Absorption cross sectionskouichi.hagino/lectures/... · Nuclear force Short range, attractive...
Transcript of Absorption cross sectionskouichi.hagino/lectures/... · Nuclear force Short range, attractive...
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Absorption cross sections
Reaction processes
Elastic scatt.
Inelastic scatt.
Transfer reaction
Compound nucleus
formation (fusion)Loss of incident flux
(absorption)
reaction cross sections
total scattering cross section - elastic cross section
• fusion
• inelastic
• transfer
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Interaction cross sections and halo nuclei
11Li something else
target nuclei
interaction cross section sI
= cross section for the change
of Z a/o N in the incident nucleus
transmission method
Nin Nout
d
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Interaction cross sections and halo nuclei
11Li something else
target nuclei
interaction cross section sI
= cross section for the change
of Z a/o N in the incident nucleus
RI(P)
Projectile
Target Slide: A. Ozawa
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I. Tanihata, T. Kobayashi, O. Hashimoto
et al., PRL55(‘85)2676; PLB206(‘88)592
Discovery of halo nuclei
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b
Glauber theory (optical limit approximation:OLA)
straight-line trajectory (high energy scattering)
adiabatic approximation
simplified treatment for multiple scattering:
Reaction cross sections
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Density distribution which explains
the experimental sR
M. Fukuda et al., PLB268(‘91)339
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Heavy-ion subbarrier fusion reactions
Inter-nucleus potential Two forces:
1. Coulomb force
Long range,
repulsive
2. Nuclear force
Short range,
attractive
Potential barrier due
to the compensation
between the two
(Coulomb barrier)
•above barrier
•sub-barrier
•deep subbarrier
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rtouch
rtouch
154Sm16O
Strong absorption
Automatic compound
nucleus formation once
touched (assumption of
strong absorption)
Three important features of heavy-ion reactions
1. Coulomb interaction: important
2. Reduced mass: large (semi-) classical picture
concept of trajectory
3. Strong absorption inside the Coul. barrier
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Partial decomposition of reaction cross section
Taken from J.S. Lilley,
“Nuclear Physics”
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Fusion: compound nucleus formation
courtesy: Felipe Canto
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Strong absorption
: can access to the strong absorption
region classically
b (impact parameter)
classical fusion cross sections
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1/Vb
pRb2
Taken from J.S. Lilley,
“Nuclear Physics”
Classical fusion cross section is proportional to 1 / E :
sfus vs 1/E (~70’s)
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OK for relatively light systems
underestimates sfus for heavier systems at subbarrier energies
Simple potential model:
Fusion cross sections at subbarrier energies
Fusion cross sections of structure-less nuclei (a potential model)
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Potential model:Reproduces the data
reasonably well for
E > Vb
Underpredicts sfus for
E < Vb
cf. seminal work:
R.G. Stokstad et al., PRL41(‘78)465
PRC21(‘80)2427
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Strong target dependence at E < Vb
low-lying collective excitations?
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0+2+
4+
6+
8+
00.082
0.267
0.544
0.903
(MeV)
154Sm
Excitation spectra of 154Sm cf. Rotational energy of a rigid body
(Classical mechanics)
154Sm is deformed
Effect of deformation on subbarrier fusion
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154Sm 16O
The barrier is lowered for =0 because an attraction works from large
distances. Def. Effect: enhances sfus by a factor
of 10 ~ 100
Fusion: interesting probe for
nuclear structure
The barrier increases for =p/2. because the rel. distance has
to get small for the attraction to work
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154Sm 16O
T
M. Dasgupta et al.,
Annu. Rev. Nucl. Part. Sci. 48(’98)401
Fusion barrier distributions
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Investigate nuclear shape through barrier distribution
Nuclear shapes
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By taking the barrier distribution, one can very clearly see
the difference due to b4!
Fusion as a quantum tunneling microscope for nuclei
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rtouch
rtouch
154Sm16O
strong absorption
Compound nucleus:
automatically formed
once touched
(strong absorption)
Fusion of medium-heavy systems:
Fusion of heavy and super-heavy systems
[This happens for Z1*Z2 > 1600 ~ 1800.]
Heavy-ion subbarrier fusion reactions in the SHE region
Large probability of re-separation (due to the strong Coulomb repulsion)
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C.-C. Sahm et al.,
Z. Phys. A319(‘84)113
extra push
Z1*Z2 = 2000
Z1*Z2 = 1296
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2-body potential before touching
1-body potential after touching
The red potential has to be
overcome even if the blue
potential has been overcome.
Re-separation if failed
(quasi-fission)
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CN
ER
contact
fusion
evaporation
Quasi-fission
fission
CN = compound nucleus
ER = evaporation residue
cannot distinguish
experimentallyn
experimentally detected
10-22
10-20
typical time-scale (sec.)
10-19
~10-18
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Heavy-ion fusion for SHE
Yuri Oganessianisland of stability around Z=114, N=184W.D. Myers and W.J. Swiatecki (1966), A. Sobiczewski et al. (1966)
modern calculations: Z=114,120, or 126, N=184 e.g., H. Koura et al. (2005)
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UraniumThorium
Lead
Continent
Island of
stability
(SHE)
Yuri Oganessian
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Element 113 (RIKEN, K. Morita et al.)
K. Morita et al., J. Phys. Soc. Jpn. 81(‘12)103201
only 3 events for 553 days experiment
70Zn (Z=30) + 209Bi (Z=83) 278113 + n
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CN = compound nucleus
ER = evaporation residue
CN
ER
contact
fusion
evaporation
Quasi-fission
fission
n
Theoretical treatment
Pcap
PCN
Psur
statistical model
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E
Pcap: quantum
mechanics
(C.C.)
energy
dissipation
thermal
motion
2-body potential
1-body potential
compound
nucleus
Langevin
approach
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Theory: Lagenvin approach
multi-dimensional extension of:
q: ・internuclear separation (z),
・deformation (d),
・asymmetry of the two
fragments (a)
g: friction coefficient
R(t): random force
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Chemistry of superheavy elements
Are they here in the periodic table?
That is, does e.g., Lv show the same chemical properties
as O, S, Se, Te, and Po?
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relativistic effect : important for large Z
E = mc2
Solution of the Dirac equation (relativistic quantum mechanics)
for a hydrogen-like atom:
relativistic effect
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Famous example of relativistic effects: the color of gold
Gold looked like silver if there was no relativistic effects!
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5d
6s
4d
5s
Gold (Au)Silver (Ag)
Non-Rel.Non-Rel.
Rel.
Rel.
3.7 eV 2.4 eV
2.76 eV 1.65 eV
cf. visible spectrum
2.4 eV3.7 eV
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Gold (Au)Silver (Ag)
Non-Rel.Non-Rel.
Rel.
Rel.
3.7 eV 2.4 eV
Au
blue: absorbed
Ag
no color
absorbed
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Chemistry of superheavy elements
How do the relativistic effects alter the periodic table for SHE?
a big open question