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Test of Level Density models from Nuclear Reactions. Babatunde M. Oginni Ohio University. Nuclear Seminar. December 3, 2009. Outline. Introduction - Methods of determining level densities - Some level density models - Motivations - Goals for our study

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test of level density models from nuclear reactions

Test of Level Density models from Nuclear Reactions

Babatunde M. Oginni

Ohio University

Nuclear Seminar

December 3, 2009

outline
Outline
  • Introduction
  • - Methods of determining level densities
  • - Some level density models
  • - Motivations
  • - Goals for our study
  • The Lithium induced reactions
  • - Edwards Accelerator Laboratory
  • - Level densities from evaporation of 64Cu
  • The A = 82 compound nuclear reactions
  • - Wright Nuclear Structure Laboratory
  • - Some results
  • Summary and Conclusion
introduction
Introduction
  • What is Nuclear Level Density (NLD) ?

E

E

methods of determining nld i
Methods of determining NLD (I)
  • Counting of levels

E

- Main drawbacks – level resolution & missing levels

  • Counting of neutron resonances
  • - Main drawback – narrow ranges of excitation energy,
  • spin and parity ratio
methods of determining nld ii
Methods of determining NLD (II)
  • Evaporation from compound nucleus – Hauser Feshbach Theory

=

with

methods of determining nld iii
Methods of determining NLD (III)
  • Evaporation from compound nucleus

- Level densities obtained for the residual nuclei

- Main drawback – contributions from other reaction mechanisms

  • Ericson fluctuation
  • - Level densities obtained for the compound nucleus
analysis idea
Analysis Idea

0

E

En~8 MeV

figure from http://inpp.ohiou.edu/~voinov/index.html

some models of nld i
Some models of NLD (I)
  • Fermi gas model (FG) [*]
  • 2 assumptions – nucleons are non-interacting fermions
  • -- single particle states are equidistant
  • in energy.

- Main challenge is to determine ‘a’ and ‘δ’ accurately for each nucleus

* H. A. Bethe, Phys. Rev. 50, 336 (1936)

some models of nld ii
Some models of NLD (II)
  • Many ideas have been suggested for a:

Al-Quraishi [**]

ROHR [*]

a = 0.071*A + V

V = 1.64 A ≤ 38

V = 3.74 38 < A ≤ 69

V = 6.78 69 < A ≤ 94

V = 8.65 94 < A < 170

a = 0.108*A + 2.4 A ≥ 170

α = 0.1062, β = 0.00051

α = 0.1068, γ = 0.0389

* G. Rohr, Z Phys. A – Atoms and Nuclei 318, 299 – 308 (1984);

** S.I. Al-Quraishi et al, Phys. Rev. C63, 065803(2001).

some models of nld iii
Some models of NLD (III)
  • Constant temperature model (CT) [*]
  • Gilbert Cameron Model [**]
  • - combine CT and FG models.
  • Hartree-Fock-BCS model
  • - microscopic statistical model

* A. Gilbert et al, Can. J. Phys. 43, 1248 (1965); ** A. Gilbert et al, Can. J. Phys. 43, 1446 (1965)

motivations
Motivations
  • Astrophysical applications
  • - evaluating reliable reaction rates for the production of nuclei
  • Production cross sections of radioactive isotopes
  • - help answer some salient questions; FRIB
  • Fission Product Yields [*]
  • Medical Applications

* P. Fong, Phys. Rev. 89, 332 (1953); P. Fong, Phys. Rev. 102, 434 (1956)

goals for study
Goals for study
  • Better understanding of the NLD problem
  • Two main projects were undertaken:
  • (1.) 6Li + 58Fe  64Cu; 7Li + 57Fe  64Cu
  • * Edwards Accelerator Laboratory, Ohio University,
  • Athens, Ohio
  • (2.) 18O + 64Ni  82Kr; 24Mg + 58Fe  82Sr; 24Mg + 58Ni  82Zr
  • * Wright Nuclear Structure Laboratory, Yale University,
  • New Haven, Connecticut
slide14

Experimental Facilities (II)

Si

Si

Si

Si

Si

Target

beam

2m flight path

Si

Si

Si

Si

Si

64 cu compound nucleus
64Cu compound nucleus

+

6Li

58Fe

p

+

63Ni

64Cu

α

+

60Co

+

57Fe

7Li

experiments particle id
Experiments: particle ID

6Li – induced rxn: 23.5, 37.7, 68.0, 98.0, 142.5 and 157.5 angles

7Li – induced rxn: 37.7, 142.5 and 157.5 angles

  • Si detectors were used to detect the charged particles:
  • TOF and Energy information.
  • helions and tritons
  • cannot be differentiated
  • from each other!
experiments calibration
Experiments: calibration

