Nuclear Structure and Gamma Spectroscopy · Nuclear Structure and Gamma Spectroscopy ... 1 - The nucleus is a many-body system ... Shell Model Pairing Collective models
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Second Andean School (2014)Second Andean School (2014)
Nuclear Structure and Nuclear Structure and Gamma SpectroscopyGamma Spectroscopy
Prof. José Roberto Brandão de OliveiraDFN-IFUSP
Brazil
IntroductionIntroduction
About my group @ LAFN/IFUSP
Why to study nuclear physics
Why to study nuclear structure
Why to use gamma-spectroscopy
N. S. & N. S. & -spec.-spec. @ IFUSP @ IFUSPPersonnel: J.R.B.O., N.H.Medina, L. Gasques (profs); J. Alcántara-Núñez (Post-Doc); V. Zagatto, V. Aguiar, A. Souza, J. Duarte (grad. students); undergraduate sutdents; and, Many collaborators: (IFUFF, IPEN, UNAL, LNS).Our spectrometer (Saci Perere)Pelletron Tandem Accelerator (8MV), LAFN (Laboratório Aberto de Fís. Nuc.)Research topics: odd-odd nuclei, chiral bands, isomers, LSSM tests, nuclear reaction mechanisms with γ-particle coincs. and weakly bound nuclei, nuclear rainbow scattering
The 4 forces of natureThe 4 forces of natureGravitational
Electromagnetic
Weak
Strong, or Nuclear 5730 a5730 a
Electroweakunification
β-decay
These 3 have a role inNuclear Physics
Quantum electrodynamicsQuantum electrodynamicsFeynman diagrams
Electron g-factor
α=1
137α
2≪α
ggexpexp
((ee)=−2.002319304 36153(53))=−2.002319304 36153(53)
...
Standard ModelStandard ModelParticles and interactions
Hadrons – color neutral:Mesons (qq) – ex: + (ud); Baryons (3q) – ex.: nucleons p(uud); n(udd)
Color: Color: RRGGBBchargescharges
Higgs*
(α)
Weak interactionWeak interactionBeta decay
β-
β+
p-p cycle energy (and neutrino)production at the Sun
n pe– e
p p H2 ee+
Δmν≠0(!?)
Why Nuclear PhysicsWhy Nuclear PhysicsNuclear force is the poorest understood of all the forces of nature
It is peculiarly STRONG – cannot be treated in perturbation theory like electro-weak interactions (except at very high energy)
It is very complex, and (therefore) very rich, particularly at low energy: short range central force, strong spin-orbit interaction, tensor force, pairing, 3-body forces.
Etc.
The atomic nucleus scaleThe atomic nucleus scaleConsists of p & n (lightest baryons)
0.5 nm 5 fm ~1 fm <<1 fm
Atom Nucleus nucleon partons3 val. quarks
Energyradius
The N-N force The N-N force
Paris potential(central part)
fm fm
MeV
S - singleto (S=0)T – tripleto (S=1)E – par (L=0, 2...)O – ímpar (L=1, 3...)(TE, SO) T=0; (TO, SE) T=1
p n
Δ tΔE≈ℏ
c Δ t mc2≈ℏ c
Δ R=cΔ t≈ℏ c
mc2
ℏ c≈200 MeV. fmΔ E=mc2
mπ c2≈140 MeV
Δ R≈1.4 fm
Pion1947
Meson theoryYukawa, 1935
S - singlet (S=0)T – triplet (S=1)E – even (L=0, 2...)O – odd (L=1, 3...)(TE, SO) T=0; (TO, SE) T=1
Why nuclear structureWhy nuclear structure Because it has interesting peculiarities (at low energy):1 - The nucleus is a many-body system (but not “too-many”, like in condensed matter physics: A < 300 << NA=6x10²³)2 - It presents an interplay between collective and single-particle degrees of freedom3 - It (and only it - together with nuclear reactions) involves the nuclear force (at low energy) 4 – It involves geometric and dynamical symmetries5 – It can provide precise tests of beyond-standard-model physics (e.g. double-β decay)6 – It is important for nuclear astrophysics
Nuclear AstrophysicsNuclear AstrophysicsPrimordial nucleosynthesis
pp cycle (Sun)
CNO cycle
r (supenova) and rp procs.
