Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon Strength...

Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007

Photon Strength Functions of Heavy Photon Strength Functions of Heavy Nuclei:Nuclei:

Achievements and Open ProblemsAchievements and Open Problems

František Bečvář


The major part of the reported results were achieved thanks to hard work of my colleagues

Michael Heil

Jaroslav Honzátko

Franz Kaeppeler

Milan Krtička

Rene Reifarth

Ivo Tomandl

Fritz Voss

Klaus Wisshak

– FZK Karlsruhe

– NPI Řež

– FZK Karlsruhe

– CU Prague

– LANL Los Alamos

– NPI Řež

– FZK Karlsruhe

– FZK Karlsruhe


Outline

The relation between the photon strength functions (PSFs) and the photoabsorption cross section. Fragmentation of photon strength. Brink hypothesis

Models for E1 and M1 PSFs

Comparison between the high-energy (n,) data and the photonuclear data

DICEBOX algorithm as a tool for testing the validity of models for PSFs at intermediate -ray energies

Two-step cascades: the essentials of the method and the survey of the results obtained

Evidence for scissors resonances of excited nuclei

Supporting results from Karlsruhe -calorimetric measurements

Comparison with the data from (,’), (3He,3He’,) and (3He,) reactions

Conclusions


Cornerstones of the extreme statistical model of decay

• A notion of strength function (fragmentation of strength of simple nuclear states)

• Porter-Thomas fluctuations of partial radiation widths

• Brink hypothesis

• The principle of the detailed balance

… and rather problematic absence of width correlation


(γ,

x)

γ a

bs =

(γ

, x)

+

(γ,γ

’)<γ abs>…an energy-smoothedphotoabsorption x-section

Eγ

Eγ

Eγ

Bn

Bn

(γ,γ’)

≈10 eV

≈15 MeV

≈0.1 eV

Photonuclear x-section

Photoabsorption x-section

Fragmentation of the GDER and the paradigm of the photon strength function

Fluctuations



(γ,

x)

γ a

bs =

(γ

, x)

+

(γ,γ

’)<γ abs>

Eγ

Eγ

Eγ

Bn

Bn

(γ,γ’)

≈10 eV

≈15 MeV

≈0.1 eV


n

γ

n n

γ“equivalent to”

The principle of the detailed balance:

ii

g.s.g.s.




(γ,

x)

γ a

bs =

(γ

, x)

+

(γ,γ

’)<γ abs>

Eγ

Eγ

Eγ

Bn

Bn

(γ,γ’)

≈10 eV

≈15 MeV

≈0.1 eV


n

γ

n n



ii

g.s.g.s.

<iγg.s.> = f (E1)(Eγ) Eγ3/(Ei)

f (E1)(Eγ) = <γ abs(Eγ)>/(3 π2 h2 c2 Eγ)

If E1 transitions dominate

Photoabsorption x-sectionGDR

— Photon strength function


(γ,

x)

γ a

bs =

(γ

, x)

+

(γ,γ

’)<γ abs>

Eγ

Eγ

Eγ

Bn

Bn

(γ,γ’)

≈10 eV

≈15 MeV

≈0.1 eV


n

γ

n n



ii

g.s.g.s.


<iγg.s(XL)

.> = f (XL)(Eγ) Eγ2L+1/(Ei)

In a general case


f (XL)(Eγ) = <γ abs(XL)(Eγ)>/[(2L+1)π2 h2 c2 Eγ]

<γ abs (Eγ)> = XL <γ abs(XL)(Eγ)>

The paradigm of PSF: f(XL) and ρ are primordial, not derived quantities


Photoexcitation pattern does not depend on initial excitation energy of a target nucleus

g.s.

Qua

sico

ntin

uum

NRF experiments

Brink hypothesis

Fictitious photoexcitation experiments


n

γ

n n

γ=

ii

ff

<iγf(XL)

.> = f (XL)(Eγ) Eγ2L+1/(Ei)



Brink hypothesis: generalization “g.s.” “f”

n

γ

n n

γ=

ii

g.s.g.s.

<iγg.s(XL)

.> = f (XL)(Eγ) Eγ2L+1/(Ei)



A target in photonuclear/photoabsorption experiment is in the ground state

Identical !

Photoexcitation pattern of an excited target nucleus

g.s.

