Strength of Giant Resonances

Giant ResonancesFirst Experiments:G.C.Baldwin and G.S. Klaiber, Phys.Rev. 71, 3 (1947)General Electric Research Laboratory, Schenectady, NYTheoretical Explanation:M. Goldhaber and E. Teller, Phys. Rev. 74, 1046(1948)University of IllinoisUniversity of ChicagoIt is an oscillation of the neutrons against the protons!Think electric dipolePositive “charge” is the collection of protons.Negative “charge” is the collection of neutrons.The Isovector Giant Dipole Resonance(this E. Teller is Edward Teller – think Hydrogen bomb)

40Ca20n20pIsovector Giant Dipole ResonanceAnalogous to charge distributionsMonopole L=0Dipole L=1Quadrupole L=2Octupole L=3Etc.There should be lots of “Giant Resonances”Isovector (n’s and p’s 180 o out of phase)Isoscalar (n’s and p’s in phase)Spin (spin up and down 180 o out of phase)

Shape Oscillations“Giant Resonance”1. Many Nucleons involved in motion (~ 10 in 40 Ca).2. Contains “most of” strength for that multipole.

Limit on strength for each multipole.Electromagnetic Operator Q L =∑ i r iLY LM (θ i )Y LM is a spherical harmonicfor multipole L, magnetic substate M.∑ n E n || 2 = S LEnergy Weighted Sum Ruleif there are no velocity dependent forces.E n is excitation energy of state|0> represents wave function of ground state“Giant Resonance”Contains ~90-99% of this strengthRest of strength in low lying states of nucleus.

1970: Only Dipole had been observed.Theorists: Came up with reasons why others weren’tthere!1971:Graduate Student: Ranier PitthanAdvisor: Thomas WalcherElectron scattering off of Ce, La, Pr targetsDarmstadt, GermanyElectrons interact only with the protons(no nuclear force)Excite Isoscalar and Isovector states ~ same.

Texas A&M1973

One in particular:Isoscalar Giant Monopole ResonanceThe “breathing mode”A 3 dimensional harmonic oscillatorSHO: =(k/m) 1/2 and E= ħLiquid drop model of nucleus:E GMR =(ħ/3roA 1/3 )*(KA/m) 1/2ro is nuclear radiusA is #(protons + neutrons)m is mass of nucleonKA is compressibility of nucleusCan get compressibility of nucleus from ISGMRIF WE CAN FIND IT!

Strength of Giant ResonancesLight Blue is what you see (the sum of strengths).Red is the Isoscalar Giant Monopole Resonance(what you want to measure)0.6Strength0.40.2Giant ResonancesISGMRLE ISGDRHE ISGDRISGQRHEORLEORIVGDRIVGQRTotal00 10 20 30 40E x (MeV)How do you separate out the Monopole??

Use an alpha particle beam to excite them!Alpha particle (2p, 2n): excites Isoscalar states strongly.Isovector states weakly.0.6Strength0.40.2Giant ResonancesISGMRLE ISGDRHE ISGDRISGQRHEORLEORIVGDRIVGQRTotal00 10 20 30 40E x (MeV)0.5Average Cross Section0.40.30.20.1Excite with AlphaParticles00 10 20 30E x (MeV)Need to do more!40

Distorted Wave Born ApproximationCalculationInelastic scattering E α =240MeV1000100d/d (mb/sr)101L=0L=1L=2L=3116 Sn(')E =240 MeV0.10 1 2 3 4 5 6 7 8 9 10 11 c.m. (deg)Measure at different scattering angles!Could separate Monopole from Quadrupoleby measuring 1.5 o to 4 o

Monopole Enhanced at 0 o .0.30 o Cross Section0.20.1Measure at 0 oThe Monopole!00 10 20 30 40Ex(MeV)0.34 o Cross Seciton0.20.1Measure at 4 oThe Quadrupole!00 10 20 30 40E x (MeV)

At Small anglesBeam would destroy detectors.Use Magnet to separate beam from inelastic scatteringBUT!Beam must be transported without hitting anything!Nobody had done 0 o inelastic scattering.

Measure over the minimum in the monopole.

later we succeeded at 0 o .oBUT average angle ~2 .

Built:New cyclotron - higher energy.New beam analysis/transport system - Clean beams.MDM spectrometer

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E GMR =ħ(K A /m) 1/2: mean square nuclear radiusm: nucleon massK A: compressibility of nucleusCompressibility of Nuclear MatterSimple Picture: Leptodermous ExpansionK A =K NM + K Surf A -1/3 +K vs ((N-Z)/A) 2 +K Coul *Z 2 /A 4/3K vs = K Sym + L(K’/K v -6)Where K NM : curvature of E/A around oK Sym : curvature of symmetry energyNote that E GMR depends on K NM AND K Sym !The Right Way to get K NMCalculate E GMR using effective interactions(each results in a specific K NM )Compare to experiment!Vretenar et al. PRC 68,024310(2003).Agrawal et al. PRC 68,031304(2003).Colò et al. PRC 70,024307(2004).Role of K v and K Sym in Infinite nuclear matter.

