lemar& low)energy&magne0c&radiaon&

LEMAR Low-‐Energy Magne0c Radia0on

S. Frauendorf Department of Physics University of Notre Dame

In collabora0on with: M. Beard, University Notre Dame A. C. Larsson, University Oslo E. Litvinova, Western Michigan University M. Mumpower, University Notre Dame R. Schwengner, HZDR, Dresden K. Wimmer, Central Michigan University

arXiv:1310.7667 PRL 111, 232504 (2013) New: arXiv:1407.1721

Low-‐Energy MAgne0c Radia0on LEMAR

•  Descrip0on by Shell Model •  Mechanism that generates radia0on •  Sta0s0cal proper0es of the transi0ons •  Predic0on of regions/relevance •  Impact on r-‐process •  Low-‐Energy Electric Radia0on

0 2 4 6 8 10

0

1

2

3

4

5

E

I

E

1

2

3

(He,He'γ )(n,γ )

(γ,γ ' )

many transitions ⇒ average propertiestransmission coefficient (average rate to decay with Eγ / energy unit )

Tγ (Eγ ,Ei ) = 2π f (Eγ ,Ei )Eγ3

∝ strength function x photon phase space radiatve strength function f (Eγ ,Ei )∝B(E1,M1,Eγ ,Ei ) ρ(Ei )number states /energy unit ρ(E)average reduced transition probability/state B(E1,M1,Eγ ,Ei )

common assumption: f (Eγ ,Ei ) "Brink- Axel hypothesis"

Ronald Schwengner | Institut für Strahlenphysik | http://www.hzdr.de

Dipole strength in 94Mo

(MeV)γ

-ray energy Eγ0 2 4 6 8 10 12 14 16

)-3

-ray

stre

ngth

func

tion

(MeV

γ

-910

-810

-710

-610Mo, Oslo data, E&B2009 norm.94He’)3He,3 (

,x) γMo(94 E1 strength M1 strength

Sum of E1 and M1

Dipole strength function

f1 = σγ/[3(πh̄c)2Eγ]

f1 = Γ ρ(Ex , J)/E 3γ

94Mo(3He,3He’):

M. Guttormsen et al.,

PRC 71, 044307 (2005)

Emission from the compound nucleus

What is it?

0 2 4 6 8 10

0

1

2

3

4

5

E

I

E

1

2

3

(He,He'γ )(n,γ )

(γ,γ ' )


Dipole strength in 94Mo


f1 = σγ/[3(πh̄c)2Eγ]

f1 = Γ ρ(Ex , J)/E 3γ

(γ, γ’) up to 4 MeV:

N. Pietralla et al., PRL 83, 1303 (1999)

Absorp0on from the ground state


Experimental B(M1) and B(E1) values in nuclei around A = 90

0 500 1000 1500 2000Eγ (keV)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

B(M

1) (µ

N2 )

B(E1

) (10

−2 e

2 fm2 )

88 A 98= =< <

M1: 312 transitionsE1: 171 transitions

Data taken from NNDC data base:

http://www.nndc.bnl.gov/nudat2/

What is it?


Shell-model calculations around N = 50

Configuration space SM2:

π ν

0g0g1p

1p0f

5/2

3/2

1/2

9/2 9/2

28

Core Ni68

50

28 38

1d5/2

0g7/2

Code: RITSSCHIL

Two-body matrix elements:

ππ:empirical from fit to N=50 nuclei, 78Ni core;X. Ji, B.H. Wildenthal, PRC 37 (1988) 1256

πν, νν (0g9/2,1p1/2):emp. from fit to N=48,49,50 nuclei, 88Sr core;R. Gross, A. Frenkel, NPA 267 (1976) 85

πν (π0f5/2,ν0g9/2):experimental from transfer reactions;P.C. Li et al., NPA 469 (1987) 393