Ciclo CNO
Why Why γγ-spectroscopy-spectroscopyNucleus is too small – we cannot measure with mechanical or electrical instruments
Gamma (electromagnetic interaction) is very well known (QED)
Provides access to detailed information of the quantum states of the nucleus (level scheme)
Typical Typical γγ-spect. experiment-spect. experiment
GeHP
GeHP
GeHP
GeHP
in-beam spectra
Level scheme
Model
High resolution detectors
Liquid Drop ModelLiquid Drop Model
Nuclear radius:
Semi-empirical mass formula
R=R0 A13 (R0=1.2 fm)
ρ0≈0.17 fm−3
rNN≈1/ 3√ρ0=1.8 fm
The shell modelThe shell model
3D harmonic oscillator
2
8
40
70
20
112
Mean field Occupation
Parabolicpotential
well
Independentparticle
Magic numbers
n l (n+1)(n+2) N
0 0 2 2 ✔
1 1 6 8 ✔
2 0, 2 12 20 ✔
3 1, 3 20 40 ✔ ?4 0, 2, 4 30 70
5 1, 3, 5 42 112
E*(n)=(n+3 /2)ℏ ω
ℏωdegeneracy
sz=±12
Shell model with spin-orbitShell model with spin-orbit
Spin-orbit interaction
Magic numbers OK!
HHso so = k l.s= k l.sHHso so = k l.s= k l.s
l = r p
s
p
r
Realistic Shell ModelRealistic Shell ModelWoods-Saxon pot. for n & p + V(Coul.)
Ex. Ex. 116116SnSn
p.b. excitation
E=∑ Ei p.b.
0+
CharacteristicLevel-scheme
J
j1
j2
T≈1 W.U.
VWS r =V 0
1er−r0
a
PairingPairing
Coupling of time reversed orbits to J=0
J=0+
j,mj
j,-mjV r−r '≈r−r '
Pairing correlations – beyond mean field.Nucleus is analogous to a supercondutor.
(gap)
Large Scale Shell Model (LSSM)Large Scale Shell Model (LSSM)
SM+realistic residual interactions between valence particles (exs.: KB3, SDPF...) Ex. 46Ti: Core: 40Ca (N=Z=20) PhysRevC.70.034302
LSSM transition probabilities LSSM transition probabilities Reduced t. p. in 46Ti
Ground-state band
Negative parity band (Kπ = 3-)PR C 70, 034302 (2004)
□○ - LSSM calcs
Collective modelsCollective modelsParameters for description of deformed shapesHill-Wheeler
θ
φ
z
x
y
R
Lund convention
Prolate collective
Oblate noncollective
Triaxial collective
Oblate collectiveProlate noncollective
Spherical
Quadrupole deformations
Vibrational ModelVibrational Model
Vibrations of the nuclear surface
0+
2+
0+,2+,4+
Level scheme
J
Harmonic quadrupole vibration
0+,2+,3+...
=t
Spherical equilibrium deformationE*(n)=n ℏω
T∝n≫1 W.U.
Rotational modelRotational modelQuadrupole deformation rotating perpendicularly to symmetry axis
Permanent deformation
0+
Level scheme
J
2+
4+
6+
8+ 152DySD
T=T (J )≫1 W.U.
