QRPA calculations for beta-decay i di li in medium-mass nuclei P.Sarriguren Instituto Estructura de la Materia, CSIC, Madrid E Moya de Guerra E. Moya de Guerra O. Moreno R Al Rdi R. Alvarez-Rodriguez A. Escuderos Int. Workshop on strong, weak, and electromagnetic interactions to probe spin-isospin excitations, ECT*, Trento 2009
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QRPA calculations for beta-decay i di l iin medium-mass nuclei
P.Sarriguren
Instituto Estructura de la Materia, CSIC, Madrid
E Moya de Guerra E. Moya de Guerra
O. Moreno
R Al R d i R. Alvarez-Rodriguez
A. Escuderos
Int. Workshop on strong, weak, and electromagnetic interactions to probe spin-isospin excitations, ECT*, Trento 2009
QRPA calculations for beta-decay
Motivation : Describe β decay process within a microscopic selfconsistent approachDescribe β-decay process within a microscopic selfconsistent approach
Selfconsistent method to derive the single-particle potential
Variational principle: Variational principle:
Search for the best Slater determinant minimizing the energy
Assume that the resulting residual interaction is smallAssume that the resulting residual interaction is small
Two body interaction: zero range limit of a finite range force
Skyrme effective interactions
Two-body interaction: zero-range limit of a finite range force
• leading term: delta-function with strength t0 and spin exchange x0
• leading finite range corrections t x t x (finite range = momentum dependence)• leading finite range corrections t1 , x1 , t2 , x2 (finite range = momentum dependence)
• short-range spin-orbit interaction with strength W0
Three-body interaction: Short-range density-dependent two-body force t3 x3 αThree body interaction: Short range density dependent two body force t3, x3 , α
( ) ( ) ( ) ( )( )2 21 1 '1V t P k kt P δδ+ + + +ur urur ur
( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )
2 20 0 1 1
2 02
1 '2
1 '
1
'i j i
ij ii j j
i j j
V t x P r r k k
t x P k r r iW k r r
t P r
k
x r
k
σ
σ
σ
σ σ δ
δ
δ
δ= + + + − +
+ + ⋅ − +
−
+ ⋅ × −uur ur ur r uur uur uur ur ur r( ) ( ) ( )
( ) ( )3 31 16 2
i ji j
r rt x P r r α
σ δ ρ⎛ ⎞+
+ + − ⎜ ⎟⎜ ⎟⎝ ⎠
ur urur ur
6 ⎝ ⎠
Parameters (10) fitted using nuclear matter properties and ground state properties of a selected set of nuclei (binding energies, charge radii,…)
• Redistribution of the strengthph : shift to higher energiespp : shift to lower energiespp : shift to lower energies
•Reduction of the strength
Stable nuclei in Fe-Ni mass region: Theory vs experiment
Main constituents of stellar core in presupernovaeMain constituents of stellar core in presupernovae
Comparison with :
exp. (n,p), (p,n)
SM calculations
GT properties: Test of QRPAGT properties: Test of QRPASM: NPA 653, 439 (1999)
QRPA: NPA 716, 230 (2003)
Constrained HF+BCS
Medium mass proton rich nuclei: Ge, Se, Kr Sr
Waiting point nuclei in rp-processes
Shape coexistenceShape coexistence
Large Q-values
Isotopic chains approaching the drip lines
Energy vs. deformation Shape coexistenceBeyond full Shell Model
Medium mass proton rich nuclei: Ge, Se, Kr SrConstrained HF+BCS
Waiting point nuclei in rp-processes
Shape coexistenceShape coexistence
Large Q-values
Isotopic chains approaching the drip lines
Beyond full Shell ModelEnergy vs. deformation Shape coexistence
Medium mass proton rich nuclei: Ge, Se, Kr SrGT strength distributionsGT strength distributions
Medium mass proton rich nuclei: Ge, Se, Kr SrGT strength distributionsGT strength distributions
Dependence on deformationNPA 658, 13 (1999)
β−decay: Nuclear Structure: Deformation
Gamow-Teller strength: Gamow Teller strength: Theory and Experiment
oblate prolateprolateoblate
p
Total absorption spectroscopy
74Kr76Sr
oblate
prolate
Exp: Poirier et al. PRC69, 034307 (2004) Exp: Nacher et al. PRL92, 232501 (2004)
Gamow-Teller strength: Theory and Experiment
High resolution spectroscopyExp: Piqueras et al. EPJA 16, 313 (2003)
SLy4
QEC= 5.070 MeV
Gamow-Teller strength: Theory and Experiment
SLy4
Half-lives: Theory and Experiment
( ) ( ) ( )0 20 01
,,W
f Z W pW W W dWZ Wβ λ± ±= −∫( )2
21 /eff
/A V ECg gT f I Iβ β
+− +∑ phase space Coulomb effecteff1/ 2 6200
f
f iI
T f I Iβ β= ∑1 11
2 22 2
2 K LC
LKE
K Lf q BgqBgπ ⎡ ⎤= + +⎣ ⎦L
phase space
Neutrino energy
Coulomb effect
( ) ( )/ 0 74 /g g g g= Neutrino energyRadial components of the bound state e-wf at the origin
Exchange and overlap corrections
( ) ( )eff bare/ 0.74 /A V A Vg g g g=
EPJA 24, 193 (2005)
Good agreement with experiment:Reliable extrapolations
Exotic Nuclei : Nuclear AstrophysicsQuality of astrophysical models depends critically on the quality of input (nuclear)
Exotic Nuclei play a relevant role in explosive events
Very limited experimental information ⇒ Network calculations based on model predictions
rp-process: Proton capture reaction rates orders of magnitude faster than the mp tin β+ d scompeting β+ -decays
Waiting point nuclei: When the dominant p-capture is inhibited: the reaction flow waits for a slow beta-decay to proceedf y p
5758
5
Ru (44)Rh (45)Pd (46)Ag (47)
Waiting points
5455
56
Sr (38)Y (39)
Zr (40)Nb (41)
Mo (42)Tc (43)Waiting points
45464748
49505152
535455
G (32)As (33)
Se (34)Br (35)Kr (36)Rb (37)
Sr (38)
272829303132333435363738394041424344Ga (31)
Ge (32)
Schatz et al. Phys. Rep. 294, 167 (1998)
Weak decay rates in rp-process
X-ray bursts: Generated by thermonuclear runaway in the hydrogen rich environment of an accreting neutron star hydrogen-rich environment of an accreting neutron star, which is fed from a binary red giant companion.
