Nuclear Reactions

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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

武藤一雄氏（東工大）

(2)

a a b

A  B A(a,b)B reaction

a a

a

A

_gs

 A

_gs

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

(3)

a a b

A  B A(a,b)B reaction

a a

a

A

_gs

 A

_gs

elastic scattering

fundamental interaction between a and A

a a

a’

A

_gs

 A*

inelastic scattering

excitation spectrum of a nucleus A

E

_a

(4)

a a b

A  B A(a,b)B reaction

16

O

17

O

208

Pb

_gs



²⁰⁷

Pb

transfer reaction

(below: an example of pick-up reaction)

level schem of

²⁰⁷

Pb

a

a (a+A)

A

_gs

 X

fusion reaction

• interaction between a and A

• structure of a and A

16

O

¹⁷

O

16

O

208

Pb

_gs



²⁰⁹

Pb

transfer reaction (below: an example of stripping reaction)

level schem of

²⁰⁹

Pb

17

O

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p

⁺

p

⁺

K

⁺

A

_gs

 A

_L

(p

⁺

,K

⁺

) reaction

excitation spectrum of a hypernucleus A

_L

p

^-

K

^-

A

_gs

 A

_L

(K

^-

,p

^-

) reaction

K

^-

12

C (p

^+,

K

⁺

)

¹²_L

C reaction

O. Hashimoto and H. Tamura,

Prog. in Part. and Nucl. Phys. 57 (‘06)564

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K

⁺

e

^-

e

^-

A

_gs

 A

_L

(e,e’K

⁺

) reaction

e

^-

12

C(e,e’K

⁺

)

¹²_L

B

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

cm

²

= 100 fm

²

(1 mb = 10

^-3

b = 0.1 fm

²

)

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Cross sections (experiments)

t target thickness S

beam intensity:

the number of target nucleus:

detection

efficiency

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Cross sections (theory)

a a

b

A  B A(a,b)B reaction

center of mass frame

a A

transition

b

B

q

_cm

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Cross sections

 center of mass frame

a A

b

B

q

_cm

 laboratory frame

a A

b

B

q

_lab

 transformation energy and momentum conservations

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Born approximation

q

perturbation V(r)

transition rate for elastic scattering:

(13)

Born approximation

q V(r)

incident flux:

q

momentum

transfer

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Electron scattering

Form factor

e

^-

e

^-

* relativistic correction:

(15)

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

D V(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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Impulse approximation

example:

^A

Z(K

^-

,p

^-

)

^A_L

Z reaction

K

^-

n

p

^-

L

 high energy

 single scattering approximation

 (other nucleons: spectator)

effective K-n interaction

(including multiple scattering)

(20)

Impulse approximation

example:

^A

Z(K

^-

,p

^-

)

^A_L

Z reaction

K

^-

n

p

^-

 high energy L

 single scattering approximation

elementary process

kinematical factor

• Plane wave impulse approximation (PWIA)

• Distorted wave impulse approximation (DWIA)

(21)

O. Hashimoto and H. Tamura,

Prog. in Part. and Nucl. Phys. 57 (‘06)564 excitation energy (MeV)

T. Motoba et al., PRC38(‘88)1322 1s

_1/2

1p

_3/2

1p

_1/2

n L

1s 1p

Dl=0 Dl=0

Dl=1

m

_n

+m

_K

= 1432 MeV m

_p

+m

_L

= 1255.3 MeV m

_p

+m

_n

= 1079.2 MeV m

_K

+m

_L

= 1609.4 MeV

Q > 0

Q < 0

(22)

relation between q and Dl

K

^-

n L p

^-

b (impact parameter)

l ~ kb (classically)

D l ~ b(p’-p) = bq

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O. Hashimoto and H. Tamura,

Prog. in Part. and Nucl. Phys. 57 (‘06)564 excitation energy (MeV)

T. Motoba et al., PRC38(‘88)1322

1s

_1/2

1p

_3/2

1p

_1/2