Beta Decay Studies in nuclear structure Escuela de doctorado de Física Nuclear Santiago 1 de Marzo de 2007 Introducción Cómo hacer una medida Un ejemplo Berta Rubio IFIC (CSIC-Univ. Valencia) B. Rubio. Escuela Doctorado FN, Santiago 2007
Most unstable nuclei decay by either β + or β - decay Proton Drip Line 265 stable About 3000 out of 6000 synthesised in our laboratories, only about 100 fission Fission B. Rubio. Escuela Doctorado FN, Santiago 2007 Neutron Drip Line
There are two ways (mainly) to study nuclei, reactions and decay Reactions have the advantage of the flexibility, Decay is God given but it is very selective and can Bring us very far from stability B. Rubio. Escuela Doctorado FN, Santiago 2007
Typical constants Pion-nucleon ( strong ) 1 Electromagnetic 10-2 β decay ( weak ) 10-5 Gravitational 10-39 Weak process p Introduction: what is β decay? n W- e- u ν e d W- e- B. Rubio. Escuela Doctorado FN, Santiago 2007 ν e
Test of the standard model: yes but only when we can eliminate the nuclear structure factor. But we are not so much concerned with The weak force but rather with the beta decay and nuclear structure Something to remember: because of the weak interaction beta Half-lives are long As soon as particle emission is possible, it will dominate B. Rubio. Escuela Doctorado FN, Santiago 2007
Far of stability beta decay is often the first piece of information we encounter: Few atoms per day: Existence Half life (even an inaccurate number) Mass (even an inaccurate number) Some atoms per second Spin, excited states 100 to 1000 atoms per second Full or very complete spectroscopy B. Rubio. Escuela Doctorado FN, Santiago 2007
i f proton neutron B. Rubio. Escuela Doctorado FN, Santiago 2007
The real process β - : n p + e - + ν β + : p n + e + + ν EC : p + e- n + ν Always in competition with β + β - : In real nuclei A Z X N A X Z + 1 N 1 + e + ν e ß+ β + : A Z X N A X Z 1 N + 1 + e + + ν e ß- EC : A Z A X + e + ν N N e + Z 1 + 1 X X ray B. Rubio. Escuela Doctorado FN, Santiago 2007
B. Rubio. Escuela Doctorado FN, Santiago 2007 ) ( ) ( 1 1 + + + e N N X X N A Z N A Z ) ( ) ( 1 1 + + e N N X X N A Z N A Z β - : β + : ) ( ) ( 1 1 X X N A Z N A Z e N + + EC : The β decay Q-value N=nuclear masses If we use atomic masses!!! Q β - = Q β + = Q EC = [ ] 2 1 1 ) ( ) ( c M M X X N A Z N A Z + [ ] 2 2 1 1 2 ) ( ) ( c m c M M e N A Z N A Z X X + [ ] e N A Z N A Z B c M M X X + 2 1 1 ) ( ) ( (Normally the mass excess is used- Audi tables)
I = 0,1 Quantum numbers and the selection rules for allowed β-decay l s = π = r r r r Ii = I f + s( e ) + s( ν ) r v r r r I = Ii I f = s( e ) + s( ν ) r r r r I = L + s = s = 0 0,1 0 Selection rules 0 + to 0 + Gamow Teller forbidden!!! B. Rubio. Escuela Doctorado FN, Santiago 2007 e - e - ν ν Single state, Fermi Triplet state Gamow Teller
The operator responsible for the process στ στ Gamow-Teller Or τ Fermi 28 2 p 1/2 1 f 5/2 2 p 3/2 1 f 7/2 στ 28 1 f 5/2 2 p 3/2 1 f 7/2 τ B. Rubio. Escuela Doctorado FN, Santiago 2007
The isospin formalism: p and n are the same kind of particles with a different isospin state (T) The third component T z is very clear: T Z N Z = 2 τ Fermi Can only change the third component of isospin: Only one state called Isobaric Analog State (IAS) στ στ Gamow-Teller Can change the spin and the isospin: Many possible final states B. Rubio. Escuela Doctorado FN, Santiago 2007
