Nuclear Excitations probed by Strong, EM and Weak ......Nuclear Excitations probed by Strong, EM and Weak Interactions-Gamow-Teller Transition Strength in Exotic Nuclei-Euroschool@Santiago,

Nuclear Excitations probed by Strong, EM and Weak Interactions

-Gamow-Teller Transition Strength in Exotic Nuclei-

Euroschool@Santiago, SpainSeptember 4 - 10, 2010

Yoshitaka FujitaOsaka Univeristy

Lecture 1: Nuclear Excitations and Isospin Symmetry

Snake of Sizes

The Nature

is alive! （自然は生きている！）

Mont Blanc: 4,810 mthe highest in Europe

225 My ago 200 My ago

150 My ago 65 My ago

Present day 現在

first idea byAlfred Wegener

Continental Drift

-Plate tectonics-

Eruption of Kilauea, Hawaii (1970’s)

地熱：ウラン等、放射性元素の核分裂の熱Terrestrial heat: originates from Radio Activity like 235U

Supernova Cycle

mainly by

&

K.L &G.M-PRev.Mod.Phys.75(’04)819

(A,Z)=nuclei in theFe, Ni region

Crucial Weak Processes

during the Collapse

Layer Structure of Nature (by Glashow)

Particle

Molecule

Quark

1 fm

1.4 billion light years

Micro world and Macro worldare tightly connected!

How can we study the Nuclear Weak Processes in Stars?

(GT and Fermi transitions)

1) Can we study by using Weak Interaction itself ?-induced reaction: the cross-section is too small ! -decay: accessible range of excitation is narrow !

Study of High Ex region by means of (3He,t) reaction.

2) Can we study them from Unstable Nuclei ?Unstable Nuclei: the production is too small

for the precise study !

Deduction by means of Isospin Symmetry in Nuclei.

Scale : 10-14 m (10 fm x 10 fm)

Protons & Neutrons in 12C

Why Protons with charge are confined

in such a small Nucleus?

Strong & Weak Interactions

1H (p)

4He: Nuclear Reaction in a Stardecay: leptons

are involved 1) weak process: slow

2) charge change

Neptune driving Waves 波を操る海神ネプチューン

Powerful Waves=強い相互作用(strong interaction)

Neptune=弱い相互作用(weak interaction)

How Nuclei are defined ?*Quantum Finite Many-body System

=> quantum numbers are importantL, S, J, K, T

=> selection rules of Q-numbers are importnat*Active forces in nuclei:

3 out of 4 fundamental forcesstrength: strong >> electro-magnetic >> weaktime : fast middle slow

(~10-20s) (~10-15s) (~10-1s)*they struggle to make their territory larger !

We can use 3 forces for the study of nuclei !

Roles of 3 forces

Strong: nuclear reactions[(p, p’), (’),.., (p, n), (3He,t) etc]

EM: (e, e’), Coulomb ex., -decayWeak: -induced reactions, -decay

[(x , x ’), (e , e-),…]

*if Strong can play a role, other two are hidden!*if EM , Weak*if Strong and EM cannot play roles,

then Weak will appear on the stage.

in Nuclear excitation & decay

**World of Nuclear

Structure Physics

Nuclear Reaction Study

Nuclear Decay Study

QuantumMechanics

Electro-Magnetism

NuclearStructure

Structure information form Transitions

*Transition strength: proportional to |<f| Op |i>|2Hi |i>= Ei |i>, Hf |f>= Ef |f>

*B(Op) : reduced transition strength ex B(E2) or B(GT)is proportional to |<f| Op |i>|2

Nuclear Transitions give us Structure information

*Studied by: Nuclear Reactions, DecaysReaction: Excitation + SpectroscopyDecay: Spectroscopy

*Mode of Excitation (Transition) Op

For the study of Nuclear Structure

We have two different tools!1) Decay Studies

-decay: in beam -study, source study -decay: -ray study, -delayed , p or n

2) Reaction StudiesInelastic Scattering: simply giving Energy Charge Exchange Reaction:

charge-exchange & giving EnergyPick-up Reaction, Transfer Reaction, …

-decay

(安定核)

(Z=13,N=14)

