Photon Strength Functions below GDR Maximum: Present Status and Outlook

CGS13, Cologne, August 25, 2008

Photon Strength Functions below GDR Maximum: Present Status and Outlook

An attempt to summarize experimental information about photon (-ray) strength functions at the low-energy tail of GDER with an emphasis on (possible) resonance structures

Milan Krtička


(γ,

x)

EγBn ≈15 MeV

Photonuclear x-section

Fragmentation of the GDER

γ a

bs =

(γ

, x)

+

(γ,γ

’)

Photoabsorption x-section

EγBn

Eγ

(γ,γ’)

≈10 eV

≈0.1 eV

Porter-Thomas fluctuations

(χ2ν=1 distribution)

<γ abs>

…an energy-smoothedphotoabsorption x-section


Photon Strength FunctionsDetailed balance principle

-d

ecay

ph

otoa

bso

rpti

on

exci

tati

on e

ner

gy

PSF describes energy distribution of photon emission from “highly-excited” states


Photon Strength Functions

What quantities can PSFs depend on:

– type of transitions (E1, M1, E2, …) – gamma-ray energy – microscopic properties of the level (energy,J) ? Brink hypothesis

Restrictions:• Energies below 10 MeV

• Low spins

• Medium-weight and heavy nuclei

• Near the valley of stability


Brink hypothesis

• The energy dependence of the photoeffect is independent of thedetailed structure of the initial state

dependence only on -ray but not on excitation energy (T), J,…

Validity of the hypothesis?• at least approximately - from (n,) reactions and hot nuclei• some signs for temperature dependence

01

n

Ex

n

10

Ex

fi(E) fi(E)

E

E

-Decay

Photoexcitation

f0(E) = f1(E) = fn(E) = f(E)


Where could we learn about PSFs from?

• photoexcitation techniques (,particle) NRF experiments – (,’)

• primaries from (n,) reaction• two-step cascades spectra - (n,)• spectrum fitting methods

single spectra coincidence spectra

• inelastic scattering of charged particles(e,e’), (p,p’), …

• sequential extraction (Oslo - 3He-induced)• Coulomb dissociation• …

Bn


Photonuclear experiments

• photoabsorption - above particle threshold (,particle)

• only GS PSF can be obtained• does not allow to distinguish

among different transition types dominance of E1 assumed

• Lorentzian shape of the resonance (classical ED, basic principles)

• photonuclear data on majority of nuclei (not all) confirms the shape above the neutron threshold

how is it below Bn?

From B.L. Berman, S.C. Fultz, Rev. Mod. Phys. 47 (1975) 713


PSFs below Bn

• Does an universal model of PSFs exist for all nuclei?• Is the E1 PSF of Lorentzian shape?• Is the decay dominated by E1 in the whole energy region?• Are the PSFs “smooth” or are there any resonance-like structures?


Spectra from 4 ballNeutroncapturingstatesE1

E2

E4 Ground state

E3

Bn+En

0

200

159Gd

Multiplicity 1 - 15

0

10Multiplicity = 1

0

20

Multiplicity = 2

0 3000 60000

50 Inte

nsity

(ar

b. u

nits

)

Inte

nsity

(ar

b. u

nits

)

Energy sum (keV)

Multiplicity = 3

0 3000 60000

50Multiplicity = 4

Energy sum (keV)

0 3000 60000

50Multiplicity > 4

Energy sum (keV)

0 3000 60000

200

Multiplicity > 4

Inte

nsity

(ar

b. u

nits

)

Energy (keV)

0 3000 60000

100

Energy (keV)

Multiplicity = 4

0

50Multiplicity = 3

0 3000 60000

10

Energy (keV)

Multiplicity = 2

0

10Multiplicity = 1

E1

E2E3

E4


Does a universal model exist?


PSFs below Bn

• Does an universal model of PSFs exist for all nuclei?• Is the E1 PSF of Lorentzian shape?• Is the decay dominated by E1 in the whole energy region?• Are the PSFs “smooth” or are there

any resonance-like structures?


PSFs below Bn

• Does an universal model of PSFs exist for all nuclei? NO

• Is the E1 PSF of Lorentzian shape?• Is the decay dominated by E1 in the whole energy region?• Are the PSFs “smooth” or are there

any resonance-like structures? There ARE structures


PSFs below Bn

• Does an universal model of PSFs exist for all nuclei? NO• Is the E1 PSF of Lorentzian shape?• Is the decay dominated by E1 in the whole energy region?• Are the PSFs “smooth” or are there



PSFs below Bn


• Is the E1 PSF of Lorentzian shape? NO

• Is the decay dominated by E1 in the whole energy region?

