astrophysical, observational and nuclear-physics aspects of r-process nucleosynthesis t 1/2 pnpn...
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Astrophysical, observational and nuclear-physics aspects of r-process nucleosynthesis
T1/2
Pn
Sn
sng
Sinaia, 2012
B2FH
Karl-Ludwig Kratz
Part I
1859 first spectral analysis of the sun and stars by Kirchhoff & Bunsen “chemistry of the
cosmos”
1932 discovery of the previously unknown neutron by Chadwick
1937 first systematic tabulation of solar abundances
by Goldschmidt
1957 fundamental paper on nucleosynthesis by Burbidge, Burbidge, Fowler & Hoyle (B2FH) Rev. Mod. Phys. 29, 547 (1957)
Some early milestones
Historically,nuclear astrophysics has always been concerned with• interpretation of the origin of the chemical elements
from astrophysical and cosmochemical observations,• description in terms of specific nucleosynthesis processes.
B²FH, the „bible“ of nuclear astrophysics
…55 years ago:
„…it appears that in order to explain all the features of the abundance curve, at least eight different types of synthesizing processes are demanded…“
(Suess and Urey, 1956)
Solar abundance observables at B²FH (1957)
1. H-burning2. He-burning3. -process4. e-process5. s-process
7. p-process8. x-process
neutrons
6. r-process
Neutron-capture paths for the s- and r-processes
Neutrons produce ≈75% of the stable isotopes, but only 0.005% of the total SS abundances….
H 30,000
C 10
Fe 1
Au 2·10-7
(from “Cauldrons in the Cosmos”)
r-process path
s- and r-abundances today about equal
scaled theoretical solar r-processscaled solar r-process
Nb
Zr
Y
SrMo
Ru
Rh
Pd
Ag
Ba
La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Hf
Os
Ir
Pt
Au
Pb
ThU
GaGe
CdSn
Elemental abundances in UMP halo stars
r-process observables
Solar system isotopic Nr, “residuals”
Isotopic anomalies in meteoritic samples and stardust
CS 22892-052 abundances
T9=1.35; nn=1020 - 1028
r-Process observables today
Pb,Bi
Observational instrumentation
• meteoritic and overall solar-system abundances
• ground- and satellite-based telescopes like Imaging Spectrograph (STIS) at Hubble, HIRES at Keck, and SUBARU
• recent „Himmelsdurchmusterungen“ HERES and SEGUE
Presolar SiC grainsand nano-diamonds
e.g.isotopic composition
of heavy metalsZr, Mo, Ru, Te, Xe, Ba, Pt
„Static“ calculation
• assumptions iron seed (secondary process) „waiting-point“ concept (global (n,) (,n) and ß-flow equilibrium) instantaneous freezeout
Fit of Nr, from B²FH
Reproduction of Solar system isotopic r-process abundances
(mainly from r-only nuclei)
The "waiting-point"concept in astrophysics (1)
Rate of n-captures:
(1)
Photodisintegration: (2)
cross section averaged over Maxwell-Boltzmann velocity distribution to T9
Nuclear Saha equation
The "waiting-point"concept in astrophysics (2)
Nuclear Saha equation:simplified
• high nn "waiting-point" shifted to higher masses• low Sn "waiting-point" shifted to higher masses• low T "waiting-point" shifted to higher masses
Equilibrium-flow along r-process path:
- governed by β-decays from isotopic chain Z to (Z+1)
T1/2 ("w.-p.") ↔ Nr,ʘ
„Static“ calculation
• assumptions iron seed (secondary process) „waiting-point“ concept (global (n,) (,n) and ß-flow equilibrium) instantaneous freezeout
• astrophysical conditions explosive He-burning in SN-I
T9 1 (constant)nn 1024 cm-3 (constant)r 100 s
• neutron source:21Ne(,n)
Fit of Nr, from B²FH
Reproduction of Solar system isotopic r-process abundances
(mainly from r-only nuclei)
Seeger, Fowler & Clayton, ApJ 98 (1965)
Speculations about r-process scenario: SN-I (as in B2FH) unlikely Explosion of massive stars M > 104 Mʘ
Conventional SNe
"long-time" solution
…however, all components with the same neutron-density of 1024 n/cm3 !