Charged Particle Energy Calibration

-elastic scattering of 6Li on Gold

-elastic scattering of 7Li on Gold

-elastic scattering of d on Gold

-alpha source of 3 known peaks

  • Energy = mean (channel #) + offset
experiments optical parameters i
Experiments: Optical Parameters (I)
  • The transmission coefficients of the entrance and exit channels and the level
  • densities of the residual nuclei are input parameters in the Hauser-Feshbach
  • codes that were used in our calculations.
  • Most of the optical parameters for the exit channels are well documented in
  • the literature [*].
  • For the entrance channels, we made use of our elastic scattering distribution.
  • The optical parameters for our experiments are given in the table:
  • The Coulomb radius parameter used was 1.41 fm

* National Nuclear Data Center

experiment optical parameters ii
Experiment: Optical Parameters (II)
  • We compared our data with results of calculations using the optical
  • parameters that were obtained:
results proton angular distribution
Results: Proton angular distribution
  • Angular distribution of compound nuclear reaction is expected
  • to be symmetric about 90 degree.
results break up study i
Results: Break Up Study (I)

6Li  α + d (Q = -1.47MeV)α + n + p (Q = -3.70MeV) 5He + p (Q = -4.59MeV)

7Li  α + t (Q = -2.47MeV)α + d + n (Q = -8.72MeV)5He + d (Q = -9.61MeV)6He + p (Q = -9.98MeV)α + 2n + p (Q = -10.95MeV)5He + n + p (Q = -11.84MeV)

  • Is the break up a 1-step process or a 2-step process ?

6Li 6Li*  … 7Li 7Li*  …

results break up study ii
Results: Break up study (II)
  • Direct break up of 6Li is into alpha and deuteron [1-4] while 7Li breaks
  • up into alpha-triton and alpha-deuteron-neutron components [4-6]
  • Sequential break up of 6Li* and 7Li* require looking up level schemes
  • The dominant contribution to break up
  • reaction among the excited levels of 6Li
  • is the 3+ level at 2.18 MeV [3, 4,7]

Table from TUNL website

(1.) J. M. Hansteen et al. Phys. Rev. 137, B524 (1965); (2.) K. Nakamura, Phys. Rev. 152, 955 (1966);

(3.) E. Speth et al, Phy. Rev. Lett. 24, 1493 (1970); (4.) K. O. Pfeiffer et al. Nucl. Phys. A 206, 545 (1973);

(5.) D. K. Srivastava et al. Phys. Lett. B, 206, 391 (1988); (6.) V. Valkori et al. Nucl. Phys. A 98, 241 (1967);

(7.) A. Pakou et al. Phys. Lett. B, 633, 691 (2006).

results break up study iii
Results: Break up Study (III)
  • The low energy levels of 7Li are given in the table below:

Table from TUNL website

  • The threshold of emitting proton in sequential break up of 7Li is about 10 MeV; most of
  • the break up will be through the α-t and α-d-n components
results break up study iv
Results: Break up study (IV)
  • In order to better understand our break up process, we use the
  • method Goshal [*] showed about compound reactions
  • We look at this ratio:

A represent proton cross sections

B could be alpha, deuteron or triton cross sections

* S. N. Ghoshal, Phys. Rev. 80, 939 (1950)

results break up study v
Results: Break up study (V)
  • We safely conclude that the protons and high energy alphas at
  • backward angles are mostly from compound nuclear reactions.
  • Thus we can get NLD information from protons and high energy alphas
results
Results
  • Using this equation:

we obtain the level density information of 63Ni and 60Co

conclusion ii

6Li + 58Fe

p + 63Ni

64Cu

α + 60Co

7Li + 57Fe

6Li + 55Mn

p + 60Co

61Ni

d + 59Co

n + 60Ni

CONCLUSION (II)
  • B. M. Oginni et al., Phys. Rev. C
  • 80, 034305 (2009).

CT with T = 1.4 MeV.

