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.

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) ?

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);

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)

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

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).

d, 3He

neutronsNE213

Flight path 8m

target

Swinger facility

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.

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

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

A.Voinov et al, PRC 74, 014314 (2006)

55Mn(d,n)56Fe, Ed=7.5 MeV

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

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 58Fe59Cod+ +

61Ni

np

α

60Ni60Co

57Fe

3He+ 58Fe

d+ 59Co

n p α

A.Voinov et al, PRC, accepted for publication

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.

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);

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

Some results of Some results of γγ-strength functions for rare-earth nuclei-strength functions for rare-earth nucleiFrom Oslo Cyclotron Lab

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).

γ-strength function of molybdenum isotopes

M. Guttormsen et al, Phys. Rev. C, 71, 044307 (2005).

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

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

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

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. MasseyOslo University: M. Guttormsen, S.Siem et alLivermore 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.