~24h ，观测结果．1.2.6测量与计算于温箱内取出孵育后的检测平板，翻转平放台面上，用游标卡尺测量其抑菌环直径（如抑菌环出现复层，以最外层为准）．如样品溶液抑菌环直径大于标准品300倍稀释液抑菌环直径，或小于标准品600倍稀释液抑菌环直径，视为无效结果，应对样品重新估量稀释，重新点样培养．将测量数据代入效价计算公式，所得结果乘以样品与标准品的稀释倍数比（K ），即为样品实际效价值．效价计算公式如下：lg++式中：为标准溶液的效价（IU/mg ）；为低剂量样品溶液所致的抑菌圈直径（mm ）；为低剂量标准溶液所致的抑菌圈直径（mm ）；82河北工业大学学报第34卷２结果与讨论由于Nisin 在无保护剂的情况下很容易失活[7]，因此检测过程中标准品溶液和样品溶液的失活现象是最重要的影响因素．２．１标准品溶液中Ｎｉｓｉｎ的失活配制稀释300倍的标准品溶液，每隔20min 测定其效价，结果如图1．由图1可见，Nisin 的标准品溶液活性下降极快，2h 后效价几乎全部丢失．Nisin 的稳定性和溶液的pH 值有密切关系．在中性条件下Nisin 的溶解度不高且稳定性很差．因此标准品溶液配制后必须马上使用，如果待测样品较多，则必须每测一个样品更换一次标准品溶液．２．２发酵液中Ｎｉｓｉｎ的失活发酵结束后，每隔30min 测定发酵液效价，结果如图2．由图2可见，在发酵结束后3h 内效价没有多大变化．但应当注意，发酵稀释后也必须马上检测．２．３ｐＨ值对发酵液中Ｎｉｓｉｎ活性的影响pH 值对Nisin 的活性也有较大的影响[8]．在发酵结束后，取5个样品分别将其pH 调至2.0，2.5，3.0，3.5，4.0，然后分别在0h ，6h ，12h ，18h 和24h 测样品的效价，结果如图3．由图3可见Nisin 的抑菌活性与pH 值成反比，在pH 为2.5时发酵液效价相对比较稳定，效价降低速度比较缓慢，因此在发酵结束后应将发酵液pH 值调到2.5以下．２．４乳链菌肽失活原理无论标准品溶液还是发酵液在pH 值较高时都存在失活现象，其原理可解释如下．乳链菌肽（1~34）溶于pH 值为2的盐酸中，即使高温处理，其活性仍能保持较长时间；但当pH 值大于7时，其生物图1标准液效价变化曲线Fig.1The mutative curve of potency in standard solution 图2发酵液效价变化曲线Fig.2The mutative curve of fermented potency1.02.03.025002000150010005000/h效价/(I U /m L )12图3不同pH 值下发酵液效价变化曲线Fig.3The mutative curve of fermented potency along with different pH10203060004000200083辛宇，等：二剂量法测定乳链菌肽效价及其C++运算程序第1期活性迅速降低；当pH 值升为11时，60℃处理30min 其活性会完全丧失．Chan 等对此进行了研究，发现新制备的乳链菌肽其结构只有一种，但若用盐酸或醋酸处理，其结构发生变化，形成活性大小不同的几种分子．其中有二种是主要的：乳链菌肽（1~32）和（des △Ala5）乳链菌肽（1~32）．其中乳链菌肽（1~32）只有32个氨基酸残基，它缺失了DHB33和Lys34，而V al32（V al-NH 2）增加了一个氨基．在（des △Ala5）乳链菌肽（1~32）中，位点5(DHA5或Ala5)的DHA 被降解，由-△Ala5-Leu-变成-Pyr5-Leu6-．对两者抗菌活性的研究发现，同乳链菌肽（1~34）相比，乳链菌肽（1~32）的活性基本不变，而（des △Ala5）乳链菌肽（1~32）的活性至少降低了500倍．这个发现证明C-末端的△Ala33（或DHA33）、LYS34对于乳链菌肽的杀菌活性不是必需的，起关键作用的是△Ala5（或DHA5）．当乳链菌肽溶于pH 值为2左右的盐酸或醋酸中时，乳链菌肽（1~34）大部分变成乳链菌肽（1~32），因此总活性几乎不下降；当pH 逐渐升高时，（des △Ala5）乳链菌肽（1~32）所占的比例逐渐增高，总活性降低；当pH 升到11左右时，乳链菌肽主要以（des △Ala5）乳链菌肽（1~32）的形式存在，故活性基本丧失．２．５效价计算程序目前效价的计算普遍采用标准曲线的方法，但在检测过程中，发酵液的效价变化范围很大，可以从1000单位到20000单位，而标准曲线只有在较小的效价范围内才准确，特别需要指出的是，不同的检测平板差异较大，使用同一标准曲线误差较大，因此效价计算方法应该改进．如果利用二剂量法计算公式直接计算即可以解决以上问题，但当测量数据较多时利用此计算公式计算量太大，因此可编一个C++运算程序，利用计算机处理数据，程序如下：float X =0.0,t1,t2,t3；UpdateData (true )；t1=((m_R+m_r )-(m_d+m_D ))/((m_R+m_D )-(m_r+m_d ))；t2=t1*log10(2.0)；t3=pow (10.0,t2)；if (m_d<=m_R &&m_R<=m_D &&m_r<=m_d )X =2000.0；else if (m_d<=m_r &&m_r<=m_D &&m_R>=m_D )X =1000.0；else if (m_R>=m_D &&m_r>=m_D )X =1000.0；else if (m_R<=m_d &&m_r<=m_d )X =2000.0；else if (m_d<=m_R &&m_R<=m_D &&m_r>=m_d &&m_r<=m_D )X =2000.0；else if (m_R>=m_D &&m_r<=m_d )X=2000.0；elseX=0；m_Result =t3*X ；UpdateData (false )；该程序应用时将同一平板上实验得到的标准Nisin 溶液抑菌圈直径()和样品抑菌圈直径()数据按顺序输入程序，计算机将判断数据有无意义，并给出样品中Nisin 效价．