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, 1046(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)

20n 20p

40Ca

Isovector Giant Dipole Resonance

Analogous to charge distributions

Monopole L=0 Dipole L=1 Quadrupole L=2 Octupole L=3

Etc. There should be lots of “Giant Resonances” Isovector (n’s and p’s 180o out of phase) Isoscalar (n’s and p’s in phase) Spin (spin up and down 180o out of phase)

Shape Oscillations

“Giant Resonance”

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

Limit on strength for each multipole.

Electromagnetic Operator QL=∑iriL YLM(θi)

YLM is a spherical harmonic for multipole L, magnetic substate M. ∑nEn|<n|QL|0>|2 = SL Energy Weighted Sum Rule if there are no velocity dependent forces. En is excitation energy of state |0> represents wave function of ground state <n| represents wave function of excited state

For L ≥ 2 SL= (ħ2 L(2L+1)A)/2m * < r2L-2>

“Giant Resonance”

Contains ~90-99% of this strength

Rest of strength in low lying states of nucleus.

1970: 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: EGMR=(ħ/3roA1/3)*(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)

0

0.2

0.4

0.6

0 10 20 30 40

Ex(MeV)

Str

eng

th

ISGMR

LE ISGDR

HE ISGDR

ISGQR

HEOR

LEOR

IVGDR

IVGQR

Total

Giant Resonances

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

0.2

0.4

0.6

0 10 20 30 40

Ex(MeV)

Str

eng

th

ISGMR

LE ISGDR

HE ISGDR

ISGQR

HEOR

LEOR

IVGDR

IVGQR

Total

Giant Resonances

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30

Ex(MeV)

Ave

rag

e C

ross

Sec

tio

n Excite with Alpha Particles

40

Need to do more!

Distorted Wave Born Approximation Calculation

Inelastic scattering Eα=240MeV

0.1

1

10

100

1000

0 1 2 3 4 5 6 7 8 9 10 1c.m. (deg)

d /d

(m

b/sr

)

1

L=0L=1L=2L=3

116Sn(')E=240 MeV

Measure at different scattering angles!

Could separate Monopole from Quadrupole

by measuring 1.5o to 4o

Monopole Enhanced at 0o.

0

0.1

0.2

0.3

0 10 20 30 4

Ex(MeV)

0o C

ross

Sec

tio

n Measure at 0o

The Monopole!

0

0

0.1

0.2

0.3

0 10 20 30 4

Ex(MeV)

4o C

ros

s S

ec

ito

n Measure at 4o

The Quadrupole!

0

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 0o inelastic scattering.

Measure over the minimum in the monopole.

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

o

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

90Zr Spectrum

0

2000

4000

0 10 20 30 40 50 60 7

Ex(MeV)

Co

un

ts/c

ha

nn

el

90Zr( ')

c.m. = 0.4o

0

Multipole Distributions

E0

0

0.1

0.2

5 10 15 20 25 30 35 40

Fra

cti

on

E0

EW

SR

/MeV

0.1

E2100+-12%

05 10 15

Fra

c

0.2

20 25 30 35 40

tio

n E

WS

R/M

eV

E2

88+11-8%

E1

0

0.05

0.1

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

ctio

n E

1 E

WS

R/M

eV

81+-10%

0

0.05

0.1

5 10 15 20 25 30 35 40Ex(MeV)

Fra

ctio

n E

3 E

WS

R/M

eV

E3

78+9-15%

We can separate multipoles!

EGMR=ħ(KA/m<r2>)1/2 <r2>: mean square nuclear radius

m: nucleon mass KA: compressibility of nucleus

Compressibility of Nuclear Matter

Simple Picture: Leptodermous Expansion

KA=KNM + KSurfA-1/3+Kvs((N-Z)/A)2 +KCoul*Z2/A4/3 Kvs= KSym + L(K’/Kv-6)

Where KNM: curvature of E/A around o KSym: curvature of symmetry energy

Note that EGMR depends on KNM AND KSym!

The Right Way to get KNM

Calculate EGMR using effective interactions (each results in a specific KNM)

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 Kv and KSym in Infinite nuclear matter.

Microscopic Calculations:

Non_Relativistic: Skyrme, Gogny effective interactions.

m s. GMR

Relativistic: NL1, NL3, etc. p ara eter set

Compare calculated to experimental E280

Knm obtained by comparing GMR energies and RPA calculations with

Gogny teraction. in

260

24Mg

200

0 250

K

208Pb

L

Qu

pendent.

)

nm=231+-5 MeV

90Zr 144

Sm40Ca

240

nm

(MeV

K

220116

Sn28Si dhy et al. PR 82,691 (1999)

dhy et al. PRC80,064318 (2009)

50 100 150 200A

24Mg, 4 2007)28Si Péru,Goutte,Berger,NPA788, 4(

asiParticle RPA HFB Gogny D1S -

KNM interaction deSymmetry Energy dependence.