"short-time" solution
Speculations about various r-process components:
1.77 s0.44 s
3.54 s
Cycle time: 4.9 s
r-Process scenarios since B2FH
For long time suspect, that puzzle of r-process siteis closely intertwined with puzzle of SN explosion mechanism
(see e.g. Reviews by Hillebrandt 1978; Meyer & Brown 1997)
…original papers "core-collapse SN", e.g. Bethe & Wilson (1985); Mayle & Wilson (1988, 1991);…first papers "neutrino-driven winds", e.g. Duncan, Shapiro & Wasserman (1986); Woosley & Hoffman(1992); Takahashi, Witti & Janka (1994).
…other suggested scenarios:- He-core flashes in low-mass stars - He- and C-shells of stars undergoing SN explosions- Neutron-star mergers- Black-hole neutron-star mergers- Hypernovae- Electron-capture SNe- r-Process without excess neutrons- Gamma-ray bursts- SNe with active-sterile neutrino oscillations- Jets of matter from collapse of rotating magnetized stellar cores
…becoming more and more "exotic"
„Static“ calculation
• assumptions iron seed (secondary process) „waiting-point“ concept (global (n,) (,n) and ß-flow equilibrium) instantaneous freezeout
• astrophysical conditions explosive He-burning in SN-I
T9 1 (constant)nn 1024 cm-3 (constant)r 100 s
• neutron source:21Ne(,n)
• nuclear physics: Q − Weizsäcker mass formula + empirical corrections (shell, deformation, pairing)
T1/2 – one allowed transition to excited state, logft = 3.85
Fit of Nr, from B²FH
Reproduction of Solar system isotopic r-process abundances
(mainly from r-only nuclei)
Parameter checks
• Do r-abundance deficiencies disappear when changing the nuclear-physics input ?
• Can effects of masses (Sn) and T1/2 & Pn be studied separately ?
• To what extent is the "waiting-point" assumption valid ?
keep it simple !
Fitting r-process abundances: a nuclear-structure learning effect or discussing the fifth leg of an elephant ?
Nuclear-data needs for the classical r-process
nuclear massesSn-values r-process path / “boulevard”Qb, Sn-values theoretical b-decay properties, n-capture rates
neutron capture rates
fission modes
sRC + sDC smoothing Nr,prog during freeze-out in “non-equilibrium” phase(s)
SF, bdf, n- and n-induced fission “fission (re-) cycling”; r-chronometers
b-decay properties
T1/2 r-process progenitor abundances, Nr,prog
Pn smoothing Nr,prog Nr,final (Nr,) modulation Nr through re-capture
b-decayfreeze-out
nuclear structure development
- level systematics- “understanding” b-decay properties- short-range extrapolation into unknown regions
Nuclear masses
D. Lunney et al., Rev. Mod. Phys. 75, No. 3 (2003)
• Weizsäcker formula• Local mass formulas (e.g. Garvey-Kelson; NpNn)• Global approaches (e.g. Duflo-Zuker; KUTY)• Macroscopic-microscopic models (e.g. FRDM, ETFSI)• Microscopic models (e.g. RMF; HFB)
Comparison to NUBASE (2001) // (2012)
FRDM (1995) srms = 0.669 // 0.564 [MeV]ETF-Q (1996) srms = 0.818 // 0.729 [MeV]HFB-2 (2002) srms = 0.674 [MeV]HFB-3 (2003) srms = 0.656 [MeV]HFB-4 (2003) srms = 0.680 [MeV]
HFB-8 (2004) srms = 0.635 [MeV]HFB-9 (2005) srms = 0.733 [MeV]
HFB-21 (2011) srms = 0.577 [MeV]
Over the years, development of various types of mass models / formulas:
No significant improvement of srms
J. Rikovska Stone, J. Phys. G: Nucl. Part. Phys. 31 (2005)
Main deficiencies at Nmagic and in shape-transition regions !