计算机的应用大大简化了数据处理工作，尤其适合于大批量实验数据的处理．２．６两种效价计算方法的比较取一发酵液样品，在两块平板上点样，测量抑菌环直径，分别用标准曲线法和二剂量法计算效价，结果见表1．从表1结果可以看出采用二剂量法重复检测同一样品，效价相差127IU/mg ，而用标准曲线法重复检测同一样品，效价相差640IU/mg ，是二剂量法的5倍．配合以计算机程序，可以得出结论，二剂量法具有简便、准确的优点．84河北工业大学学报第34卷表１效价计算结果Ｔａｂ．１Ｒｅｓｕｌｔｏｆｐｏｔｅｎｃｙ标准曲线法二剂量法标准品(300~600)抑菌圈直径/mm 样品(600~1200)抑菌圈直径/mm效价/(IU/ml)标准品(300~600)抑菌圈直径/mm样品(600~1200)抑菌圈直径/mm效价/(IU/ml)16.08原液17.00487016.08原液17.00453213.9213.9413.9213.9416.44原液17.56423016.44原液17.556440515.0214.5215.0214.52３结论二剂量法检测发酵液中乳链菌肽效价有效的避免了标准曲线法造成的人为误差．由于使用二剂量法，只有对标准品和样品产生差异的一些因素才能对测定结果影响较大，这就排除了检测平板制备过程中诸多因素对检测结果造成的影响，大大简化了检测操作程序．应用计算机程序，简化了数据处理工作，尤其适于大批量数据的运算．综上所述，二剂量法具有快速、准确、可靠等优点．参考文献：[1]Hirsch A．Growth and nisin production of a strain of Streptococcus lactis[J]．J Gen Microbiol，1951(5)：208-221．[2]Berridge NJ，Barret J．Nisin production from Lactococcus lactis A.T.C. C.7962using supplemented whey permeate[J]．J Gen Microbiol，1952(6)：14-20．[3]Tramer J，Fowler GG．Estimation of nisin in foods[J]．Sci Food Agr，1964，15（8）：522-528．[4]刘稳，马桂荣．一种乳链菌肽生物测定方法及其FORTRAN运算程序[J]．食品与发酵工业，1997，23（3）：36-41．[5]邬行言，熊宗贵，胡章助．抗生素生长工艺学[M]．北京：化学工业出版社，1982．429-440．[6]吴琼．乳链菌肽效价测定方法的研究[J]．食品科学，1999，20（6）：56-59．[7]蒋永福，张焜，黎碧娜．天然防腐剂-乳酸链球菌素的研究进展[J]．精细化工，2002，19（8）：453-456．[8]侯革非，何仁．乳酸链球菌素抑菌效果的研究[J]．广西工学院学报，2001，12（4）：63-65．。

Effective Potential Models for Hadrons

HEPHY-PUB 621/95 UWThPh-1995-16 December 1995
arXiv:hep-ph/9601263v1 13 Jan 1996
EFFECTIVE POTENTIAL MODELS FOR HADRONS
Wolfgang LUCHA
Institut f¨ ur Hochenergiephysik, ¨ Osterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Wien, Austria
Contents
1 Nonrelativistic Potential 1.1 Nonrelativistic limit . . . . . . . . . . . . . . . 1.2 Static potential in quantum electrodynamics . 1.3 Static potential in quantum chromodynamics . 1.4 Lorentz structure of an interquark interaction 2 Relativistic Corrections 2.1 Spin-dependent corrections . . . . . . . . 2.2 Interaction with vector Lorentz structure 2.3 Interaction with scalar Lorentz structure 2.4 Generalized Breit–Fermi Hamiltonian . . . . . . . . . . . . . . 1 3 4 9 13 26 27 30 33 35
Chapter 1 Nonrelativistic Potential

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Determination of the spin-dependent potentials with the multi-level algorithm
Miho Koma
T
B E
Ntsl
r1
r2
r
Figure 1: How to construct By (r, 0)Ez (r, τ ) functions are constructed in a similar way.
