Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 A. Brondi, G. La Rana, R. Moro, M. Trotta, E. Vardaci Università di Napoli Federico II, and Istituto Nazionale di Fisica Nucleare, Napoli, Italy Search for isospin effects on nuclear level density The Physics Opportunities with Eurisol Trento, January 16-20, 2006

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Why is it important to study the level density ? Level density is a basic ingredient for x-section calculations Astrophysical processes “Astrophysical Reaction Rates from Statistical Model Calculations”, ADNDT 75 (2000) SHE’s production Capture of two nuclei in the attractive potential pocket. Survival probability against fission. Probability of forming a compact compound nucleus (CN). Fluctuation-dissipation dynamics: Fokker-Plank or Langevin equations Evaporative process: Statistical Model

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Study of isospin effects on level density through fusion-evaporation reactions Temperature, Angular momentum, Pairing & Shell effects: a,  Isopin (?) Isospin comes in through: Isospin Distribution Symmetry Energy P(U o,J o,  l,U,J)   (U,J). T l ( 

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Isospin distribution A reduction of level density with increasing |T 3 | is predicted Statistical mechanics

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Level densities in n-rich and n-deficient nuclei Isospin distribution 20<A<70 ENSDF Form A: Form B: Form C:

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Level density in n-deficient Dy nuclei n-richn-deficient 140 Dy

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Study of the level density in n-deficient Dy nuclei Which observables? “… complete level schemes up to 2.5 MeV will be difficult to obtain for higher A and for nuclei far off the valley of stability. Thus further tests of this level density approach will likely be based on evaporation spectra…” Al Quraishi et al., Phys. Rev. C 63, Method: observation of evaporative xp channels Observables: E.R. yields and energy spectra To what extent such effects on level density can be observed? Statistical model calculations (Lilita_N97) 76 Kr + 64 Zn  140 Dy E x = 50 MeV - xp channels Standard a = A/8,

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Study of level density in n-deficient Dy nuclei Enhanced effects using Z-Zo prescription

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Study of level density in n-deficient Dy nuclei Decay channels involving a small number of particles – Low E x St.N-ZZ-Z O   p (  b)  1n (  b)  1  (  b) Owing to the higher average energy, 1particle decay channels are enhanced using Z-Zo prescription Best condition:

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Why is it important to study the symmetry energy ? E sym =b sym (T)(N-Z) 2 /A As a part of the nuclear Equation Of State it may influence the mechanism of Supernova explosion General theoretical agreement on its temperature dependence (LRT+QRPA vs. large scale SMMC) Possible consequences of T dependence of E sym on core-collapse Supernova events still debated Effects enhanced by the instrinsic isospin dependence of E sym Fusion-evaporation reactions: E sym affects the particle B.E.

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 SYMMETRY ENERGY m  (T) 0 < T < 3 MeV - 98Mo, 64Zn, 64Ni -Hartree-Fock – coupling s.p.s. to c.v. -LRT – QRPA Decrease of the effective mass  Increase of E sym E sym (T)= b sym (T) x (N-Z) 2 /A bsym(T)=bsym(0)+(h 2 k o 2 m/6m k )[m  (T) -1 – m  (0) -1 ] m  (T)=m + [m  (0) – m]exp(-T/T o )

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Study of the level density in n-rich Mo nuclei Method: observation of evaporative xn channels (1n, 2n) Observables: E.R. yields and energy spectra Statistical model calculations (Lilita_N97) 105 Zr + 4 He  109 Mo E x = MeV - 1n, 2n channels 98 Kr + 12 C  110 Mo E x = MeV - 5n, 6n channels Standard a = A/8, Symmetry energy: prescription of P. Donati et al. Isospin distribution:

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Effect of symmetry energy Effect EXEX

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Symmetry energy and isospin distribution effects E sym effect dominates at low E x

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Moving to higher excitation energies More channels involved, including charged particle emission Higher cross sections Higher angular momenta  (mb) J(h)

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Single effects on different evaporative channels No effects are observed for E sym

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Isospin effects on energy spectra shapes No effects are observed for E sym 5n channel 1n channel

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 In program….. - Refinements of the model: microscopic level density based on single-particle level schemes obtained from Hartree-Fock calculations on the basis of the Gogny effective interaction, taking into account for parity, angular momentum, pairing corrections as well as collective enhancements. S. Hilaire et al., Eur. Phys. J. A, 169 (2001) - Estention of calculations to other exotic nuclei - Measurements with existent RIB and SB facilities

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Summary and perspectives The availability of n-rich and n-deficient RNB’s will allow to study isospin effects on fusion-evaporation reactions. These may have strong implications in nuclear astrophysics and affect the estimation of SHE’s production cross sections. Such studies require: - High intensity n-rich and p-rich beams - High selectivity, high granularity, high efficiency detectors Such tasks may be accomplished using: - SPES, SPIRAL II, EURISOL beams - Neutron + Charged particle detectors; High efficiency, large solid angle ER separators (PRISMA in GFM, VAMOS); Gamma tracking arrays (AGATA).

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Testing realistic effective interactions on exotic nuclei around closed shells Covello, L. Coraggio, A. Gargano, and N. Itaco Università di Napoli Federico II, and Istituto Nazionale di Fisica Nucleare, Napoli, Italy

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Theory B(E2;0 +  2 + ) = e 2 b Sn Coulex (Oak Ridge) B(E2;0 +  2 + ) = 0.029(4) e 2 b 2 Expt. Theory 726 keV Lowest first-excited 2+ level in semi-magic even-even nuclei

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006

Theory B(E2;0 +  2 + ) = 0.18 e 2 b Te Coulex (Oak Ridge) B(E2;0 +  2 + ) = 0.103(15) e 2 b 2 New measurement larger value: ~ 0.13(15) e 2 b 2

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Theory with free g-factors: B(M1) = 25 x (n.m.) 2 Theory with effective M1 operator: 4 x (n.m) 2 B(M1;5/2 +  7/2 + ) = 0.29 x (n.m.) 2 (OSIRIS, Studsvik) N/Z = 1.65 : most exotic nucleus beyond 132Sn for which there is information on excited states From 133 Sb: ε 5/2 = 962 keV 282 keV

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Mechanism of Supernova explosion When the n-rich core of a massive star reaches a mass limit, it begins to collapse. The increased density induces electron captures on both free protons and protons bound in nuclei, driving the matter in the core towards successively more n-rich nuclei. As long as the density remains lower than the “trapping density”, the neutrinos produced escape freely from the core, releasing energy. Influence of symmetry energy: The larger the symmetry energy, the more difficult is to change protons into neutrons. Via the EOS, the symmetry energy influences the amount of free protons in the core, that in the late stage of the collapse are believed to be the main source for electron capture. Larger symmetry energy  smaller electron capture rate  less energy lost by neutrino escape  stronger shock wave  Supernova explosion

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Isospin effects on …… 105 Zr + 4 He  109 Mo 98 Kr + 12 C  110 Mo

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Isospin effects on 1n and 2n channel yields 105 Zr + 4 He  109 Mo

Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006 Single effects on different evaporative channels No effects are observed for E sym