QRPA calculations of stellar weak-interaction rates P. Sarriguren Instituto de Estructura de la Materia CSIC, Madrid, Spain Zakopane Conference on Nuclear Physics: Extremes of Nuclear Landscape. August 28 - September 4 (2016)
Problem : Weak-decay rates determine late stages of stellar evolution. Experimental extrapolations or theoretical predictions: Reproduce exp information on T 1/2 and BGT under terrestrial conditions. Theoretical approach : Weak-decay rates Deformed HF+BCS+QRPA formalism with Skyrme forces and residual interactions in both ph and pp channels. Results : Weak-decay rates at various (,T) in stellar scenarios pf-shell nuclei. Main constituents of stellar core in presupernova formations: Sc, Ti, V, Mn, Fe, Co, Ni, Zn isotopes. BGT measured in laboratory (Charge exchange reactions) and compared with benchmark Shell Model calculations. Neutron rich Zr-Mo isotopes: r process. Neutron-deficient waiting-point isotopes (Ni-Sn) at (,T) typical of rpprocess.
Weak-decay rates ln 2 ln 2 T ( ) if 1 1/2 Pi T Bif, D if T Initial states thermally populated 2Ji 1 PT i( ) e, G2J1 e G Nuclear structure Ei /( kt ) Ei /( kt ) i i 2 2 g A k k Bif ( GT ) f t i gv k eff P ( 0) 1 ig.. s T Phase space factors : EC if if if +, EC : - : if if are different from laboratory (P i, cec)
Q if Q if 1( Q ) F( Z 1, ) 1 S 1 S ( Q ) d 2 2 if 1 if p if cec 2 2 if if e if Phase space factors 1( Q ) F( Z 1, ) 1 S 1 S ( Q ) d 2 2 if 1 if e if 1( Q ) F( Z, ) S 1 S ( Q ) d oec 2 2 2 2 qk gk BK ql g 1 L B 1 L 1 2 q Neutrino energy g Radial components of the e-wf at r=0 B Exchange and overlap corrections Distribution functions S p =S S e : Fermi-Dirac distribution 1 Se exp e / kt 1 1 Q M M E E if 2 p d i f mc e
Nuclear Structure Skyrme HF + def + BCS + QRPA (ph,pp) Redistribution and reduction of the strength Smooth occupations New excitations Skyrme HF Fragmentation pnqrpa with separable forces Transition amplitudes t q X q Y K K K K 0 q u v, q v u, K K K K
Neutron-rich isotopes: Ge - Pd 80-94 Ge, 86-100 Se, 90-104 Kr, 94-108 Sr, 100-114 Zr, 104-118 Mo, 110-124 Ru, 114-128 Pd r-process: supernovae, n-star mergers Nucleosynthesis of heavy elements
Zr-Mo B(GT)
Zr-Mo Half-lives
Impact of deformation Average position Mean square fluctuation r M log T calc 1/2 10 T1/2 exp r 1 n n i 1 r 1 n r ri Mr n i1 i 2 1/2 10 Mr r Global Sph 1.105 10.213 def 0.937 3.088 0.25 < < 4 sph 0.260 3.285 def 1.062 1.518 P.S. PRC 91, 044304 (2015)
Weak decay rates in pf-shell nuclei Main constituents of stellar core in presupernovae. Comparison with : exp. (n,p), (p,n) SM calculations GT properties: Test of QRPA SM: NPA 653, 439 (1999) QRPA: NPA 716, 230 (2003)
Weak decay rates in pf-shell nuclei Calculations for several isotopes: Sc, Ti, V, Fe, Mn, Ni, Co, Zn exp: charge exchange reactions QRPA (n,p) B ( GT ) f t i if 2 Shell Model Accumulated GT strength A.L. Cole PRC 86, 015809 (2012) P.S. PRC87, 045801 (2013), PRC93, 054309 (2016)
Weak decay rates in pf-shell nuclei, T P i ( T) B if if, T if Electron Capture from e - plasma cec 1( Q ) F( Z, ) S e if 2 2 if Se 1 S ( Qif ) d 1 exp e / kt 1 1 Q M M E E if 2 p d i f mc e Si burning Ia Supernova