Miho Koma∗
Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan E-mail: miho.koma@desy.de
2. Numerical procedures
We describe the procedure how to compute the ﬁeld strength correlator with the PLCF background using the multi-level algorithm (here we restrict to the lowest level). The standard Wilson action is most preferable for the multi-level algorithm because its action density is locally deﬁned. Thus we shall use this action in our simulation. Periodic boundary conditions are imposed in all directions. The essence of the multi-level algorithm is to construct the desired correlation function from the “sublattice average” of its components. In our case the corresponding parts are the twolink correlator and the ﬁeld-strength-inserted two-link correlator. For a schematic understanding, see Fig. 1, which illustrates the computation of the correlation function, By Ez , for V1′ . The sublattice is deﬁned by dividing the lattice volume into several layers along the time direction and thus a sublattice consists of a certain number of time slices. We then take averages of the components of the correlation function at each sublattice by updating the gauge ﬁeld (with a mixture of HB/OR), while the space-like links on the boundary between sublattices remain intact during the update. We repeat the sublattice update until we obtain stable signals for the components. Then, we multiply these averaged components in a desired way and complete the correlation function. This is how the correlation function is constructed from “one” conﬁguration. We then update the whole links without specifying any layers to obtain another independent gauge conﬁguration and start the above sublattice averaging for the next conﬁguration. In order to beneﬁt from this algorithm, we need to optimize the number of time slices in each sublattice Ntsl , and the number of the internal update Niupd for sublattice averaging. They depend on the coupling β and on the distances to be investigated. In principle, these parameters can be determined by looking at the behavior of the correlation function as a function of Niupd for several Ntsl . An empirical observation shows that aNtsl = 0.3 − 0.4 fm is optimal in order to suppress the ﬂuctuation of the correlation function among conﬁgurations. 216 / 3
PoS(LAT2005)216
(s1 · r)(s2 · r) s1 · s2 s1 · s2 − V4 (r) , V3 (r) + r2 3 3m1 m2
(1.1)
where the locations of quark and antiquark are r1 , r2 (r ≡ |r1 − r2 |). m1 , m2 (= m) denote their masses, s1 , s2 the spins, l1 = −l2 = l the orbital angular momenta. V0 (r) is the spin-independent static potential and Vi (r) (i = 1, . . . , 4) the spin-dependent potentials, which are expressed in terms of the correlation function of two ﬁeld strength operators attached to the quark and antiquark, respectively. The prime denotes the derivative with respect to r. The determination of these potentials through lattice Monte Carlo simulations goes back to the 1980s [2, 3, 4, 5]. The latest investigations are found in refs. [6, 7]. The qualitative (quantitative to some extent) ﬁndings which seem to be established are that while the spin-orbit potential V1 (r) contains the long-ranged nonperturbative component, all other potentials are only relevant to the short range as explained by one-gluon exchange interaction. However, the observed spin-dependent potentials from even the latest studies [6, 7] suffer from large numerical errors, which obscure the behaviors already at intermediate distances. For the phenomenological use of these potentials, it is clearly important to determine the form of the potentials as accurately as possible. For this purpose, we employ the multi-level algorithm [8] with a certain modiﬁcation as applied to the measurement of the electric-ﬂux proﬁle between static charges [9]. The problem is quite similar to this, since we need to measure the correlation function between the quark source and the ﬁeld strength operator. This algorithm also allows us to use the Polyakov loop correlation function (PLCF: a pair of Polyakov loops P separated by a distance r) as the quark source instead of † )/2i, where Uµν the Wilson loop. We use the ﬁeld strength operator deﬁned by Fµν = (Uµν − Uµν is the plaquette variable. The electric and magnetic ﬁelds are then Ei = F4i and Bk = Fi j . Noting Fµν Fρσ ≡ Fµν Fρσ P† P / P† P , where Fµν Fρσ P† P is the two ﬁeld strength correlator with the PLCF background, the spin-dependent potentials with the PLCF, for r = (r, 0, 0), are expressed as V1′ (r) = 2 V2′ (r) = 2 V3 (r) = 2 V4 (r) = 2