Test of Level Density models from Nuclear Reactions

Babatunde M. OginniOhio University

Nuclear Seminar December 3, 2009

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• What is Nuclear Level Density (NLD) ?

E

E

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

Methods of determining NLD (II)

=

with

• Evaporation from compound nucleus – Hauser Feshbach Theory

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

0 En~8 MeV E

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

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

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

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• 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

• 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 (I): Edwards Accelerator Facility

beamTarget

Si

Si

Si

SiSi

Si Si

Si

Si

Si

2m flight path

14

Experimental Facilities (II)

64Cu compound nucleus

6Li 58Fe

7Li 57Fe

64Cu

63Ni

60Co

p

α

+

+ +

+

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

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

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

Experiment: Optical Parameters (II)

• We compared our data with results of calculations using the optical parameters that were obtained:

Results: Proton angular distribution

• Angular distribution of compound nuclear reaction is expected to be symmetric about 90 degree.

Results: particle energy distribution (I)

Results: particle energy distribution (II)

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)• 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

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)• 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:

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• Using this equation:

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

Results: NLD (I)

Results: Particle energy distribution (III) -- GC

Results: NLD (II)

Conclusion (I)

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).

A = 82 Project

Layout of the WNSL tandem accelerator

Experimental Facilities (III): WNSL

Experimental Facilities (IV)

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

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

beam

detectorcorrect for Doppler

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)

• 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 γ will be used

78Kr

How decision on the γs are made

Summary of data obtained

24Mg on 58Ni

24Mg + 58Ni

24Mg on 58Fe

24Mg on 58Fe

24Mg + 58Fe

Al - Quraishi

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• 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

Thanks for your attention!

k

Emitted particle energy spectra

Taking a peep away from stability!

Al - Quraishi

Summary of Results!

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

Optical Model

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

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

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

Energy calibration of the leaf detectors

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.

Origin of the “clover”

Efficiency

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

Error Propagation

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

* ?? Picture of targets and Si detector

58Ni 0.525 mg/cm2

59Co 0.89 mg/cm2

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