Erot=12
I ω2 L=I ω Erot=L2
2 I
Erot=ℏ2 J (J+1)
2 IEγ=ΔErot (Δ J=2)
Erot=ℏ2 J (J+1)
2 I
ΔEγ=4 ℏ2
I
ℏω=Eγ
2
I=moment of inertia
Rotational or vibrational?Rotational or vibrational?Nuclide chartRatio of energies between 4+ and 2+
states(eve-even nuclei)
E4+/E2+Vib.= 2.0Rot.= 3.3
Www.nndc.bnl.gov
Cranking shell model - CSMCranking shell model - CSM
Nilsson+Coriolis interactionRouthian e '=e−ω J x
Energy in the intrinsic frame
““BackbendingBackbending” at high spins” at high spinsCoriolis induced pair breaking
0+
Level schemeJ
2+
4+
6+
8+10+
12+
14+
156Dy
HCoriolis=−ℏω jx
ℏω=Eγ
2
Example of study at IFUSPExample of study at IFUSPJ.A.Alcántara-Núñez, PhD, IFUSP, 2003
Saci Perere spectrometer – Pelletron accelerator
B.Q.
105Rh
Symmetry and phase transitionsSymmetry and phase transitions
Ex. X(5) critical point of the rotation-vibration phase transition
Casten triangle
IBM: s, d bosonsDynamical symmetries
LSSM x Collective rotationLSSM x Collective rotation
Rotor behavior built up from SM + residual interactions
Backbending
1f7/2
Ab Initio - NCSMAb Initio - NCSM
Effective interactions (χEFT) from bare NN and NNN interactions – No Core Shell Model
J.P. Vary ntse-2014(Nucl. Theory in the Supercomputing Era), Russia
1
Gamma spectroscopyGamma spectroscopy
Gamma detectors and Electronics
Coincidence technique
Compton suppressor
Large spectrometers (Why so complex?)
The concepts of resolving power and observational limits
Tracking arrays
Other techniques
2
HPGe semiconductor crystals
Liquid N2 T=77K
High Voltage (2-5 kV)
Energy resolution 2-3keVTime resolution 20 ns
Hiperpure Germanium detectorHiperpure Germanium detector
1k$/%
3
Basic electronicsBasic electronics
Energy spectrum
Det. PCAmp.Spec.
HV
FA CFD
PreE
TADC
bits
Canal
Analog pulseFrom Spec. Amp. (linear)
Analog to digital conversion
4
Comparison between “ideal”, NaI(Tl) Comparison between “ideal”, NaI(Tl) and HPGeand HPGe
Energy resolution (FWHM)
5
γ-γγ-γ coincidence circuit coincidence circuit
Amp.Spec.
HV
CFD
PreE
T
Det.
PC
Amp.Spec.
HV
FA
PreE
T
FA
CFD
CO
GDG
GDG
Det.
GDG
TAC/SCA
startstop
ADC
scat
in1
2
3gate
CC
camac
7
- - Matrix Matrix Biparametric spectrum E1 x E2
Total Projection
Matrix in perspective
Event: Event: EE11,E,E
22,T,T
22-T-T
11
1 2γ
1γ
2
8
Gates x Level SchemeGates x Level Scheme
Gate BGate C
Gate ATotal
projection E
#
A
B
C
A B C
MatrixMatrix
E1
E2
Gates:
A
BC
Level scheme
Spectra:
10
Typical Typical γγ spectrometer system spectrometer system
PRISMA-CLARALNL-INFN
Why is it so complex?