Nuclear masses
effect of Sn around N=82 shell closure catchword “shell-quenching”
K.-L. Kratz et al. Nucl. Phys. A630 (1998)
“static” calculations (Saha equation) break-out at N=82 130Cd
astrophys. parameters (T9, nn, τn) and T1/2 kept constant
“time-dependent” calculations (w.-p.) r-matter flow at A=130 peak
B. Pfeiffer et al. Nucl. Phys. A693 (2001)
Effects of N=82 "shell quenching"
g9/2
g 9/2
i13/2
i13/2
p1/2
f5/2
p 1/2
p3/2
p3/2
f7/2
f7/2
h9/2
h 11/2
h 11/2
g7/2g 7/2 d3/2
d 3/2
s1/2
s1/2
d 5/2
d 5/2
g 9/2g9/2
f5/2f5/2
p1/2
p1/2
h 9/2 ;f 5/2
N/Z
112
70
40
50
82
126
B. Pfeiffer et al.,Acta Phys. Polon. B27 (1996)
100% 70% 40% 10%
Strength of ℓ 2-Term
5.0
5.5
7.0
6.5
6.0
Sin
gle
– N
eutr
on E
nerg
ies
( Uni
ts o
f hw
0)
• high-j orbitals (e.g. nh11/2)• low-j orbitals (e.g. nd3/2)• evtl. crossing of orbitals• new “magic” numbers / shell gaps (e.g. 110Zr70, 170Ce112)
"Shell quenching"
…reduction of the spin-orbit coupling strength; caused by strong interaction between bound and continuum states; due to diffuseness of "neutron-skin" and its influence on the central potential…
• shell-gaps• deformation• r-process path (Sn)
• r-matter flow (τn)
change of
The N=82 shell gap as a function of Z
FRDM
DZ
Groote
EFTSI-Q
Exp
A≈130 Nr, peak
The N=82 shell closure dominates the matter flow of the „main“ r-process (nn ≥ 1023).Definition „shell gap“: S2n(82) – S2n(84) ↷ paired neutrons.Therefore request:
experimental masses and reliable model predictions for the respective N=82 waiting-point nuclei 125Tc to 131In
HFB-14
Exp
Deviation from SS-r: FRDM vs. ETFSI-Q
How to fill up the FRDM A 115 “trough” ?
• if via T1/2 (as e.g. suggested by Nishimura, Kajino et al.; PRC 85 (2012)), on average all r-progenitors between 110Zr and 126Pd should have7.5 x T1/2(FRDM) 350 ms → 2 x T1/2(130Cd) at top of r-peak
• it must be the progenitor masses, via Sn (and correlated deformation ε2)
Nuclear-data needs for the classical r-process
nuclear massesSn-values r-process path / “boulevard”Qb, Sn-values theoretical b-decay properties, n-capture rates
neutron capture rates
fission modes
sRC + sDC smoothing Nr,prog during freeze-out in “non-equilibrium” phase(s)
SF, bdf, n- and n-induced fission “fission (re-) cycling”; r-chronometers
b-decay properties
T1/2 r-process progenitor abundances, Nr,prog
Pn smoothing Nr,prog Nr,final (Nr,) modulation Nr through re-capture
b-decayfreeze-out
nuclear structure development
- level systematics- “understanding” b-decay properties- short-range extrapolation into unknown regions
Effects of T1/2 on r-process matter flow
T1/2 : 3
r-matter flow too slow r-matter flow too fast
Mass model: ETFSI-Q
- all astro parameters (T9, nn, τn) kept constant
r-Process model: “waiting-point approximation“
T1/2 x 3
T1/2 (GT + ff)
130Cd – the key isotope at the A=130 peak
already B²FH (Revs. Mod. Phys. 29; 1957) C.D. Coryell (J. Chem. Educ. 38; 1961)
…hunting for nuclear properties ofwaiting-point isotope 130Cd…
K.-L. Kratz (Rev. Mod. Astr. 1; 1988)climb up the N= 82 ladder ...A 130 “bottle neck“
“climb up the staircase“ at N=82;major waiting point nuclei;“break-through pair“ 131In, 133In;
“association with the rising side of majorpeaks in the abundance curve“
132Sn50
131In8249
133In8449
129Ag8247
128Pd8246
127Rh8245
126
127
128
129
130
131
132
133
Pn~85%165ms278ms
46ms(g)
r-processpath
(n,)
(n,)
(n,)135 136 137
134 135
131 132 133
130
134
158ms(m)
130Cd8248
162ms
b
T1/2(130Cd) Nr,ʘ(130Te) ?
