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,

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


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) 1-351

SHE’s production

Capture of two nuclei in the attractive potential pocket.

ER capture PCN Psurv

Survival probability against fission.

Probability of forming a compact compound nucleus (CN).

Fluctuation-dissipation dynamics: Fokker-Plank or Langevin equations

Evaporative process: Statistical Model


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(Uo,Jo,l,U,J) (U,J) . Tl(


Isospin distribution

A reduction of level density with increasing |T3| is predicted

Statistical mechanics


Level densities in n-rich and n-deficient nuclei Isospin distribution

20<A<70 ENSDF

Form A:

Form B:

Form C:


Level density in n-deficient Dy nuclei

n-rich n-deficient

140Dy


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, 065803

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)

76Kr + 64Zn 140Dy Ex = 50 MeV - xp channels

Standard a = A/8,


Study of level density in n-deficient Dy nuclei

Enhanced effects

using Z-Zo prescription


Study of level density in n-deficient Dy nuclei

Decay channels involving a small

number of particles – Low Ex

St. N-Z Z-ZO

p (b) 1.3 0.32 1322

1n (b) 1.3 1.3 225

1(b) 1890 3500 2478

Owing to the higher average

energy, 1particle decay

channels are enhanced

using Z-Zo prescription

Best condition:


Why is it important to study the symmetry energy ?

Esym=bsym(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 Esym on core-collapse Supernova events still debated

• Effects enhanced by the instrinsic isospin dependence of Esym

Fusion-evaporation reactions: Esym affects the particle B.E.


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 Esym

Esym(T)= bsym(T) x (N-Z)2/A

bsym(T)=bsym(0)+(h2ko2m/6mk)[m(T)-1 – m(0)-1]

m(T)=m + [m(0) – m]exp(-T/To)


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)

105Zr + 4He 109Mo Ex = 14-20 MeV - 1n, 2n channels

98Kr + 12C 110Mo Ex = 50-85 MeV - 5n, 6n channels

Standard a = A/8,

Symmetry energy: prescription of P. Donati et al.

Isospin distribution:


Effect of symmetry energy

Effect

EX


Symmetry energy and isospin distribution effects

Esym effect

dominates

at low Ex


Moving to higher excitation energies

1

10

100

1000

10000

40 45 50 55 60 65 70 75 80 85 90

Ex(MeV)

fus(mb)

Lfus(h)

98Kr + 12C 110Mo Elab=285 - 605 MeV

More channels involved, including charged particleemission

Higher cross sections

Higher angular momenta(mb)

J(h)


Single effects on different evaporative channels

No effects are observed for Esym


Isospin effects on energy spectra shapes


5n channel

1n channel


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


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).


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


Theory

B(E2;0+ 2+) = 0.033 e2b2

134Sn Coulex (Oak Ridge)

B(E2;0+ 2+) = 0.029(4) e2b2

Expt. Theory

726 keV

Lowest first-excited2+ level in semi-magiceven-even nuclei



Theory

B(E2;0+ 2+) = 0.18 e2b2

136Te Coulex (Oak Ridge)

B(E2;0+ 2+) = 0.103(15) e2b2

New measurement larger value: ~ 0.13(15) e2b2


Theory with free g-factors: B(M1) = 25 x 10-3 (n.m.)2

Theory with effective M1 operator: 4 x 10-3 (n.m)2

B(M1;5/2+ 7/2+) = 0.29 x 10-3 (n.m.)2 (OSIRIS, Studsvik)

N/Z = 1.65 : most exotic nucleus beyond 132Sn for which there is information on excited states

From 133Sb: ε5/2 = 962 keV

282 keV


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


Isospin effects on ……

105Zr + 4He 109Mo

98Kr + 12C 110Mo


Isospin effects on 1n and 2n channel yields

105Zr + 4He 109Mo


Single effects on different evaporative channels


Documents

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,