Transcript Document

The Physics Opportunities with Eurisol
Trento, January 16-20, 2006
Search for isospin effects on nuclear level density
A. Brondi, G. La Rana, R. Moro, M. Trotta, E. Vardaci
Università di Napoli Federico II,
and Istituto Nazionale di Fisica Nucleare, Napoli, Italy
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) 1-351
SHE’s production
 ER   capture  PCN  Psurv
Capture of two nuclei
in the attractive
potential pocket.
Probability of forming a
compact compound
nucleus (CN).

Fluctuation-dissipation dynamics:
Fokker-Plank or Langevin equations
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Survival probability
against fission.
Evaporative process:
Statistical Model
Study of isospin effects on level density through
fusion-evaporation reactions
P(Uo,Jo,e,l,U,J)  r(U,J) . Tl(e)
Temperature, Angular momentum, Pairing & Shell effects: a , ,d
Isopin (?)
Isospin comes in through:
Isospin Distribution
Symmetry Energy
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin distribution
Statistical mechanics
A reduction of level density with increasing |T3| is predicted
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Level densities in n-rich and n-deficient nuclei
Isospin distribution
Form A:
Form B:
20<A<70 ENSDF
Form C:
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Level density in n-deficient Dy nuclei
n-rich
n-deficient
140
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Dy
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,
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
Best condition:
Decay channels involving a small
number of particles – Low Ex
St.
N-Z
Z-ZO
1p (mb)
1.3
0.32
1322
1n (mb)
1.3
1.3
225
1a(mb)
1890
3500
2478
Owing to the higher average
energy, 1particle decay
channels are enhanced
using Z-Zo prescription
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
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.
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
SYMMETRY ENERGY
mw(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)[mw(T)-1 – mw(0)-1]
mw(T)=m + [mw(0) – m]exp(-T/To)
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)
105Zr
+ 4He 
109Mo
Ex = 14-20 MeV - 1n, 2n channels
98Kr
+ 12C 
110Mo
Ex = 50-85 MeV - 5n, 6n channels
Isospin distribution:
Standard a = A/8,
Symmetry energy: prescription of P. Donati et al.
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Effect of symmetry energy
Effect
EX
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Symmetry energy and isospin distribution effects
Esym effect
dominates
at low Ex
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Moving to higher excitation energies
10000
98
Kr + 12C
110
fus(mb)
Mo
Elab=285 - 605 MeV
Higher cross sections
1000
(mb)
Higher angular momenta
100
Lfus(h)
J(h)
10
1
40
45
50
55
60
65
70
75
80
85
90
Ex(MeV)
More channels involved,
including charged particle
emission
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Single effects on different evaporative channels
No effects are observed for Esym
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin effects on energy spectra shapes
5n channel
1n channel
No effects are observed for Esym
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
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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
Lowest first-excited
2+ level in semi-magic
even-even nuclei
726 keV
Expt.
134Sn
Coulex (Oak Ridge)
B(E2;0+ 2+) = 0.029(4) e2b2
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Theory
Theory
B(E2;0+ 2+) = 0.033 e2b2
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
136Te
Theory
Coulex (Oak Ridge)
B(E2;0+ 2+) = 0.103(15) e2b2
New measurement
B(E2;0+ 2+) = 0.18 e2b2
larger value: ~ 0.13(15) e2b2
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
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
B(M1;5/2+  7/2+) = 0.29 x 10-3 (n.m.)2
(OSIRIS, Studsvik)
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
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Mechanism of Supernova explosion
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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 ……
105Zr
+ 4He 
109Mo
98Kr
+ 12C 
110Mo
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
Isospin effects on 1n and 2n channel yields
105Zr
+ 4He 
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006
109Mo
Single effects on different evaporative channels
No effects are observed
for Esym
Giovanni La Rana, EURISOL Workshop, Trento, January 16-20, 2006