11
Complexity of the spectraComplexity of the spectra Ex.: Fusion-evaporation reaction Ex.: Fusion-evaporation reaction
Singles spectrum
Coincidence spectrum
Compromise: efficiency x resolving power (R)
12
The resolving power conceptThe resolving power concept
The P/B ratio improves each time a gate selection is made
The improvement factor is the
resolving power: R=SEγ
Δ Eγ
P /T
is the average energy separation between γ peaks within a cascade is the energy resolution
is the peak to total ratio of the detector
Δ Eγ
P /T
SEγ
SEγ
Δ Eγ
SEγ
P
B
T
13
Multiple Multiple γγ coincidences coincidences
α: observational limit of the spectrometerR – Resolving powerph – Photo-peak efficiency
Number of rays detectedOptimum:
R=SEγ
Δ Eγ
P /T
αback=(P /B)FR0(kR )
F
αstat=N F
N ε0(k εph)F
αback≈αstat
N F=100 ;(P /B)F=0,2
14
γγ-spectrometer examples-spectrometer examples
HERA – LBLHERA – LBL20 GeHP20 GeHP
Gammasphere LBNL/ANLGammasphere LBNL/ANL~100 GeHP~100 GeHP
Multi-detector GeHP/CS systems
15
The Saci-Perere spectrometer The Saci-Perere spectrometer IFUSPIFUSP
Sistema Ancilar de Cintiladores (Saci)Pequeno Espectrômetro de Radiação Eletromagnética com Rejeição de Espalhamento (Perere)
4 GeHP c/ AC11 E-E ( 85% of 4π)
16
Ancillary systemsAncillary systems
Charged particle detectors (4π)
SACI – sistema ancilar de cintiladores plásticos
(phoswich)
17
Plastic Plastic Phoswich Phoswich scintillatorsscintillators
Two types, with different decay time constants
Z=2
O
1818O + O + 110110PdPd
EE
Saci
Z=1
Z=0
PMTΔ E
E
Charged particleEnergyloss
18
Observacional limit of Saci-PerereObservacional limit of Saci-Perere
1% - typical SD band intensity
20
Composite/segmented Composite/segmented detectors detectorsClover (4 segments) / Multi-segmented
EXOGAM(Ganil)
AGATA (EU)
GRETA (USA)
21
New generation: New generation: γ-γ-ray ray trackingtrackingPositions of interactions in 3 dimensions with mm precision
Reconstruction of the scattering sequence
Pulse-shape discriminationDSP (FPGA)Segmented Ge detectors
22
Tracking spectrometersTracking spectrometers
Gretina/Greta (USA)
Agata (EU)
Large efficiencies (50%)Excellent resolution (2keV)
24
Other Other γγ spectroscopy techniques spectroscopy techniques
Angular distributions and correlations
Lifetime measurements
g-factor measurements
25
Angular distributions →Angular distributions → JJ
Determinação da multipolaridade de uma transição
Beam
Target
r
=1 =1 (M1, E1)(M1, E1)=1 =1 (M1, E1)(M1, E1)
=2 =2 (M2, E2)(M2, E2)=2 =2 (M2, E2)(M2, E2)
M1
M1
M2
3+
4+
5+
6-
E1
E2
l=r×pp ml=0 z
Beam
Compound nucleus
W
26
Directional correlation Directional correlation
QDCO versus mixing ratio
(Q - Stretched quadrupole gate)
2
4
5
1+21+2
22gate
Saci-Perere 37o/101o
27
Doppler shift attenuation methodDoppler shift attenuation method
Lineshapes
v
E
#
v t
t ps10
Velocity distribution
v
t
48V
ExpLSSM
v
Eγ=E0(1+βcosθ)
28
Plunger (~ns)Plunger (~ns)
Recoil distance method - RDM
E=E0 1vc
cos
Doppler effect
EE0
E
E
E
d=vt
vRecoil velocity
beam
L.G.R. Emediato (IFUSP)133Ce Triax. PRM x IBFMPRC 55 (1997) 2105
29
RSM - “SISMEI”RSM - “SISMEI” γ-γ(t), p-γ(t) coincidences
Time spectra - 20ns-10s
stop
start
Dennis Toufen – Mestrado IFUSP Rev. Sci. Instr. 85, 073501 (2014)
30
g-factor measurements g-factor measurements
Larmor precession
Modulation spectra for 176W in Pb. B=27.2kGTDPAD
μ=g J
B
S
N
B
Z
Application- Hauser Alloys (114In)
31
Recoil in vacuum - RIVRecoil in vacuum - RIVA. Stuchbery (ANU) 2012
..
.
B∼103 T
Detector ringAzimuthal angle φ
B=0
φBeamz
130Te+12C ORNL (Hyball+Clarion @ HRIBF)
|g|
S electron CC
PerturbedPerturbedNon-Non-perturbedperturbed
B=0B∼103 T
32
Transient magnetic fieldTransient magnetic field
Triple target
Rotation of W(θ)
Bext ⇒ polarization
BT~1000 T (τ∼ps)
Polarized unpaired s electrons
NN
SS
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