Nuclear Astrophysics

K. E. Rehm

Physics Division

Argonne National Laboratory

2x50 minutes for (13.7±0.13)x109

years

(a ratio of 1.39x10‐14

!)

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Outline•Why astrophysics?

•The life of a star

•Astrophysical jargon: Big Bang nucleosynthesis, Jeans 

criterion, quiescent and 

explosive  burning, reaction rate, Gamow window, 

S‐factor, resonance strength,..

•Examples                                                  (p,) reaction in X‐ray bursts                     

n‐rich nuclei and the r‐process

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LiteratureC. Rolfs & W. Rodney:

Cauldrons in the Cosmos, University of Chicago Press, 1988

C. Iliadis:

Nuclear Physics of Stars, Wiley 2007

I. Thompson and F. Nunes

Nuclear Reactions for Astrophysics, Cambridge Univ. Press 2009

B2FH:

Burbidge,Burbidge,Fowler, Hoyle: Rev. Mod. Phys. 29, 15(1957)

Annual Review of Nuclear and Particle Physics

Annual Review of Astronomy and Astrophysics

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Why astrophysics? What is astrophysics?

Forefront science

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Particle Physics

Atomic Physics

Neutrinos 0.7%

Plasma Physics

Cosmology Nuclear Physics

Gravitation

Dark Energy 73.4%

Dark Matter 22.1%

-mass 0.7%

H, He 4.1%

Heavy Elements 0.07%

Neutrino Physics

Astronomical Observations

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Lab/Earth Stars

gravitation 9.81 m/sec2 Black hole

magnetic field 91.4 T 10‐100x109

T

Acc. energy 7x1012

eV 1020

eV

density 22.5 g/cm3 1013

g/cm3

‐flux 1020

/sec 1058

in ~1 s

Whatever stars do, they do it to the extreme

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Nuclear Astrophysics – goals:

•Understanding the birth and death of stars

•Understanding the energy that powers the stars

•Understanding the formation of the elements

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Nuclear Astrophysics - Challenges:•Extremely small cross sections

•backgrounds

•Reactions involving unstable nuclei

Frontiers:•High-current accelerators

•Underground laboratories

•Gas targets

•Radioactive ion beams

•High efficiency detectors

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T ~ 109 K,

t ~ 3 min

1H 0.75

2H 2.5x10‐5

3He 4x10‐5

4He 0.23

7Li 5x10‐9

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Burles, Nollett, Turner, ApJ

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The elements after the Big Bang The elements today

What the stars did for us

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C

C

RGMU

2

53

NkTK23

H

C

mMN

Virial

theorem:  2K + U = 0

Collapse: 2K < ‐U

C

C

H

C

RGM

mkTM 2

533

3/1)43(

C

CC

MR

2/12/3 )4

3()5(CH

J mGkTM

Jeans criterion (1902)

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C

C

RGMU

2

53

NkTK23

H

C

mMN

Virial

theorem:  2K + U = 0

Collapse: 2K < ‐U

C

C

H

C

RGM

mkTM 2

533

3/1)43(

C

CC

MR

2/12/3 )4

3()5(CH

J mGkTM

Jeans criterion (1943)

MJ

= 45M

TK3/2 N‐1/2

For T=3000K and N=6x103

cm‐3

MJ

=105M

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Two paths to ‘cook’ the elements in stars:Slowly (quiescent)

~(109 years)

Example : the sun

hydrogen helium

Fast (explosive)

~( a few seconds)

Example:Supernova

iron

heavy elements

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Experiments with stable beams and targets:

provide data for BB nucleo-synthesis and quiescent burning scenarios

Need:•High beam intensities

•thick targets, that can tolerate the beams

•low backgrounds

•long runs

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LUNA Gran Sasso

DUSEL

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Experiments with radioactive beams:

provide data for explosive burning scenarios:

Need:•Beams of unstable nuclei (low intensities, contaminants)

•thick targets (to compensate for the intensity)

•long runs

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Targets for experiments with radioactive beams: controlled by stellar abundance pattern

Most reactions induced by:

p,

(16O,12C, n)

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Critical reactions in nuclear astrophysics

(p,)

(novae, rp‐process)

()

(red giants)

(,p)

(rp‐process)

12C + 12C fusion

(supernovae)

(n,)

(r‐process, s‐process)

GT transitions

(supernovae)

(,n)

(s‐process, red giants)

(p,)

(novae)

(,p), (,n), () (p‐process)

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Ap,

(v)

In Nature:

v: Maxwellian distribution

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target A

p,

(with velocity vo )

(vo )

In the laboratory:

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Reactions between Charged Particles(astrophysical reaction rate, Gamow window, S-factor, resonance strength)

Example: 12C(p,13N

Nc : 12C particles/cm3

Np : protons/cm3

v: relative velocity between C and p

Astrophys. reaction rate: r=Nc •Np • v• p

(v)

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Plasma: velocity distribution (v)

v

<v>= (v)•v•(v) dv

(<v> reaction rate per particle pair)

Particle densities Ni :

=Ni weight of a particle

=Ni A/NA NA : Avogadro’s Number

Ni =NA /A

Or, for a multiparticle gas with Xi as a mass fraction:

Ni =NA /A Xi

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Example: particle density in the center of the sun:

~150 g/cm3

Xi =0.73

Np =6.6 1025 particles/cm3

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In normal stellar matter (not in neutron stars)

i (vi )=4vi2( )3/2 exp(- ) (Maxwellian)

<v>= (v1 )(v2 )(vrel )vrel dv1 dv2

v1 =V + m2 /(m1 +m2 )v V : center-of-mass velocity

v2 =V - m1 /(m1 +m2 )v v : relative velocity (v1 -v2 )

<v>= (V)(v) v (v) dv dV

kTm2 kT

mv2

2

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Where:

(V)=4V2( M/(2kT))3/2 exp(- MV2/(2kT))

M=m1 +m2

(v)=4v2(/(2kT))3/2 exp(-v2/(2kT))

=m1 m2 /(m1 +m2 )

<v>= (v)v(v)dv

Because (V)dV=1

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<v>=4( )3/2 v3 (v) exp(- )dv

or

<v>=( )1/2 ( )3/2 (E) E exp(- ) dE

kT

2 kTv

2

2

8

kT1 kT

E

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vN

QREvNNR

2

121212

2112

1)1(

Reactions/(cm3 sec) in a plasma consisting of N1 and N2 particles/cm3

Rate of energy release (MeV/(cm3 sec)

Life time (sec) of particle 1 in a plasma consisting of N2 particles/cm3

Some useful expressions:

Need to measure (v) (or (E))

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Need (E):

Non-resonant cross sections resonant cross sections

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Probability of tunneling through the Coulomb barrier:

P~ exp(-2); 2Z1 Z2 (/Ecm )1/2 ;

in amu, E in keV

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2.1 Non-resonant Reactions:

=/k2 l

lTl 2)12(

at low energies only l=0 collisions contribute:

=/k2|T0 |2 = /k2 (F,G:Coulomb functions)221

oo GF

With asymptotic values (Abramowitz-Stegun):

~ 1/E exp(-2)

Where =Z1 Z2 e2/(v) Sommerfeld parameter

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To eliminate the strong energy dependence, one takes out the trivial factors : e-2/E and defines a new parameter S (S-Factor) which contains the ‘non-trivial’ energy dependence:

=S(E)/E e(-2)

S(E)=E e(2)

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With S(E) one can rewrite <v>:

<v>=( )1/2 ( )3/2 S(E)exp(-E/kT-b/E1/2) dE

argument of the exponent:

8

kT1

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Maximum of the argument at E0 :

E0 =(bkT/2)2/3 with b=(2)1/2 e2Z1 Z2 /

or

E0 =1.22( )1/3 [keV] Gamow peak26

22

21 TZZ

T6 : temperature in 106 K

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56

22

21 TZZ

System Eo

[keV] [keV] 3He + 3He 21 12.1 49.7

p + 12C 24 12.8 55.4

+ 12C 56 19.6 130.216O + 16O 237 40.4 550.9

Example of Gamow window values

T6

=15 K    T=15x106

K

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From C. Angulo

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Example: reactions in the CNO cycle

reaction times long compared to Nuclear reactions occur on stable nuclei

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Increasing the temperature by a factor of 10:

Reaction times are comparable to decay times.

unstable nuclei become part of the reaction network

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2.2 Resonance Reactions

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resonance : Breit-Wigner shape

if = 2k

)12)(12(12

21

JJJ

22 )2/()(

r

fi

EE

J: spin of the resonance

J 1,2 : spin of the particles in the entrance channel

k: wave number

i,f : widths (decay probabilities) in the entrance or exit channel

Er : resonance energy

: total width (i +f +..)

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<v>=( )1/2 ( )3/2 BW E exp(-E/kT) dE

<v>=( )1/2( ) 3/2 Er exp(-Er /kT) BW (E) dE

8

kT1

8

kT1

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BW (E) dE = i f /2)

=22/k2 =

=22/k2

: resonance strength

2k

fi

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<v>=( )3/2 2

exp(-Er /kT)

For several non-overlapping resonances:

<v>=( )3/2 2 i exp(-Ei /kT)

kT2

kT2

High rates for:

1. Large

2. low resonance energies Ei

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spin-parity selection rules, e.g.14O + : 0+, 1-, 2+,3-..17F(5/2+) + p(1/2+): 2+,3+,1-,2-,..

