10-19sec 10-22 sec
10-15 sec
10-9sec
Elab = 147 MeV E* = 53.8 MeV T = 1.7 MeV
M
γ~ 20-30
40Ar +124Sn → 164-xEr + xn
Compound Nucleus
Decay
lCN=10h
lCN=20h
lCN=32h
19F+27Al 76MeV
Cascade Code
Pulhöfer et al., NPA280(1977)267
d ~ 10-1000 keV d ~ eV-keV
B
nCN formation
► Compound nucleus reactions populate excitation energy region of
high level density
(high number of states per MeV)
►
impossibility of counting individual nuclear levels►
need of statistical concepts:level density ρ
excitation energy E*
temperature T
∆E≈eV
τ=h/∆E≈10-16-10-18s
Level density of Nuclear States
Equidistant spacing model for level density evaluation
being E the total energy of the system how can one distribute A nucleons
in equidistant single particle levels (respecting Pauli’s principle) ?
E E n
∆
= ∆ ) ρ(
level density
E=4ε ε
equivalent problem:
decomposition of n=E/ε in n1+n2+ …
4=… p(n)=(4 3n)−1exp
[
π(2n/3)1/2]
Ramanujan & Hardy
[ ]
[
1/2]
2 / 1 4
/ 5 4 / 1
) ( 2 exp ) 0 (
) ( 2 exp )
12 / ( ) (
aE
aE E
a E
ρ π ρ
=
= − −
a [MeV-1 ]
A
example: A=100, E=50MeV ⇒ ρ = 1020MeV-1 !!
Nuclear System:
Z protons N neutrons
2 particles per state (spin up & down)
Fermi Gas
Thermodynamics in Nuclear Physics
With some care: the nucleus contains few particles
compared to macroscopic systems described by statistical models
entropy S ( E ) k
Bln ( E ) ln ( E )
def
= ρ = ρ
Requirement
full statistical equilibrium
yield
E
Maxwell-Boltzmann distribution:
( / )
(
kin)
kin.
Ekin TN E ∝ E e
−kinetic temperatures
Experimental Thermometers:
particles and γ energy distribution
)
1(
−
∂
= ∂
E E T S
def
temperature
[ ]
E a E
a E
E E T
aE E
a E
≈ +
−
∂ =
= ∂
= − −
1 4 5 )
( ln 1
) ( 2 exp )
12 / ( )
( 1/4 5/4 1/2
ρ π ρ
leading term
aT 2
E =
Examples:
a=A/8=160/8=20
CN formation (5MeV/A): E=50MeV, T=1.6MeV Binding Energy: E=8 MeV, T=0.6 MeV
Limit of discrete spectroscopy: E=1 MeV, T=0.2 MeV
HOT Giant Dipole Resonance
Eγ ~ 15 MeV
FWHM ~ 5-7 MeV
Pγ/Ppart≈ 10-3
GDR
64Ni (@300MeV) + 68Zn → 132Ce
yield
E Maxwell-Boltzmann
distribution
) /
) (
(E e E T N γ ∝ − γ statistical decay of compound nucleus by γ-ray emission
Caloric curve of nuclear matter
Caloric curve of nucleus Caloric curve of water
Excitation energy per Nucleon (MeV)
Temperature (MeV)
liquid
gas
Multifragmentation: T≈5 MeV, E*≈4-5/A MeV Vaporization: T>6 MeV, E*>10/A MeV
J. Pochodzalla et al., Phys. Rev. Lett. 75(1995)1040
Heavy Ions Fusion Reactions:
population of excited (0<E<8 MeV), high spins states (
>40 h)
0 10 20 30 40 50 60 70
0 2 4 6 8
<U> [MeV]
Spin [h]
168
Yb
γ-flow
E1/E2
compound nucleus formation
ground state
10-9 sec 10-19
sec 10-15 sec
(70,2) (70,4) (70,5.5) (40,8) (50,8)
(70,8)
Most of the experimental works on γ spectroscopy focus on
high spins and low excitation energies (E-Eyrast)=U≤ 2 MeV, T ≤ 0.3 MeV
yrast
1) 2 (
) (
2 +
= ℑ I I I
E h
I[h],<U>[MeV]
Døssing, Vigezzi, NPA587(1995)13.