νν (0g9/2,1d5/2):exp. from energies of the multiplet in 88Sr;P.C. Li, W.W. Daehnick, NPA 462 (1987) 26

remaining:MSDI;K. Muto et al., PLB 135 (1984) 349


Level energies in 94Mo

0 1 2 3 4 5 6 7 8 9 10J

0

1

2

3

4

5

6

7

E x (M

eV)

94Mo shell model SM1π = +

0 1 2 3 4 5 6J

0

1

2

3

4

5

6

7

8

9

10E x

(MeV

)

94Mo shell model SM2π = +


Average M1 strengths in 90Zr and 94Mo

0 2000 4000 6000 8000Eγ (keV)

0

0.1

0.2

0.3

0.4

0.5

B(M

1) (µ

N2 )

90Zr shell model SM2

(π = +, 14279 transitions)(π = −, 14278 transitions)

J = 0i to 6i, i = 1 to 40

0 2000 4000 6000 8000Eγ (keV)

0

0.1

0.2

0.3

B(M

1) (µ

N2 )

94Mo shell model SM2


J = 0i to 6i, i = 1 to 40

⇒ Enhancement of M1 strength toward very low transition energy in the N = 50 nuclide 90Zr as well.

⇒ Total M1 strength of 1+→ 0+

1transitions around 8 MeV in 90Zr is in agreement with results of an

experiment at HIγS [G. Rusev et al., PRL 110, 022503 (2013)].

averages over bins of 100 keV

LEMAR LEMAR


Average M1 strengths in 95Mo and 94Mo

0 2000 4000 6000 8000Eγ (keV)

0

0.1

0.2

0.3

B(M

1) (µ

N2 )



J = 1/2i to 13/2i, i = 1 to 40

0 2000 4000 6000 8000Eγ (keV)

0

0.1

0.2

0.3

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

◦ Average B(M1) values in bins of 100 keV of transition energy.

⇒ Enhancement of M1 strength toward very low transition energy in the two isotopes.

⇒ ν(1d2

5/20g1

7/2) configuration preferred to ν(1d3

5/20g−1

9/20g1

7/2) configuration in 95Mo.


M1 strength function in 94Mo

0 2000 4000 6000 8000 10000Eγ (keV)

0

1

10

100

f M1 (

10−9

MeV

−3)


(3He,3He’) data

J = 0i to 6i, i = 1 to 40

M1 model


f1 = 11.5473 B(M1) ρ(Ex , J)

ρ(Ex , J) - level density

of the shell-model states,

includes π = +, π = −,

all spins from 0 to 6.

94Mo(3He,3He’):

M. Guttormsen et al.,

PRC 71, 044307 (2005)

0 2 4 6 8 10 12 14 16 18Ea (MeV)

10−2

10−1

100

101

102

103

f M1 (

10−9

MeV

−3)

94Mo(3He,3He’) data

shell model SM2M1

E1 + M1

(a,n) data

E1f

fM1 ≈ f0 exp(−Eγ /TF ), f0 = 3710−9MeV −3, TF = 0.50MeV

GLO

LEMAR is an exponen0al func0on of gamma energy

LEMAR accounts for the Oslo experiments



0 2000 4000 6000 8000 10000 12000Ei (keV)

0

0.2

0.4

0.6

0.8

1

1.2

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

0 2000 4000 6000 8000Ei (keV)

0

0.2

0.4

0.6

0.8

1

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

◦ Average B(M1) values in bins of 100 keV of excitation energy.

◦90Zr: Large peaks between about 5.9 and 7.5 MeV for π = – arise from states dominated by

the configuration π(1p−1

1/20g1

9/2) ν(0g−1

9/21d1

5/2).

◦94Mo: Large peaks between about 1.5 and 3.0 MeV for π = + and π = – arise from states dominated by

the configurations π(0g2

9/2) ν(1d2

5/2) and π(1p−1

1/20g3

9/2) ν(1d2

5/2), respectively.

Where does the strength come from?



0 1 2 3 4 5 6Ji

0

0.05

0.1

0.15

0.2

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

0 1 2 3 4 5 6Ji

0

0.05

0.1

0.15

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

◦ Average B(M1) values vs. initial spin.

