spectroscopy

Nucle

ar S

pect

rosc

opy

Spectroscopy

W. Udo Schröder, NCSS 2012

1

NUCLEARSPECTROSCOPY

SURVEY

Nucle

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rosc

opy

Chemical Evolution of our Universe


2

Nucle

ar S

pect

rosc

opy


3

S. Mason. Chemical Evolution (Clarendon Press, 1992), pp. 40-45.

Chemical Evolution of our Universe

Nuc

lear

Spe

ctro

scop

y4


Probes for Nuclear Structure

To “see” an object, the wavelength l of the light used must be shorter than the dimensions d of the object (l ≤ d). (DeBroglie: p=ħk=ħ2p/l)Rutherford’s scattering experiments dNucleus~ few 10-15 mNeed light of wave length l < 1 fm, equivalent energy E

) ) ) )

2

2 2 2 22

2 2

4 2 2

2

200: 2 6 1.21

( ) , . ., ( 1), 0.9 :

200 22 2 2 1.8

80 10 1 800

( 100) : 1

p p

p

c MeV fmPhotons E pc kc GeVfm

Massive m Am particle e g proton A m c GeV

k ck MeV fmpEm m Am c AGeV

MeV fm MeVAGeV fm A

Heavy ions A fm cla

pl

pl

l

ssical particles

Not easily available as light

Can be made with charged particle acceleratorsScan energy states of nuclei. Bound systems have discrete energy

states unbound E continuum

Nucle

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What Structure? - Spectroscopic Goals


5

Bound systems have discrete energy states unbound E continuum Scan energy states of nuclei.

Desired information on nuclear states (“good quantum numbers”):

• Energy relative to ground state (g.s.) (Ei, i=0,1,…; E*)

• Stability, life time against various decay modes (a, b, g,…)

• Electrostatic moments Qj see below• Magnetostatic moments Mi see below

• Angular momentum (nuclear spin)• Parity (=spatial symmetry of quantum y)

• Nucleonic (neutron & proton) configuration (e.g., “isospin” quantum #)

Nuclear Level

Scheme+

0

-

E*

Nucle

ar E

xper

imen

t

Particle and g Spectroscopy

W. Udo Schröder, 2011

6

Individual ormulti detector setups, spectrometersOff-line activation measurements

Identify scattered/transmuted projectile & target nuclei, measure m, E, A, Z, I,.. of all ejectiles (particles and g-rays).

Nucle

ar S

pect

rosc

opy

How to Excite Nuclei: Inelastic Nuclear Reactions

Coulomb excitation of rotational motion for deformed targets or vibrations.


7

p, n,..transfer rxns,e.g., (d, n), (3He,d).Final state is excited

Target

Projectile

Fusion/compound nucleus reactions, Final state is highly excited, thermally metastable

Scan the bound nuclear energy level scheme

Defl. angles , L

Defl. angles , L

Coulomb Excitation (Semi-Classical)

)

238Deformed ChargeDistribution U

r RI

sphericaldeformed

0I I L

) )Ruthi fi f

d dP

d d

Excitation probability in perturbation theory:

)* *2( )

i E E tfii fi fi f

f

Coul

iP b b dt e f H t i

Transition amplitude Fourier transform of transition MEelm projectile - target interaction H V j A

For small energy losses (weak excitations: * *

i fE E

tt(R0)

Vcoul(t)

0

1R

tcoll

) ) )

0:

1 1 sin 2 2 arctana

R L

1800

-

Torque exerted on deformed target excitation of collective nuclear rotations Transfer of angular momentum from relative motion:

Angular dependence of excitation probability:

21 2e Z ZSommerfeld Parameter :

Adiabaticity Condition:Fast “kick” will excite nucleus

Otherwise adiabatic reorientation of deformed nucleus to minimize energy

)

)

11 * *0

* *

.2 1

1: 14

coll fiifrel

fi coll ifrel

Collision time rot period

R E E

E

Adiabaticity param

E

eter

t

t

!

