test of level density models from nuclear reactions
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/1.jpg)
Test of Level Density models from Nuclear Reactions
Babatunde M. OginniOhio University
Nuclear Seminar December 3, 2009
![Page 2: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/2.jpg)
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
![Page 3: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/3.jpg)
Introduction• What is Nuclear Level Density (NLD) ?
E
E
![Page 4: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/4.jpg)
Methods of determining NLD (I)
• Counting of levels
- Main drawbacks – level resolution & missing levels
• Counting of neutron resonances
- Main drawback – narrow ranges of excitation energy, spin and parity ratio
E
![Page 5: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/5.jpg)
Methods of determining NLD (II)
=
with
• Evaporation from compound nucleus – Hauser Feshbach Theory
![Page 6: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/6.jpg)
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
![Page 7: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/7.jpg)
Analysis Idea
0 En~8 MeV E
figure from http://inpp.ohiou.edu/~voinov/index.html
![Page 8: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/8.jpg)
Some models of NLD (I)
• Fermi gas model (FG) [*] 2 assumptions – nucleons are non-interacting fermions
-- single particle states are equidistantin energy.
* H. A. Bethe, Phys. Rev. 50, 336 (1936)
- Main challenge is to determine ‘a’ and ‘δ’ accurately for each nucleus
![Page 9: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/9.jpg)
Some models of NLD (II)
9
• Many ideas have been suggested for a:
ROHR [*] Al-Quraishi [**]
** S.I. Al-Quraishi et al, Phys. Rev. C63, 065803(2001).
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
* G. Rohr, Z Phys. A – Atoms and Nuclei 318, 299 – 308 (1984);
α = 0.1062, β = 0.00051
α = 0.1068, γ = 0.0389
![Page 10: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/10.jpg)
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)
![Page 11: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/11.jpg)
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)
![Page 12: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/12.jpg)
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
![Page 13: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/13.jpg)
Experimental Facilities (I): Edwards Accelerator Facility
![Page 14: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/14.jpg)
beamTarget
Si
Si
Si
SiSi
Si Si
Si
Si
Si
2m flight path
14
Experimental Facilities (II)
![Page 15: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/15.jpg)
64Cu compound nucleus
6Li 58Fe
7Li 57Fe
64Cu
63Ni
60Co
p
α
+
+ +
+
![Page 16: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/16.jpg)
Experiments: particle ID
• Si detectors were used to detect the charged particles: TOF and Energy information.
•helions and tritons cannot be differentiated from each other!
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
![Page 17: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/17.jpg)
Experiments: calibration
17
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
![Page 18: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/18.jpg)
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:
* National Nuclear Data Center
• The Coulomb radius parameter used was 1.41 fm
![Page 19: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/19.jpg)
Experiment: Optical Parameters (II)
• We compared our data with results of calculations using the optical parameters that were obtained:
![Page 20: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/20.jpg)
Results: Proton angular distribution
• Angular distribution of compound nuclear reaction is expected to be symmetric about 90 degree.
![Page 21: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/21.jpg)
Results: particle energy distribution (I)
![Page 22: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/22.jpg)
Results: particle energy distribution (II)
![Page 23: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/23.jpg)
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* …
![Page 24: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/24.jpg)
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
(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).
•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
![Page 25: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/25.jpg)
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
![Page 26: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/26.jpg)
Results: Break up study (IV)• In order to better understand our break up process, we use the method Goshal [*] showed about compound reactions
* S. N. Ghoshal, Phys. Rev. 80, 939 (1950)
A represent proton cross sections B could be alpha, deuteron or triton cross sections
• We look at this ratio:
![Page 27: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/27.jpg)
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
![Page 28: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/28.jpg)
Results• Using this equation:
we obtain the level density information of 63Ni and 60Co
![Page 29: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/29.jpg)
Results: NLD (I)
![Page 30: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/30.jpg)
Results: Particle energy distribution (III) -- GC
![Page 31: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/31.jpg)
Results: NLD (II)
![Page 32: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/32.jpg)
Conclusion (I)
![Page 33: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/33.jpg)
CONCLUSION (II)
6Li + 58Fe
7Li + 57Fe
p + 63Ni
6Li + 55Mn
d + 59Co n + 60Ni
p + 60Co
64Cu
61Ni
α + 60Co
CT with T = 1.4 MeV.