• Are the PSFs “smooth” or are there any resonance-like structures? There ARE structures


PSFs below Bn





• Pigmy (small) resonances in nuclei– Scissors mode in deformed nuclei– Low-energy mode in medium-weight (Fe, Mo) nuclei

– Resonances near Bn:

• Gold region

• Spherical N=82 nuclei


p n

n p

M1 - SCISSORS

E1 - GDR

M1 - SPIN-FLIP

np

np

n

p

E2

Scissors mode

• Experimentally observed in many reactions: (e,e’), (,’), (n,), (3He,)

• Majority of data from NRF:– Dynamitron, S-DALINAC, ELBE, HIS

– only GS excitations– in principle, allow to distinguish

among different XL (Compton polarimeter, HIS)

– problems with exp. threshold relation between exp. and actual strength?

– M1 strength is stronger than E1 near 3 MeV

H. Maser et al., PRC 53 (1995) 2749


Scissors mode - strength

0

2

B

(M1)

( N

2)

200180160140A

4

Redrawn from J. Enders et al., PRC 59 R1851 (1999)

Summing interval for B(M1): 2.5 - 4.0 MeV

Summing interval for B(M1): 2.7- 3.7 MeV

164Dy (NRF)

Summing interval for B(M1): 2.5 - 4.0 MeV - deduced from data in original paper of J. Margraf et al., PRC 52, 2429 (1995)

Odd or odd-oddEven-even

6

Phenomenological sum rule:Lo Iudice, Richter, Phys. Lett. B304 193 (1993)

p n

n p

M1 - SCISSORS

E1 - GDR

M1 - SPIN-FLIP

np

np

n

p

E2


TSC spectra

Neutroncapturing state

E1

E2

Fixed final level

Ground State

Intermediatelevels ofquasicontinuum

Low-energylevels

Bn

Ef

7400 7600 78000

5000 SE

P (

80 k

eV)

SE

P (

0 ke

V)

261

keV

, 4+

80 k

eV, 2

+

0 ke

V, 0

+

Cou

nts

Energy Sum (keV) E1+ E

HPGe detectors

target

beam of thermal neutrons

E1

E2

capture of thermal neutrons known initial Jđ

2000 4000 60000

200

T

SC

Inte

nsity

(ar

b. u

nits

)

Gamma-Ray Energy (keV)

0

30

E1E2


TSCs in the 162Dy(n,γ)163Dy reaction

SRs assumed to be built only on all levels

below 2.5 MeV


TSCs in the 162Dy(n,γ)163Dy reaction

Scissors resonances assumed to be built on

all 163Dy levels



0

2

B

(M1)

( N

2)

200180160140A

4




164Dy (NRF)


Odd or odd-oddEven-even

163Dy (TSC)Value from TSCs in 163Dy:total sum Σ B(M1)

Value from TSCs in 163Dy;

summing interval for B(M1): 2.5 - 4.0 MeV 163Dy (TSC)

6


p n

n p

M1 - SCISSORS

E1 - GDR

M1 - SPIN-FLIP

np

np

n

p

E2


Scissors from (3He,γ) and (3He,3He’γ)f (

E1)(E

γ) +

f (M1)(E

γ)

(MeV

)

Eγ (MeV) E. Melby et al., PRC 63 (2001) 044309

167Er (3He,γ)168Er 167Er (3He,3He’γ)167Er

SR ≈ 1.30 MeV SR ≈ 1.45 MeV


Scissors from (3He,γ) and (3He,3He’γ)f (

E1)(E

γ) +

f (M1)(E

γ)

(MeV

)

Eγ (MeV) E. Melby et al., PRC 63 (2001) 044309

167Er (3He,γ)168Er 167Er (3He,3He’γ)167Er

SR ≈ 1.30 MeV SR ≈ 1.45 MeV

Contradictions with the NRF and TSC data:

(1) the strength of the 3 MeV resonance is too small compared to the E1 strength at 3 MeV

(2) the resonance is wider by a factor of two or more


Scissors from (3He,γ) and (3He,3He’γ)

172Yb(3He,3He’γ)172Yb

Data taken from A. Schiller et al., Physics of Atomic Nuclei 62 (2001) 1186

It does not seem to be the case:

– the position of the 3 MeV peak is remarkably stable with changing the initial excitation


PSFs below Bn





• Pigmy (small) resonances in nuclei– Scissors mode in deformed nuclei

– Low-energy mode in medium-weight (Fe, Mo) nuclei


• Gold region

• Spherical N=82 nuclei


PSFs below Bn

• Does an universal model of PSFs exist for all nuclei? NO• Is the E1 PSF of Lorentzian shape? NO• Is the decay dominated by E1 in the whole energy region?