* *i finitial E final E


Mea

n Fie

ld 9

Observation of Collective Nuclear Rotations2

0 04( , ) 1 ( , ) 3 5

RR R YR

p b b

z

b ab := quadrupole deformation parameter

Quadrupole moment (Deviation from spherical nucleus )

Wood et al.,Heyde

2

15 182

Typical values

keV

;2a bR R a b

)

b

bp

20

20

2

:2 1 0.31

12

5:

98

rig

I

irr

even Ionly

Rigid body momentofi nertia

MR

Hydro dynamical

MR

E I I

)p

b b 3 2 2 2

0 03( ) 3cos 1 1 0.165eZQ eZ d r r r R

Deexcitation-Gamma Spectra

Measured energies (keV)

Nucle

ar E

xper

imen

t

Method: Particle Spectroscopy


10

(A+a) Excited states

Energy Spectrum of Products b

Particle Energy Eb

Coun

ts

Excited States g.s.

Particle a Beam

QuadrupoleMagnet

Faraday Cup Populate (excite) the spectrum of

nuclear states. Measure probabilities for excitation and de-excitation

Reconstruct energy states Ei,Ii,pi from energy, linear and angular momentum balance.Obtain structure information from probabilities.

Bound systems have discrete energy states unbound E continuum

Reaction A(a,b)B*E

Nucle

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opy

Method: Simultaneous Absorption & Emission Spectroscopy


11

Reaction 64Ni(p,p’)64Ni* :inelastic proton scattering, absorb E from beam64Nigs+g1+g2+g3+…

g

pE

pDpC

pB

pA

Scattered Proton Spectrum p-energy loss

Deexcitation g Spectrum

Nucle

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pect

rosc

opy

Example: Inelastic Particle Scattering


12

238U+d 238U*+d’

Scattered deuteron kinetic energy spectrum

E’d = E’d (d , Ed)

Beam

HPGeHPGe

HPGe

Deexcitation-g Spectrum

Coincident g cascades

Coincident g cascades indicate nuclear band structure (rotational, vibrational,...)

Measuring Energy Transfer: The Q Value Equation

Cross Section, Kinematics & Q Values

W. U

do S

chrö

der,

2008

13

i i i

3 3 4 4

3 3 4 4 1

3 4 1

Lab System (target initially at rest , p 0) :p 2m Ep sin p sinp cos p

linear momentum

Process Energy Releasee.g. : mass loss (

y compone

Q 0),inter

ntx compone

nal excitat

cos pQ E E

ion(

nt

Q

E

0)

3 4

3p

4p

1Projectile p

)3 3 31 3 13 1

14

34

34

2 m m Em mQ 1 E 1 coE , sm m m

E E

Measure kinetic energy E3 vs. angle 3 to determine reaction Q value.Predict energies of particles at different angles as functions of Q.

4, 4Eliminate E

How to interpret energies of scattered particles:

Nucle

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opy

Transmutation in Compound Nucleus Reactions


14

Q

Decay of CN populates states of the “evaporation residue” nucleus

Use mass tables to calculate Q

g.s.

EER*

Excited levels of ER

Nucle

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opy

Technology: Typical Setups Particle Experiments


15

Modified, after K.S. Krane, Introduction to Nuclear Physics, Wiley&Sons, 1988

Simultaneous measurement of time of flight, specific energy loss and residual energy of particles E, Z, A

Simultaneous measurement of specific energy loss DE and residual energy E of particles E, Z, (A)

Particle

Particle

E-E/TOF Setup

E-E Setup

= Total Energy

Residual Energy

E

= ToF

Time of Flight

Tota

l Ene

rgy

Nucle

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16


Particle ID (Z , A, E) Specific energy loss, spatial ionization density, TOF

Particle ID with Detector Telescopes

Si Telescope Massive Reaction Products SiSiCsI Telescope (Light Particles)