Microscopic Calculations:Non_Relativistic:Skyrme, Gogny effective interactions.Relativistic:NL1, NL3, etc. parameter sets.280Compare calculated to experimental EK nm obtained by comparing GMR energies and RPA calculations withGognyinteraction.GMR26024 Mg)40 Ca90 Zr144 SmKnm =231+-5 MeVKnm(MeV240208 Pb220116 Sn28 Si dhy et al. PRL82,691 (1999)dhy et al. PRC80,064318 (2009)2000 50 100 150 200250A24 Mg, 28 Si Péru,Goutte,Berger,NPA788, 44(2007)QuasiParticle RPA-HFB Gogny D1SK NM interaction dependent.Symmetry Energy dependence.Present: K NM ~ 220-240 MeV

Nuclear Matter Equation of StateA parametrization of the EOS to order 2 :(M. Farine et al. NPA 615,135(1997))E/A= A v +(K NM /18) 2 +[( n - p )/] 2 {J+(L/3) + (K Sym /18) 2 +..}+..Where =(- o )/ o and ( n - p )/ ~ (N-Z)/ASecond derivative leaves K NM and K SYM .K SYM goes as (N-Z)/A) 2

Present ResearchIncrease (N-Z/A) for K symMove away from stable nucleiD.H. YoungbloodY.-W.LuiJonathon Button(thesis project)Will McGrew (REU)Yi Xu (post doc joins 8/30/12)Hanyu Li (undergrad joins 9/1/12)Use unstable nuclei as beams:upgraded Cyclotron facility.Inverse reactions – Problem: Helium targetSolution: Use 6 Li targetX. Chen’s Thesis: 240 MeV 6 Li on 24 Mg, 28 Si, 116 Sn.Prove 6 Li scattering good for GMR.

Inelastic Scattering to Giant Resonances40006 116240 MeV Li + SnntsCou2000116 Sn avg =1.08 0 60 7000 10 20 30 40 50E x (MeV)d/d(mb/sr)1000100101116 Sn( 6 Li, 6 Li')E x =16.0MeVL=0L=1 T=0L=20 2 4 6 8(deg) cmL=3

Multipole Distributions116 SnFraction E0 EWSR/MeV0.30.20.16 LiE0Fraction E2 EWSR/MeV0.250.20.150.10.05E2005 15 25 35 5 15 25 35E x (MeV)E x (MeV)28 Si GMR0.1628 Si E0 EWSR/MeVFraction E0 EWSR/MeV0.120.080.046Li scatteringalpha scattering05 15 25E x (MeV)6 Li, agree for GR’s 116 Sn, 28 Si, 24 Mg.35

To study GMR in 27 Si6LiStops in targetto decay detector27Si6Li4.12sTarget27Si*10 -20 s23Mg11.32sto magneticspectrometer

Decay detector – Jonathan Button thesisWill McGrew: Analyzing dataTest runCalibrationDesigning Faraday Cup/Beam Stop

Other Monopole ThingsFraction E0 EWSR0.20.150.10.0590 Zr E016.9 MeV84%24.9 MeV22%Fraction E0 EWSR0.160.120.080.0492 M0 E016.6 MeV42%23.9 MeV65%05 10 15 20 25 30 35 40E x (MeV)0.1605 10 15 20 25 30 35 40E x (MeV)0.16Fraction E0 EWSR0.120.080.0492 Zr E016.5 MeV62%25.5 MeV38%Fraction E0 EWSR0.120.080.0496 M0 E016.2 MeV83%23.8 MeV20%05 10 15 20 25 30 35 40E x (MeV)05 10 15 20 25 30 35 40E x (MeV)0.16m1/m090 Zr 17.87 MeV92 M0 19.62 MeVFraction E0 EWSR0.120.080.04100 M0 E015.5 MeV97%23.6 MeV14%05 10 15 20 25 30 35 40E x (MeV)E GMR 92 Mo should be below 90 Zr??

KA(MeV)220200180160140K A for Mass 92 very different.K A from HF radiiZrMo12010088 90 92 94 96 98 100 102A92 MoK A 5 from expected value!

Nuclear equation of state influences many astrophysical processesDouble pulsar rotation (astro-ph 0506566)Binary mergers (astro-ph 0512126)Neutron star formation:Life of a type II supernovaProtonneutron star has aboutthe same density as nucleiStolen from :C. Hartnack and J. AichelinSubatech/University of NantesH. OeschlerTechnical University of Darmstadt