QEC

(不安定核)

0

4

8

12

基底状態

基底状態励起状態

励起状態

27Al 27Si(Z=14,N=13)

-decay

-decay

Sn

n-decay

Sp

p-decayNuclear Decays

Exci

tatio

n En

ergy

GroundState

GroundState

ExcitedStates

GT Transitions from 42Ti :

decay

proton: f7/2 neutron f7/2proton: f7/2 neutron f5/2

one-particle one-hole excitation

Direct Reactions with Light Projectiles

Projectile

Target

Coulomb Excitation

Elastic Scattering

Inelastic Scattering

Pick-up Stripping

Charge-exchange

Similarity with

decay!

by Berta Rubio

|i> |f>

interaction(operator)

1p-1h Excitations (reaction)

*mesons are exchanged! Eout =Ein -Ex

“energy spectrum”

Resolutions Now and Then

Y. Fujita et al.,EPJ A 13 (’02) 411.

H. Fujita et al.,PRC 75 (’07) 034310

“energy spectrum”

High resolution brings higher quality!

Projectile

Stable target

Charge exchange

Charge Exchange Reaction and -decay

+ or - decay

β - : n → p + e- + νβ + : p → n + e+ + νEC : p + e- → n + ν

B.Rubio

3He t

(p, n) or (3He,t) reaction

bystrong

interaction

byweak

interaction

Ejectile

Transitions from 42Ca : CE Reaction

neutron: f7/2 proton f7/2neutron: f7/2 proton f5/2

Transitions from 42Ti :

decay

proton: f7/2 neutron f7/2proton: f7/2 neutron f5/2

decay and CE reaction makeIsospin Analogous transitions

(mirror transitions in proton and neutron)

Our Scope: Nuclear Excitations

by Charge Exchange Reaction and -decay

Study of Weak Response of Nucleiby means of

Strong Interaction !

- established in the 1980s -

***Nucleus = Bell Operators = Hammers ??

Transition strength=Int. strength x

|<f |Vint | i>|2

Vint : various kinds of Operators (Op)

Hit a Bell ! Hit a Nucleus!

at Todaiji templeNara, Japan

from Lucia collection

Todaiji Temple in Nara

from Lucia collection

Todaiji Great

Buddha

Various Operators / Various Hammers!

The sound from the bell is different depending on hammas!

hammers=operators

The mode of nuclear excitation is decided by an operator!

wooden hammers metal hammers

***Operators and Excitations

Vibration Modes in Nuclei (Operators)

Vibration Modes in Nuclei (Schematic)

Vibration Modes in Nuclei (Operators)

T=1: IV excitation(isospin related!)

S=1: spin excitation

Gamow-Teller Giant Resonances for A>90 Nuclei

Ex= h

***Giant Resonances*** (collective excitations)

- absorbs a large fraction of the total sum rule strength -

1p-1h Configu-

rations making

GQR in 208Pb

Z=82,N=126

Many 1p-1h configurations can make 2+ states !Both proton & neutron configurations move “in phase.”

Therefore, such excitations are “Coherent”!

How can we study Nuclear Weak Transitions?-induced reaction, -decay

*caused by the Weak Interaction: |<f| VintW|i>|2

*main part L =0 (GT:

and Fermi: -type operator)*very slow process (interaction is weak!)

Nuclear reaction*caused by the Strong Interaction: |<f| Vint

S|i>|2*various components, and

includs L =0 (

and -type operator)*fast process (interaction is strong!)

Vibration Modes in Nuclei (Schematic)

Gamow-Teller mode

()

(p, n) spectra for Fe and Ni Isotopes

Fermi

GT

Fermi

GT

GTFermi

58Ni(p, n)58CuEp = 160 MeV

58Ni(3He, t)58CuE = 140 MeV/u

Cou

nts

Excitation Energy (MeV)0 2 4 6 8 10 12 14

Comparison of (p, n) and (3He,t) ０o spectra

Y. Fujita et al.,EPJ A 13 (’02) 411.

H. Fujita et al.,PRC 75 (’07) 034310

Sp

J. Rapaport et al.NPA (‘83)

T> states

GTGR

Vibration Modes and Ex (Harmonic Osc.)

