Astrophysical, observational and nuclear-physics
aspects of r-process nucleosynthesis
B2FH
Part I
sng

Karl-Ludwig Kratz
Sinaia, 2012
Some early milestones
1859
1932
first spectral analysis of the sun and stars by
Kirchhoff & Bunsen
“chemistry of the
cosmos”
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)
B²FH, the „bible“ of nuclear astrophysics
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.
…55 years ago:
Solar abundance observables at B²FH (1957)
(Suess and Urey, 1956)
„…it appears that in order to explain all the
features of the abundance curve, at least
eight different types of synthesizing
processes are demanded…“
1. H-burning
2. He-burning
3. -process
4. e-process
5. s-process
6. r-process
7. p-process
8. x-process
neutrons
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….
s- and r-abundances today about equal
H 30,000
C
Fe
Au
10
1
2·10-7
(from “Cauldrons in the Cosmos”)
r-Process observables today
Observational instrumentation
Solar system isotopic Nr, “residuals”
• meteoritic and overall solar-system
abundances
T9=1.35; nn=1020 - 1028
Pb,Bi
• ground- and satellite-based telescopes
like Imaging Spectrograph (STIS) at
Hubble, HIRES at Keck, and SUBARU
• recent „Himmelsdurchmusterungen“
HERES and SEGUE
r-process observables
CS 22892-052 abundances
scaled solar r-process
scaled theoretical solar r-process
Zr
Ru Cd
Sn
Ga Sr
Mo Pd
Ge
Ba Nd
Dy
Gd
Ce Sm ErYb
Ir
Hf
Y
Rh
Nb Ag
Presolar SiC grains
and nano-diamonds
e.g.
isotopic composition
of heavy metals
Zr, Mo, Ru, Te, Xe, Ba, Pt
Pt
Os
Pb
La Eu Ho
Pr Tb
Lu
Tm
Au
Th
U
Elemental abundances in UMP halo stars
Isotopic anomalies in meteoritic samples
and stardust
Fit of Nr, from B²FH
„Static“ calculation
Reproduction of Solar system
isotopic r-process abundances
(mainly from r-only nuclei)
• assumptions
iron seed (secondary process)
„waiting-point“ concept
(global (n,g)  (g,n) and
ß-flow equilibrium)
instantaneous freezeout
The "waiting-point"concept in astrophysics (1)
Rate of n-captures:
(1)
cross section averaged over MaxwellBoltzmann velocity distribution to T9
Photodisintegration:
(2)
Nuclear Saha equation
The "waiting-point"concept in astrophysics (2)
Nuclear Saha equation:
simplified
• high nn
• low Sn
• low T
"waiting-point" shifted to higher masses
"waiting-point" shifted to higher masses
"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
Fit of Nr, from B²FH
„Static“ calculation
Reproduction of Solar system
isotopic r-process abundances
(mainly from r-only nuclei)
• assumptions
iron seed (secondary process)
„waiting-point“ concept
(global (n,g)  (g,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)
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
Speculations about various r-process
components:
"short-time" solution
0.44 s
1.77 s
3.54 s
Cycle time: 4.9 s
"long-time" solution
…however, all components with the
same neutron-density of 1024 n/cm3 !
r-Process scenarios since B2FH
For long time suspect, that puzzle of r-process site
is 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"
Fit of Nr, from B²FH
„Static“ calculation
Reproduction of Solar system
isotopic r-process abundances
(mainly from r-only nuclei)
• assumptions
iron seed (secondary process)
„waiting-point“ concept
(global (n,g)  (g,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
Parameter checks
Fitting r-process abundances:
a nuclear-structure learning effect or
discussing the fifth leg of an elephant ?
•
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 !
Nuclear-data needs for the classical r-process
 nuclear masses
Sn-values
 r-process path / “boulevard”
Q, Sn-values  theoretical -decay properties, n-capture rates
 -decay properties
T1/2  r-process progenitor abundances, Nr,prog
-decay
Pn  smoothing Nr,prog freeze-out Nr,final (Nr,)
modulation Nr through re-capture
 neutron capture rates
sRC + sDC  smoothing Nr,prog during freeze-out in
“non-equilibrium” phase(s)
 fission modes
SF, df, n- and n-induced fission
 “fission (re-) cycling”; r-chronometers
 nuclear structure development
- level systematics
- “understanding” -decay properties
- short-range extrapolation into unknown regions
Nuclear masses
Over the years, development of
various types of mass models / formulas:
• 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]
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 !
