Astrophysical, observational and nuclear-physics aspects of r-process nucleosynthesis

Astrophysical, observational and nuclear-physics aspects of r-process nucleosynthesis

T1/2P

nS

nsng

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

Sr MoRu

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,g) (g,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



• 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

"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"



• 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

• 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”Q, Sn-values theoretical -decay properties, n-capture rates

neutron capture rates

fission modes

sRC + sDC smoothing Nr,prog during freeze-out in “non-equilibrium” phase(s)

SF, df, n- and n-induced fission “fission (re-) cycling”; r-chronometers

-decay propertiesT1/2 r-process progenitor abundances, Nr,prog

Pn smoothing Nr,prog Nr,final (Nr,) modulation Nr through re-capture

-decayfreeze-out

nuclear structure development- level systematics- “understanding” -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

p1/2f5/2

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 5/2d 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

Sing

le –

Neu

tron

Ener

gies

(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

N=82 shell-quenching

WARNING: FRDM not appropriate for r-process calculations !

FRDM “trough”

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)




fission modes





-decayfreeze-out


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

127Rh8245126

127

128

129

130

131

132

133

Pn~85%165ms278ms

46ms(g)

r-processpath

(n,g)

(n,g)

(n,g)135 136 137

134 135

131 132 133

130

134

158ms(m)

130Cd8248

162ms

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 [S(E)]

“Theoretical” definition (Yamada & Takahashi, 1972)

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

“Experimental” definition (Duke et al., 1970)

S(E) =b(E)

f(Z, Q-E) · T1/2

[s-1MeV-1]

b(E) absolute -feeding per MeV,f(Z, Q-E) Fermi function,T1/2 -decay half-life.

T1/2 as reciprocal ft-value per MeV

T1/2 = S(Ei) x f (Z,Q-Ei)0Ei Q

11

1

f(Z, Q-Ei) (Q-Ei)5 S(E)

E*[MeV]

Q

Fermi function

T1/2 sensitive to lowest-lying resonances in S(Ei)Pn sensitive to resonances in S(Ei) just beyond Sn

↷ easily “correct” T1/2 with wrong S(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↷ Q, 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 S(E)

SnQ

(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 -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)




fission modes





-decayfreeze-out


E(2+) - landscape 90 A 150

• reduced pairing• rigid rotors• ng7/2 pg9/2 interaction• shell quenching

• magic shells/subshells• shape transitions/coexistence• intruder states• identical bands

N

ZE(2+)

90Zr

96Zr132Sn

r-process path

50

40

82

60

56

50

nd5/2

ns1/2

ng7/2

nh11/2

nd3/2

pg9/2

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

130In81130In81

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

1731 keV

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%

Ilog(ft)

S1n=2.84MeV

S1n=1.81MeV

1/2+

T1/2 determined by Q-E7/2

Short range extrapolation

Known ! partly known extrapolation

Experiment: T1/2 = 68 ms; Pn = 3.4 %

Surprising -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 (III)

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. SurmanAp.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

Astrophysical, observational and nuclear-physics aspects of r-process nucleosynthesis

Documents

rprocess scenario

nuclearphysics aspects

cosmosrprocess paths

solarsystem abundances

n fit of nr

solar abundance observables

rate of n

concept global n