"Waiting-point" estimate T1/2(130Cd)
If the historical "waiting-point" concept is valid for the A ≈ 130 Nr,ʘ-peak, then in the simplest version with Sn(N=82)=const.
From this assumption, in 1986 the waiting-point prediction for T½(130Cd) ≈ 595 ms.
With a more realistic approach,taking into account that • the breakout from N=82 involves 131In und 133In (≈ 1:1)
• 133In has a known Pn ≈ 90%
…to be compared to the 1986 exp. value of 195 (35) ms, and to the 2001 improved value of 162 (7) ms.
1,E -01
1,E +00
1,E +01
1,E +02
1,E +03
1,E +04
1,E +05
1,E +06
1 2 3 4 5 6 7 8 9 10
1
103
106
Nuclear models to calculate T1/2
Theoretically, the gross β-decay quantities, T1/2 and Pn, are interrelated via the so-called β-strength function [Sb(E)]
“Theoretical” definition (Yamada & Takahashi, 1972)
Sb( )E = D-1 · M(E) ² · (E) [s-1MeV-1]
M(E) average b-transition matrix element (E) level density D const., determines Fermi coupling constant gv²
“Experimental” definition (Duke et al., 1970)
Sb(E) =b(E)
f(Z, Qb-E) · T1/2
[s-1MeV-1]
b(E) absolute b-feeding per MeV,f(Z, Qb-E) Fermi function,T1/2 -b decay half-life.
T1/2 as reciprocal ft-value per MeV
T1/2 = Sb(Ei) x f (Z,Qb-Ei)
0Ei Qb
11
1
f(Z, Qb-Ei) (Qb-Ei)5
Sb(E)
E*[MeV]
Qb
Fermi function
T1/2 sensitive to lowest-lying resonances in Sb(Ei)Pn sensitive to resonances in Sb(Ei) just beyond Sn
↷ easily “correct” T1/2 with wrong Sb(E)
same T1/2 !
1 5 10
1
3x103
6x105
“Typical spherical example”:
note: effects on T1/2 and Pn !
T1/2 and Pn calculations in 3 steps – (I)
(1) Mass model FRDM↷ Qb, Sn, e2
Folded-Yukawa wave fcts.
SP shell model QRPA (pure GT) with input from FRDM potential: Folded Yukawa
pairing-model: Lipkin-Nogami
(2) as in (1) with empirical spreading of SP transition strength, as shown in experimental Sb(E)
SnQb
(3) as in (2) with addition of first-forbidden strength from Gross Theory
…and a typical “deformed” case:
Note: low-lying GT-strength; ff-strength unimportant!
T1/2 and Pn calculations in 3 steps – (II)
spreading of SP strength to deformed “Nilsson spaghetti”
Möller, Nix & Kratz; ADNDT 66 (1997) Möller, Pfeiffer & Kratz; PRC 67 (2003)
Pn effects at the A≈130 peak
Significant differences
(1) smoothing of odd-even Y(A) staggering
(2) importance of individual waiting-point nuclides, e.g. 127Rh, 130Pd, 133Ag, 136Cd
(3) shift left wing of peak
Global T1/2 & Pn – calc. vs. exp.
Total Error = 5.54
Total Error = 3.52
Total Error = 3.73
Total Error = 3.08
Pn-valuesHalf-lives
(Möller, Pfeiffer, KratzPR C67, 055802 (2003))
T1/2, Pn gross b-strength properties from theoretical models, e.g. QRPA in comparison with experiments.