D. Lunney et al., Rev. Mod. Phys. 75, No. 3 (2003)
Nuclear masses
effect of Sn around N=82 shell closure
catchword “shell-quenching”
astrophys. parameters (T9, nn, τn) and T1/2 kept constant
“static” calculations (Saha equation)
break-out at N=82 130Cd
K.-L. Kratz et al.
Nucl. Phys. A630 (1998)
“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"
Single – Neutron Energies (Units of h w0)
"Shell quenching"
N/Z
g 9/2
126
7.0
g 9/2
p 1/2
f 5/2
p 3/2
112
h 9/2 ;f 5/2
p 1/2
i 13/2
6.5
h 9/2
f 7/2
p 3/2
f 7/2
82
6.0
5.5
70
h 11/2
g 7/2
h 11/2
g 7/2
d 3/2
d 3/2
s 1/2
s 1/2
d 5/2
d 5/2
50
5.0
i 13/2
g 9/2
g 9/2
40
p 1/2
f 5/2
…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…
• 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)
f 5/2
p 1/2
100%
70%
40%
10%
Strength of ℓ 2 -Term
B. Pfeiffer et al.,
Acta Phys. Polon. B27 (1996)
change of
• shell-gaps
• deformation
• r-process path (Sn)
• r-matter flow (τn)
The N=82 shell gap as a function of Z
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
A≈130 N peak
r,
FRDM
Exp
DZ
Groote
EFTSI-Q
Exp
HFB-14
N=82 shell-quenching
FRDM “trough”
WARNING: FRDM not appropriate for r-process calculations !
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
have
7.5 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 masses
Sn-values
 r-process path / “boulevard”
Q, Sn-values  theoretical -decay properties, n-capture rates
 -decay properties
T1/2  r-process progenitor abundances, Nr,prog
-decay
Pn  smoothing Nr,prog freeze-out Nr,final (Nr,)
modulation Nr through re-capture
 neutron capture rates
sRC + sDC  smoothing Nr,prog during freeze-out in
“non-equilibrium” phase(s)
 fission modes
SF, df, n- and n-induced fission
 “fission (re-) cycling”; r-chronometers
 nuclear structure development
- level systematics
- “understanding” -decay properties
- short-range extrapolation into unknown regions
Effects of T1/2 on r-process matter flow
Mass model: ETFSI-Q
T1/2 (GT + ff)
- all astro parameters (T9, nn, τn)
kept constant
r-Process model:
“waiting-point approximation“
T1/2 x 3
r-matter flow too slow
T1/2 : 3
r-matter flow too fast
130Cd
– the key isotope at the A=130 peak
…hunting for nuclear properties of
waiting-point isotope 130Cd…
already B²FH (Revs. Mod. Phys. 29; 1957)
C.D. Coryell (J. Chem. Educ. 38; 1961)
132Sn
50
131
(n,g)
134
135
136
132
133In
84
49
134
135
132
133
133
Pn~85%
“climb up the staircase“ at N=82;
major waiting point nuclei;
“break-through pair“ 131In, 133In;
“association with the rising side of major
peaks in the abundance curve“
r-process
path
(n,g)
130
131In
82
49
129
130Cd
82
48
131
128
129Ag
82
47
130
127
128Pd
82
46
126
127Rh
82
45
(n,g)
K.-L. Kratz (Rev. Mod. Astr. 1; 1988)
climb up the N= 82 ladder ...
A  130 “bottle neck“
T1/2(130Cd)
Nr,ʘ(130Te) ?
137
"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 P ≈ 90%
n
…to be compared to the 1986 exp. value of 195 (35) ms,
and to the 2001 improved value of 162 (7) ms.
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 [S(E)]
“Theoretical” definition (Yamada & Takahashi, 1972)
“Experimental” definition (Duke et al., 1970)
S(E) = D-1 · M(E) ² · w(E) [s-1MeV-1]
M(E)  average -transition matrix element
w(E)
level density
D
const., determines Fermi coupling constant gv²
T1/2 =
106
103

b(E)
absolute -feeding per MeV,
f(Z, Q-E) Fermi function,
T1/2
-decay half-life.

