Transcript Slide 1

We use compound nuclear reactions to study nuclear structure.
We study nuclear structure to calculate compound reaction cross
sections.
The concept of compound nuclear
reaction:
a+B  C  d+F
d ( E' ) ~ Td (E' )F (E* )dE'
The particle transmission coefficients T are usually known from cross
sections of inverse reactions (from optical model parameters).
Level densities and
gamma-transmission coefficients
are most uncertain values !!!
How is nuclear level density estimated (current status) ?
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
 (E) 
exp( 2 a( E   )
12 2 a1/ 4 ( E   )5 / 4
a, δ -parameters
σ = f(a, δ)
Bn
Excitation energy
E
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);
The Oslo method is based on the measurements of particle-gamma
coincidences from ( 3He, αγ) and ( 3He, 3Heγ) reactions
(M. Guttormsen et al)
ρ(E) = ρ’(E)·A·exp(BE)
Level density
A,B are uncertain
Bn
Excitation energy
E
The level density from particle spectra of compound
nuclear reactions
The concept:
d ( E ) ~  C ( E )
Td ( E ' )  f ( E * )
T
dE
di
i
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 angles
3. Compare reactions with different targets and incoming species
leading to the same final nuclei
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 (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 accelerator
Q-reactions are positive (5-15 MeV).
Swinger facility
d, 3He
target
neutrons
Flight path 8m
NE213
Si
Scheme of experimental set-up for
charge-particle spectra measurements
Edward’s Accelerator Lab,
Ohio University
Si
Si
Si
Si
Target
beam
Si
Si
Si
Si
Si
Experimental level densities from (d,n) reactions
measured at Edwards Lab.
Testing the level density with
Level density of
28
27Al(d,n)28Si
Si
Experiment, from 27Al(d,n)28Si reaction
From counting of discrete levels
2
10
Level density, 1/MeV
1
10
0
10
-1
10
-2
10
0
2
4
6
8
10
Excitation energy, MeV
12
14
16
55Mn(d,n)56Fe,
Ed=7.5 MeV
56Fe
4
Level density (MeV
-1
)
10
3
10
2
10
1
10
0
10
0
2
4
6
8
10
Excitation energy (MeV)
12
14
55Mn(d,n)56Fe,
Ed=7.5 MeV
A.Voinov et al,
PRC 74, 014314 (2006)
65Cu(d,n)66Zn,
Ed=7.5 MeV
Level density of
66
4
8
Zn
5
10
4
Level density, 1/MeV
10
3
10
2
10
1
10
0
10
0
2
6
Excitation energy, MeV
10
12
14
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
Reactions with deuterons and He-3
3He
+
58Fe
d
61Ni
n
60Ni
α
p
60Co
57Fe
+
59Co
n
p
α
3He+ 58Fe
d+ 59Co
A.Voinov et al, PRC, accepted for publication
We also measured reactions with 12C, 6Li and 7Li projectiles
The following reactions have been measured:
6Li+ 55Mn
61Ni
6,7Li+ 58,57Fe
12C+ 27Al
(=d+ 59Co and 3He+ 58Fe)
64Cu
39K
Main result:
all of these reactions can be used for the measurement
of 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.
B. Zhuravlev et al, Phys.Atomic Nuclei 69, 363 (2006);
16
a, MeV
-1
18
14
12
12
14
16
18
20
(N - Z)
22
24
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].
γ – strength function in continuum
3
E Di
~
 abs ( E )
Particle separation threshold
f ( E ) 
( E )
E
i
f ( E )
Excitation energy
0.1
0.01
From (γ,n) reactions
1E-3
1E-4
0
0
5
10
15
γ- Energy (MeV)
20
Some results of γ-strength functions for rare-earth nuclei
From Oslo Cyclotron Lab
γ-strength function of iron isotopes
Low energy upbend phenomenon
- 56Fe
- 57Fe
Eγ (MeV)
A.Voinov et al, Phys.Rev. Lett., 93, 142504 (2004).
γ-strength function of molybdenum isotopes
M. Guttormsen et al, Phys. Rev. C,
71, 044307 (2005).
Method of two-step γ – cascades from
neutron capture reactions
History:
Bn
Proposed:A.M. Hoogenboom, NIM 3,57(1958)
E1
Intensity
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, 2001
A.Voinov, E. Algin et al Budapest, 2002
E2
Intensity
E1+E2
Ground state
Problem: level density is needed !!!
Eγ
Measurement of gamma-strength function at
Edwards Lab.
(p,2γ)
(d,n)
To the same product nucleus
Strategy
1. We obtain a level density from neutron evaporation spectra.
2. We obtain a γ-strength function from 2γ- spectra
The first candidate is 59Co(p,2γ) 60Ni reaction at Ep=1.9 MeV
The level density of 60Ni has already been measured
from 59Co(d,n) 60Ni reaction:
A.Voinov et al, PRC, accepted for publication
First results from
59Co(p,2γ)
59
p+ Co, 13 hours of measurements
400
Single escape peaks
Counts
300
Real peaks
200
100
0
9000
10000
11000
12000
E2
0
2
+
59
p+ Co -->
60Ni
1.33 MeV
E1
60
Ni+ 
E1+E2, keV
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. !!!)
Collaborators :
OU:
S.Grimes, A.Schiller, C.Brune, T. Massey
Oslo University: M. Guttormsen, S.Siem et al
Livermore Lab: U. Agvaanluvsan,
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.