Nuclear Structure and Gamma Spectroscopy · Nuclear Structure and Gamma Spectroscopy ... 1 - The nucleus is a many-body system ... Shell Model Pairing Collective models

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)

Strong interaction, QCDStrong interaction, QCDConfinement x asymptotic freedom

Unification

α=1

137

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

Other terms of N.F.Other terms of N.F.

Tensor

Spin-orbit

3-body

LS

s

D(r) l . s

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

Level schemesLevel schemes

Manifest the nuclear structure

Nuclear ModelsNuclear Models

Liquid DropShell ModelPairingCollective modelsNilssonCSM, TACIBM

Binding energy per nucleonBinding energy per nucleon

EB/AEB/A

(E = Mc2)

EB = (NMn+ZMH-M(Z,A))c2

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

Magic NumbersMagic Numbers

N: 2, 8, 20, 28, 50, 82, 126

… at least near the stability valley!

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

Nilsson modelNilsson modelSingle particle shell model states in a deformed potential

140Gd

K=∑Ωi

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

Band terminationBand termination

Alignment of all the valence particles

Termination

Chiral symmetry breakingChiral symmetry breaking

Tilted Axis Cranking105RhNearly degenerateM1 bands

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

Precision theoretical calculationsPrecision theoretical calculations

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

6

Todays electronicsTodays electronics

Ex.: Gretina Digitizer and Timing & control modules

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:

9

The Compton SupressorThe Compton Supressor

Anti-coincidence with BGO signals (b)

Normal

Suppressed

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

19

-p (-p (1616O+O+2727Al)Al)J.A.Alcántara-Núñez (Mestrado IFUSP)

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)

23

Evolution of the resolving powerEvolution of the resolving power

I-Y. Lee

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

33

Measurement

H

TMF TMF

Proposal LAFNUnal/USP