Medium-mass neutron-deficient isotopes X-ray bursts: Source of intense X-ray emissions generated by thermonuclear runaway in the H-rich environment of an accreting n-star, fed from a binary red giant companion. Nucleosynthesis mechanism: rp capture process rp-process: Proton capture reaction rates are orders of magitude faster than the competing -decays. Waiting point nuclei: When the dominant p-capture is inhibited, the reaction flow waits for a slow beta-decay to proceed further. Time scale Isotope abundances Light curve profile Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38) Rb (37) Kr (36) Br (35) Se (34) As (33) Ge (32) Ga (31) Ag (47) Pd (46) Rh (45) Ru (44) 424344 272829303132333435363738394041 45464748 5455 53 5152 4950 56 5758 5
Medium-mass neutron-deficient isotopes Constrained HF+BCS Waiting point nuclei in rp-processes Shape coexistence Beyond full Shell Model Ni,Zn,Ge,Se,Kr,Sr,Zr,Mo,Ru,Pd,Cd,Sn (N=Z and neighbors)
Gamow-Teller strength: Theory and Experiment ISOLDE: Total absorption spectroscopy Exp: Poirier et al. PRC69, 034307 (2004) Exp: Nacher et al. PRL92, 232501 (2004)
+ /EC half-lives: Theory and Experiment g / g 2 2 1 A V eff / EC 1/2 6200 f T f i g / g 0.74 g / g A V eff A V bare 1( Q ) F( Z, ) d if 1 Q if 2 2 if EC 2 2 2 2 qkgkbk ql g 1 L B 1 L 1 2 Good agreement with experiment: Reliable extrapolations to high and T
Weak decay rates in rp-process 74 Sr Deformed pn-qrpa B(GT) and T 1/2 : Good agreement with experiment Competition +/EC P.S. PRC83, 025801 (2011) 78 Sr
Weak decay rates in rp-process 74 Sr 76 Sr (WP) P.S. PRC83, 025801 (2011) 78 Sr
Conclusions Nuclear structure model (deformed Skyrme HF+BCS+QRPA) o o Study of decay properties in different mass regions. Astrophysical applications. Reproduce half-lives and main features of GT strength distributions extracted from beta-decay and/or charge exchange reactions. o Weak-decay rates at (,T) typical of astrophysical scenarios: pf-shell nuclei (presupernova): EC rates from QRPA comparable quality to benchmark SM calculations. Neutron-rich Zr-Mo isotopes (r process). Neutron-deficient WP nuclei (rp-process): EC/ + competition
1 E Vph r r 16 ( ) ( ) ph Residual interactions Particle-hole residual interaction consistent with the HF mean field 2 ss' tt' 1 ( 1) 1 2 1 ( 1) 1 2 1 2 sts'' t st r1 s ' t ' r2 2 1 ss' tt' E ( 1) ( 1) 1 21 2 1 2 16 sts'' t st ( r1 ) s ' t '( r2) V r r 1 2 2 2 4t 0 2t1kF 2t2kF t3 1212 r1r2 16 3 Average over nuclear volume Separable forces V 2 ( 1), t a a ph ph K GT GT K K K K K K 0, 1 pp 2 pp ( 1) K GT GT K K, K K K 0, 1 V P P P a a ph GT 3 1 2 1 3 t0 kf t1t2 t3 8 R 2 6
pnqrpa with separable forces Phonon operator pnqrpa equations K K X A Y A, A K K K K K K n p K 0 0, 0 K K K t M K K Transition amplitudes 0 K K K K M q X qy M q X q Y K K K q u v, q v u, K K K K Single-particle states from deformed Skyrme Hartree-Fock u, v: Occupation amplitudes from BCS pairing B(GT) in the lab. system IiKi00I fk f 1 K 2 2 0 0 0 1 1 1 B ( GT ) t 0 2 t 0
Isotopic evolution (, r c ): Ge-Pd n-rich isotopes
Shape dependence of GTdistributions in neutron-deficient: Pb isotopes B(GT) strength distributions Not very sensitive to : Skyrme force and pairing treatment Sensitive to : Nuclear shape Signatures of deformation PRC 72, 054317 (2005), PRC 73, 054302 (2006) prolate oblate spherical QEC
decay patterns: Theory vs. Experiment 192 Pb 190 Pb Preliminary experimental data (unpublished) TAS (ISOLDE/CERN) A.Algora et al.
Weak decay rates in pf-shell nuclei (Q<0) large: sensitive low-lying exc. P.S. PRC87, 045801 (2013)
Weak decay rates in pf-shell nuclei Q small
Odd-A nuclei. Excited states
Odd-A nuclei: Contributions of excited states