◦94Mo: Staggering of the values for π = +. Large B(M1) values for transitions from states with the mainconfiguration π(0g2

9/2) ν(1d2

5/2) and even spins.

The M1 strength comes from many small transi0ons Between states at 4-‐6MeV and I=0-‐6

Mechanism that generates radia0on


Shell-model calculations for 94Mo

Configurations that generate large M1 transition strengths(active orbits with jπ != 0 and jν != 0):

◦ π = +: π(0g2

9/2) ν(1d2

5/2)

π = –: π(1p−1

1/20g3

9/2) ν(1d2

5/2)

◦ π = +: π(0g2

9/2) ν(1d1

5/20g1

7/2)

π = –: π(1p−1

1/20g3

9/2) ν(1d1

5/20g1

7/2)

◦ π = +: π(0g2

9/2) ν(1d2

5/20g−1

9/20g1

7/2)

π = –: π(1p−1

1/20g3

9/2) ν(1d2

5/20g−1

9/20g1

7/2).

◦ π = +: ν(1d2

5/20g−1

9/20g1

7/2)

⇒ “Mixed-symmetry” and spin-flip configurations.

jπ

jν

jπ

jν

µν

µπ

µtrans

J

J −1

J

Large B(M1)

Large matrix elements between different states of one and the same configura0on that are related by mutual re-‐alignment of the spins of the ac0ve high-‐j orbitals. Without residual interac0on the states have the same energy -‐> no radia0on Residual interac0on mixes the states and generates the energy differences between them. Introduces randomness. -‐>LEMAR The radia0ng mixed states s0ll contain a substan0al components of the re-‐aligned mul0plet states

Sta0s0cal proper0es of the transi0ons

Constant temperature level density ρ(E) = ρ0 exp(E /T )v. Egidy, Bucurescu PHYSICAL REVIEW C 72, 044311 (2005)95 Mo ρ0 =10.3MeV −1, T = 0.87MeV

0 1000 2000 3000 4000 50000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

π =+ π =- sum

lnρ

E(keV)

T=0.66MeVρ0=3.3MeV-1

94Mo

0 1000 2000 3000 4000 50000.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

95Mo

lnρ

E(keV)

π =+ π =- sum

T=0.59MeVρ

0=5.4MeV−1

Transi0on from paired to unpaired state

8/27/14 3:38 PMRIPL-3 (Plot of Total Level Densities)

Page 1 of 1https://www-nds.iaea.org/cgi-bin/ripl_density_plot.pl?Z=42&A=94

Plot of Total Level DensitiesZ=42, A=94

Description

Levels: Cumulative Plot of Discrete Levels

Nmax : Last level of the complete level scheme

T=0.63 MeV

from RIPL3

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )


(/ = +, 14279 transitions)(/ = −, 14278 transitions)

J = 0i to 6i, i = 1 to 40

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )



J = 1/2i to 13/2i, i = 1 to 40

Dependence on γ − energy nearly exponential decreaseB(M1,Eγ ) ≈ B0 exp(−Eγ /TB )

TM = 0.32MeV TM = 0.48MeV

TM = 0.49MeV

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )



J = 0i to 6i, i = 1 to 40

0 2000Ea (keV)

10−3

10−2

10−1

100

B(M

1) (µ

N2 )



J = 1/2i to 13/2i, i = 1 to 40

Better described by

B(M1,Eγ ) = B0

exp(Eγ /T )−1T from level density "thermal temperature"

TM = 0.32MeV TM = 0.48MeV

TM = 0.49MeV

0.5 1.0 1.5 2.0 2.5 3.0

-4

-2

2

4

0.5 1.0 1.5 2.0 2.5 3.0

-4

-2

2

4

0.5 1.0 1.5 2.0 2.5 3.0

-6

-4

-2

2

4

T = 0.66MeV from level density

T = 0.59MeV from level density

T = 0.50MeV

Spectral distribu0on of the emission probability

P∝Eγ3B(M1,Eγ )

P(Eγ ) = P0Eγ

3

exp(Eγ /T )−1T from level density "thermal temperature"

Planck’s Law for black body radia0on Could be used as a thermometer.

