nuclear excitations probed by strong, em and weak ......nuclear excitations probed by strong, em and...
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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!***