What are the important levels in the compound nucleus (18Ne)? Example: 14O(,p)17F

Angular momentum barrier:

Vint =Z1 Z2 e2/R +2 l(l+1)/(2R2)

tunneling inhibited for higher l

preference for l=0 transitions

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Example I:

X-ray bursts –

Reactions on the surface of a neutron star

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X-ray bursts

~1.5 M

radius ~ 10 km

~ 106-14 g/cm3

T ~ 107 K

donor star

neutron star

accretion disk

normal H, He star

period: hours-100d

distance~ 10-3– 1AU

accumulation rate ~10-8-10-10 M

/y

(50-0.5 kg/cm2/s)

~200 MeV/u

KS 1731-260

D=23 kly

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X-ray Bursts

•~repetition rate hours-days

•duration of ~10 sec

•E=1038 erg/s (sun 1033 erg/s)

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56Ni(p,)57Cu

b

T1/2 (56Ni)=6.1d

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What are the observables? a) Time dependence of the luminosity

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L. Boirin et al.,

A&A 2007

Observables cnt’d:multiplets

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Galloway et al., ApJ 601,466(2004)

Observables cnt’d:‘aging’ effects in X-ray bursts

Observations 

in 1997‐98 

and in 2000

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Observables cnt’d:Energy shift of Fe-absorption line (ionization)

Nature 420, 51

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Observables cnt’d:Long (‘super’) bursts

Strohmayer & Brown ApJ 566, 1045(2002)

~ 3hrs

Nuclear reactions deeper inside the neutron star

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0 12

3 45 6

7 8

9 10

111213

14

1516

17181920

2122

2324

25262728

2930

3132

33343536

3738

n (0)H (1)

He (2)Li (3)

Be (4) B (5) C (6) N (7)

O (8) F (9)

Ne (10)Na (11)

Mg (12)Al (13)Si (14) P (15)

S (16)Cl (17)

Ar (18)K (19)

Ca (20)Sc (21)

Ti (22)V (23)

Cr (24)Mn (25)

Fe (26)Co (27)

Ni (28)Cu (29)

Zn (30)Ga (31)

Ge (32)As (33)

( )

X-ray bursts and Nuclear PhysicsTypical rp-process reaction network

(p,)

(,p)

+ decay

Need:•Proof of particle stability

•masses

•T1/2 (+)

•Cross sections

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Shock front

atmosphere Sedimentation of the reaction products

Egr /mc2=GMNS /(RNS c2) ~ 0.2

•Relativistic treatment

•Three-dimensional

•Rotations

•Turbulences

•Sedimentation

•‘Ashes’ (e.g. 12C) can burn as well

•Magnetic fields

Theoretical treatment of X-ray bursts

FLASH Center ANL

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Which reactions have been measured?

Direct measurement

Indirect measurement

Under investigation

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0 12

3 45 6

7 8

9 10

111213

14

1516

17181920

2122

2324

25262728

2930

3132

33343536

3738

n (0)H (1)

He (2)Li (3)

Be (4) B (5) C (6) N (7)

O (8) F (9)

Ne (10)Na (11)

Mg (12)Al (13)Si (14) P (15)

S (16)Cl (17)

Ar (18)K (19)

Ca (20)Sc (21)

Ti (22)V (23)

Cr (24)Mn (25)

Fe (26)Co (27)

Ni (28)Cu (29)

Zn (30)Ga (31)

Ge (32)As (33)

( )

X-ray bursts and Nuclear PhysicsTypical rp-process reaction network

(p,)

(,p)

+ decay

Need:•Proof of particle stability

•masses

•T1/2 (+)

•Cross sections

21Na(p,)22Mg

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(p,) reactions

Center of activities with radioactive beams

Mainly resonant 

Example  21Na(p,)22Mg (TRIUMF)

S. Bishop et al. PRL90, 162501(2003)

J. d’Auria

et al. PRC69, 065803(2004)

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Gamow windows

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Need 200-900 keV 21Na (T1/2 =22.8 s) beams and hydrogen gas target

Reaction studied as: p(21Na,22Mg)21Na

22Mg

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Conversion from cross section to reaction rate

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Other Recoil Separators for Astrophysics

Used to measure 21Na(p,)22MgDRAGON at TRIUMF ISAC

ARES at Louvain-la-NeuveUsed to measure 19Ne(p,)20Na

DRS at ORNL HRIBFUsed to measure 17F(p,)18Ne

FMA at ANL ATLASUsed to measure 18F(p,)19Ne

Future: SECAR at NSCL

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rp-process

Nuclei involved in Astrophysics

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Example 2:

Nucleosynthesis beyond 56Fe:

(r and s-processes)

Coulomb barrier too high for charged-particle reactions

reactions involving neutrons

from the mass distributions: at least two processes

slow neutron capture (s-process)

rapid neutron capture (r-process)

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Relative abundances as f(A)

~3% of 56Fe

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Where does nature produce neutrons in stars?