Peak conditions of ρ=10 6-7 g.cm-3 and T=1-3 GK are reached
Mechanism is the rp capture process
Nuclear models should be able to describe at least the experimental information (Half-lives and GT strength distributions) available under terrestrial conditions
Decay rates λ (ρ,T)• Effect of T: Thermal population of excited states in the parent • Effect of T: Thermal population of excited states in the parent nucleus
• Effect of ρ and T: Atoms are completely ionized. Electrons form d l d a degenerate plasma obeying Fermi-Dirac distribution: Continuum
electron capture becomes possible.
Weak decay rates in rp-process
( )/( ) /( )2 1 E kT E kTJ +∑ ∑
Weak interaction rates
( )/( ) /( )2 1 , 2 1 i iE kT E kTii i
i i
J e G J eG
λ λ − −+= = +∑ ∑
Thermal population of excited states
72,74KrKr76,78Sr
Weak decay rates in rp-process
( )/( ) /( )2 1 , 2 1 i iE kT E kTii i
J e G J eG
λ λ − −+= = +∑ ∑
i iG
( )ln 2 B Tρλ λ= = Φ∑ ∑ ( ),i iff
ifif
fDB Tρλ λ= = Φ∑ ∑
Nuclear structure Phase space factor
( () )B B GT B F= +
p
( () )if if ifB B GT B F= +2 2
( ) 1 k kAg f iB TG⎛ ⎞⎜ ⎟ ∑
eff
( )2 1
k kA
ki Vif
g f t iJ
B Tg
G σ ±= ⎜ ⎟+ ⎝ ⎠∑
( ) ( )/ /( ) ( )eff bare/ 0.74 /A V A Vg g g g=
Ph
Weak decay rates in rp-process
cECif if if
β +
Φ = Φ + Φ
Phase space
f f f
( )2 21( ) ( , ) 1 ( )cECif if e ifQ F Z S S Q dνω
ω ω ω ω ω ω ω∞
⎡ ⎤Φ = − + − +⎣ ⎦∫ll
( )2 2
11( ) ( 1, ) 1 1 ( )ifQ
if if p ifQ F Z S S Q dβνω ω ω ω ω ω ω
+
⎡ ⎤ ⎡ ⎤Φ = − − − + − − −⎣ ⎦ ⎣ ⎦∫
( )2
1if p d i f
e
Q M M E Em c
= − + −
Se,p,ν (ω): Distribution functions (inhibit/enhance the phase space available)
S S 0
( ) ( )1
exp / 1ee
SkTω μ
=− +⎡ ⎤⎣ ⎦
Se: Fermi-Dirac distributionSp=Sν=0
( , )e Tμ ρ
Weak decay rates in rp-process
6 -310 g cmρ = 10 g cmρ
PLB 680, 438 (2009)
Shape dependence of GTdistributions in neutron-deficient Hg, Pb, Po isotopes
• Triple shape coexistence at low excitation 6+
...
(MeV)Triple shape coexistence at low excitation energy
• Search for signatures of deformation on 2+
4+
6+
1their beta-decay patterns 0+
0+
e-e-γ
0+
186Pb0
Shape dependence of GTdistributions in neutron-deficient: Pb isotopes
• Not very sensitive to : Skyrmeforce and pairing treatmentp g
• Sensitive to : Nuclear shape
Signatures of deformation
l t
g
PRC 72, 054317 (2005), PRC 73, 054302 (2006)
prolate
oblate
h lspherical
QEC
Conclusions
Theoretical approach based on a deformed Skyrme HF+BCS+QRPA
Used to describe spin-isospin nuclear properties (GT & M1) in stable and exotic nuclei in various regions along the nuclear chart exotic nuclei in various regions along the nuclear chart
Find
• Good agreement with experimentGood agreement with experiment