Present: KNM~ 220-240 MeV

Nuclear Matter Equation of State

A parametrization of the EOS to ord(M. Farine et al. NPA

er 2: 615,135(1997))

E/A= Av+(KNM/18)2+ [(n-p)/]2 {J+(L/3) + (KSym/18)2+..}+..

Where =(-o)/o and (n-p)/ ~ (N-Z)/A

Second derivative leaves KNM and KSYM.

KSYM goes as (N-Z)/A)2

To get KSYM: Change (N-Z)/A Sn 112-124

112Sn - 124Sn GMR

0.5

1.5

50-Kvs (MeV

MeV

Experiment Limits

Farine et al. NPA615,135(1997) Modified Skyrme

0.7

0.9

1.1

1.3

)

150 250 350 450 550)

Chossy & Stocker

224 MeV

PRC56,22518(1997) RMF

220 MeV240 MeVNLC

E (

200 MeV

220 MeV217 MeVSkM*

180 MeV

Kvs= K= KSym + L(K’/Kv-6) K < -375 MeV

KNM vs K

150

200

250

300

350

400

-800 -700 -600 -500 -400 -300 -200 -100 0K

RMF

(MeV)

Skyrme

NL-Z

NL1

NLC

NL3

NL-RA

NL-SH

SkM*

RATP

SkA

S3

SkK180

SkK200

SkK220

SkK240

SkKM

KNM=2315MeV

Data: EGMR 112Sn-124Sn : Lui et al. PRC70,014397(2004).

Disagree withTAMU data

Agrees with TAMUdata

Ksat,2=-370 120 MeV

Chen et al. PRC80, 014322(2009)

KN

M(M

eV)

Increase (N-Z/A) for Ksym

Move away from stable nuclei Present Research D.H. Youngblood Y.-W.Lui Jonathon 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 target Solution: Use 6Li target

X. Chen’s Thesis: 240 MeV 6Li on 24Mg,28Si,116Sn.

Prove 6Li scattering good for GMR.

Inelastic Scattering to Giant Resonances

240 MeV Li + Sn

6 116

4000

116Snnts

avg=1.080

60 70

Ex(MeV)

2000

Co

u

0

0 10 20 30 40 50

116Sn(6Li,6Li')1000

Ex=16.0MeV

1

10

100

0 2 4 6 8(deg)

d

/d

(mb/s

r)

L=0

L=1 T=0

L=2

cm

L

=3

Multipole Distributions

116 n S

0

0.1

0.2

0.3

5 15 25 35

Ex(MeV)

Fra

ctio

n E

0 E

WS

R/M

eV

6Li

E0

0

0.05

0.1

0.15

0.2

0.25

5 15 25 35

Ex(MeV)

Fra

cti

on

E2

EW

SR

/Me

V E2

28Si GMR

28Si E0 EWSR/MeV

0

0.04

0.08

0.12

0.16

5 15 25Ex(MeV)

Fra

ction E

0 E

WS

R/M

eV

35

6Li scattering

alpha scattering

6Li, agree for GR’s 116Sn, 28Si, 24Mg.

To study GMR in 27Si

6Li

27Si*

6Li27Si

23MgTar

t

to decay detector

to magnetic spectrometer

Stops in target

10-20s

4.12s

.32sge

11

Decay detector – Jonathan Button thesis

Will McGrew: Analyzing data Test run Calibration Designing Faraday Cup/Beam Stop

Other Monopole Things

m1/m0

90Zr 17.87 MeV92M0 19.62 MeV

92M0 E00.12

16.6 MeV42%

0

0.04

0.08

0.16

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

ctio

n E

0 E

WS

R

23.9 MeV 65%

90Zr E0

0

0.05

0.1

0.15

0.2

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

ctio

n E

0 E

WS

R

16.9 MeV84%

24.9 MeV 22%

96M0 E0

0

0.04

0.08

0.12

0.16

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

ctio

n E

0 E

WS

R

16.2 MeV 83%

23.8 MeV 20%

100M0 E0

0

0.04

0.08

0.12

0.16

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

cti

on

E0

EW

SR

15.5 MeV 97%

23.6 MeV 14%

92Zr E0

0

0.04

0.08

0.12

0.16

5 10 15 20 25 30 35 40

Ex(MeV)

Fra

ctio

n E

0 E

WS

R

16.5 MeV 62%

25.5 MeV 38%

EGMR 92Mo should be below 90Zr??

KA for Mass 92 very different.

KA from HF radii

100

120

140

160

180

200

220

88 90 92 94 96 98 100 102A

KA(M

eV

) Zr

Mo

92Mo

KA 5 from expected value!

Life of a type II supernova

Protonneutron star has about the same density as nuclei

Nuclear equation of state influences many astrophysical processesDouble pulsar rotation (astro-ph 0506566)

Binary mergers (astro-ph 0512126)Neutron star formation:

Stolen from : C. Hartnack and J. Aichelin Subatech/University of Nantes H. Oeschler Technical University of Darmstadt