Fermi transitions 74 36 Kr 38 T T Z =1 =1 T=8 T Z =7 88 37 Rb 51 β - β + 74 35 Br 39 T 1, T = T Z = 2 2 T=8 T Z =8 88 36 Kr 52 In β + Fermi, forbidden for N>Z In β - allowed but energetically difficult B. Rubio. Escuela Doctorado FN, Santiago 2007
Gamow Teller transitions 74 36 Kr 38 T T Z =1 =1 T=8 T Z =7 88 37 Rb 51 β - β + 74 35 Br 39 T Z T = 2 = 2 T=8 T Z =8 88 36 Kr 52 In β + Gamow Teller allowed In β - Gamow Teller allowed B. Rubio. Escuela Doctorado FN, Santiago 2007
The β+ process is hindered due to the occupation Л ν β+ B. Rubio. Escuela Doctorado FN, Santiago 2007
Not a problem on the β- side Л ν β- B. Rubio. Escuela Doctorado FN, Santiago 2007
Transition probability i τ στ f BF = ψ f τ ± ψ i 2 BGT = ψ f στ ± ψ i 2 B GT and B F can be calculated using microscopic models!!! This is the main message of this talk!!!! B. Rubio. Escuela Doctorado FN, Santiago 2007
We will learn in the next lectures how to MEASURE the B GT or B F,, but before that two comments. B. Rubio. Escuela Doctorado FN, Santiago 2007
The Ikeda sum rule: MODEL INDEPENDENT π ν S - -S + =B GT- -B GT+ =3(N-Z) β- B GT- (p,n) B GT+ (n,p) In principle β- decay is more interesting because most of the nuclei have more neutrons than protons, and then most of the Ikeda sum rule in the β- side. B. Rubio. Escuela Doctorado FN, Santiago 2007
Before we go to the experimental techniques, one word about charge exchange reactions B. Rubio. Escuela Doctorado FN, Santiago 2007
Charge exchange reactions Target Exchange of a proton for a neutron Projectile Ejectile The are experimentally very different from the β decay experiments They involve different nuclei The i> state is But they are governed by the same operator!!!!, a and stable are therefore nucleus intimately related B. Rubio. Escuela Doctorado FN, Santiago 2007
Two possible explanations: 1232 Higher order configuration mixing: interpretation and normalisation of a reaction spectrum An experimental problem (to analyse the background properly) K.Yako et al CM 2002 B. Rubio. Escuela Doctorado FN, Santiago 2007
BGT = ψ f στ ± ψ i 2 BGT = I β ft 1/ 2 B. Rubio. Escuela Doctorado FN, Santiago 2007
FIN parte 1 B. Rubio. Escuela Doctorado FN, Santiago 2007
Beta decay experiments Production of exotic nuclei, the reaction Separation of the radioactive activity Detection techniques Extraction of the B GT B.Rubio. Es. Doc. Santiago 2007
The reaction Any in principle, beta decay will not depend on it B.Rubio. Es. Doc. Santiago 2007
In the following example: Isol technique (far from stability: fragmentation in flight technique) B.Rubio. Es. Doc. Santiago 2007
Accelerator target Ion source Mass Separator recoil. Time=0 β Z A N γ Time>1 s γ Z-1 A N+1 γ β B.Rubio. Es. Doc. Santiago 2007 Transport system
Off beam Projectile Target Fusion evaporation projectile fragmentation, target spallation, fission... n p α n γ γ γ γ ν T1/2=1 s β+ β+ Particle evaporation 10-19 s Gamma deexcitation fs,ns,µs,ms B.Rubio. Es. Doc. Santiago 2007 Beta-decay ms, s,min,days,years
Difference between in beam fusion evaporation and off beam beta decay B.Rubio. Es. Doc. Santiago 2007