HeLiBe

NaNe

F

O

N

CB

20Ne + 12C @ 20.5 MeV/u - lab = 12°

E

E-E

E-E Telescope

Nucle

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17


THE CHIMERA DETECTOR

Chimera mechanical structure 1m

1°

30°

REVERSE EXPERIMENTAL APPARATUSTARGET

BEAM

Experimental Method

E-E ChargeE-E E-TOF Velocity, MassPulse shape Method LCP

Basic element Si (300m) + CsI(Tl) telescope

Primary experimental observables

TOF t 1 nsKinetic energy, velocityE/E Light charged particles 2%Heavy ions 1%

Total solid angle /4p

94%

Granularity 1192 modules

Angular range 1°< < 176°

Detection threshold

<0.5 MeV/A for H.I. 1 MeV/A for LCP

CHIMERA characteristic features

688 telescopes

Laboratori del Sud, Catania/Italy

Nucle

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18

GRETA Detector ConfigurationTwo types of irregular hexagons, 60 each,3 crystals/cryostat= 40 modulesDetector – target distance = 15 cm$750k GRETINA

Technology in g spectroscopy Greta HPGe Array

Realistic coverage: Ω/4p=0.8Spatial resolution: ∆x=2 mm

Nucle

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opy


19

I.-Y. Lee, LBNL, 2011

Use Compton scattering laws to identify & track interactions of all g’s. Conventional method requires many detectors to retain high resolution and avoid summing.

g-Ray Tracking with HPGe Detector Array

) ) 2

11 1 cose

E EE m c

g gg

Nucle

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Characteristic Examples of Level Schemes


20

Single-particle spectra: Irregular sequence, half-integer spins, various parities.

Collective vibrations:

O+ g.s., even spins & parity, regular sequence with bunching of (0+,2+,4+) triplet

Collective rotations: Regular quadratic sequence 0+,2+,4+,….

Only even or only odd spins, I=2, uniform parity.

Nucle

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opy


21

Characteristic Level Schemes-Light Nuclei

Different densities of states.

Similarities in energies, spin, parity sequence for mirror nuclei:(N, Z)=(a, b)=(b,a)mirror


Gam

ma

Deca

y 2

2

Gamma Decay of Isobaric Analog States

For same T, wfs for protons and neutrons are similar “Mirror Nuclei” 19Ne and 19F

W.u.

Nucle

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23

Examples of Level Schemes: SM vs. Collective

Nucle

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24

Example ofg –particle

Spectroscopy


Prin

ciple

s Mea

s 2

5

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120

a Energy (keV) - 5 MeV

g En

ergy

(k

eV)

a-Decay of 241Am, subsequent g emission from daughter

Find coincidences

(Ea, Eg)9 g-rays, 5 a


Prin

ciple

s Mea

s 2

6

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)

a-Decay of 241Am, subsequent g emission from daughter

Find coincidences

(Ea, Eg)9 g-rays, 5 a


Prin

ciple

s Mea

s 2

7

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)


Prin

ciple

s Mea

s 2

8

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)


Prin

ciple

s Mea

s 2

9

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)


Prin

ciple

s Mea

s 3

0

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)


Prin

ciple

s Mea

s 3

1

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)

No ag coincidences ! must be g.s. transition


Prin

ciple

s Mea

s 3

2

Example

159

103766033

0

241Am

237Np

5.378 MeV

5.433 MeV

5.476

MeV

5.503

MeV

5.546

MeV

380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

30

40

50

60

70

80

90

100

110

120


g En

ergy

(k

eV)

Nucle

ar S

pect

rosc

opy


33 Exercises

Exercises: Nuclear Electrostatic Moments

Consider a nucleus with a homogeneous, axially symmetric charge distribution 1. Show that its electric dipole moment Q0 is zero.2. Assume for the charge distribution a homogenously

charged rotational ellipsoid with semi axes a and b, given by .

