Level Densities, Decay Probabilities and Cross sections in the Actinide Region

J.N. Wilson, EFNUDAT workshop, CERN, August 2010

Level Densities, Decay Probabilities and Cross sections in the Actinide Region

J.N. WilsonInstitut de Physique Nucléaire, Orsay


1. Fundamental physics – NLD and GSF fine structure, statistical properties of the hot compound nucleus

2. Indirect cross section measurements via surrogate reactions

3. Level density knowledge helps cross section calculations where direct measurements are difficult or impossible

NLD Measurements in the Actinides: Goals & Motivations


Spectroscopy oflow lying states

Resonance spacingsat the neutron binding energy

1. Fundamental Physics

Oslo method

Extrapolation


2. Indirect Measurements


S. Boyer et al. Nucl.Phys. A775, 175 (2006)

2. 233Pa Capture Experiment Results


3. x-section calculations


Part I

First Experimental Data


Oslo Cyclotron Experiments

Si Ring Cactus NaI array


The Silicon Ring

• High efficiency/high angular resolution detection of the outgoing particles (<2°)

• E/ΔE collimators not necessary


2. The Thorium Cycle

235U233U 234U232U

232Pa

231Th 233Th232Th230Th

231Pa

a

233Pa

a

234Pa

236U

(n, g) (n, 2n)

(n, g) (n, 2n)

(n, 2n) (n, g) (n, g) (n, g)

(n, g)

b-b-

b- b- b-

FISSION FISSION


232Th(d,x) @ 12 MeV 232Th(3He,x) @ 24 MeV

351 M events 135 M events

Experiment 232Th: 01/12/09 – 13/12/09

Reaction Compound Nucleus

Ex-Eg counts

3He,p 234Pa 13 M

3He,d 233Pa 6.0 M

3He,t 232Pa 0.57 M

3He,a 231Th 0.79 M

Reaction Compound Nucleus

Ex-Eg counts

d,p 233Th 23 M

d,d’ 232Th 0.24 M

d,t 231Th 1.2 M



Ring 0

16O (d,d’)

12C (d,d’)

12C(d,p) 13C

16O(d,p) 17O ex1

12C(d,p)13C ex1

12C(d,p)13C ex2



Part II

Extracting the Level Density


The Brink Axel hypothesis

)()(),( gg ETEEEP fi

Assuming dominance of dipoleradiation (E1 and M1)

Level density TransmissionCoefficient

Gamma strength function



2.15 MeV ???

3.1 MeV

3.9 MeV3.6 MeV

0.87 MeV



MCNP simulations of Cactus detector response




Cactus Response Matrix


Matrix *response;Spec *after=before->SubtractComptons(response);


233Th* - After Compton Subtraction


233Th* -Primary gamma rays


Part III

The surrogate method


ε = k EγSuppose detector has this property:

d

d kEEEREW ggg ),()(

Then effeciency of detecting a cascade becomes proportional to cascade energy and independent of cascade path!!

Decay probability measurementEfficiency of detecting a cascade, Ec of m gammas is:

)1(1..1

mj

jc

mj

jc..1

If ε is small, then:


« With four parameters, I could fit an elephant, with five I could make him wiggle his trunk »

W(E) = a + bE + cE2 + d E3 + eE4 + f E5

d

d kEEEREW 0),()( ggg

Minimisation with the Downhill simplex method


Weighting Function Matrix



17O




Primary gamma rays

n,gamma spectral extrapolation below n,n’threshold

(New Technique)

n,n' correctionto measureddecay probability


Results


Compare results with TALYS calculations: Since 232Th(n,g) has been measured directly at nTOF we can perform a direct test of the optical model and the validity of the surrogate method.

TALYScalculations


Level density measurements possible in:

233Th - d,p (0- 5 MeV)232 Th - d,d’ (0- 3.5 MeV)231Th - d,t (0 – 3 MeV)

Surrogate reaction & decay probability measurements possible in:

233Th* - d,p230Ac* - d,a234Pa* - 3He,p232Pa* - 3He,t231Th - 3He,4He

Conclusions


• Fission detectors

• 233U, 231Pa, 234U targets

The Future


IPN OrsayJ.N. WilsonB. Leniau

Oslo CyclotronS. SiemS. RoseA. BürgerM. GuttormsenA-C. LarsenT. WiborgH. Toft

CEA SaclayF. GunsingA. Georgen

ThankyouTakkMerci

Lawrence Livermoore LabM. WeidekingL. Bernstein


147Sm

146Sm


Hauser-Feshbach Formalism

Differential cross section depends on transmission coefficients, Γ and level densities of the residual nuclei, ρ

a + A B + b


Level Densities Theory and Experiment

- Level density changes due to collectivity, deformation etc.- Large effects can occur over a small number of nucleons

J.N. Wilson, EFNUDAT workshop, CERN, August 2010 44

(n, g)

Nuclei where direct measurements are difficult

239Pu

245Cm

241Am 242Am

242Pu

243Am

238U

240Pu 241Pu

246Cm 247Cm242Cm 243Cm 244Cm

244Am

243Pu

239Np

239Ub-

236U 237U

(n, 2n)

(m)

238Np237Np

238Pu

a

234U 235U233U

233Pa

232U

231Th 233Th232Th230Th

231Pa

229Th

a

a

a

a

Target activity > 109 Bq/mg

69 y

88 y

163 d

26 h 22 m

6.8 d5.0 h

26 h


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Level Densities, Decay Probabilities and Cross sections in the Actinide Region

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