NO - at least in deformed nuclei• Are the PSFs “smooth” or are there



Exists, but problems (strength,

width) – Low-energy mode in medium-weight (Fe, Mo) nuclei


• Gold region• Spherical N=82 nuclei


PSFs below Bn






width) – Low-energy mode in medium-weight (Fe, Mo,…) nuclei




Fe, Mo, … – softpole

• Data from Oslo strong enhancement of PSF at low -ray energies


TSC data - 96Mo


TSC data - 96Mo

Pictures with comparison similar but correct statistical analysis excludes also this model at 99.8 % confidence levelKrticka et al., PRC 77 054319 (2008)

the enhancement is very weak if any analysis of data from DANCE confirm this


DANCE data (4BaF2 detector) - 96Mo

Exactly the same results were obtained from analysis of spectra with different multiplicities measured with the DANCE detectorSheets et al., submitted to PRC

Strong enhancement No enhancement

J = 2+ J = 2+


PSFs below Bn




• Pigmy (small) resonances in nuclei

– Scissors mode in deformed nuclei Exists, but problems (strength,

width)

– Low-energy mode in medium-weight (Fe, Mo,…) nuclei




PSFs below Bn






width) – Low-energy mode in medium-weight (Fe, Mo,…) nuclei

Weak – if any




PSFs below Bn






width) – Low-energy mode in medium-weight (Fe, Mo) nuclei

Weak – if any




Pygmy resonance in 198Au

Photonuclear data

Isolated neutron resonances

Fast n-capture, CTF

“Depressed”Lorentzian GDR

Lorentzian GDR

Redrawn from S. Joly, D. M. Drake and L. Nilsson, PRC 20 (1979) 2072

Is there, indeed, an E1 pygmy resonance at 5.5 MeV?

… or a mere deficiency and/or a redistribution of E1 photon strength?

197Au(n,)198Au reaction

Fast n-capture, BSFG

?

data obtained before 1980


Pygmy resonance in 198Au revisited

data from the Karlsruhe 4π BaF2 γ calorimeter

Pygmy resonance at 5.5 MeVNo pygmy resonance postulated Suppression of PSF below 5 MeV

… but postulating a pygmy resonance leads to too large total radiation widthNo difference in fits


Pygmy resonance in 198Au revisited


NRF in N = 82 nuclei

A.Zilges et al., Phys. Lett. B542 (2002) 43

Profile of beam



• Only G.S. strength• Relation actual vs.

observed strength very complicated – decays to excited levels expected

• Is the fragmentation of PSF valid here?

A.Zilges et al., Phys. Lett. B542 (2002) 43


NRF experiment

• relation actual GS vs. observed GS strength very complicated

• some estimates can be made from measurement with “monoenergetic beam” (HIS experiment)

see talk of A.P.Tonchev

G.S. (0+)

1- many weak (unobservable) transitions – corrections are needed



Is there really a resonance?


PSFs below Bn





Exists, but problems (strength, width) – Low-energy mode in medium-weight (Fe, Mo,…) nuclei

Weak – if any


• Gold region • Spherical N=82 nuclei


PSFs below Bn






Weak – if any


• Gold region Change in a shape of a PSF• Spherical N=82 nuclei


Summary



• Is the decay dominated by E1 in the whole energy region? NO - at least in deformed

nuclei




Weak – if any


• Gold region Change in a shape of a PSF• Spherical N=82 nuclei Further study required


Many thanks to

F. Becvar (Charles University Prague)

I. Tomandl, J. Honzatko (NPI Rez near Prague)

F. Kappeler, F. Voss, K. Wisshak, M. Heil, R. Reifarth,… (FzK Karlsruhe)

G.E. Mitchell (NCSU)