Show that

3. From the measured 242Pu and 244Pu g spectra determine the deformation parameters b of these two isotopes.


Nucle

ar D

efor

mat

ions

34

)r

)

)

2 2 20

2 4 45 5 5

1 ; ;2

Q eZ b a eZR R eZR

R a b R b a R R

)2 2 2 2 2 1x y a z b

Alpha-Gamma Spectroscopy

• 251Fm247Cf


Nucle

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ions

35

Nucle

ar S

pect

rosc

opy


36

g SpectroscopyTheoretical Tools

Spectroscopic vs. Intrinsic Quadrupole Moment


Gam

ma

Deca

y 3

7

mI=I

z

)1I I

I )2

01ˆ 3cos 12z

I I

I IQ Q Q

m I m I

I≠0: Transformation body-fixed to lab system

) )

1 cos cos1I

Im I I II I

) 0 (2 12 0 ,1 2)1 0z for IIQ Q

I

) )23 ( 1) ( )2 1I

z I z Im I IQ m Q m I

I I

Any

orientationquadratic dependence of Qz on mI

“The” quadrupole moment

Electromagnetic RadiationGa

mm

a-Ga

mm

a Co

rrela

tions

38

Protons in nuclei = moving charges emits electromagnetic radiation, except if nucleus is in its ground state!

Heinrich Hertz

E. Segré: Nuclei and Particles, Benjamin&Cummins, 2nd ed. 1977 Point

ChargesNuclearCharge

Distribution

Monopole ℓ = 0

Dipole ℓ = 1

Quadrupole ℓ =2

Propagating Electric Dipole Field

Gam

ma-

Gam

ma

Corre

latio

ns 3

9

Nuclear Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I) and total parity (p):

222

.( ) ( , )mi

Initial Nucl Statej r Y

Ip2+

1-

0+

Ei

g g gp p p

i fi fi fE E E I I I

111

.( ) ( , )mf

Final Nucl Statej r Y gy

( ) ( , )ImE

Photon WFr Y

Consider often only electric multipole transitions.Neglect weaker magnetic transitions due to changes in current distributions.

Ip2+

1-

0+

Ef

g

Initial Ni spatial symmetry retained in overall combination Nf +g

Illustration conserved spatial symmetry

Gam

ma-

Gam

ma

Corre

latio

ns 4

0

Selection Rules for Electromagnetic Transitions Conserved: Total energy (E), total angular momentum (I, Iz), total parity (p):

g g gp p p

i fi fi fE E E I I I

iiIp

ffI p

iI

z

mi

mf

fI

mg

)

i f

i f

i fi f

fi i fi i

i f

Electric dipole radiation

Angular momenta I Idirection undetermi

I I I

nedProjections conservedm m m m m

Other types magnetic and multipolaritieshave other se

m m

I I I

m

Ig

g

g

[ 1( )]

,.

, ,

( )

:, 1 , 1

lection rules.

g

Coupling of Angular Momenta

Quantization axis : z direction. Physical alignment of I possible (B field, angular correlation)

g


Gam

ma

Deca

y 4

1

Transition Probabilities: Weisskopf’s s.p. Estimates

Consider single nucleon in circular orbit (extreme SM)

2 12 2 21

24.4( 1) 3 10( ) 3 197(2 1)!!

RP EMeV fm s

2 12 2 2 21

21.9( 1) 3 10( ) 2 197(2 1)!!

RP MMeV fm s

WeisskopfEstimates

) )

) ) )

Nucleus NucleusLow energy long wave length limit k R R fmMeV fmE c k MeV fm k MeV

fm

krj kr for kr j kr j kr k k

g

g g g

g

1 1

/ : 1, 10200200 2010

( ) 1 ( ) ( ) :2 1 !!


Gam

ma

Deca

y 4

2

Weisskopf’s Eℓ Estimates

T1/2 for solid lines have been corrected for internal conversion.

2 1 2 3:

( )single particleP E E Ag

Experimental E1: Factor 103-107 slower than s.p. WE Configurations more complicated than s.p. model, time required for rearrangementExperimental E2: Factor 102 faster than s.p. WE Collective states, more than 1 nucleon.Experimental Eℓ (ℓ>2): App. correctly predicted.


Gam

ma

Deca

y 4

3

Weisskopf’s Mℓ Estimates

T1/2 for solid lines have been corrected for internal conversion.