i
6x105
i
f(Z, Q-Ei)  (Q-Ei)5
1,E+05
1,E+04
[s-1MeV-1]
 S (E ) x f (Z,Q -E )
0Ei Q
1,E+06
f(Z, Q-E) · T1/2
1
T1/2 as reciprocal
ft-value per MeV
S(E)
b(E)
S(E) =
3x103
Fermi function
T1/2 sensitive to lowest-lying resonances in S(Ei)
Pn sensitive to resonances in S(Ei) just beyond Sn
1,E+03
1,E+02
Q
same T1/2 !
1,E+01
↷ easily “correct” T1/2 with wrong S(E)
1
1
1
11,E+00
1,E-01
1
1
2
3
4
5
5
6
7
8
9
10
10
E*[MeV]
T1/2 and Pn calculations in 3 steps – (I)
“Typical spherical example”:
(1)
Mass model FRDM
↷ Q, Sn, e2
Folded-Yukawa wave fcts.
SP shell model QRPA (pure GT)
with input from FRDM
potential: Folded Yukawa
pairing-model: Lipkin-Nogami
SnQ
(2) as in (1) with empirical spreading of SP transition
strength, as shown in experimental S(E)
(3) as in (2) with addition of first-forbidden strength
from Gross Theory
note: effects on T1/2 and Pn !
T1/2 and Pn calculations in 3 steps – (II)
…and a typical “deformed” case:
spreading of SP strength to deformed
“Nilsson spaghetti”
Möller, Nix & Kratz; ADNDT 66 (1997)
Möller, Pfeiffer & Kratz; PRC 67 (2003)
Note: low-lying GT-strength; ff-strength unimportant!
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.
T1/2, Pn
gross -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.
Total Error = 3.73
Half-lives
QRPA (GT)
Total Error = 5.54
Pn-values
QRPA (GT)
QRPA (GT+ff)
QRPA (GT+ff)
(Möller, Pfeiffer, Kratz
PR C67, 055802 (2003))
Total Error = 3.08
Total Error = 3.52
Nuclear-data needs for the classical r-process
 nuclear masses
Sn-values
 r-process path / “boulevard”
Q, Sn-values  theoretical -decay properties, n-capture rates
 -decay properties
T1/2  r-process progenitor abundances, Nr,prog
-decay
Pn  smoothing Nr,prog freeze-out Nr,final (Nr,)
modulation Nr through re-capture
 neutron capture rates
sRC + sDC  smoothing Nr,prog during freeze-out in
“non-equilibrium” phase(s)
 fission modes
SF, df, n- and n-induced fission
 “fission (re-) cycling”; r-chronometers
 nuclear structure development
- level systematics
- “understanding” -decay properties
- short-range extrapolation into unknown regions
E(2+) - landscape 90  A  150
Z
E(2+)
• reduced pairing
• rigid rotors
• ng7/2  pg9/2 interaction
• shell quenching
90Zr
132Sn
96Zr
50
nd5/2
56
110Zr
60
ns1/2
ng7/2
nh11/2
• magic shells/subshells
• shape transitions/coexistence
• intruder states
• identical bands
nd3/2
50
82
pg9/2
40
N
What is known experimentally ?
Known 1+ states in n-rich even-A In isotopes
1+
OXBASH
(B.A. Brown, Oct. 2003)
1+
2120
2181
(new)
1+
3+
243
0
124In
75
1+
688
3+
0
126In
77
1731 keV
1+
1173
3+
0
128In
79
1382
(old)
Reduction of
the TBME (1+)
by 800 keV
3+
389
3+
473
1-
0
1-
0
130In
Configuration 1- : nh11/2  pg9/2
Configuration 3+ : nd3/2  pg9/2
Configuration 1+ : ng7/2  pg9/2
1+
81
130In
81
Dillmann et al.; PRL 91 (2003)
determines T1/2
Short range extrapolation
Known !