U. Agvaanluvsan (LLNL, Stanford)

M. Guttormsen, S. Siem, … (University of Oslo)

…


HIS

By courtesy of A.P. Tonchev

E1 M1

G.S. transitions in 138Ba

Transitions to 21+

Simulations within statistical model

I L L U S T R A T I O N

IGS/Iprim = 6(1) Eini = 8.4 MeV


P R E

L I

M I

N A R

Y

95Mo – comparison with simulations (2+)


P R E

L I

M I

N A R

Y

95Mo – comparison with simulations (2+)

BA



172Yb(3He,3He’γ)172Yb

Data taken from A. Schiller et al., Physics of Atomic Nuclei 62 (2001) 1186

It does not seem to be the case:

– the position of the 3 MeV peak is remarkably stable with changing the initial excitation


Eγ (MeV)

f (E

1)(E

γ) +

f (M1)(E

γ)

(MeV

)

Data taken from E. Melby et al., PRC 63 (2001) 044309

NRFNRF



Primaries from (n,) reaction

Two possibilities:1. measurement from a large number of isolated resonances

(absolute value of PSF can be deduced)2. average resonance capture (ARC) - simultaneous population of a

large number of resonances by the capture of n’s with energy spread over a relatively wide interval (only relative PSFs can be deduced)

f(E1)/f(M1) 5-7 for A > 100


Inelastic proton scattering

• Inelastic scattering experiment with protons with Ep 200 MeV at forward angles is sensitive to spin-flip M1 transitions

• experiments performed on rare-earth (deformed) nuclei


How is it with M1 strength @ 7 MeV?

• Problem with M1 strength data from (n,) and (p,p’)

for deformed rare-earth nuclei are not in a good agreement

a) shapeb) assuming the ratio E1/M1

from (n,) data and Lorentz shape of E1 PSF the strength from (p,p’) is 3x lower than those deduced from (n,)

f(E1)/f(M1) 5-7 for A > 100


Scissors mode - strengthC

ount

s pe

r 1

.2 k

eV

Gamma-ray energy (keV)

A. Nord et al., PRC 67, 034307 (2003)

Spectrum of γ-rays scattered off 163Dy

Even if all 163Dy transitions observed are M1 we get only B(M1) = 1.53 N2

94 lines from 163Dy

41 lines from 164Dy

background lines

-ray energies 2.3-3.3 MeV:

line spacing of 7 keV

Even if all 163Dy transitions observed are M1 we get only B(M1) = 1.53 N2

… while TSC 163Dy data yield total B(M1) = 6.2 N2

Probably a large number of

unresolved lines here ...

Limits of NRF?


KMF+BA

SRSF

EGLO

f(E

,T

=0

) (M

eV

-3)

SP

wrong PSF model in deformed nucleus

2(152Eug.s.) = 0.29


Pygmy resonance in 198Au revisiteddata from the Karlsruhe 4π BaF2 γ calorimeter

Enhancement of level density at Eexc ≈ 1.0 MeV by a factor of 8

… a not satisfactory explanation of the observed effects


Pygmy resonance in 198Au revisitedTSC data from Řež

No pygmy resonance postulated



Pygmy resonance at 5.9 MeV



Abrupt suppression of PSF below 5 MeV

The best fit obtained – it does not seem that there is a pygmy resonance in 198Au


Photonuclear experiments

• Classical ED: response of a point-like charge with damping to external electric dipole field is given by Lorentzian shape

• majority of photonuclear data confirms above neutron threshold• but there exist nuclei violating this shape - puzzle how is it below n threshold


Decay of excited states

• decay of low-lying levels (low density) is experimentally known (structure effects - calculations)

• decay of highly excited levels?• is it possible to predict it?

• Solution in medium-weight and hevavy nuclei:– use of statistical approach– description via photon strength

functions


D. Savran et al., PRL 95 (2005) 132501



0

2

B

(M1)

( N

2)

200180160140A

4



164Dy (NRF)


163Dy (TSC)Value from TSCs in 163Dy:total sum Σ B(M1)

Value from TSCs in 163Dy;

summing interval for B(M1): 2.5 - 4.0 MeV 163Dy (TSC)

6


Theory of E. Lipparini and S. Stringari, Phys. Rep. 175 (1989) 103


p n

n p

M1 - SCISSORS

E1 - GDR

M1 - SPIN-FLIP

np

np

n

p

E2

Photon Strength Functions below GDR Maximum: Present Status and Outlook

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