the concept of compound nuclear reaction: a+b c d+f the particle transmission coefficients t are...
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The concept of compound nuclear reaction:
a+B C d+F
')()'(~)'( * dEEETEd Fd
The particle transmission coefficients T are usually known from cross sections of inverse reactions (from optical model parameters).
Level densities andgamma-transmission coefficients are most uncertain values !!!
We use compound nuclear reactions to study nuclear structure. We study nuclear structure to calculate compound reaction cross sections.
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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)
How is nuclear level density estimated (current status) ?
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Test of the formulas proposed in the work for the LD at the neutron resonance energy. The dashed lines mark a difference by a factor of 2 between experimental and calculated values.
T.von Egidy, D.Bucurescu, Phys.Rev. C 72, 044311 (2005);
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Excitation energy
Leve
l den
sity
Bn
The Oslo method is based on the measurements of particle-gammacoincidences from ( 3He, αγ) and ( 3He, 3Heγ) reactions
E
ρ(E) = ρ’(E)·A·exp(BE)
A,B are uncertain
(M. Guttormsen et al)
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The level density from particle 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 the outgoing particles at backward angles3. Compare reactions with different targets and incoming species leading to the same final nuclei
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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 dominatesDrawback (for us): Negative Q-values of reactions that require higher energy beams not available from our tandem accelerator of Edwards Lab.
Our options:
d, 3He, 12C, 6Li, 7Li … beams available from our tandem acceleratorQ-reactions are positive (5-15 MeV).
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d, 3He
neutronsNE213
Flight path 8m
target
Swinger facility
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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
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Experimental level densities from (d,n) reactions measured at Edwards Lab.
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
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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
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A.Voinov et al, PRC 74, 014314 (2006)
55Mn(d,n)56Fe, Ed=7.5 MeV
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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
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Main results from (d,n) experiments:
1. Neutron spectra measured at backward angles are suitable for level density determination.
2. For many nuclei we got different level densities (shape and absolute numbers) compared to predictions from recent level density systematics based on neutron resonance spacings
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Reactions with deuterons and He-3
3He 58Fe59Cod+ +
61Ni
np
α
60Ni60Co
57Fe
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3He+ 58Fe
d+ 59Co
n p α
A.Voinov et al, PRC, accepted for publication
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We also measured reactions with 12C, 6Li and 7Li projectilesThe following reactions have been measured:
6Li+ 55Mn 61Ni (=d+ 59Co and 3He+ 58Fe)6,7Li+ 58,57Fe 64Cu 12C+ 27Al 39K
Main result: all of these reactions can be used for the measurementof level densities of residual nuclei.
The next steps: 1. Determining level density parameters from particle evaporation spectra for more nuclei to build new level density systematics which will be different from that based on neutron resonance spacing. Improve empirical formulas. 2. Investigate level density for nuclei off stability line. 24Mg+ 58Ni experiment is scheduled at Yale Lab. in ~ one month.
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Fig.6. Dependence of nuclear level density parameter “ã” from (N-Z) for Sb isotopes. o – present work, - [12]. Curve – calculation according a=A/exp[(N-Z)2] with = 0.154 and = 0.00064 [10].
B. Zhuravlev et al, Phys.Atomic Nuclei 69, 363 (2006);
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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
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Some results of Some results of γγ-strength functions for rare-earth nuclei-strength functions for rare-earth nucleiFrom Oslo Cyclotron Lab
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γγ-strength function of iron isotopes-strength function of iron isotopesLow energy upbend phenomenonLow energy upbend phenomenon
Eγ (MeV)
- 56Fe
- 57Fe
A.Voinov et al, Phys.Rev. Lett., 93, 142504 (2004).
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γ-strength function of molybdenum isotopes
M. Guttormsen et al, Phys. Rev. C, 71, 044307 (2005).
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Method of two-step γ – cascades fromneutron capture reactions
Ground state
Bn
E1
E2
E1 +
E2
History:
Proposed:A.M. Hoogenboom, NIM 3,57(1958)
Developed in Dubna(Russia): (A. Sukhovoj) (since ~1980); PhD thesis: A.Voinov (1994)F. Becvar (Prague) (since ~1992)A.Schiller, A.Voinov et al, Los Alamos, 2001A.Voinov, E. Algin et al Budapest, 2002
EγProblem: level density is needed !!!
Intensity
Intensity
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Measurement of gamma-strength function at Edwards Lab.
(p,2γ)(d,n) To the same product nucleus
1. We obtain a level density from neutron evaporation spectra.2. We obtain a γ-strength function from 2γ- spectra
Strategy
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: A.Voinov et al, PRC, accepted for publication
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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
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We have unique opportunity to study level densities and γ-strength function needed for the basic physics and applications. Edwards Lab. has unique facilities to do such kind of research.
Our strategy is based on combinations of different experimental techniques including particle evaporation spectra and (p,2g) measurements at Edwards Lab, measurements of level density and γ-strength function in collaboration with Oslo Cyclotron Lab.
We also plan to start studying level densities for nuclei off stability line (The first experiment is scheduled next month at Yale Lab. !!!)
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Collaborators :
OU: S.Grimes, A.Schiller, C.Brune, T. MasseyOslo University: M. Guttormsen, S.Siem et alLivermore Lab: U. Agvaanluvsan,
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Motivation
1. Curiosity. We think that what we can measure has not been measured before. This will bring new knowledge about nuclei. Edwards Lab. has unique facilities to do such kind of research.
2. The practical application. The new knowledge will allow us to calculate reaction cross sections more accurately. Astrophysics, reactor physics.