Giant Resonances First Experiments: G.C.Baldwin and G.S. Klaiber, Phys.Rev. 71, 3 (1947) General Electric Research Laboratory, Schenectady, NY Theoretical Explanation: M. Goldhaber and E. Teller, Phys. Rev. 74, 146(1948) University of Illinois University of Chicago It is an oscillation of the neutrons against the protons! Think electric dipole Positive 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)
4 Ca 2n 2p Isovector Giant Dipole Resonance Analogous to charge distributions Monopole L= Dipole L=1 Quadrupole L=2 Octupole L=3 Etc. There should be lots of Giant Resonances Isovector (n s and p s 18 o out of phase) Isoscalar (n s and p s in phase) Spin (spin up and down 18 o out of phase)
Shape Oscillations Giant Resonance 1. Many Nucleons involved in motion (~ 1 in 4 Ca). 2. Contains most of strength for that multipole.
Limit on strength for each multipole. Electromagnetic Operator Q L = i r i L Y LM (θ i ) Y LM is a spherical harmonic for multipole L, magnetic substate M. n E n <n Q L > 2 = S L Energy Weighted Sum Rule if there are no velocity dependent forces. E n is excitation energy of state > represents wave function of ground state <n represents wave function of excited state For L 2 S L = (ħ 2 L(2L+1)A)/2 m * < r 2L-2 > Giant Resonance Contains ~9-99% of this strength Rest of strength in low lying states of nucleus.
197: Only Dipole had been observed. Theorists: Came up with reasons why others weren t there! 1971: Graduate Student: Ranier Pitthan Advisor: Thomas Walcher Electron scattering off of Ce, La, Pr targets Darmstadt, Germany Electrons interact only with the protons (no nuclear force) Excite Isoscalar and Isovector states ~ same.
Texas A&M 1973
One in particular: Isoscalar Giant Monopole Resonance The breathing mode A 3 dimensional harmonic oscillator SHO: =(k/m) 1/2 and E= ħ Liquid drop model of nucleus: E GMR =( ħ/3roa 1/3 )*(KA/m) 1/2 ro is nuclear radius A is #(protons + neutrons) m is mass of nucleon KA is compressibility of nucleus Can get compressibility of nucleus from ISGMR IF WE CAN FIND IT!
Strength of Giant Resonances Light Blue is what you see (the sum of strengths). Red is the Isoscalar Giant Monopole Resonance (what you want to measure).6 Strength.4.2 Giant Resonances ISGMR LE ISGDR HE ISGDR ISGQR HEOR LEOR IVGDR IVGQR Total 1 2 3 4 E 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..6 Strength.4.2 Giant Resonances ISGMR LE ISGDR HE ISGDR ISGQR HEOR LEOR IVGDR IVGQR Total 1 2 3 4 E x (MeV).5 Average Cross Section.4.3.2.1 Excite with Alpha Particles 1 2 3 E x (MeV) Need to do more! 4
Distorted Wave Born Approximation Calculation Inelastic scattering E α =24MeV 1 1 d /d (mb/sr) 1 1 L= L=1 L=2 L=3 116 Sn( ') E =24 MeV.1 1 2 3 4 5 6 7 8 9 1 11 c.m. (deg) Measure at different scattering angles! Could separate Monopole from Quadrupole by measuring 1.5 o to 4 o
Monopole Enhanced at o..3 o Cross Section.2.1 Measure at o The Monopole! 1 2 3 4 Ex(MeV).3 4 o Cross Seciton.2.1 Measure at 4 o The Quadrupole! 1 2 3 4 E x (MeV)
At Small angles Beam would destroy detectors. Use Magnet to separate beam from inelastic scattering BUT! Beam must be transported without hitting anything! Nobody had done o inelastic scattering.
Measure over the minimum in the monopole.
later we succeeded at o. o BUT average angle ~2.
Built: New cyclotron - higher energy. New beam analysis/transport system - Clean beams. MDM spectrometer
Measuring only horizontal angle. Average over vertical angle.