• A. V. Voinov, B. M. Oginni, et al., Phys. Rev. C 79, 031301 (R) (2009).
• B. M. Oginni et al., Phys. Rev. C 80, 034305 (2009).
![Page 34: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/34.jpg)
A = 82 Project
![Page 35: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/35.jpg)
Layout of the WNSL tandem accelerator
![Page 36: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/36.jpg)
Experimental Facilities (III): WNSL
![Page 37: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/37.jpg)
Experimental Facilities (IV)
![Page 38: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/38.jpg)
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
![Page 39: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/39.jpg)
152Eu• Within the energy range that was considered during the experiment, the source has fifteen prominent peaks with known emission probabilities
![Page 40: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/40.jpg)
Artist View of the set up
beam
detectorcorrect for Doppler
![Page 41: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/41.jpg)
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
![Page 42: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/42.jpg)
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.
![Page 43: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/43.jpg)
How to decide if the γ will be used
78Kr
![Page 44: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/44.jpg)
How decision on the γs are made
![Page 45: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/45.jpg)
Summary of data obtained
![Page 46: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/46.jpg)
24Mg on 58Ni
![Page 47: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/47.jpg)
24Mg + 58Ni
![Page 48: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/48.jpg)
24Mg on 58Fe
![Page 49: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/49.jpg)
24Mg on 58Fe
![Page 50: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/50.jpg)
24Mg + 58Fe
Al - Quraishi
![Page 51: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/51.jpg)
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
![Page 52: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/52.jpg)
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
![Page 53: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/53.jpg)
Thanks for your attention!
![Page 54: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/54.jpg)
![Page 55: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/55.jpg)
k
![Page 56: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/56.jpg)
Emitted particle energy spectra
![Page 57: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/57.jpg)
Taking a peep away from stability!
Al - Quraishi
![Page 58: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/58.jpg)
Summary of Results!
![Page 59: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/59.jpg)
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
![Page 60: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/60.jpg)
Optical Model
![Page 61: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/61.jpg)
61
Nuclear Processes in stars and stellar explosions
neutrons
protons
rp processrp process
r-process(SNII)
r-process(SNII)
s-process (AGB)
s-process (AGB)
Heavy-element burning(Massive stars)
Heavy-element burning(Massive stars)
Big BangBig BangH(1)
Fe (26)
Sn (50)
Pb (82)
Proton-rich(SNII)
Proton-rich(SNII)
C(6)
CNO Breakout
Novae, SNIaX-ray bursts
W. Tan
![Page 62: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/62.jpg)
NLDNLD 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 magneticfield
![Page 63: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/63.jpg)
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
![Page 64: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/64.jpg)
Energy calibration of the leaf detectors
![Page 65: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/65.jpg)
![Page 66: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/66.jpg)
mAgga
JEEUU
aUa
IJJE
Ea
aEE
ppnn
rotFG
FG
)()(6
parameter density -level
)( ,2exp
12212),(
2exp
12)(
2
*2
2/32*
4/5*4/1
**
Fermi-gas level-density expressions
1) Single-particle model, no many-body effects
2) Used in most statistical-model calculations.
![Page 67: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/67.jpg)
Origin of the “clover”
![Page 68: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/68.jpg)
![Page 69: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/69.jpg)
Efficiency
![Page 70: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/70.jpg)
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
![Page 71: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/71.jpg)
Error Propagation
![Page 72: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/72.jpg)
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}
![Page 73: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/73.jpg)
Experiment
* ?? Picture of targets and Si detector
58Ni 0.525 mg/cm2
59Co 0.89 mg/cm2
![Page 74: Test of Level Density models from Nuclear Reactions](https://reader035.vdocuments.us/reader035/viewer/2022062520/5681592a550346895dc65209/html5/thumbnails/74.jpg)
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