Requests: (I) prediction / reproduction of correct experimental “number” (II) full nuclear-structure understanding
↷ full spectroscopy of “key” isotopes, like 80Zn50 , 130Cd82.
QRPA (GT)
QRPA (GT+ff)
QRPA (GT)
QRPA (GT+ff)
Nuclear-data needs for the classical r-process
nuclear massesSn-values r-process path / “boulevard”Qb, Sn-values theoretical b-decay properties, n-capture rates
neutron capture rates
fission modes
sRC + sDC smoothing Nr,prog during freeze-out in “non-equilibrium” phase(s)
SF, bdf, n- and n-induced fission “fission (re-) cycling”; r-chronometers
b-decay properties
T1/2 r-process progenitor abundances, Nr,prog
Pn smoothing Nr,prog Nr,final (Nr,) modulation Nr through re-capture
b-decayfreeze-out
nuclear structure development
- level systematics- “understanding” b-decay properties- short-range extrapolation into unknown regions
E(2+) - landscape 90 A 150
• reduced pairing• rigid rotors• g7/2 g9/2 interaction• shell quenching
• magic shells/subshells• shape transitions/coexistence• intruder states• identical bands
N
ZE(2+)
90Zr
96Zr
132Sn
r-process path
50
40
82
60
56
50
d5/2
s1/2
g7/2
h11/2
d3/2
g9/2
110Zr
What is known experimentally ?
Reduction of the TBME (1+)by 800 keV
OXBASH(B.A. Brown, Oct. 2003)
3+ 0 3+ 3893+ 03+ 0 3+ 473
1- 0 1- 0124In75
126In77
130In81
130In81
128In79
1+ 2431+ 688
1+ 1173
1+ 2120 1+ 2181(new)
1+ 1382
(old)
Known 1+ states in n-rich even-A In isotopes
Configuration 3+ : nd3/2 pg9/2
Configuration 1+ : ng7/2 pg9/2
Configuration 1- : nh11/2 pg9/2
17
31
ke
V
Dillmann et al.; PRL 91 (2003)
determines T1/2
0
0,5
1
1,5
2
2,5
3
Beta-decay odd-mass, N=82 isotonesnSP states in N=81 isotones
0nh11/2
282nd3/2
ns1/2
ng7/2
524
2565 26077/2+ 7/2+ 7/2+
1/2+
1/2+
1/2+
3/2+3/2+ 3/2+ 3/2+
11/2- 11/2- 11/2- 11/2-2.3%6.3
0.9%6.4
1.2%6.3
0.6%6.4
0.5%6.45
89%4.0
88%4.0
67%4.1
45%4.25
24%4.5
ng7/22648 2643 2637
601
331
728
414
814
472
908
536
S1n=5.246MeV S1n=3.98MeV S1n=3.59MeV
Pn=4.4% Pn=9.3%P1n=29%P2n= 2%
P1n=39%P2n=11%P3n= 4.5%
P1n=25%P2n=45%P3n=11%
131Sn8150
129Cd81127Pd81
125Ru81123Mo81
48 46 44 42
E*[MeV]
P4n= 8.5%P5n= 1%
Iblog(ft)
S1n=2.84MeV
S1n=1.81MeV
1/2+
T1/2 determined by Qb-E7/2
Short range extrapolation
Known ! partly known extrapolation
Experiment: T1/2 = 68 ms; Pn = 3.4 %
Surprising b-decay properties of 131Cd
QRPA predictions:
later, g-spectroscopic confirmation of decay scheme at ISOLDE
T1/2(GT) = 943 ms;
Pn(GT) = 99 %
T1/2(GT+ff) = 59 ms;
Pn(GT+ff) = 14 %
…just ONE neutron outside N=82 magic shell
nuclear-structure requests: higher Qβ, main GT lower, low-lying ff-strength;
The FK2L waiting-point approach (I)
known r-process isotopes at that time:N=50 79Cu, 80Zn, 81GaN=82 130Cd, 131In
30
e.g.: Cameron, Clayton, Schramm,Truran, Kodama, Arnould,Woosley, Hillebrandt, Thielemann…
The FK2L waiting-point approach (II)
Classical assumptions:
global steady flow of r-process through N=50 80Zn, N=82 130Cdand N=126 195Tm
r-process matter flow atfreeze-out temperature ;
at N=82 “imperfect” peak,r-process through 40 s 132Sn,instead of 195 ms 130Cd…
Calculation:
The FK2L waiting-point approach (IV)
birth of N=82“shell-quenching” idea …
“…best fit so far…;long-standing problem solved…” W. Hillebrandt
“…call for a deeper study…before rushing into numericalresults… and premature comparisonswith the observed abundances” M. Arnould
Wide-spread ignorance of experimental r-process data
Two typical examples:
I. Dillmann & Y.A. LitvinovProg. Part. Nucl. Phys. 66 (2011)“Up to now, one could only “scratch” the regions where the r-process
takes place.”