Added measurement of vertical angle 9 Zr Spectrum 4 Counts/channel 2 9 Zr( ') c.m. =.4 o 1 2 3 4 5 6 7 E x (MeV) Multipole Distributions Fraction E EWSR/MeV Fraction E1 EWSR/MeV.2.1.1.5 E 1+-12% 5 1 15 2 25 3 35 4 E1 81+-1% 5 1 15 2 25 3 35 4 E x (MeV) tion E2 EWSR/MeV Frac Fraction E3 EWSR/MeV.2.1.1.5 5 1 15 E3 78+9-15% We can separate multipoles! E2 88+11-8% 2 25 3 35 4 5 1 15 2 25 3 35 4 E x (MeV)
E GMR =ħ(k A /m<r 2 >) 1/2 <r 2 >: mean square nuclear radius m: nucleon mass K A: compressibility of nucleus Compressibility of Nuclear Matter Simple Picture: Leptodermous Expansion K A =K NM + K Surf A -1/3 +K vs ((N-Z)/A) 2 +K Coul *Z 2 /A 4/3 K vs = K Sym + L(K /K v -6) Where K NM : curvature of E/A around o K Sym : curvature of symmetry energy Note that E GMR depends on K NM AND K Sym! The Right Way to get K NM Calculate E GMR using effective interactions (each results in a specific K NM ) Compare to experiment! Vretenar et al. PRC 68,2431(23). Agrawal et al. PRC 68,3134(23). Colò et al. PRC 7,2437(24). 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. 28 Compare calculated to experimental E K nm obtained by comparing GMR energies and RPA calculations with Gogny interaction. GMR 26 24 Mg ) 4 Ca 9 Zr 144 Sm Knm =231+-5 MeV Knm(MeV 24 28 Pb 22 116 Sn 28 Si dhy et al. PRL82,691 (1999) dhy et al. PRC8,64318 (29) 2 5 1 15 2 25 A 24 Mg, 28 Si Péru,Goutte,Berger,NPA788, 44( 27) QuasiParticle RPA-HFB Gogny D1S K NM interaction dependent. Symmetry Energy dependence. Present: K NM ~ 22-24 MeV
Nuclear Matter Equation of State A 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)/A Second derivative leaves K NM and K SYM. K SYM goes as (N-Z)/A) 2
1.5 112-124 To get K SYM : Change (N-Z)/A Sn Experiment Limits 1.3 Farine et al. NPA615,135(1997) Modified Skyrme Chossy & Stocker PRC56,22518(1997) RMF 112 Sn - 124 Sn GMR MeV ) 1.1 NLC 22 MeV 24 MeV E (.9 2 MeV 217 MeV SkM* 224 MeV 22 MeV.7 18 MeV.5 5 15 25 35 45 55 -K vs (MeV) K vs = K = K Sym + L(K /K v -6) K < -375 MeV 4 KNM(MeV) 35 3 25 NL-SH NL-RA NL3 RMF Skyrme S3 SkA SkK24 NLC RATP K NM vs K Data: E GMR 112 Sn- 124 Sn : Lui et al. PRC7,14397(24). Agrees with TAMUdata Disagree withtamu data K NM =231 5 MeV 2 NL1 SkK22 SkKM SkM* K sat,2 =-37 12 MeV Chen et al. PRC8, 14322(29) SkK2 NL-Z SkK18 15-8 -7-6 -5-4 -3-2 -1 K (MeV)
Present Research Increase (N-Z/A) for K sym Move away from stable nuclei D.H. Youngblood Y.-W.Lui Jonathon Button(thesis project) Will McGrew (REU) Yi Xu (post doc joins 8/3/12) Hanyu Li (undergrad joins 9/1/12) Use unstable nuclei as beams: upgraded Cyclotron facility. Inverse reactions Problem: Helium target Solution: Use 6 Li target X. Chen s Thesis: 24 MeV 6 Li on 24 Mg, 28 Si, 116 Sn. Prove 6 Li scattering good for GMR.
Inelastic Scattering to Giant Resonances 4 6 116 24 MeV Li + Sn nts Cou 2 116 Sn avg =1.8 1 2 3 4 5 E x (MeV) 6 7 d /d (mb/sr) 1 1 1 116 Sn( 6 Li, 6 Li') E x =16.MeV L= L=1 T= L=2 L=3 1 2 4 6 8 (deg) cm
Multipole Distributions 116 Sn Fraction E EWSR/MeV.3.2.1 6 Li E Fraction E2 EWSR/MeV.25.2.15.1.5 E2 5 15 25 35 5 15 25 35 E x (MeV) E x (MeV) 28 Si GMR.16 28 Si E EWSR/MeV Fraction E EWSR/MeV.12.8.4 6Li scattering alpha scattering 5 15 25 E x (MeV) 6 Li, agree for GR s 116 Sn, 28 Si, 24 Mg. 35
To study GMR in 27 Si 6 Li Stops in target to decay detector 27 Si 6 Li 4.12s T a r g e t 27 Si* 1-2 s 23 Mg 11.32s to magnetic spectrometer
Decay detector Jonathan Button thesis Will McGrew: Analyzing data Test run Calibration Designing Faraday Cup/Beam Stop
Other Monopole Things Fraction E EWSR.2.15.1.5 9 Zr E 16.9 MeV 84% 24.9 MeV 22% Fraction E EWSR.16.12.8.4 92 M E 16.6 MeV 42% 23.9 MeV 65% 5 1 15 2 25 3 35 4 E x (MeV).16 5 1 15 2 25 3 35 4 E x (MeV).16 Fraction E EWSR.12.8.4 92 Zr E 16.5 MeV 62% 25.5 MeV 38% Fraction E EWSR.12.8.4 96 M E 16.2 MeV 83% 23.8 MeV 2% 5 1 15 2 25 3 35 4 E x (MeV) 5 1 15 2 25 3 35 4 E x (MeV).16 m1/m 9 Zr 17.87 MeV 92 M 19.62 MeV Fraction E EWSR.12.8.4 1 M E 15.5 MeV 97% 23.6 MeV 14% 5 1 15 2 25 3 35 4 E x (MeV) E GMR 92 Mo should be below 9 Zr??
KA(MeV) 22 2 18 16 14 K A for Mass 92 very different. K A from HF radii Zr Mo 12 1 88 9 92 94 96 98 1 12 A 92 Mo K A 5 from expected value!
Nuclear equation of state influences many astrophysical processes Double pulsar rotation (astro-ph 56566) Binary mergers (astro-ph 512126) Neutron star formation: Life of a type II supernova Protonneutron star has about the same density as nuclei Stolen from : C. Hartnack and J. Aichelin Subatech/University of Nantes H. Oeschler Technical University of Darmstadt