In beam spectroscopy γ Projectile Target γ γ Ex Information about Yrast or near Yrast states (we can change E and J) I B.Rubio. Es. Doc. Santiago 2007 (D.R.LaFosse et al. P.R.L 78 (1997)614
ν β+ Parent Beta Decay: low angular momentum, and high exc. Energy sometimes, but given by nature Ex Daughter Parent β+ Daughter Daughter B.Rubio. Es. Doc. Santiago 2007
How to measure the B(GT) Theoretical quantity BGT = ψ f σkτ ± k ψi k 2 Strength function S ( E) β Experimental quantity: = I ( E) β 1 2 f ( Qβ E) T / S β Relationship 1 6147 ± 7 g g 1 E A ( E) = B( GT ) i f 2 B.Rubio. VEs. Doc. E Santiago E 2007 f
The Strength Function Beta-feeding S β ( E) = f ( Q β I β ( E) E, Z) T 1/ 2 Fermi function Phase space factor and Coulomb interaction between the β and the nucleus, tabulated, Nuclear Data Tables A10 (1971): Quantities to be measured E= Exc. En. Daugther Q β B.Rubio. Es. Doc. Santiago 2007 β Half life I% ( E) S( E) = = ft 1 ft
B.Rubio. Es. Doc. Santiago 2007
Q β -measurements, associated to the process Fermi Kurie plot: we measure the maximum energy of the e - B.Rubio. Es. Doc. Santiago 2007
Fermi Kurie plot silicon detector to detect electrons Keller et el. NIM A300(1991)67 β B.Rubio. Es. Doc. Santiago 2007
But today very precise mass measurements are Possible by other means, and the Q β -value Is calculated as a difference of ground state atomic masses B.Rubio. Es. Doc. Santiago 2007
The principle of Penning traps z r 0 0 z0 r A Penning trap can be defined as the superposition of a homogeneous magnetic field and an electrostatic quadrupole field. ω c = Q m B B.Rubio. Es. Doc. Santiago 2007
ISOLTRAP, CERN Measurement trap Purification trap RFQ buncher B.Rubio. Es. Doc. Santiago 2007
Stopping chamber RFQ buncher Transfer section Purification trap Measurement trap B.Rubio. Es. Doc. Santiago 2007
Other methods Mass measurements at storage rings The Euschool Lectures on Physics with Exotic Beams G. F. Bosch Mass measurements at Isolde with Mistral Lunney D, Pearson JM, Thibault C Recent trends in the determination of nuclear masses REVIEWS OF MODERN PHYSICS 75 (3): 1021-1082 JUL 2003 B.Rubio. Es. Doc. Santiago 2007
dn/dt Half life measurement Z A N β N( t) = N 0 e λt dnγ/dt γ Z-1 A N+1 1 λ = τ = Ln2 T 1/ 2 Nγ t t t t t t
Ln( Nγ/ t) A Very simple!!!! A/2 T 1/2 B.Rubio. Es. Doc. Santiago 2007 t
Z A N β+? γ γ Beta-feeding Impossible We have to use the gamma Z-1 A N+1 γ1 γ2 B.Rubio. Es. Doc. Santiago 2007
B.Rubio. Es. Doc. Santiago 2007 The CLUSTERCUBE A set-up of six EUROBALL CLUSTER detectors at GSI
B.Rubio. Es. Doc. Santiago 2007 EXOGAM, GANIL
1 - states SINGLES 0+ B.Rubio. Es. Doc. Santiago 2007
The Pandemonium problem B.Rubio. Es. Doc. Santiago 2007
Beta-feeding far from stability B( GT ) = ψ σ τ ± f k k ψi στ k 2 2 Q β Many states, daughter One state (g.s) parent ψ f ψ f ψ f ψ f ψ f B.Rubio. Es. Doc. Santiago 2007 Further from stability, higher Q β -values
For high Q-values, Ge detectors Traditionally fail to detect γ1 γ2 β-feeding at high Z A N excitation energy!!! Z A N B.Rubio. Es. Doc. Santiago 2007
We use Ge detectors to construct the decay scheme From the γ-balance we stract the β -feeding What happens if we miss some gamma intensity??? B.Rubio. Es. Doc. Santiago 2007
Z A N B.Rubio. Es. Doc. Santiago 2007 β-feeding Aparent β-feeding!!!!!!!!!!
