Double-beta decay matrix elements and nuclear shapes

Transcription

1 Double-beta decay matrx elements and nuclear shapes E. Moya de Guerra UCM and CSIC Madrd (Span) December 2005

2 Collaborators P. Sarrguren R. lvarez-rodrguez O. Moreno

3 Contents Overvew of underlyng theory: QTDHF pplcaton to charge-exchange exctatons: a smplfed scheme Numercal applcatons and ther accuracy Sngle beta-decay Magnetc dpole mode Double beta-decay Summary and outlook

4 OVERVIEW OF UNDERLYING THEORY QTDHF has been formulated by varous groups wth dfferent ams. The startng pont s the varatonal prncple δi δψ,,,, ψ = ψ(t) tme dependent many-body nuclear wave functon Reducton to a few collectve, slowly varyng degrees of freedom ( ) when ψ S.D. TDHF (or TDHFB) V.P. set of selfconsstency condtons for φ s and Q s I- δφ H φ = 0 t eulbrum { = 0 } I- HF or HFB II- δi = δψ = * 0 I t = 2 12 ψ t Σ pq ( ( t), p ( t) ) e φ( ) ψ ( t) Ψ V = δφ V [ H, Q ] φ = 0 φ H φ φ [ Q ] φ = δ P j P M M 1 = φ [ H, Q ], Q ]φ j 1 * L( ψ, ) dt * ) * L( ψ, ψ = ψ H ψ t V = 0, Normal modes of the system 2 V 2 = K > 0 δφ0 H φ0 = 0 II- RP or QRP δφ0 [ H, Γ ] ω Γ φ0 = 0 Γ = M ω 2 Q P 2M ω

5 QUNTIZTION OF CLSSICL DYNMICS OF COL. MODES V.P.,,,, Let s go back to the t-dependent many body wave functon: near eulbrum Mcroscopc many-body aspect contaned n Q s, P s and f 0 Collectve aspect s, p s classcal uantze, Defne collectve phonon operator: and phonon bass Relevant Physcal Quanttes: Expectaton values for any operator θ between uantal many body collectve states ψ n, ψ m : 0 ) ( ) ( φ P Q p e t = Ψ ˆ p = ˆ = ω ω M p M ˆ ˆ 2,..., 1 f 0 f ,, 0 = = = n n f n f f f f m n m n m n f f f p f d ), ˆ( ) ( ) ˆ, ˆ( ) ( * = = = θ θ θ ψ ψ have to p = & = K V V ) ( ) ( ) ( p = & H = M p V 2 ) ( 2 H H

6 ... )] (, [ ), ˆ( ) ( ) ( 0 Γ Γ = = Γ Γ Γ Γ φ θ θ φ φ θ φ θ e e Quantal representaton of the operator n collectve space... ) ( ), ˆ( 1,1 1,0 0,1,0 0 = θ θ θ θ θ [ ] [ ] [ ] ,0 0,, ],, [ 2 1 φ θ θ θ φ φ θ φ θ = z.p. correcton wth Matrx elements: 0 0,1 0 ], [ φ θ φ θ = [ ] [ ] 0 0,1 1 ],, [ ],, [ 2 1 φ θ θ φ θ = m n m n ψ θ ψ θ =, Moya de Guerra and Vllars, NP 285 (1977) 287; NP 298 (1978) 109; PRL 48 (1982) 922

7 QUNTIZTION OF CLSSICL DYNMICS OF COL. MODES V.P.,,,, Let s go back to the t-dependent many body wave functon: near eulbrum Mcroscopc many-body aspect contaned n Q s, P s and f 0 Collectve aspect s, p s classcal uantze, Defne collectve phonon operator: and phonon bass Relevant Physcal Quanttes: Expectaton values for any operator θ between uantal many body collectve states ψ n, ψ m : 0 ) ( ) ( φ P Q p e t = Ψ ˆ p = ˆ = ω ω M p M ˆ ˆ 2,..., 1 f 0 f ,, 0 = = = n n f n f f f f m n m n m n f f f p f d ), ˆ( ) ( ) ˆ, ˆ( ) ( * = = = θ θ θ ψ ψ have to p = & = K V V ) ( ) ( ) ( p = & H = M p V 2 ) ( 2 H H H = ω 0,0 H^