  • A. V. Voinov, B. M. Oginni, et al.,
  • Phys. Rev. C 79, 031301 (R) (2009).
calibration of the clover detectors
Calibration of the clover detectors
  • We did two types of calibrations:
  • energy and the efficiency calibrations
  • The idea of the calibration is to
  • move from the “known”to the “unknown”
  • - So we made use of 152Eu source with known activity
152 eu
152Eu
  • Within the energy range that was considered during the
  • experiment, the source has fifteen prominent peaks with
  • known emission probabilities
slide40

Artist View of the set up

correct for Doppler

detector

beam

experimental idea i
Experimental Idea (I)
  • For even-even nuclei, most gamma rays
  • pass through the 2+ to 0+ levels.
  • Production cross section of the 2+ gamma
  • is proportional to the production cross
  • sections of the nucleus [*].
  • Since we know the even-even nuclei that
  • are expected from each reaction, we use
  • the gamma level schemes to determine the
  • gamma energies associated with each
  • residual nucleus.

* R. P. Koopman, PhD Thesis, Lawrence Livermore Laboratory

experimental idea ii
Experimental Idea (II)
  • Not all the 2+ gammas were used in the analysis
  • RULES FOR SELECTION
  • There must be a noticeable gamma peak at the
  • energy corresponding to the 2+ gamma
  • Since most of the gammas were produced in
  • coincidence! We place a gate on each 2+ gamma
  • peak and check for other gammas detected in
  • coincidence; the gammas used in the analysis
  • had at least one gamma decayed in coincidence.
24 mg 58 fe
24Mg + 58Fe

Al - Quraishi

summary
Summary
  • I talked about the different methods of determining LDs
  • I presented some LD models
  • I presented the level densities that we obtained for 63Ni
  • and 60Co
  • I also presented some results from our A = 82 nuclear
  • compound reactions
  • A better constraint will be achieved in the Yale experiment
  • if both the evaporated particles and gammas are detected
  • in coincidence
list of collaborators
List of Collaborators
  • S. M. Grimes, C. R. Brune, T. N. Massey, A. Schiller, A. V. Voinov
  • - Ohio University, Athens, OH
  • A. S. Adekola
      • Triangle University Nuclear Laboratory, NC
  • Z. Heinen
  • - Savannah River Site, Aiken, SC
  • D. Carter, D. Jacobs, J. O’Donnell
  • - Ohio University, Athens, OH
  • Andreas Heinz (Yale University)
    • - Yale University, New Haven, CT
state level density
State & Level density
  • Each level of spin J comprises 2J+1 degenerate states with
  • different projections of J

where

= state density

= level density

 cumulative number of levels

nuclear processes in stars and stellar explosions
Nuclear Processes in stars and stellar explosions

s-process

(AGB)

Pb (82)

protons

Proton-rich

(SNII)

r-process

(SNII)

Sn (50)

rp process

Novae, SNIa

X-ray bursts

Fe (26)

Heavy-element burning

(Massive stars)

CNO Breakout

C(6)

neutrons

H(1)

Big Bang

W. Tan

slide62
NLD

NLD from neutron resonances: Levels are excited by the absorption of

neutrons with zero angular momentum, the number of resonances

in the energy interval is

 for target nuclei

 for J = 0 target nuclei

F = qvB = (mv^2)/R

 R = mv/qB  Radius of curvature in a magnetic field

slide63
NLD
  • Rapid increase in # of levels at high energy is expected from simple
  • thermodynamics considerations, from probability arguments and
  • from nuclear model calculations
  • For the thermodynamics consideration

= entropy

= state density

slide66

Fermi-gas level-density expressions

1) Single-particle model, no many-body effects

2) Used in most statistical-model calculations.

errors
Errors
  • Two main error types we took into consideration: statistical & systematic
  • Statistical error is the square root of the number of counts
  • Systematic are mainly uncertainties in target thickness (15%), beam charge
  • integration (5%) and solid angles (5%)
  • We obtained our overall error by propagating the errors
gc model
GC model
  • The 3 model parameters, T, Ux, and E0, are determined by the requirement that
  • the level density and its derivative are continuous at the matching point, Ux.

{Sum over all Energies and spins}

experiment
Experiment

58Ni  0.525 mg/cm2

59Co  0.89 mg/cm2

* ?? Picture of targets and Si detector

calibration cont d
Calibration (cont’d)
  • Since we know what the energy associated with each
  • peak is, we look at the spectra from each leaf detector
  • To obtain the counts expected, we need to know the
  • activity of the source at a certain time, the half-life of the
  • source and the emission probabilities for each peak
ad