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Nuclear Level Density

Nuclear Level Density. What we know, what we do not know, and what we want to know Experimental techniques to study level densities, what has been done until now What kind of experiments we need to develop in the future. How is nuclear level density estimated ?.

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Nuclear Level Density

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  1. Nuclear Level Density • What we know, what we do not know, and what we want to know • Experimental techniques to study level densities, what has been done until now • What kind of experiments we need to develop in the future

  2. How is nuclear level density estimated ? Traditionally, for most of the nuclei, the level density is estimated on the basis of experimental information from low-lying discrete levels and neutron resonance spacing Level density is known for most of the stable nuclei Level density is unknown for most of the nuclei Level density Bn E Excitation energy

  3. Nuclear level density models Fermi-gas model : comes from consideration of noninteracting fermi-particles moving in a common potential Constant temperature model : does not have a theoretical justification for nuclei (only for classical ideal gas) Microscopical models : calculations based on different representation of nuclear potentials plus collective effects

  4. Additional problems: • spin cutoff parameter at neutron binding energy is not known • ratio of levels with negative and positive parities is not known • possible deviations of the shape of real level density from model functions assumed for interpolation might lead to extra uncertainties of total level densities We need to develop some experimental techniques capable to measure the precise energy dependence of TOTAL level densities in the whole excitation region

  5. The level density from particle evaporation spectra of compound nuclear reactions The concept: • The problem : • Make sure that the compound reaction mechanism dominates. • Possible solutions: • Select appropriate reactions (beam species, energies, targets). • Measure angular distributions to study reaction mechanism • Compare reactions with different targets and incoming species • leading to the same final nuclei

  6. Compound nulceus + (Hauser-Feshbach theory) Maxwell–Boltzmann distribution (Wikipedia)

  7. Early works on level densities from evaporation spectra: H. Vonach (Vienna, Austria): S.Grimes (OU): B.Zhuravlev (Obninsk, Russia): (n,p); (n,a); (a,n) (p,n) Beam energies: up to 15 MeV Advantage: The compound nuclear mechanism dominates. Drawback: Negative Q-values of reactions that require higher energy beams if we want to measure level density at higher excitation energies. Pre-equilibrium processes become important ! Other options: d, 3He, 12C, 6Li, 7Li … beams Q-reactions are positive (for some of them), less beam energy is needed Smaller E/A which decreases pre-equilibrium contributions.

  8. Particle evaporation measurements at Edwards Lab of Ohio University Compound nucleus formation 59Co 3He 58Fe d + + 11 MeV 7.5 MeV 6Li 55Mn + 61Ni Compound nucleus 15 MeV α n p 60Ni 57Fe 60Co Make sure that features of spectra of outgoing particles are determined by internal nuclear properties of a compound nucleus !!!

  9. Swinger facility at Edwards Lab. Ohio University d, 3He neutrons NE213 target Flight path 8m

  10. Si Scheme of experimental set-up for charge-particle spectra measurements Edward’s Accelerator Lab, Ohio University Si Si Si Si Target beam 2m flight path Si Si Si Si Si

  11. Experimental level densities from (d,n) reactions measured at Edwards Lab. of Ohio University Testing the level density with 27Al(d,n)28Si Level density, 1/MeV Excitation energy, MeV

  12. Points are from our experiment, red line the the Fermi-gas model with parameters found from the fit to discrete levels and neutron resonance spacing, black line is the Fermi-gas model fit to experimental points

  13. Simulation with Empire reaction code 60Ni+n 6Li+55Mn 60Co+p

  14. Level density off stability line S.I. Al-Quraishi, S.Grimes et al, Phys.Rev.C63, 065803 Possible theoretical explanation could be that the level density is lower off stability line because levels which have too wide width should not be counted in compound nuclear reactions because no equilibration can take place.

  15. What is next ? • Study evaporation spectra from ion induced reactions. • Advantages: • Lower E/A compared to nucleon induced reaction (n,p,a) that makes the compound nuclear mechanism dominant. • Larger energy interval for outgoing particles allowing us to study level density in a larger excitation energy range ( at least up to 20-25 MeV). • Possibility to study nuclei off stability line (proton rich nuclei). GARFIELD is the new generation state of the art spectrometer to study nuclear level density and physics of compound nuclear reactions

  16. D.R. Chakrabarty et al Nuclear Physics A 712 (2002) 23–36

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