Nuclear Reactionskouichi.hagino/lectures/nuclth15/nuclth… · Prog. in Part. and Nucl. Phys. 57...
Transcript of Nuclear Reactionskouichi.hagino/lectures/nuclth15/nuclth… · Prog. in Part. and Nucl. Phys. 57...
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Nuclear Reactions
Shape, interaction, and excitation structures of nuclei scattering expt.
cf. Experiment by Rutherford (a scatt.)
http://www.th.phys.titech.ac.jp/~muto/lectures/QMII11/QMII11_chap21.pdf
K. Muto (TIT)
projectiletarget transmitted particles
scattered
particles
detector
solid angle
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aa
b
A B
A(a,b)B reaction
a a
a
Ags Ags
elastic scattering
fundamental interaction
between a and A
p(d,d)p and n(d,d)n
K. Sekiguchi et al., PRC89(‘14)064007
3-body
interaction
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aa
b
A B
A(a,b)B reaction
a a
a
Ags Ags
elastic scattering
fundamental interaction
between a and A
a a
a’
Ags A*
inelastic scattering
excitation spectrum
of a nucleus A
Ea
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aa
b
A B
A(a,b)B reaction
16O
17O
208Pbgs 207Pb
transfer reaction
(below: an example
of pick-up reaction)
level schem of 207Pb
a
a
(a+A)
Ags X
fusion reaction
• interaction between
a and A
• structure of a and A
16O17O
16O
208Pbgs 209Pb
transfer reaction
(below: an example
of stripping reaction)
level schem of 209Pb
17O
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p+p+
K+
Ags AL
(p+,K+) reaction
excitation spectrum
of a hypernucleus AL
p-
K-
Ags AL
(K-,p-) reaction
K-
12C (p+,K+) 12LC reaction
O. Hashimoto and H. Tamura,
Prog. in Part. and Nucl. Phys. 57 (‘06)564
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K+
e-
e-
Ags AL
(e,e’K+) reaction
e-
12C(e,e’K+) 12LB
L. Tang et al., PRC90(‘14)034320
S.N. Nakamura et al.,
PRL110(‘13)012502
T. Gogami,
Ph.D. Thesis (Tohoku U.)
2014
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Cross sections
incident beam
flux = the number of particles
crossing unit area
per unit time
event rate (the number of event per unit time per target nucleus)
: proportional to the incident flux
cross section
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Cross sections
event rate (the number of event per unit time per target nucleus)
: proportional to the incident flux
cross section
differential cross sections (angular distribution)
units: 1 barn = 10-24 cm2 = 100 fm2 (1 mb = 10-3 b = 0.1 fm2)
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Cross sections (experiments)
ttarget thickness
S
beam intensity:
the number of target nucleus:
detection
efficiency
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Cross sections (theory)
aa
b
A B
A(a,b)B reaction
center of mass frame
a Atransition
b
B
qcm
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Cross sections
center of mass frame
a A
b
B
qcm
laboratory frame
a A
b
B
qlab
transformation energy and momentum conservations
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Born approximation
q
perturbation
V(r)
transition rate for elastic scattering:
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Born approximation
qV(r)
incident flux:
q
momentum
transfer
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Electron scattering
Form factor
e- e-
* relativistic correction:
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cf. electron scattering off unstable nuclei (SCRIT)
T. Suda et al.,
PTEP 2012, 03C008 (2012)
PRL102, 102501 (2009)
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Distorted Wave Born approximation (DWBA)
q
perturbation
DV(r)
perturbation
“distorted waves”
inelastic scattering
transfer reactions
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Reaction processes
Elastic scatt.
Inelastic scatt.
Transfer reaction
Compound nucleus
formation (fusion)Loss of incident flux
(absorption)
Optical potential
(note) Gauss’s law
Optical model
r
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Woods-Saxon + volume &surface
imaginary parts
H. Sakaguchi et al.,
PRC26 (1982) 944
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Appendix: DWBA in ocean acoustics
Fishfinder
https://www.furuno.co.jp/technology/about/fishfinder1.html
(backward) scattering of
(ultra-)sonic waves due
to fish etc.
one can know the number
of fish NT if one knows the
differential cross sections
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J. Accoust. Soc. Am. 125 (‘09) 73
Modeling of squid
!DWBA: local wave number
inside a squid
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W.-J. Lee, A.C. Lavery, T. Stanton,
J. Accoust. Soc. Am. 131 (‘12) 4461
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Krill (オキアミ)
DWBA
measurement
K. Akamatsu and M. Furusawa,
ICES J. of Marine Science 63 (‘06) 36
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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