Qua

sico

ntin

uum

Brink hypothesis

Fictitious (γ,γ‘) and (γ,x) experiments

NRF experiments


γ a

bs

Eγ

Bn

(γ,x)

(γ,γ')

(γ,γ') – NRF, g.s. only

(n,γ) – two-step & n-step cascades (thermal and keV neutrons)(3He,3He’γ), (3He,αγ)

Singles γ-ray spectra from (n,γ), total radiation widths γ tot

(p,p’γ) at small angles of scattering

Photon strength functions: problems

(γ,x) – g.s. only

The Brink hypothesis and the paradigm of the photonstrength function: do they hold?

Is the E1 part of <γ abs(Eγ)> for energies near and below neutron threshold an extrapolation of a Lorentzian GDR?

Does the energy dependence of <γ abs(Eγ)> displayadditional, statistically significant resonance-likestructures in the region near or below the neutronthreshold?

To which extent the other multipolarities (M1, E2, …)contribute to photoabsorption cross section <γ abs(Eγ)> ?

The main obstacles in studying PSFs: - strong Porter-Thomas fluctuations of iγf

- limited knowledge of other quantities

(n,γ) at isolated neutron resonances, ARC


First evidence for validity of Brink hypothesis

Data of L. M. Bollinger and G. E. Thomas, PRL 25 (1967) 1143

195Pt(n,)196Pt at filtered neutron beam

Transitions to 0+ and 2+ levels

= 4.90.5


L. M. Bollinger and G. E. Thomas, Phys. Rev. Lett. 18 (1967) 1143:

“There is no adequate, theoretically based explanation of the E5 dependence of

the experimental widths, although an idea introduced by Brink and developed by Axel may be relevant.”

<f > E5

… the birth of the extreme statistical model for decay of nuclear levels implications for complete spectroscopy of low-lying levels (ARC method)

First evidence for validity of Brink hypothesis

For Lorentzian E1 GDR with a constant damping width for a typical heavy nucleus:

at


Further evidence …

ARC data from 147Sm(n,)148Sm reaction

... convincing?

D. Buss and R. K. Smither, PRC 2 (1970) 1513


2. Model of Kadmenskij, Markushev and Furman:The damping width due to strongly

interacting quasiparticles

Kadmenskij, Matkushev, Furman (1982)

… energy and temperature dependence

1. Axel-Brink model:

Models used for E1 PSF

An approximation for low -ray energies

Not justified for deformed nuclei

At T>0 it gives a non-zero limit for E→0

Diverges for E→ EG

Landau-Migdal parameters


Models used for E1 PSF

3. Model GLO:

R. E. Chrien, Dubna Report No. D3, 4, 17-86-747 (1987)

4. Semi-empirical model EGLO:

Divergence for E→ EG removed

J. Kopecky, M. Uhl and R. E. Chrien, PRC 47 (1993) 312, adjustable parameters

A good description for spherical, transitional and deformed nuclei achieved at energies E > 6 MeV


Model of Mughabghab and Dunforda generalization of KMF model for description of PSFs of deformed nuclei

The damping width due to strongly interacting quasiparticles

Kadmenskij, Matkushev, Furman (1982)

The condition imposed on the modified width

Problems:

The spreading width due to the interaction between dipole and

quadrupole vibrations

J. Le Tourneux, Mat. Fys. Medd. Dan. Selsk. 34 (1965) 1

Summing the damping and spreading widths not fully legitimate

For a typical deformed nucleus with β2>0.27, EG (low)

≈ 12 MeV and ΓG(low)

<3.2 MeV the damping width becomes negative

S. F. Mughabghab and C. L. Dunford, PLB 487 (2000) 155

… the model is not applicable to well deformed nuclei


Models for M1 PSF

1. The single-particle model A constant PSF

2. The spin-flip model Analogous to AB model for E1 PSF Parameters deduced from the (p,p’) data

3. The scissors-resonance temperature-independent model Photon strength assumed not to depend on nuclear temperature

F. Becvar et al., PRC52 (1995) 1278


Comparison between photonuclear and (n,) data


Single-Lorentzian fit Double-Lorentzian fit



Behavior of photonuclear data for nuclei with N ≈ 50

No (n,) data


Comparison between photonuclear and (n,) data main conclusions

PSFs of spherical and transitional nuclei in -ray energy region of 6-8 MeV are appreciably lower compared to predictions of the Axel-Brink model