Charged-particle reactions 13C(,n)16O Q=2.216 MeV (but 12C(,n)15O Q=-8.508)22Ne(,n)25Mg Q=-0.480 MeV

Cross sections for neutron capture

reactions are usually quite large.

(100-5000 mb)

Shell effects!

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s-process

slow neutron capture process

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s-process

Nuclei involved in Astrophysics

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What neutron flux is needed?

Rate equation for a nucleus A with respect to n- capture:

dNA (t)= -NA (t)/A dt

is the rate at which A is converted into A+1,

i.e. NA Nn <v>=-dNA /dt

A Nn =1/<v>

dtdN A

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n

~1/v <v> ~ constant

~ 100 mb , v ~ 108 cm/sec

Nn ~ 1017 s neutrons/cm3

To have capture times <10y (=•108 s)

Nn > 3x108 neutrons/cm3 (s-process)

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Nuclei with small n

(e.g. closed shell nuclei) have a large

and form a ‘bottleneck’

resulting in the s process abundance peaks.

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What causes the second peaks?

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The other peaks in the abundance spectra are shifted downward in mass, but can be explained with a similar mechanism: rapid capture of neutrons.

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r-process

s-process

rapid neutron capture process

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For this to happen the n capture has to occur on a much faster time scale: n ~ ms

With Nn ~ 1017

Nn ~ 1020 n/cm3

At which astrophysical sites do we have these neutron densities?

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Price and Rosswog

Where can we get these high neutron densities?

Neutron star mergers                                            

core‐collaps

supernovae

• Site of the r‐process is unknown

•

Properties of nuclei in the r‐process path are unknown 

(half‐lives, masses, n‐capture cross sections..)

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S.Wanajo

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0

20

40

60

80

100

0 50 100 150

GANIL SPEG CSS2

stable indirect

ISOLDE MISTRAL ISOLTRAP

Other Penning traps CPT (ANL) LEBIT (MSU) JYFLTRAP

neutron dripline(FRDM95)

proton dripline(FRDM95)

GSI ESR-SMS ESR-IMS SHIPTRAP

N

Z

Lunney, NIC-IX, 2006

For the r‐process path we need masses of neutron‐rich nuclei

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106 103 100 10-310-9

10-8

10-7

10-6

10-5

10-4

JYFL COOL

CPT

ESR SMS

ISOLTRAP

ESRIMS

MISTRAL

CSS2

SPEG

rela

tive

unce

rtain

ty

half life (seconds)

See: Lunney, Pearson & Thibault, Rev. Mod. Phys. 75 (2003) 1021

Most accurate mass measurements with Penning traps

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B

• constant axial magnetic field

• particle orbits in horizontal plane

• free to escape axially

mqB

c

How a Penning trap works -1

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How a Penning trap works-2

B

Add an axial harmonic potential to confine particles:

)2

(2

22

2rz

dVV o

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Motion of ions in a Penning trap

picture from http://isoltrap.web.cern.ch/isoltrap/

242

22zcc

)( BvEqF

Solve for equations of motion:

2mdeV

z

Axial oscillations:

Radial motion:

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Magnetic field lines outside the Penning trap

Ions from the Penning trap

zFF

0B

0B

MCP

OrbitalEnergy

LinearEnergy

TOFDetection

Penning trap mass spectrometry

35

40

45

50

55

60

-20 -15 -10 -5 0 5 10 15 20

Applied Frequency - 1328698.54 Hz

TOF

( s)

Sample TOF spectrum

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Penning traps

CPT at ATLAS

SHIPTRAP

ISOLTRAP

JYVLTRAP

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Need information of n‐rich nuclei in the r‐process path

T1/2

, masses, n‐capture rates

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T1/2

known

Mass known

RIKEN 2010

RIKEN 2011

CARIBU 2011

A very active field – stay tuned!

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r-process

sn1006

rp-process

s-process

Nuclear Physics in Astrophysics

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97Thanks for listening ‘til the bitter end.