spectroscopy w. udo schröder, ncss 2012 nuclear spectroscopy 1

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Spectroscopy

W. Udo Schröder, NCSS 2012

1

NUCLEARSPECTROSCOPY

SURVEY

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Chemical Evolution of our Universe


2

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

Chemical Evolution of our Universe

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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 m

Need light of wave length l < 1 fm, equivalent energy E

2

2 2 2 22

2 2

4 2 2

2

200: 2 6 1.2

1

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

200 2

2 2 2 1.8

80 10 1 800

( 100) : 1

p p

p

c MeV fmPhotons E pc kc GeV

fm

Massive m Am particle e g proton A m c GeV

k ck MeV fmpE

m m Am c AGeV

MeV fmMeV

AGeV fm A

Heavy ions A fm cla

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

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What Structure? - Spectroscopic Goals


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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*

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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).

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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

q

Defl. angles , L

Coulomb Excitation (Semi-Classical)

238

Deformed Charge

Distribution U

r RI

spherical

deformed

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 ME

elm 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

18

00-q

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 Z

Sommerfeld Parameter :

Adiabaticity Condition:Fast “kick” will excite nucleus

Otherwise adiabatic reorientation of deformed nucleus to minimize energy

11 * *0

* *

.

2 1

1: 1

4

coll fiifrel

fi coll ifrel

Collision time rot period

RE E

E

Adiabaticity param

E

eter

!

* *i finitial E final E


Mean

Fie

ld 9

Observation of Collective Nuclear Rotations

20 0

4( , ) 1 ( , )

3 5R

R R YR

z

b ab := quadrupole deformation parameter

Quadrupole moment (Deviation from spherical nucleus )

Wood et al.,Heyde

2

15 182

Typical values

keV

;2

a bR R a b

20

20

2

:

21 0.31

12

5:

98

rig

I

irr

even I

only

Rigid body moment

ofi nertia

MR

Hydro dynamical

MR

E I I

3 2 2 2

0 03

( ) 3cos 1 1 0.165

eZQ eZ d r r r R

Deexcitation-Gamma Spectra

Measured energies (keV)

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Method: Particle Spectroscopy


1

0

(A+a) Excited states

Energy Spectrum of Products b

Particle Energy Eb

Counts

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

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Method: Simultaneous Absorption & Emission Spectroscopy


1

1

Reaction 64Ni(p,p’)64Ni* :inelastic proton scattering, absorb E from beam

64Nigs+g1+g2+g3+…

g

pE

pD

pC

pB

pA

Scattered Proton Spectrum p-energy loss

Deexcitation g Spectrum

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Example: Inelastic Particle Scattering


1

2

238U+d 238U*+d’

Scattered deuteron kinetic energy spectrum

E’d = E’d (qd , Ed)

Beam

HPGe

HPGe

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,

20

08

1

3

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 E

p sin p sin

p cos p

linear momentum

Process Energy Release

e.g. : mass loss (

y compone

Q 0),

inter

nt

x compone

nal excitat

cos p

Q 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 , s

m m mE E

Measure kinetic energy E3 vs. angle q3 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:

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Transmutation in Compound Nucleus Reactions


1

4

Q

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

Use mass tables to calculate Q

g.s.

EER*

Excited levels of ER

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Technology: Typical Setups Particle Experiments


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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

DE-E/TOF Setup

DE-E Setup

= Total Energy

Residual Energy

E

= ToF

Time of Flight

Tota

l En

erg

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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

C

B

20Ne + 12C @ 20.5 MeV/u - qlab = 12°

DE

E-DE

E-E Telescope

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THE CHIMERA DETECTOR

THE CHIMERA DETECTOR

Chimera mechanical structure 1m

1°

30°

REVERSE EXPERIMENTAL APPARATUS

TARGETBEAM

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 /4

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

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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

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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

1

1 1 cose

E EE m c

g gg

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Characteristic Examples of Level Schemes


2

0

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.

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1

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

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2

Gamma Decay of Isobaric Analog States

For same T, wfs for protons and neutrons are similar

“Mirror Nuclei” 19Ne and 19F

W.u.

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2

3

Examples of Level Schemes: SM vs. Collective

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2

4

Example ofg –particle

Spectroscopy


Pri

nci

ple

s M

eas

2

5

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)

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

Find coincidences

(Ea, Eg)

9 g-rays, 5 a


Pri

nci

ple

s M

eas

2

6

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)

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

Find coincidences

(Ea, Eg)

9 g-rays, 5 a


Pri

nci

ple

s M

eas

2

7

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)


Pri

nci

ple

s M

eas

2

8

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)


Pri

nci

ple

s M

eas

2

9

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)


Pri

nci

ple

s M

eas

3

0

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)


Pri

nci

ple

s M

eas

3

1

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)

No -a g coincidences ! must be g.s. transition


Pri

nci

ple

s M

eas

3

2

Example

159

1037660

33

0

241Am

237Np

5.378 MeV

5.433 M

eV

5.47

6 M

eV

5.50

3 M

eV

5.54

6 M

eV

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 E

nerg

y

(keV

)

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3

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.