partly known
S1n=5.246MeV
S1n=3.98MeV
Beta-decay odd-mass, N=82 isotones
nSP states in N=81 isotones
extrapolation
E*[MeV]
3
ng7/2
2565
2,5
89%
4.0
7/2+
2607
S1n=3.59MeV
88%
4.0
2
Pn=4.4%
1,5
7/2+
S1n=2.84MeV
2648 67%
264345%
4.1
0,5
ns1/2
nd3/2
0
524
P4n= 8.5%
P5n= 1%
282
nh11/2
131Sn
81
50
2.3%
0 6.3
728
814
601
3/2+
3/2+
1/2+
331
11/2-
129Cd
81
48
1.2%
6.3
3/2+
414
11/2127Pd
81
46
0.9%
6.4
472
11/2125Ru
81
44
4.5
S1n=1.81MeV
1
1/2+
263724%
P1n=25%
P2n=45%
P3n=11%
T1/2 determined by Q-E7/2
1/2+
ng7/2
4.25
P1n=39%
P2n=11%
P3n= 4.5%
P1n=29%
P2n= 2%
Pn=9.3%
7/2+
0.6%
6.4
1/2+
908
3/2+
536
11/2123Mo
81
42
0.5% I
6.45 log(ft)
Surprising -decay properties of 131Cd
…just ONE neutron outside N=82 magic shell
Experiment: T1/2 = 68 ms; Pn = 3.4 %
QRPA predictions:
T1/2(GT) = 943 ms;
T1/2(GT+ff) = 59 ms;
Pn(GT) = 99 %
Pn(GT+ff) = 14 %
nuclear-structure requests: higher Qβ, main GT lower, low-lying ff-strength;
later, g-spectroscopic confirmation of decay scheme at ISOLDE
The FK2L waiting-point approach (I)
e.g.:
Cameron, Clayton, Schramm,
Truran, Kodama, Arnould,
Woosley, Hillebrandt,
Thielemann…
30
known r-process isotopes at
that time:
N=50 79Cu, 80Zn, 81Ga
N=82 130Cd, 131In
The FK2L waiting-point approach (II)
Classical assumptions:
global steady flow
of r-process through
N=50 80Zn, N=82 130Cd
and N=126 195Tm
Calculation:
r-process matter flow at
freeze-out temperature ;
at N=82 “imperfect” peak,
r-process through 40 s 132Sn,
instead of 195 ms 130Cd…
The FK2L waiting-point approach (III)
The FK2L waiting-point approach (IV)
“…best fit so far…;
long-standing problem solved…”
W. Hillebrandt
“…call for a deeper study…
before rushing into numerical
results…
and premature comparisons
with the observed abundances”
M. Arnould
birth of N=82
“shell-quenching”
idea …
Wide-spread ignorance of experimental r-process data
Two typical examples:
I. Dillmann & Y.A. Litvinov
Prog. 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
T1/2 of N=50 “waiting-point” isotope 540 ms
80Zn
(top of A ≈ 80 Nr, peak)
• at the ISOL facility SC-ISOLDE
T1/2 of N=82 “waiting-point” isotope 195 ms
130Cd
(top of A ≈130 Nr, peak)
Both act as major “bottle-necks” for the matter flow of the
classical r-process starting from an Fe-group seed
Experimental information on r-process nuclides
Today,
82
altogether ≈ 80 r-process nuclei known
g9/2
p1/2
p3/2
f5/2
f7/2
42
Z
86
Ba
Cs
Xe
I
Te
Sb
heaviest isotopes with measured T1/2
new (MSU, 2009; RIKEN 2011)
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
84
N
44
46
g9/2
48
50
52
d5/2
54
56
58
s1/2
60
62
64
g7/2
66
68
d3/2
70
72
74
76
h11/2
78
80
82
88
90
92
94
nn
Classical r-process path for nn=1020
=1020
82
Ba
Cs
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
42
Z
N
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
„waiting-point“ isotopes at nn=1020 freeze-out
78
80
82
84
86
88
90
92
94
nn
Classical r-process paths for nn=1020 and 1023
=1020
82
84
86
88
90
92
94
Ba
Cs
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
nn=1023
42
Z
N
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
„waiting-point“ isotopes at nn=1023 freeze-out
(T1/2 exp. : 28Ni – 31Ga, 36Kr – 40Zr, 47Ag – 51Sb)
nn
r-Process paths for nn= 1020, 1023 and 1026
=1020
r-process “boulevard”
82
84
86
88
90
92
94
Ba
Cs
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
nn=1023
nn=1026
42
Z
N
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
„waiting-point“ isotopes at nn= 1026 freeze-out
(T1/2 exp. : 28Ni, 29Cu, 47Ag – 50Sn)
78
80
82
Summary “waiting-point” model
seed Fe (still implies secondary process)
superposition of nn-components
…largely site-independent!
T9 and nn constant;
instantaneous freezeout
“weak” r-process
(later secondary process;
explosive shell burning?)
“main” r-process
(early primary process; SN-II?)
Kratz et al., Ap.J. 662 (2007)