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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



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).


A 82 project
A = 82 Project





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


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.


How to decide if the will be used
How to decide if the γ will be used

78Kr




24 mg on 58 ni
24Mg on 58Ni


24 mg 58 ni
24Mg + 58Ni


24 mg on 58 fe
24Mg on 58Fe


24 mg on 58 fe1
24Mg on 58Fe


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



  • k





    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


    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


    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



    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


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