8 pplcaton to charge-exchange exctatons Deformed Hartree-Fock wth Skyrme forces Sngle partcle states (axally symmetrc even-even nucle) smplfed scheme Expanson nto egenfunctons of deformed h.o. f a (R,s) wth Parng correlatons n BCS approxmaton and Resdual nteractons consstent wth the HF mean feld pnqrp phonon operator for GT exctatons QRP euatons (ω Κ, X ω K πν, Y ω K πν ) Transton ampltudes n the ntrnsc frame c ph, k pp verage over nuclear volume

9 Even-even nucle K (0p 2p) Type of GT transtons E ex,2p = ω E p0 E n0 Odd- nucle I p K I fp K f Phonon exctatons : (1p 3p) Odd nucleon acts as a spectator E ex,3p =ωe n, spect E p0 > 2 Transtons nvolvng the odd nucleon state : (1p 1p) E ex,1p =E p E p0

10 General behavour of matrx elements (b ) Sphercalf Def BCS QRP (ph,pp) Redstrbuton and reducton of the strength N=Z Smooth occupatons New exctatons Fragmentaton Selfconsstent method wth Skyrme forces Sutable for extrapolatons to unknown regons and processes

11 Ferm & Gamow-Teller 2p

12 Stable nucle n Fe-N mass regon Man consttuents of stellar core n presupernovae formatons Gamow-Teller propertes. Comparson wth expermental (n,p) Comparson wth SM calculatons. Test of our QRP method.

13 Stable nucle n Fe-N mass regon. GT strength: Theory and experment Total B(GT ) strength exp. QRP HFBCS SM 51 V 1.2 (0.1) Fe 3.5 (0.7) Mn 1.7 0(.2) Fe 2.9 (0.3) N 3.8 (0.4) Co 1.9 (0.1) N 3.11 (0.08) N 2.53 (0.07) N 1.72 (0.09) Fe 56 Fe 58 N 60 N Total B(GT ) strength Exp. 7.8 (1.9) 9.9 (2.4) 7.5 (1.8) 7.2 (1.8) QRP SM SM : Caurer et al. NP 653(99)439 QRP: Sarrgurenet al. NP 716(2003)230

14 Medum-mass proton-rch nucle : Ge, Se, Kr, Sr Watng ponts n rp process Shape coexstence. Large Q values Isotopc chans approachng drp lnes Beyond full Shell Model

15 Energy vs. deformaton Mnmzaton of the energy under the constrant of holdng the nuclear deformaton fxed Shape coexstence More than one local mnmum at close energy Sarrguren et al. NP 658 (1999) 13

16 Test of b-decay shape dependence predctons 74 Kr op shape coexstence 76 Sr prolate Gamow-Teller strength: Theory and Experment oblate oblate prolate prolate 74 Kr 76 Sr oblate prolate Exp: Porer et al Exp: Nácher et al. 2004

17 Q EC and T 1/2 : Theory and Experment When z.p. energy correctons are taken nto account Q th Q exp and T th T exp

18 Beta-decay half-lves of watng pont nucle Good agreement wth experment : Relable extrapolatons MNK: Moeller et al. t. Data and Nucl. Data. Tables 66 (1997) 131; Sarrguren et al. Eur. Phys. J. 24 (2005) 193

19 Recent predctons on neutron-defcent Pb sotopes... (MeV) e - e - γ Pb ndreyev et al, Nature 405 (2000) 430 trple shape coexstence at low exctaton energy 186 Pb Unue laboratory to study the phenomenon of nuclear shape coexstence Search for sgnatures of deformaton on ther b-decay patterns

20 Energy-deformaton curves : Pb sotopes Influence of Skyrme force and parng Influence: Relatve energy of mnma Sarrguren et al. PRC (2005) n press Lttle nfluence : locaton of mnma

21 GT strength dstrbutons : Pb sotopes GT strength dstrbutons show specfc sgnatures, dfferent for each eulbrum deformaton, whch hardly change when the ngredents n the formalsm are modfed

22 Rare earths: M1 exctatons n deformed nucle orbtal (e,e ) (γ,γ ) spn (p,p ) (p,p ) Trumf 90 s (e,e ) Darmstadt 1984 (γ,γ ) Stuttgart 90 s Scssors mode ~ b 2 Nojarov et al. NP 563 (1993) 349

23 ORBITL M1 exctatons n deformed nucle: Theory and experment Characterstc of M1 exctatons Orbtal exctaton spectra centered around 3 MeV and b 2 dependence Moya de Guerra et al. PRC 49 (1994) 3354 / 47 (1993) 811

24 SPIN M1 exctatons n deformed nucle: Theory and experment Spn M1 strength: sospn counterpart ( T z =0) of GT strengths ( T z =±1) Total strength and peak structures n agreement wth experment Sarrguren et al. PRC 54 (1996) 690

