nuclear level density 1.what we know, what we do not know, and what we want to know 2.experimental...
TRANSCRIPT
Nuclear Level Density
1. What we know, what we do not know, and what we want to know
2. Experimental techniques to study level densities, what has been done until now
3. What kind of experiments we need to develop in the future
Excitation energy
Leve
l den
sity
Bn
Level density is knownfor most of the stable nuclei
Level density is unknown formost of the nuclei
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
E
How is nuclear level density estimated ?
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
Additional problems:
1. spin cutoff parameter at neutron binding energy is not known2. ratio of levels with negative and positive parities is not known3. 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
The level density from particle evaporation spectra of compound nuclear reactions
The concept:
dET
EETEEd
idi
fdC
)()'()(~)(
*
The problem :
Make sure that the compound reaction mechanism dominates.
Possible solutions:
1. Select appropriate reactions (beam species, energies, targets).2. Measure angular distributions to study reaction mechanism 3. Compare reactions with different targets and incoming species leading to the same final nuclei
Compoundnulceus
+
dEEEETEd exf )()(~)(
(Wikipedia)Maxwell–Boltzmann distribution
(Hauser-Feshbach theory)
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)
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 higherexcitation 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.
Beam energies: up to 15 MeV
Particle evaporation measurements at Edwards Lab of Ohio University
3He 58Fe59Cod+ +
61Ni
np
α
60Ni60Co
57Fe
Compound nucleus
Make sure that features of spectra of outgoing particles are determined by internal nuclear properties of a compound nucleus !!!
Compound nucleus formation
6Li 55Mn+
11 MeV
15 MeV
7.5 MeV
d, 3He
neutronsNE213
Flight path 8m
target
Swinger facilityat Edwards Lab. Ohio University
beamTarget
Si
Si
Si
SiSi
SiSi
Si
Si
Si
2m flight path
Scheme of experimental set-up for charge-particle spectra measurementsEdward’s Accelerator Lab, Ohio University
Experimental level densities from (d,n) reactions measured at Edwards Lab. of Ohio University
Testing the level density with 27Al(d,n)28Si
0 2 4 6 8 10 12 14 16
10-2
10-1
100
101
102
Experiment, from 27Al(d,n)28Si reaction From counting of discrete levels
Leve
l densi
ty, 1
/MeV
Excitation energy, MeV
Level density of 28Si
Excitation energy, MeV
Level densi
ty,
1/M
eV
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
0 5 10 15 20 2510-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
experiment Fermi-gas Constant Temperature
Cro
ss s
ect
ion, m
b/M
eV
Proton energy, MeV
6Li+55Mn ---> 60Co+p
0 5 10 15 20 2510-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
0 5 10 15 20 2510-7
103
0 5 10 15 20101
102
103
104
105
106
107
108
109
Cro
ss s
ect
ion, m
b/M
eV
Neutron energy, MeV
Proton energy, MeV
0 5 10 15 20100
101
102
103
104
105
106
107
108
109
Leve
l densi
ty, M
eV
-1
Exciation energy, MeV
60Co60Co
Simulation with Empire reaction code
6Li+55Mn60Ni+n
60Co+p
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.
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
D.R. Chakrabarty et alNuclear Physics A 712 (2002) 23–36