Distribu0on of the reduced transi0on probabili0es Expecta0on: Porter-‐Thomas

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.5

1.0

1.5

2.0

y = B(M1)i / < B(M1)>

No way!

1 0.8 0.6 0.4 0.2

χ 2 (y,ν )

It is a power law distribution! P(x) = Axν , v =1.2

0.0 0.5 1.0 1.5 2.0

1

2

3

4

5

fat tail distribu0on

B(M1)i / < B(M1)>

10−2 10−1 100

B(M1)i / B(M1)

10−3

10−2

10−1

Ni /

N

94Mo, / = +

It is a power law distribution! P(x) = Axν , v =1.2

Power laws describe the distribu0on of fluctua0ons near a second order phase transi0on paired-‐>normal phase ? Magne0sm is sensi0ve to pair correla0ons

Predic0on of regions/relevance


Generation of large M1 strengths

B(M1) ∼ µ2⊥

Analogous “shears mechanism”

in magnetic rotation

Examples near A = 90: 82Rb, 84Rb

H. Schnare et al., PRL 82, 4408 (1999).

R.S. et al., PRC 66, 024310 (2002).

199Pb

Magne0c Rota0on

Appearance of magne0c rota0on

LEMAR in the same regions?

131Cd a key player in the r-‐process

Mo, Zr

(MeV)initialE0 1 2 3 4 5 6 7 8 9 10

) N^2µ

(M1)

(B

0

1

2

3

4

5

(MeV)γE0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

) N2µ

(M1)

(B

0

0.1

0.2

0.3

0.4

0.5

0.6negative parity state

positive parity state

Eγ (keV )Ei (keV )

B(M1)[µN2 ] B(M1)[µN

2 ]

Shell model with Z=50 and N=82 corevalence orbitals: proton holes 1p3/2, 0 f5/2, 1p1/2, 0g9/2 neutron particles 0h9/2, 1 f5/2, 2p3/2, 2p1/2

G-matrix derived from CD-Bonn NN interaction

Neutron separa0on energy

102

103

104

105N

A<m

v>

M1-talysM1-LEMAR

NS

10-2

10-1

100

101

102

0.01 0.1 1 10

NA<

mv>

T9 K

130Cd(n,g)

M1-talys/ NSM1-LEMAR/ NS

Factor 2.5 enhancement

Calculation by M. Mumpower

(n,gamma) rate enhanced by

r-‐process yields in a neutron star merger

Low Energy Electric Radia0on

E. Litvinova, N. Belov, PHYSICAL REVIEW C 88, 031302(R) (2013)

Large dipole moments Small distance

Thermal excita0on

T=0.9 MeV

T=0

1 MeV radia0on 3 0mes enhanced

0 1 2 3 4 5 6 7 8 9 101E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

f E1

[MeV

-1]

E [MeV]

T = 1 MeV T = 0.8 MeV T = 0.5 MeV T = 0.3 MeV T = 0

Neutron separa0on energy

131Cd T=1MeV

T es0mated according to V. Egidy, Bucurescu PRC 72(2005)044311

1 MeV radia0on 30 0mes enhanced

Sta0s0cal approach at 2 MeV excita0on energy???

T=0.6MeV

0 1 2 3 4 5 6 7 8 9 101E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

f E1

[MeV

-1]

E [MeV]

T = 1 MeV T = 0.8 MeV T = 0.5 MeV T = 0.3 MeV T = 0

Summary-‐ques0ons •  LEMAR accounts for experimental enhancement •  M1 radia0on generated by re-‐alignment of high-‐j orbitals

•  B(M1) dependence Eγ is black body •  Power law distribu0on of B(M1) (not Porter Thomas!)

•  Which nuclei show it, which not? •  Role of deforma0on: Shim of strength into scissors mode?

•  5-‐10 0mes enhanced r-‐process rates/abundances

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