Total Absorption spectroscopy γ1 NaI β feeding γ2 γ1 E 2 E 1 γ2 N I β Ideal case B.Rubio. Es. Doc. Santiago 2007 E 2 Ex in the daughter
If the case is not ideal: One has to solve the following equation: d R i j = max j= 1 ij f j d i i j E j B.Rubio. Es. Doc. Santiago 2007
B.Rubio. Es. Doc. Santiago 2007 TAS at the dead On-line Mass separator at GSI
Lucrecia, the TAGS spectrometer at ISOLDE NaI crystal + ancillary detetcors (Ge for X-ray, plastic for β 38 cm x 38 cm B.Rubio. Es. Doc. Santiago 2007
FIN parte 2 B.Rubio. Es. Doc. Santiago 2007
The deformation of the N=Z nucleus 76 Sr in its ground state Physics motivation Production and separation of 76 Sr activity Experimental set-up Raw data Analysis of the data Final results and interpretation ED Santiago 2007
The shape of a nucleus and the concept of deformation ED Santiago 2007
The Shape of the nucleus Near closed shells: spherical g 9/2 ED Santiago 2007
When we depart from closed shells, the simplest deformation is quadrupole deformation R ( θ, φ ) = R 0 (1 + β 2Y 20 ( θ, φ )) [413]7/2 36 42 34 32 38 g p f p f s d 9/2 [301]3/2 [301]1/2 (MeV) 0 [422]5/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 ED -0.4 Santiago -0.3-0.2 2007-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 40 [404]9/2 [303]5/2 28 38 [431]3/2 [440]1/2 [312]3/2-5 [310]1/2 30 [321]1/2 [303]7/2 [312]5/2-10 [321]3/2 [330]1/2 [200]1/2 [202]3/2 [211]1/2-15 ε 0.95 β 2
How to measure the deformation B(E2): 4+ 2+ 0+ E2(2 + 0 + ) E2(4+ 2+)- E2(2+ 0+) Or to measure the electrical quadrupole moment, By interaction with external gradient electric field, not for even even ED Santiago 2007
Static quadrupole moment measurements Finite range droplet model Q 3 β2 + 5π 2 7 2 2 0 = ZR0 5/ π β 2 S.Raman et al At. Dat and Nucl. Dat. Tables 78 (2001) Not for even-even and not very far from stability ED Santiago 2007
B(E2) g.s 2+ 0+ B(E2) measurements γ-half-life τ γ ( ) [ ] 13 5 2 2 1+ α = 40.81 10 E B( E2) / e 1 = τ b The model dependent relationship with deformation: [ ] 2 B( E2) 1/ 2 β = ( 4π / 3ZR e 2 0 ) / S.Raman et al At. Dat and Nucl. Dat. Tables 78 (2001) ED Santiago 2007 Other experiments like Electron Scat., Coulomb exc. Difficult far of stability
Future: Coulomb excitation: REX-Isolde, GANIL Electron scattering: FAIR, GSI ED Santiago 2007
Far from stability: level spacing 8+ 6+ E = E2(4+ 2+)- E2(2+ 0+) n γ E 4+ 2+ 0+ 4 h E The empirical (2) 2 J dynamic = Grodzin s formula β 2 J 2 1225 A 7 /3 E + 1/ 2 = 2 5 AMR 2 1 (2 β cos( ) O θ + 120º ) 5 4π For axially symmetric rotor θ=90º E γ ED Santiago 2007
However, none of these methods will give us the sign of the deformation [413]7/2 36 42 34 32-0.4-0.3-0.2-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ED Santiago 2007 38 g p f p f s d 9/2 [301]3/2 [301]1/2 (MeV) 0 [422]5/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 40 [404]9/2 [303]5/2 28 38 [431]3/2 [440]1/2 [312]3/2-5 [310]1/2 30 [321]1/2 [303]7/2 [312]5/2-10 [321]3/2 [330]1/2 [200]1/2 [202]3/2 [211]1/2-15 OBLATE ε 0.95 β 2 PROLATE
In this context, the N Z region around mass 70 is particularly interesting Strong oblateprolate competition Why? Strong def. Rapid shape transitions Shape mixing (MeV) 0-5 -10-15 36 42 34 32 [404]9/2 [211]1/2 g p 38 f p f s d 9/2 1/2 5/2 3/2 28 7/2 20 1/2 3/2 [303]5/2 [413]7/2 [301]1/2 [312]3/2 [321]1/2 [303]7/2 [312]5/2 [321]3/2 [330]1/2 [200]1/2 [440]1/2 [310]1/2 [202]3/2 [301]3/2 [431]3/2-0.4-0.3-0.2-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 40 28 38 [422]5/2 30 Oblate ED Santiago 2007 Prolate
Strong deformation Ref. Gelletly et al P.L.B253 (1991)287 ED Santiago 2007
The sign of the deformation??? ED Santiago 2007