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Defo

rmati

on

s 3

4

r

2 2 20

2 4 4

5 5 51

; ;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


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Defo

rmati

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s 3

5

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3

6

g SpectroscopyTheoretical Tools

Spectroscopic vs. Intrinsic Quadrupole Moment


Gam

ma D

eca

y 3

7

mI=I

z

q 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 cos1

II

m I I II I

0 (2 1

20 ,1 2)

10z for I

IQ Q

I

23 ( 1)

( )2 1

Iz I z I

m I IQ m Q m I

I I

Any orientation

quadratic dependence of Qz on mI

“The” quadrupole moment

Electromagnetic Radiation

Gam

ma-G

am

ma C

orr

ela

tion

s 3

8

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-G

am

ma C

orr

ela

tion

s 3

9

Nuclear Electromagnetic Transitions

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

222

.

( ) ( , )mi

Initial Nucl State

j r Y

Ip

2+

1-

0+

Ei

g g g

i fi fi fE E E I I I

111

.

( ) ( , )mf

Final Nucl State

j r Y g ( ) ( , )I

mE

Photon WF

r Y

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

Ip

2+

1-

0+

Ef

g

Initial Ni spatial symmetry retained in overall combination Nf +g

Illustration conserved spatial symmetry

Gam

ma-G

am

ma C

orr

ela

tion

s 4

0

Selection Rules for Electromagnetic Transitions

Conserved: Total energy (E), total angular momentum (I, Iz), total parity (p):

g g g

i fi fi fE E E I I I

iiI

f

fI

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 I

direction undetermi

I I I

ned

Projections conserved

m m m m m

Other types magnetic and multipolarities

have 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


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1

Transition Probabilities: Weisskopf’s s.p. Estimates

Consider single nucleon in circular orbit (extreme SM)

2 12 2 21

2

4.4( 1) 3 10( )

3 197(2 1)!!

RP E

MeV fm s

2 12 2 2 21

2

1.9( 1) 3 10( )

2 197(2 1)!!

RP M

MeV fm s

WeisskopfEstimates

Nucleus NucleusLow energy long wave length limit k R R fm

MeV 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, 10

200200 20

10

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


Gam

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2

Weisskopf’s Eℓ Estimates

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

2 1 2 3

:

( )

single particle

P E E Ag

Experimental E1: Factor 103-107 slower than s.p. WE Configurations more complicated than s.p. model, time required for rearrangement

Experimental E2: Factor 102 faster than s.p. WE Collective states, more than 1 nucleon.

Experimental Eℓ (ℓ>2): App. correctly predicted.


Gam

ma D

eca

y 4

3

Weisskopf’s Mℓ Estimates

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

2 1 ( 1)2 3

:

( )

single particle

P M E Ag

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


Gam

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4

Isospin Selection Rules

Reason: n/p rearrangements multipole charge distributions

photon interacts only with 1 nucleon (t = 1/2) DT = 0, 1

Example E1 transitions:

zE p cm i cmp i i

O e r R e r R iso vector op 11ˆ ( )2

Enhanced (collective) E2, E3 transitions DT = 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 operator

n

O g s g s

I g g s g g s l

g

P

1

0

11ˆ : (1 2 )2 0

1 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 D

eca

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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

Zd r r

Zd r r

er r

e rV r e d r

r r

e e Z

e e Z

e e ZZd r

e r dr r

Qr

r err


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6

Electrostatic Multipole (Coulomb) Interaction

Monopoleℓ = 0

Dipole ℓ = 1 Quadrupole ℓ =2

Point Charges

Nuclear charge distribution

|e|Z

e

q

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 d

azimuth polar angles

d r r

2 1.44e MeV fm


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4

7

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 r

A r d r d r j r d r r r j rr r r r

3 30 03 3

1 1( ) ( ) .. ..

4 4( )A r d r r r j r d j r rr r

r r

03 3

3

1

1: [ ( )]

2

( )4

Magnetic dipole moment

rA r higher multipole momen Bts

r

r r j r

r

d

3

( ) ( ) . .

( ) ( ) ( ) ;

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

er j r r r p r r p L

m

e e ed r r L r L g

m m m

0B H A

70 104

VsAm

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

=0

2

current

I e r

current density

j e

A r

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4

8

End Spectroscopy

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Lecture Plan Intro to Nuclear Structure


4

9

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 w. udo schröder, ncss 2012 nuclear spectroscopy 1

Documents

nuclear experiment

nuclear structure

spectrum of nuclear

nuclear spectroscopy

udo schrder

discrete energy states

equivalent energy e

energy relative