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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



Test of level density models from nuclear reactions

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


Test of level density models from nuclear reactions

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



  • Test of level density models from nuclear reactions

    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


    Test of level density models from nuclear reactions
    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


    Test of level density models from nuclear reactions
    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



    Test of level density models from nuclear reactions

    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