For spherical and transitional nuclei near A = 100 the photonuclear data also indicate a deficit of PSF with respect to predictions of the Axel-Brink model

The KMF model for E1 PSF agrees with experimental data only in case of nuclei near A=100


Simulation of cascades by means of DICEBOX algorithm

Assumptions:

For nuclear levels below certain “critical energy” spin, parity and decay properties are known from experiments

Energies, spins and parities of the remaining levels are assumed to be a discretization of an a priori known level-density formula – a random discretization with the Wigner-type long-range level-spacing correlations

f (XL)(Eγ) Eγ2L+1/(Ei),

A partial radiation width if (XL), characterizing a decay of a level i to

a level f, is a random realization of a chi-square-distributed quantity the expectation value of which is equal to

where the PSFs f(XL) and the density ρ are also a priori known

Selection rules governing the decay are fully observed

Any pair of partial radiation widths if (XL) is statistically uncorrelated

Depopulating intensities are given by Iif = [Σ XLf Γ if (XL)] /[ Σ X΄L΄f ΄ if ΄

(X΄L΄)]


A straightforward approach to simulating cascades 1-

3 ×

106

lev

els

A complete decay scheme is known for at most

100 levels, i.e. for a 10– 2 % fraction

Probability of reaching a level after n-th step of a cascade:

,

where level energies .

“Distant past of cascading is irrelevant given knowleldge of the recent past”

… Markovian process

Necessity to generate the rest part of the decay scheme

Problem: the need to generate an enormous number of depopulating intensities Iff’ = P(f ’| f), up to 1013 ! ~

Specificity: in line with the basic assumptions the branching intensities Iif = P(f | i) are realizations

pertinent to the corresponding random variables

~


A notion of a nuclear realization

≡A set of realizations {Ifi} for all possible i,f and

a set of realizations {Ef , Jf , πf} for all levels f A nuclear realization

Of these NRs only one of characterizes the behavior of a given nucleus

Simulations of cascades based on the use of various NRs lead to mutually different predictions of the cascade-related quantities

Simulations of cascades based on the use of various NRs lead to mutually different predictions of the cascade-related quantities

To assess uncertainties of these predictions simulations of cascades are to performed for a large number of NRs

An infinite number of NRs exist for a given level-density ρ and a set of photon strength functions f (XL)


- Generate a level system (excitation energies, spins and parities); take experimentally known levels and add the levels from discretization according a chosen level-density formula

0

Bn

Getting a “nuclear realization”


0

Bn

- Ascribe at random a precursors (a random generator seed) to each level of the system



- Ascribe at random a precursors (a random generator seed) to each level of the system



- Start with the neutron capturing level- Pick up its precursor

γ-cascading


- Using this precursor generate if

- Deduce I’s

γ-cascading ...


- Generate a random number from the uniform distribution in (0,1)

γ-cascading ...


- Get the energy of the depopulating transition

γ-cascading ...


- Determine the first intermediate level- Pick up its precursor

γ-cascading ...


- Using this precursor generate if for the intermediate level- Deduce I’s

γ-cascading ...


- Generate another random number from (0,1)

γ-cascading ...


- Get the energy of the next depopulating transition

γ-cascading ...


- Determine the next intermediate level- Pick up its precursor

γ-cascading ...



γ-cascading ...


- Generate another random number from (0,1)

γ-cascading ...



γ-cascading ...


- Determine the next intermediate level

- Pick up its precursor

γ-cascading ...



γ-cascading ...


- Generate a random number from (0,1)

γ-cascading ...



- This transition reaches the ground state – the cascade ends

γ-cascading ...


The outcome of γ-cascading

- The number of steps of a given cascade is known

- The procedure described is reiterated many times. Typically a set of 100 000 cascades are obtained for a given nuclear realization

-The whole this process in repeated for an enough large number of other nuclear realizations

- Various cascade-related quantities can be deduced and their residual Porter-Thomas r.m.s. uncertainties estimated

- So also the energies of the individual transitions and the intermediate levels involved


The method of two-step γ-cascades following the thermal neutron capture

Geometry:

Data acquisition: - Energy E1

- Energy E2

- Detection-time difference

Three-parametric, list-mode


Spectrum of energy sums

Bn-Ef

Essentials of accumulating the TSC spectra

E1

Det

ectio

n-tim

e di

ffere

nce

Tim

e re

spon

se fu

nctio

n

Energy sum Eγ1+ Eγ2

List-mode data

i=-1 i=0 i=+1

j=-1

j=0

j=+1

Accumulation of the TSC spectrum from, say, detector #1:

The contents of the bin, belonging to the energy E1, is incremented by

q = ij

where ij is given by the position and the size

of the corresponding window in the 2D space “detection time”×“energy sum E1+E 2”.