25 Double beta-decay: Two neutrno mode One of the most rare events n nature T 1/2 ~ years (,Z) (,Z2)2e - 2n 2n : 2 successve β decays through ntermedate vrtual states. Second order process n the weak nteracton. Observed n 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 150 Nd (T 1/2 ~ years)

26 Double beta-decay and deformaton Descrpton of the nuclear structure nvolved n the process

27 Bndng energy profles of DBD partners Q exp Parent Daughter β exp lvarez-rodrguez et al. PRC 70 (2004) Q exp

28 Double beta-decay and Deformaton GT strengths of DBD partners

29 GT strength n the sngle-beta branches of double beta partners

30 M 2n 2b vs. κ pp and deformaton Dependence on partclepartcle nteracton Dependence on deformaton

31 Summary We have tested our selfconsstent approach on GT strengths and related propertes along the nuclear chart. We fnd: Good agreement wth experment: * GT strength dstrbutons : Fe-N and 2νββ emtters. * Half- lves : Proton-rch nucle. Watng pont nucle. * Spn M1 strengths : Rare earth and actnde. Important dependence on nuclear shapes. Suppresson mechansm for DBD matrx elements. Sgnatures of deformaton n GT strengths of neutron-defcent Pb. Far agreement on 2ν DBD M.E. for reasonable values of κ pp and nuclear deformaton selfconsstently determned.

32 Outlook Further exploratons of theory and numercal calculatons: Take nto account zero pont correctons (bndng energes, Q EC s, ). Test other Skyrme forces. Test local parng nteractons. Go from 2ν DBD to 0ν DBD

33 THE END &

34 PPENDIX

35 Role of resdual nteractons Redstrbuton of the strength ph : shft to hgher energes pp : shft to lower energes Reducton of the total strength Sarrguren et al. NP 635 (1998) 55

36 Theoretcal approach Deformed Hartree-Fock wth Skyrme forces Resdual nteractons Sngle partcle states (axally symmetrc even-even nucle) Expanson nto egenfunctons of deformed h.o. f a (R,s) Ν=11 pnqrp phonon operator for GT exctatons Parng correlatons n BCS approxmaton Fxed gaps taken from phenomenology QRP euatons (ω Κ, X ω K πν, Y ω K πν ) Transton ampltudes n the ntrnsc frame Partcle-hole resdual nteracton consstent wth the HF mean feld

37 2p / TD / RP Skyrme force GT strength n the lab frame even-even nucle TD : (Y 0); 2p : (V res 0)

38 Role of parng Exstng peaks: decrease wth ncreasng D (at low energy) New peaks appear: ncrease wth ncreasng D (at hgh energy)

39 Role of deformaton p obl n obl p sph n sph p prol n prol 74 Kr Z=36 N=38 llowed GT transtons π= sphercal/deformed Fragmentaton of the strength oblate/sphercal/prolate Dfferent scenaros

40 Gamow-Teller strength dstrbutons Kr sotopes

41 Beta-decay half-lves of watng pont nucle rp process Mechansm to understand nucleosynthess of heavy p-rch nucle Expected n scenaros of hgh r and T : X-ray bursts bnary systems (red gant neutron star) Proton capture reacton rates (p,g) are orders of magntude faster than the competng b -decays When the domnant p-capture s nhbted, the reacton flow wats for the slow b-decay (WITING POINTS) T 1/2 of watng ponts determne : rp tme scales abundances of elements watng ponts Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38) Rb (37) Kr (36) Br (35) Se (34) s (33) Ge (32) Ga (31) g (47) Pd (46) Rh (45) Ru (44) Schatzet al

42 Dependence of T 1/2 on deformaton Dependence of T 1/2 on k pp pp

43 Double beta-decay: Test of the Standard Model One of the most rare events n nature T ~ years 2 decay modes (,Z) (,Z2)2e - 2n (,Z) (,Z2)2e - 2n : 2 successve β decays through ntermedate vrtual states. Second order process n the weak nteracton. Observed n 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 150 Nd (T ~ years) 0n : Lepton number not conserved. Forbdden n the SM. ν emtted s absorbed : Massve Majorana partcle. (T ( 76 Ge) > years)

44 Double beta matrx elements as a functon of deformaton Suppresson mechansm due to deformaton

45 Double beta matrx elements HF-QRP WS-QRP

46 GT strength n the sngle-beta branches of double beta partners

47 Odd- nucleus