Sherical HarmonicY1 : L=1Y2 : L=2Y3 : L=3

:

Radialr1 : h=1r2 : h=2, 0r3 : h=3, 1:

Operator and Excitations

main subh~8 MeV

Role of Residual Int. (attractive)

1p-1h strength

collective strength

(GR)

stre

ngth

stre

ngth

Ex

Ex

Ex

negative=attractive

Graphical solution of theRPA dispersive eigen-equation

Single particle-holestrength distribution

Collective excitation formedby the attractive residual interaction

Role of Residual Int. (repulsive)

1p-1h strength

collective strength

(GR)

stre

ngth

stre

ngth

Ex

Ex

Ex

positive=repulsive

Graphical solution of theRPA dispersive eigen-equation

Single particle-holestrength distribution

Collective excitation formedby the repulsive residual interaction

GRs observed in (’)

Isoscalar (IS) GRs are at lower Ex than expected.

Summary

What we observe =reaction mechanism

x operator x structure

Uniqueness of nuclei : strong, weak, EM int.

Operators: IS, IV, Electric, MagneticGT : (spin-isospin-type)

B(Op) = |<f | Op | i>|2

***Isospin Symmetry

an important idea to see the connection of decays and excitations caused

by Strong, EM and Weak interactions !

T=1/2 Isospin

Symmetry

Koelner Domin Germany(157m high)

Nucleon & Coin

= Coin

back face

= Nucleon

isospin T=1/2

proton neutronsimilar mass

nearly the same interactionTz =-1/2 Tz = 1/2

Isospin of a Nucleus

Tz = (1/2)N + (-1/2)Z*z-component: conserved

AN Z

The size of a vector should be larger than its z-component!

T = or > | Tz |ex. 27Al (Z=13, N=14) : Tz =+1/2, T=1/2, 3/2, …

27Si (Z=14, N=13) : Tz = -1/2, T=1/2, 3/2, …

Isospin Analogous Structure is expected !

**only Z and N numbers are reversed !

Nucleon & Coin

= Coin

back front

= Nuclei

isospin T=1/2, 3/2, …Tz =1/2 Tz = -1/2

2714 Si13

2713 Al14

Analogous Structures and Transitions in T=1/2 System

(Z,N+1)

-decay

(stable)

-decay

g.s.

g.s.

Tz=-1/2(Z+1,N)

g.s.

Tz=+1/2

g.s.

Tz=-1/2(Z+1,N)(Z,N+1)

(stable)

Isospin Symmetry Space

QEC

(p,n)-type

Real Energy Space

(p,n)-type

Tz=+1/2-decay

-decay

-decay -decay

T=1/2, 3/2 Isospin Symmetry for A=15 Nuclei

715N8 8

15O7

915F6

615C9

Tz =+3/2T= 3/2 Tz =-3/2

T= 3/2

T=1/2 Isospin

Symmetry

Koelner Domin Germany(157m high)

T=1/2 Mirror Nuclei : Structures & Transitions

Tz=+1/2(Z,N+1) (Z+1,N)

-decay

Tz=-1/2

VV

(p,n)-typeV

M1(e,e')

-decayM1

-d ecayM1

2713 Al14

2714 Si13

GT

GT + Fermi

T=1/2 & 3/2 Symmetry

(3He,t)(p, p’)

(d,2He)

-decay

**Higher T Symmetry

T=1 Isospin Symmetry

Byodoin-temple, Uji, Kyoto

T=1 Isospin Symmetry

2612 Mg14

Tz = +1 Tz = -1

2614 Si12

Tz = 0

2613 Al13

GT GT

Transitions in real & isospin space (T=1)

Tz=+1

58 Ni

0 +

1 +

Tz=0

58 Cu

0 +

1 +

1 +

1 +

1 + Tz=-1

58 Zn

0 +

1 +

, IASQEC=9.37

QEC=8.56

Symmetry Transitions from T=1 Nuclei Tz=+1 Tz=0 Tz=-1

(in real energy space)

-decay

1 +

(stable)