2 1 ( 1)2 3:

( )single particleP M E Ag

Experimental Mℓ: Several orders of magnitude weaker than Eℓ transitions.


Gam

ma

Deca

y 4

4

Isospin Selection RulesReason: n/p rearrangements multipole charge distributionsphoton interacts only with 1 nucleon (t = 1/2) T = 0, 1 Example E1 transitions:

)zE p cm i cmp i i

O e r R e r R iso vector opt 11ˆ ( ) 2

Enhanced (collective) E2, E3 transitions T = 0 Collective (rot or vib) WF does not change in transition.

n

M i p i n ii i i

n p i n p i ii i

iso scalar iso vector

zi

z z

n

zi i i

zi

pProjection operatorn

O g s g s

I g g s g g s l

g

t

t t t

t

P

1

0

11ˆ : (1 2 )2 01 1 1ˆ ˆ ˆ ˆ(1 2 ) (1 2 ) (1 2 )2 2 2

1 1 ˆˆ ˆ ˆ( 1) ( )2 2

3

pg .8 5.6


Gam

ma

Deca

y 4

5

Gamma Decay of Isobaric Analog States

For same T, wfs for protons and neutrons are similar “Mirror Nuclei” 19Ne and 19F

W.u.

)

)

)

) )

3

32 2

2 23 3

3

2

2

23

(

1

cos

3co

)

s

. ..

1

.. .

Z

Z d r r

Z d r r

er r

e rV r e d r

r r

e e Z

e e Z

e e ZZ d r

e r dr r

Qr

r err


Nucle

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ions

46

Electrostatic Multipole (Coulomb) Interaction

Monopoleℓ = 0 Dipole ℓ =

1 Quadrupole ℓ =2

Point Charges

Nuclear charge distribution

|e|Z

e

z

)r

r

r r r

symmetry axis

Quadrupole Q ≠0,indicates deviation from spherical shape

Different multipole shapes/ distributions have different spatial symmetries

)

3 2

3

(cos ),

1

d r r dr d dazimuth polar anglesd r r

2 1.44e MeV fm


Nucle

ar S

pins

47

Magnetization: Magnetic Dipole Moments

Moving charge e current density j vector potential , influences particles at via magnetic field

r

p

e,m

r

r

)3 3 30 03

( ) 1 1( ) ( ) ( ) ..4 4j rA r d r d r j r d r r r j r

r r r r p p

)3 30 03 31 1( ) ( ) .. ..4 4 ( )A r d r r r j r d j r rr rr r

p p

p

03 3

3

1

1: [ ( )]2

( ) 4

Magnetic dipole moment

rA r higher multipole momen Btsr

r r j r

r

d

3

( ) ( ) . .

( ) ( ) ( ) ;

( ) ( )2 2 2r r R qu mech

er j r r r p r r p Lm

e e ed r r L r L gm m m

0B H A

70 104VsAm

p

Loop = I x A= current x Area(inside)current loop:

=0

p

2currentI e rcurrent densityj e

)A r

Nucle

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48

End Spectroscopy

Nucle

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Lecture Plan Intro to Nuclear Structure


49

Day Time Topic

Monday 6/25

09:00-10:0010:30-11:30

How do we know about NS? Nuclear Spectroscopy.Nucleon-Nucleon forces and 2-body Systems

Tuesday 6/26

09:00-10:0010:30-11:30

Mean Field and its Symmetries, Spin and IsospinFermi Gas Model

Wednesday 6/27

09:00-10:0010:30-11:30

Spherical Shell ModelSimple Predictions and Comparisons

Thursday 6/28

09:00-10:0010:30-11:30

Residual Interactions/ PairingDeformed Nuclei and their Spectroscopy

Friday 6/29 09:00-11:30 Final Exam

spectroscopy

Documents

nuclear experiment

nuclear spectroscopyprobes

spectrum of nuclear

nuclear structureto

udo schrder

discrete energy states

energy relative

nuclear level scheme