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Ohio University: A.V. Voinov, S.M. Grimes, C.R.Brune, T. Massey, B.M. Oginni, A.Schiller,
Oslo University: M. Guttormsen, A.C. Larsen, S.Siem, N.U.H. Syed
Experimental study of level density and gamma-strength functions at Edwards Laboratory, Ohio University
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
4/54/1 )( 212
)(2exp()(
Ea
EaE
E
a, δ -parameters
σ = f(a, δ)
Nuclear level density
The level density from particle spectra of compound nuclear reactions
The concept:
dET
EETEEd
iiout
finC
*)()'()(~)(
The problem :
Make sure that the compound reaction mechanism dominates.
Possible solutions:
1. Select appropriate reactions (beam species, energies, targets).2. Measure the outgoing particles at backward angles3. Compare reactions with different targets and incoming species leading to the same final nuclei
Reactions with deuterons and He-3
3He 58Fe59Cod+ +
61Ni
np
α
60Ni60Co
57Fe
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
d, 3He
neutronsNE213
Flight path 8m
target
Swinger facilityat Edwards Lab. Ohio University
Experimental level densities measured at Edwards Lab. of Ohio University
Testing the technique 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
Leve
l den
sity
, 1/
MeV
55Mn(d,n)56Fe, Ed=7.5 MeV
0 2 4 6 8 10 12 14100
101
102
103
104
Leve
l den
sity
(M
eV -1
)
Excitation energy (MeV)
56Fe
Points are from our experiment, line – Fermi-gas model with parameters fromsystematics T.von Egidy, D.Bucurescu, Phys.Rev. C 72, 044311 (2005);
Points are from our experiment, red line is 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
65Cu(d,n)66Zn, Ed=7.5 MeV
0 2 4 6 8 10 12 14
100
101
102
103
104
105
Leve
l den
sity
, 1/M
eV
Excitation energy, MeV
Level density of 66Zn
56Ni, 60Ni, 60Cu, 60Co, 56Fe, 57Fe, 60Zn, 64Zn, 66Zn
0 2 4 6 8 10 12 14 16 18 20
101
102
103
104
105
106
107
108
Constant temperature model Fermi-gas (Bethe) model = HF-BCS Discrete levels
data points from 59Co(d,p)
Leve
l densi
ty (
MeV
-1 )
Excitation energy (MeV)
Level density of 60Co
Fermi-gas or constant temperature ?
6Li 55Mn59Cod+ +
61Ni
np
α
60Ni60Co
57Fe
Eex=33 MeV Eex=23 MeV
15 MeV 7.5 MeV
0 2 4 6 8 10 1210-1
100
101
102
0 2 4 6 8 10 12
0 2 4 6 8 10 1210-1
100
101
102
Cro
ss s
ectio
n (m
b/M
eV)
CT FG
Empire calculations
Proton energy (MeV)
protons from 6Li+55Mn
Proton energy (MeV)
Data pointsprotons from d+59Co
Main conclusions from experimental results :
1. The functional form of the level density especially at low excitation energies is more complicated than Fermi-gas simple model.
2. The constant temperature model seems to be valid for excitation energies far beyond the particle separation energy (at least for some nuclei)
0
E
E
DE
EEf
i
)( ~
)( )( abs
3
0 5 10 15 20
1E-4
1E-3
0.01
0.1
γγ – strength function in continuum – strength function in continuum
i
Exc
itat
ion
en
erg
yE
xcit
atio
n e
ner
gy
)( Ef
γ- Energy (MeV)
From (γ,n) reactions
Par
ticle
sep
arat
ion
thr
esho
ld
γγ-strength function of iron isotopes-strength function of iron isotopesLow energy upbend phenomenonLow energy upbend phenomenon
Eγ (MeV)
- 56Fe
- 57Fe
Phys.Rev.Lett. 93, 142504 (2004)
Method of two-step γ – cascades fromneutron capture reactions
Ground state
Bn
E1
E2
E1 +
E2
EγProblem: level density is needed !!!
Intensity
Intensity
Measurement of gamma-strength function at Edwards Lab. Of Ohio University
(p,2γ)(d,n) Produce the same product nucleus
1. We obtain a level density from neutron evaporation spectra.2. We obtain a γ-strength function from 2γ- spectra
Idea
The first candidate is 59Co(p,2γ) 60Ni reaction at Ep=1.9 MeV
The level density of 60Ni has already been measuredfrom 59Co(d,n) 60Ni reaction:
First results from 59Co(p,2γ)
9000 10000 11000 120000
100
200
300
400
Real peaks
E1+E2, keV
E2
2+
Single escape peaks
Cou
nts
60N
i
p+59
Co
--> 60
Ni+
0
1.33
MeV
p+59Co, 13 hours of measurements
E1
0 2 4 6 8 10 1210-10
10-9
10-8
10-7
10-6
0 2 4 6 8 10 1210-10
10-9
10-8
10-7
10-6
0 2 4 6 8 1010-10
10-9
10-8
10-7
10-6
fM1
fE1
fE1
+fM1
0 2 4 6 8 10
100
101
Casc
ade in
tensi
ty, perc
ents
/deca
y/M
eV
Gamma energy (MeV)
0 2 4 6 8 10 1210-10
10-9
10-8
10-7
10-6
0 2 4 6 8 10 1210-10
10-9
10-8
10-7
10-6
0 2 4 6 8 1010-10
10-9
10-8
10-7
10-6
fM1
fM1 f
E1
fE1
fE1
+fM1
fE1
+fM1
0 2 4 6 8 10
100
101
Casc
ade in
tensi
ty, perc
ents
/deca
y/M
eV
Gamma energy (MeV)
cascade spectrum
Conclusions
Level density:
• The total level density exhibit step structures new region of discrete levels. The interpolation between the density of discrete levels and neutron resonance spacing with simple models do not provide a good accuracy.
• The constant temperature model of level density is valid above the particle separation threshold, at least for some nuclei.
Gamma strength function
Gamma strength function can be studied with combination of (p,2g) and (d,n) reactions. The low energy enhancement is supported by results of these experiments for the 60Ni.