2000 4000 60000

200

T

SC

Inte

nsity

(arb

. uni

ts)

Gamma-Ray Energy (keV)

0

30

2000 4000 60000

200

TS

C I

nte

nsi

ty (

arb

. u

nits

)

Gamma-Ray Energy (keV)

0

30

X 5

TSC spectrum - taken from only one of the detectors

Spectrum of energy sums

Bn-Ef

Essentials of accumulating the TSC spectra

E1

Det

ectio

n-tim

e di

ffere

nce

Tim

e re

spon

se fu

nctio

n

Energy sum Eγ1+ Eγ2

List-mode data

i=-1 i=0 i=+1

j=-1

j=0

j=+1


TSCs in the 167Er(n,γ)168Er reaction

The spectrum of -ray energy sums


The 167Er(n,γ)168Er reaction

TSCs terminating at the Jπ = 4+, 264 keV level in 168Er


DICEBOX Simulations

Řež experimental data

πf = +

πf = -

Entire absence of scissors resonances

is assumed



Scissors resonances assumed to be built on

all 168Er levels

DICEBOX Simulations


πf = +

πf = -




… still a small fraction of the overall TSC strengths

2200 2400 2600 2800

Energy of intermediate levels (keV)

2200 2400 2600 2800

Energy of intermediate levels (keV)

Ground-state band

-vibrational band

Non-statistical effects


TSCs in the 155Gd(n,γ)156Gd reaction

DICEBOX Simulations


πf = +

πf = -


is assumed



DICEBOX Simulations


πf = +

πf = -


all 156Gd levels



Origin of the two hump structure

0 Bn - Ef

resonanting

resonanting



TSCs terminating at the Jπ = 4+, 261 keV level in 158Gd

x 20


DICEBOX Simulations


πf = +

πf = -


is assumed




DICEBOX Simulations


πf = +

πf = -


all 158Gd levels


Eγ1+Eγ2 = 2 ESR

Sharpening the peak at the midpointof the TSC spectrum due to simultaneously resonating

primary and secondary transitions

TSCs in the 162Dy(n,γ)163Dy reaction

A unique possibility of a sensitive test for presence of SRs built on the levels in the quasicontinuum

M. Krticka et. al, PRL 92 (2004) 172501

Probability

Probability

Eγ1

Eγ2

3/2-

6271 keV ½+

163DyG.s. 5/2-

251 keV 5/2+

162Dy

n

SR

SR

Specifity of TSCs terminating at 251 keV level


Entire absence of SRs is assumed



A “pygmy E1 resonance” with energy of 3 MeV

assumed to be built on all levels



SRs assumed to be built only on all levels

below 2.5 MeV




all 163Dy levels

Sharpening the 3 MeV peak well reproduced


plus

a quantitative agreement between the predicted and

simulated TSC spectra


Data:

E1 M1 150Sm Gd isotopes 163Dy Er isotopes

Models for photon strength function used v.s. experimental data

Models:

E1 BA EGLO KMF

M1 SR+SF(KMF+BA) – agrees better with the NRF data on E1/M1 ratio @ 3 MeV

Photon strength functions plotted refer to the transitions from the neutron capturing level

f(E

,T

f) (M

eV-3)


SRs built on all163Dy levels …only on levels with Ef <2.5 MeV

n-step cascades following the capture of keV neutrons in162Dy

En = 90-100 keV


163Dy: optimum models for photon strength functions

Photon strength functions plotted refer to the transitions to the ground state of 163Dy

KMF+BA

SRSF

EGLO

f(E

,T

=0)

(M

eV-3) The role of E1 transitions

to or from the ground state is reduced


0

2

B

(M1)

( N

2)

200180160140A

4

6

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

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

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

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)

Scissors-mode strength B(M1):

A considerable loss due to a finite summing energy interval

The data from TSCs in odd 163Dy agree well with the NRF data at least for even-even 164Dy …

Comparison between the TSC and NRF dataI. NRF data for 29 even-even nuclei

Value from TSCs in 163Dy;

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

163Dy (TSC)

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

163Dy (TSC)

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


Cou

nts

per

1.2

keV

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

Comparison between the TSC and NRF dataII. NRF data for 163Dy

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?