Can beta decay help to solve this problem? BGT = ψ στ ± f ψ i 2 First idea, Hamamoto and collaborators Def HF +BCS+TDA [I. Hamamoto et al., Z. Phys. A353 (1995) 145] Further pursued by Sarriguren and collaborators Def HF+BCS+QRPA [P. Sarriguren et al., Nuc. Phys. A635 (1999) 13] ED Santiago 2007
In N~Z nuclei Protons and neutrons occupy partially the same orbitals Gamow-Teller decay allowed. large part of the GT strength inside the Q EC window ED Santiago 2007
Here we see the B GT distribution for Sr nuclei Q β Sarriguren ED Santiago 2007
We want to measure the beta decay of 76Sr ED Santiago 2007
Isolde at CERN ED Santiago 2007
ED Santiago 2007
In general not all of them used!!! 2.4 µ s 1.2 s (...) 1 2 3 14 1 ED Santiago 2007 16.8 s
Reaction: 1.4 GeV protons on 52g/cm 2 Nb, surface ionisation Fluorination technique. M/ M=5000 Lucrecia ED Santiago 2007
Shielding Polyethylene Lead Copper Aluminium Factor 6 ED Santiago 2007
Lucrecia, the TAGS spectrometer at ISOLDE NaI crystal + ancillary detectors (Ge for X-ray, plastic for β ) 38 cm x 38 cm ED Santiago 2007
Ancillary Detectors The plastic β detector X-ray detector Tape transport system ED Santiago 2007
Efficiency of the Total Absorption Gamma Spectrometer Lucrecia Efficiency 1 0.8 Total Efficiency 0.6 0.4 Peak Efficiency 0.2 0 0 1000 2000 3000 4000 ED Santiago 2007 Energy (kev)
About 5000 counts/s of 76Sr Symmetric cycle of 15 s (T 1/2 76Sr=9s, T 1/2 76Rb 36.8 s) Counts Counts Counts 10 10 5 5 10 4 Lucrecia 10 4 Singles 10 3 10 10 3 2 10 10 2 10 1 0 2000 4000 6000 8000 10000 1 6000 10 3 4000 10 2 2000 10 1 0 10 2 10000 10 5000 1022 kev (516+1022) kev (983+1022) kev Energy (kev) Beta Beta detector Gated 0 1000 2000 3000 4000 5000 Channel X-ray Gated X-ray detector 1 0 2000 5 10 4000 15600020 ED 8000 Santiago 25 10000 30 2007 Q EC =6240 kev Energy (kev) 76Sr activity 76Rb activity Background (1500 counts/s, intrinsic) Pile up 76 Sr + 76 Rb β + 76 Sr EC
Geant simulation The 24 Na source, also produced at Isolde At the same position 4123keV 1369keV 2754keV Black: measured source Red: Simulation with GEANT4 ED Santiago 2007
Analysis We can use the EM algorithm to calculate the feedigs But we need to assume the levels and the way they decay: Known high resolution level scheme, statistical model Statistical model High res. Data Dessagne et al EPJA20(2004)405 ED Santiago 2007
After 300 iterations. ED Santiago 2007
Results of of 76 Sr Sr β-decay Counts I β 10 6 10 5 10 4 10 3 10 2 40 30 20 10 0 1 2 3 4 5 6 7 0 1 2 3 Energy (MeV) Experiment 0.2 0.15 0.1 0.05 0 Energy (MeV) 4 5 6 Energy (MeV) The β feeding B(GT) (g A 2 /4π) B(GT) (g A 2 /4π) 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025 0 0.012 0.01 0.008 0.006 0.004 0.002 Recalculated ED Santiago 2007 0 β-delayed gamma-rays (this work) 0 1 2 3 4 5 6 β-delayed protons (Dessagne et al.) 5 5.2 5.4 5.6 5.8 6 Energy (MeV)
Comparison High Resolution versus Total Absorption I β (%) 50 40 30 20 10 B(GT)(g A 2 /4π) 0 0.2 0.15 0.1 Q EC =6240 kev 0.05 0 0 1000 2000 3000 4000 5000 6000 ED Santiago 2007 Energy (kev)
Results of of 76 Sr Sr β-decay: clearly prolate!!! ΣB(GT) (g A 2 /4π) 5 4 Theo.prolate Theo.oblate ( ) E.Nácher PRL 92 (2004)232501 76 Sr 3 2 Oblate 1 Prolate Q EC 0 1 2 3 4 5 6 7 Energy (MeV) ( ) P.Sarriguren et al.npa 658 (1999)13 Strong deformation in ED agreement Santiago 2007with [C.J. Lister Phys.. Rev. C 42 (1990) R1191], but now we have the sign Lister et al.,
74 Kr, shape admixture 76 Sr clearly prolate 74 Kr ΣB(GT) (g A 2 /4π) 5 4 3 Theo.prolate Theo.oblate E.Nácher PRL 92 (2004) 232501 ( ) 76 Sr 2 Oblate E.Poirier PRC 69 (2004) 034307, agreement with in beam studies. 1 Prolate Q EC 0 1 2 3 4 5 6 7 ED Santiago 2007 Energy (MeV) ( ) P.Sarriguren et al.npa 658 (1999)13
FIN ED Santiago 2007