M.R. Mumpower, G.C. McLaughlin & R. Surman
Ap.J. 752 (2012)
“…current experimental data on neutron-rich isotopes is sparse.” But …”recent developments using radioactive beams show promise[ Hosmer et al. (2005) 78Ni; Jones et al. (2009) 132Sn ].”
History and progress in measuring r-process nuclei
Already 26 years ago,
in 1986 a new r-process astrophysics era started:
• at the ISOL facilities OSIRIS and TRISTAN
• at the ISOL facility SC-ISOLDE
Both act as major “bottle-necks” for the matter flow of the classical r-process starting from an Fe-group seed
T1/2 of N=50 “waiting-point” isotope 540 ms 80Zn (top of A ≈ 80 Nr, peak)
T1/2 of N=82 “waiting-point” isotope 195 ms 130Cd (top of A ≈130 Nr, peak)
42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82Fe
CoNi
CuZn
GaGe
AsSe
BrKr
RbSr
YZr
NbMo
TcRu
RhPd
AgCd
InSn
Z N
SbTe
IXe
CsBa
82 84 86 88 90 92 94
Experimental information on r-process nuclides
heaviest isotopes with measured T1/2
g9/2 d5/2 s1/2 g7/2 d3/2 h11/2
g9/2
p1/2
p3/2
f5/2
f7/2
Today,altogether ≈ 80 r-process nuclei known
new (MSU, 2009; RIKEN 2011)
42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82Fe
CoNi
CuZn
GaGe
AsSe
BrKr
RbSr
YZr
NbMo
TcRu
RhPd
AgCd
InSn
Z N
SbTe
IXe
CsBa
82 84 86 88 90 92 94
Classical r-process path for nn=1020
„waiting-point“ isotopes at nn=1020 freeze-out
nn=1020
42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82Fe
CoNi
CuZn
GaGe
AsSe
BrKr
RbSr
YZr
NbMo
TcRu
RhPd
AgCd
InSn
Z N
SbTe
IXe
CsBa
82 84 86 88 90 92 94
„waiting-point“ isotopes at nn=1023 freeze-out
Classical r-process paths for nn=1020 and 1023
(T1/2 exp. : 28Ni – 31Ga, 36Kr – 40Zr, 47Ag – 51Sb)
nn=1023
nn=1020
42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82Fe
CoNi
CuZn
GaGe
AsSe
BrKr
RbSr
YZr
NbMo
TcRu
RhPd
AgCd
InSn
Z N
SbTe
IXe
CsBa
82 84 86 88 90 92 94
(T1/2 exp. : 28Ni, 29Cu, 47Ag – 50Sn)
r-Process paths for nn= 1020, 1023 and 1026
„waiting-point“ isotopes at nn= 1026 freeze-out
nn=1023
nn=1026
nn=1020
r-process “boulevard”
Summary “waiting-point” model
“weak” r-process
“main” r-process (early primary process; SN-II?)
superposition of nn-components
(later secondary process; explosive shell burning?)
seed Fe (still implies secondary process)
Kratz et al., Ap.J. 662 (2007)
…largely site-independent!T9 and nn constant;instantaneous freezeout