0

2

B

(M1)

( N

2)

180160140A

4

6

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

164Dy (NRF)

NRF data: summary of the results on the ssissors-mode

163Dy (TSC)Theory

Odd or odd-odd

A significantly higher summed reduced M1 strengths than that seen from NRF

The reputation of SR in odd nuclei seems saved

Even-even

SR’s damping width determined

Richter’s sum rule

– does not it underestimate the size of SRs ?

Consequences for the constraint on parameters of the still not discovered high-lying SR, predicted by R. Hilton (1980)

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


Eγ (MeV)

f (E

1)(E

γ) +

f (M1)(E

γ)

(MeV

-3)

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

A 3 MeV resonance seen from ( 3He,) reactions in deformed nuclei

- a “pygmy resonance” of an unknown multipolarity or the SR resonance?

NRFNRF(3He,)

(3He,)

SR’s seen are very broad A-dependence of SR energy differs differs from that observed from NRF data

- dependence of SR energy on energy of the level on which the SR resides?


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

The 3 MeV resonance-like structure in the 172Yb(3He,3He’γ)172Yb data

It does not seem to be the case:

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

Dependence of SR energy on energy of the level on which the SR resides?


Remarkable agreement

Blind validation testing of the Oslo method

Postulating a set of PSFs

Extraction of first-generation spectra

Simulation of cascades

Construction of -ray spectra corresponding

to various initial excitations

Getting a PSF

The Oslo method itself should not widen the observed SR’s

Postulated PSFExtracted by the Oslo method

RESULTS

with a SR


A comparison between the ( 3He,) and NRF data on M1 strength of 166Er and 168Er

Reaction -ray energy interval f (M1)(E) dE / f (E1)(E) dE

168Er(,΄) 168Er 2.5-4.0 MeV 1.84a)

167Er(3He,α)166Er 2.5-4.0 MeV 0.34a) Data from linear -ray polarization measurements at Stuttgart (a sets of 46 M1 transitions and 30 E1 transitions)

Effects of a temperature- or Eexc- dependent

E1 photon strength function?


Photon strength functions of 148Sm


Photon strength functions of 148Sm

A region where crucial information on PSF is missing


Photon strength functions of 96Mo


Gamma-Ray Energy (MeV)

0 5 10 15 20

PS

F (

Me

V-3

)

1e-9

1e-8

1e-7

1e-6

96Mo(,x)

92Mo(n,)93Mo

(p-wave resonances)

96Mo(3He,

3He' )96

Mo97Mo(

3He,)96

Mo

Brink-Axel

TSC data

Photon strength functions of 96Mo

Strong correlation f – n(1)


J

J

n

f

Jn

Jf

J nR

1

)0(λλγ ),(

121

R-correlation in the 173Yb(n,)174Yb reaction at isolated resonances

R-correlation: coefficient of correlation between partial radiatiation widths and reduced neutron widths averaged over final levels and resoance spins :

… statistically significant

Primary transitions from resonances to the low-lying 174Yb two-quasipartice levels

F. Becvar et al., Yadernaya fizika 46 (1987) 392


9 resonances with J = 2-

63 partial widths

14 resonances with J = 3-

140 partial widths

R-correlation in the 173Yb(n,)174Yb reaction at isolated resonances

f

JfJ qQ

λλ

and

Intercept of Q : less than 1

Are correlated parts of f

decoupled from the GDR?

)(σπhc)(3

λγ

λγ

λabs2

2λ EDE

qJ

JfJ

f

Introduce

-


SUMMARY

A strong evidence for scissors-like vibrations of excited deformed nuclei

Methods of TSCs and the n-step cascades (following the capture of keV neutrons) proved to be efficient tools for studying PSFs at intermediate -ray energies of 2 – 4 MeV

A deficit of photon strength in spherical and transitional nuclei at -ray energies of 6-8 MeV

Very large values of the reduced B(M1) strength found; a deeper revision of the NRF data would be welcome

The scissors M1 mode per se displays, indeed, resonance-like behavior


Thank you

Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon Strength...

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Transcript of Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon Strength...