The concept of compound nuclear reaction: a+B  C  d+F 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 !!! We use compound nuclear reactions to study nuclear structure. We study nuclear structure to calculate compound reaction cross sections.

Excitation energy Level density Bn Level density is known for most of the stable nuclei Level density is unknown for most 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 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, (2005);

Excitation energy Level density Bn The Oslo method is based on the measurements of particle-gamma coincidences from ( 3 He, α γ ) and ( 3 He, 3 Heγ) 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: 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, 3 He, 12 C, 6 Li, 7 Li … beams available from our tandem accelerator Q-reactions are positive (5-15 MeV).

d, 3 He neutrons NE213 Flight path 8m target Swinger facility

beam Target Si 2m flight path Scheme of experimental set-up for charge-particle spectra measurements Edward’s Accelerator Lab, Ohio University

Experimental level densities from (d,n) reactions measured at Edwards Lab. Testing the level density with 27 Al(d,n) 28 Si

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

A.Voinov et al, PRC 74, (2006) 55 Mn(d,n) 56 Fe, E d =7.5 MeV

65 Cu(d,n) 66 Zn, E d =7.5 MeV

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 3 He 58 Fe 59 Co d Ni n p α 60 Ni 60 Co 57 Fe

3 He+ 58 Fe d+ 59 Co np α A.Voinov et al, PRC, accepted for publication

We also measured reactions with 12 C, 6 Li and 7 Li projectiles The following reactions have been measured: 6 Li+ 55 Mn 61 Ni (=d+ 59 Co and 3 He+ 58 Fe) 6,7 Li+ 58,57 Fe 64 Cu 12 C+ 27 Al 39 K 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. 24 Mg+ 58 Ni 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  = and  = [10]. B. Zhuravlev et al, Phys.Atomic Nuclei 69, 363 (2006);

0 γ – strength function in continuum i Excitation energy γ- Energy (MeV) From (γ,n) reactions Particle separation threshold

Some results of γ-strength functions for rare-earth nuclei From Oslo Cyclotron Lab

γ-strength function of iron isotopes Low energy upbend phenomenon E γ (MeV) - 56 Fe - 57 Fe A.Voinov et al, Phys.Rev. Lett., 93, (2004).

γ-strength function of molybdenum isotopes M. Guttormsen et al, Phys. Rev. C, 71, (2005).

Method of two-step γ – cascades from neutron capture reactions Ground state BnBn E1E1 E2E2 E 1 +E 2 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, 2001 A.Voinov, E. Algin et al Budapest, 2002 EγEγ Problem: level density is needed !!! 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 59 Co(p,2γ) 60 Ni reaction at E p =1.9 MeV The level density of 60 Ni has already been measured from 59 Co(d,n) 60 Ni reaction: A.Voinov et al, PRC, accepted for publication

First results from 59 Co(p,2γ)

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.