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Microscopic Single Particle Potential in Nuclear Matter

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Microscopic Single Particle Potential in Nuclear Matter

    Microscopic Single Particle Potential in

    Nuclear Matter

    2007IMP&HIRFLAnnualReport

    1--5MicroscopicSingleParticle

    PotentialinNuclearMatter

    includemicroscopicthreebodyforces[,

    ZuoWei

    thefulls.p.potentialcontainsthreeparts:

    ,()Ubhf()+U.()+Ubf()(1)

    Intherighthandsideoftheaboveequation,thefirstcontributioncorrespondstothelowest

    orderBHFs.

    p.potentialandisdeterminedbytheon

    shellG-matrix.Thesecondtermstemsfromthegroundstatecor

    relationsanditgivesthesecondandhigherorderhole

    linecorrectionstothes.P.potentialaccordingto theholelineexpansionofmassoperator[.

    Theleading-ordercontributionofthesecondtermcorresponds tothecorepolarization(alsocalledPaulirearrangement).ThePaulirearrangementofG-matr

    ixgivesthe

    higherordercorrectionsinthehole

    lineexpansionofmassoperatoranddescribestheinfluenceofthe groundstatetwo

    holecorrelationsonthes.P.potentialL..Thethirdtermistherearrangementcontri

    butioninducedbytheTBF,i.e.,

    ,?专(}I1,V?惫z)A(2)

    InFig.1weshowseparatelythethreedifferentcontributionstothes.P.potentialinsymmetricn

    uclear

matter(Solidcurves:Ubhf(k);Dashedcurves:Utbf();Dot

    dashedcurves:U.(k)).Itisseenthatthe

    BHFpart(solidcurves)isstronglyattractiveatlowmomentaanditsattractionincreasesasafunctionof

    density.Thegroundstatecorrelationsleadtoarepulsivecontributiontothes.p.potentia1.Itisclear

    fromFig.1thatthePaulirearrangementcontribution(dot

    dashedcurves)affectsthes.P.potentialmain

    lYat1owmomentabelowandaroundtheFermisurfaceandisexpectedtoweakenthemomentumdepend

    enceoftheopticalpotentia1.Thecontributionofthegroundstatecorrelationsisnotonlyimportantfor

    satisfactorilyreproducingthedepthoftheempiricalnuclearopticalpotentialL,butalsocrueialforresto-

    ringtheHugenholtzVanHoretheoremL53.

    However,itcannotprovideanyappreciateimprovementof

    thehigh

    momentumBHFs.P.potentialwhichhasbeenshowntobetooattractiveathighdensitiesand whosemomentumdependenceturnsouttobetooweakfordescribingtheexperimenta1ellipticflowdataof

    highenergyHICE.TherearrangementcontributioninducedbytheTBF(dashedcurves)turnsouttobe

    completelydifferentfromthePaulirearrangementeffect.Itsrepulsionincreasesmonotonicallvandrapidly

    asafunctionofmomentumanddensity.Itseffectismorepronouncedathighermomentaanditenhances

    remarkablythemomentumdependenceoftheS.P.potentialathighmomenta. .

    p=0.085fin-.

P=0.17fin.

    PO34fin/

    

    ,

    ,-IuI

    

    

    

    _l_一,一. =_'.'

    .

    /.

    ///.//一一

    ?_

    I/

    O24024024

    k(fm-)

    Fig.1Threecontributionstos.P.potentialvs.momentuminsymmetricnuclearmatter

    ordertodiscussclearlytheTBFeffects,wecompareinFig.2[Dottedcurves:s.P.potentialatth

    e

    BHFlevelpredictedbyadoptingtheA8twobodyforce;Dashedcurves:BHFs.P.potentialincluding

    theTBFeffectattheBHFlevelviatheO-matrix;Dotdashedcurves:includingtheTBFeffectviaboththe

    帅?d

    -;

    1

    

    

    mm

    .

?B

    

    

    "

    m

    ..m

    n

    .

    w.

    

    m

    a?

    m似譬

    

    

    T

    qIp

    8IMP&HIRFLAnnualReport2007

    G-matrixandtheTBFinducedrearrangementcontribution;Solidcurves:FullS.P. potentialincludingall

    thethreetermsofEq.(1)]theS.P.potentialsinsymmetricnuclearmatterobtainedinfourdifferentca

    ses.ItiSseenthattheS.P.potentialattheBHFlevelwithoutincludinganyTBFiSmostattractive.At

    lowdensitiesbelowandaroundthenormalnuclearmatterdensity,theTBFeffectsarereasonablysmal1.

    TheTBFeffectsturnouttobecomesignificantrapidlyasthedensityincreases.TheTBFeffectviaits

    modificationoftheG-matrixattheBHFlevelprovides3nmoderaterepulsionathighdensitieswhichiS

morepronouncedatlowermomentaandweakensthemomentumdependenceoftheS.P.pote

    ntia1.Itaf-

    l00

    0

    -

    100

    P0.17fm.P:0.34fm/

    /

    //

    ..

    ,-

    /.

    

    ./,一一一一.

    一一

    :

    024024

    k(fm)

    Fig.2TheS.P.potentialsinsymmetricnuclearmatterattWOtypicaldensities

    fectstheS.P.propertiesinawiderangeofnucleonmomentum,butitsrepulsioniSshowntobe

    muchwea

    kerascomparedtotheTBFinducedrearrangementeffect.TheTBF

    inducedrearrangementeffectprovides

    anadditiona1repulsiveandstronglymomentum

    dependentcontributionathighdensitiesandhighmomen

    ta.TherepulsionoftherearrangementcontributioninducedbytheTBFreduceslargelytheattr

    actionand

    enhancesstronglythemomentum-dependenceoftheS.P.potentialatlargedensitiesandhigh

    momenta.By

comparingthesolidcurvesandthedot

    dashedcurves.weseethatinclusionofthegroundstatecorrelation

    effectmakestheS.P.potential1essattractiveatlOWmomentaaroundandbelowtheFermimomentum.

    Whereas,abovetheFermimomentum,theeffectofthegroundstatecorrelationsvanishesrapidly.

    1ferences

    I-1]

    [2]

    [3]

    [4]

    [5]

    [63

    W.Zuo,A.Lejeune,U.Lombardo,eta1.,Nuc1.Phys.,A7o6(2002)418;Eur.Phys.J.,A14(2OO2)469

    J.P.Jeukenne,A.Lejeune,C.Mahaux.,Phys.Rep.,25C(1976)83.

    M.Baldo,I.Bombaci,L.S.Ferreira,eta1.,Phys.Lett.,B209(1988)135;Phys.Lett.,B215(1988)19

    M.Baldo,I.Bombaci,G.Giansiracusa,eta1.,Phys.Rev.,C40(1989)R491. W.Zuo,I.Bombaci,U.Lombardo,Phys.Rev.,C60(1999)024605.

    P.Danielewicz,Nuc1.Phys.,A673(2000)375.

    >0苫一.)

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