(p,n)-type

Tz=+1 Tz=-1Tz=0

58 Ni 58 Cu 58 Zn

0 + 0 +0 +

1 +

1 +1 +

1 +

1 +

1 +

1 +

(p,n)-typeV

-decay

V

Symmetry Transitions from T=1 Nuclei Tz=+1 Tz=0 Tz=-1

(in isospin symmetry space*)

V

, IAS

*after the correction of Coulomb displacement energy

5828 Ni30

5830 Zn28

5829 Cu29

Analogous Transitions in A=26 Nuclei

Tz= -126Al

0+

(p,n)-type + decay

26SiTz= 0Tz= +1

26Mg

0+

g.s.IAS 0+

1+1+

1+

1+

1+

1+

V

V

1+

decay M1

(p,p')V

(e,e')M1

T=1

T=1

T=0, 1,.. T=1,..T=1,..

***Decay and Widths of States

Relationship: Decay and WidthHeisenberg’s Uncertainty Priciple

Etpx

Width E*if: Decay is Fast, then: Width of a State is Wider !

*if t =10-20 sec E ~100 keV (particle decayt =10-15 sec E ~ 1 eV (fast

decay)

-decay

(安定核)

(Z=13,N=14)

QEC

(不安定核)

0

4

8

12

基底状態

基底状態励起状態

励起状態

27Al 27Si(Z=14,N=13)

-decay

-decay

Sn

n-decay

Sp

p-decayNuclear Decays

Exci

tatio

n En

ergy

GroundState

GroundState

ExcitedStates

9Be(3He,t)9B spectrum (at various scales)

-decay

(安定核)

(Z=13,N=14)

QEC

(不安定核)

0

4

8

12

基底状態

基底状態励起状態

励起状態

27Al 27Si(Z=14,N=13)

-decay

-decay

Sn

n-decay

Sp

p-decayNuclear Decays

Exci

tatio

n En

ergy

GroundState

GroundState

ExcitedStates

9Be(3He,t)9B spectrum (II)

Isospin selection rule prohibits proton decay of T=3/2 state!

Width E*if t =10-18 sec E ~1 keV (particle decay)

**Sum Rule

As an example, sum rule for Fermi &Gamow-Teller transitions

are discussed.

Fermi & Gamow-Teller operatorsFermi operator: L=0, S=0 J=0, and T=1 (change in vector)

*transition is between the same configurationSum rule value: B(F) = N-Z

L=0, S=1 J=1, and T=1 (change in vector)*transitions are among LS-partner (j> & j< ) configurations

Sum rule value: B(GT-) - B(GT+) = 3(N-Z)

GT operator:

*if ji=0+ jf=1+ ji=3/2 jf=1/2+, 3/2+, 5/2+

*if Ti=0 Tf=1 Ti=1/2 Tf=1/2, 3/2 Ti=1 Tf=0, 1, 2

**Sum Rule (idea)Nucleus: quantum finite many-body system

The number of nucleons involved in each mode (degree of freedom): limited

Vibration of each mode has a max. amplitude.

For each operator, sum of transition strength is constant.

Sum Rule ★

simple sum rule (non-energy weighted sum rule)

S = B(operator) = const.★

energy weighted sum rule

S = Ex x

B(operator) = const.

Sum Rule (example)*Sum rule value is derived from

Commutation Relationship! (very basic!)

ex.2. Gamow-Teller transition-(GT) – +(GT) = 3(N–Z)

Think of the value<i |[T+ , T- ]| i> = <i | T+ T- - T- T+ | i>Left side: = <i | 2Tz | i> = 2 (N - Z)/2

= N–Zwhere [T+ , T- ] = 2Tz was used

Right side: using T+ | i> = 0= f <i | T+ | f > < f | T- | i>= f |<f | T- | i>|2

ex.1. Fermi transition in - decayS

(F) = f |<f | T- | i>|2 = N–Z

Fermi GT

We see N-Z particlescan participate in theFermi transition.

SummaryUnique Quantum Number in nuclei : Isospin

Life time decay width interaction strength

Sum Rule: derived from the Commutation Relationship! (very basic!)

Nuclear structures with the same A nuclei (isobars)are connected by the idea of Isospin Symmetry !

End of Lecture 1

***Thank you!***