description of proton-induced inclusive knockout reactions...wakasa et al., prc59, 3177 (1999)....
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Description of proton-induced inclusive knockout reactions
Kazuyuki Ogata
Research Center for Nuclear Physics (RCNP), Osaka University
ECT* workshop on
“Recent advances and challenges in the description of nuclear reactions at the limit of stability”
K0
K1
K2
Recent result from RIBF/RCNPS. Kawase+, PTEP2018, 021D01 (2018).
✓ Collaboration ongoing with R. Tang+ (23,25F), R. Taniuchi+ (79Cu), and L. Olivier+ (80Zn) …
✓ Benchmark study on DWIA with M. Gomez-Ramos, A. M. Moro, K. Yoshida.
Plan of this talk
I. Multistep direct process and quasi-free scattering
II. The semiclassical distorted wave (SCDW) model and its applicationsY. L. Luo and M. Kawai, PRC43, 2367 (1991).
M. Kawai and H. A. Weidenmueller, PRC45, 1856 (1992).Y. Watanabe et al., PRC59, 2136 (1999).Sun Weili et al., PRC60, 064605 (1999).
KO et al., PRC60, 054605 (1999).KO, G. C. Hillhouse, and B. I. S. van der Ventel, PRC76, 021602(R) (2007).
M. Kohno et al., PRC74, 064613 (2006).
III. Description of inclusive 1N cross section for nuclear transmutationKO, arXiv:1801.09994.
emission
1-step 2-step
incidence
multistep directprocess (MSD)
emission
Pre-equilibrium process
multistep compoundprocess (MSC)
compoundnucleus
at intermediate energies
Multistep direct process and QFS
MSD is dominant for the pre-equilibrium process for incident energies higher than several dozens of MeV.
One-step process is most important.At intermediate energies the impulse picture holds.
Emission energy
Cro
ss se
ctio
n of
(N,N
’x)
Pre-equilibrium process
Quasi-Free Scattering
We see a peak corresponding to the incident particle with a nucleon inside the nucleus at rest:. quasi-free peak
The peak has a width due to the Fermi motion of the target nucleon.
50 100 150 200 2500.10.20.30.40.50.60.70.80.9
1
DD
X (m
b / M
eV sr
) 40Ca(p,p’x) at 392 MeVf=25.5 deg.
20 70 120 1700.2
0.3
0.4
0.5
0.6
0.7
0.840Ca(p,nx) at 346 MeV
f=22 deg.
A.A. Cowley et al., PRC62, 044604 (2000). T. Wakasa et al., PRC59, 3177 (1999).
Energy transfer (MeV) Energy transfer (MeV)
QFS in observables
QFS gives an important contribution to the cross section.
A naïve (intuitive) picture of QFS
How is this picture derived from quantum mechanics?
INC, QMD, and AMDassume this picture.
Local Fermi gas model (LFG) for nuclei (for simple explanation)
DWIA formalism for QFS
Possible issues Interference between different “collision points” Two-body kinematics is not specified.
LSCA to the distorted waves
Local Semi-Classical Approxn (LSCA)
Y. L. Luo and M. Kawai, PRC43, 2367 (1991).
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Rea
l
EXACTLSCA
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-4 -3 -2 -1 0 1 2 3 4sr (fm)
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Imag
inar
y
-4 -3 -2 -1 0 1 2 3 4
s (fm)
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y
z
x
O
sr
s
s
LSCA holds within1―2 fm.
r
Validity of LSCA: p-40Ca at 350 MeV
Determination of the NN kinematics
LSCA to
NN kinematics specified
with
cf. K determines the angular distribution~ nuclear radius: oscillation~ NN interaction range: smooth
K for inclusive processes If we take the summation over all
the states, we have a delta function. If many states contribute, the range
of non-locality of K should be short.
Non-locality of the kernel
0 1 2 3 4 5 6 7 8
|r-r'| (fm)
-0.5
0
0.5
1
1.5
2
2.5
K Kernel ( w = 80 MeV )Kernel ( w = 40 MeV )
90Zr(p,p’x) at 200 MeV
Localization of the NN collision
LSCA to with .
Conservation of NN local momentum
Semi-Classical Distorted Wave model
The intuitive picture of QFS is derived (no free parameter).Y. L. Luo and M. Kawai, PRC43, 2367 (1991).
Formulation of multistep processes up to 3-step has been completed.M. Kawai and H. A. Weidenmueller, PRC45, 1856 (1992); Y. Watanabe et al., PRC59, 2136 (1999).
A Woods-Saxon s.p. wave function can be used (beyond LFG).Sun Weili et al., PRC60, 064605 (1999).
Spin observables can be calculated.KO et al., PRC60, 054605 (1999); T. Wakasa et al., PRC65, 034615 (2002);KO, G. C. Hillhouse, and B. I. S. van der Ventel, PRC76, 021602(R) (2007).
Applicable to various types of QFS/knockout reactions, e.g., (,K+) reaction.M. Kohno, M. Fujiwara, Y. Watanabe, KO, M. Kawai, PRC74, 064613 (2006).
Extension to the multistep processes Eikonal approximation to the intermediate Green function
Distortion
Fermi motion
Two-body collisiontaking account of
the Pauli’s principle
Geometrical inverse squarelaw and Absorption
No interference between processesthrough different collision points!
A cascade QFS picture derived by SCDW
Sun Weili et al., PRC60, 064605 (1999).
Momentum distribution and observables
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10-01
1000
1001
DD
X (m
b / M
eV sr
)
1+2+3STEP1STEP2STEP3STEPCowley et al.
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Energy transfer (MeV)
10-03
10-02
10-01
1000
DD
X (m
b / M
eV sr
)
1+2+3STEP1STEP2STEP3STEPCowley et al.
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Energy transfer (MeV)
10-04
10-03
10-02
10-01
1000
1+2+3STEP1STEP2STEP3STEPCowley et al.
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-04
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1000
1+2+3STEP1STEP2STEP3STEPCowley et al.
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-04
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1000
1+2+3STEP1STEP2STEP3STEPCowley et al.
50 100 150 200 250 300 350
Energy transfer (MeV)
10-05
10-04
10-03
10-02
10-01
1+2+3STEP1STEP2STEP3STEPCowley et al.
25.5 deg.
40 deg.
60 deg.
80 deg.
100 deg.
120 deg.
DDX for 40Ca(p,p’x) at 392 MeVKO, Watanabe, Sun, Kohno, Kawai, Proc. of MEDIUM02, p.231 (2003).
Exp. data: A.A. Cowley et al., PRC62, 044604 (2000).
The longstanding quasi-free Ay problem
208Pb(p,p’x)at 290 MeV
Exp. data:X.Y. Chen et al., NPA505, 670 (1989).
A naïve DWIA fails.
208Pb(p,p’x) at 290 MeV
Exp. data:X.Y. Chen et al., NPA505, 670 (1989).
0 6 12 18 24 30
0.15
0.25
0.35
0.45
full SCDW
A solution to this problem with SCDW
0 6 12 18 24 300.1
0.2
0.3
0.4
0.5
(deg)A y
w/o deflection
Fermi motion fixed w/o deflection
Fermi motion fixed(optimal momentum)
KO, G. C. Hillhouse, and B. I. S. van der Ventel, PRC76, 021602(R) (2007).
Application of SCDW to (,K+) reaction
Application of SCDW to (,K+) reaction
Nuclear Transmutation studiesImpulsing Paradigm Change through Disruptive Technologies Program・Launched FY2014 and 12 programs approved.・will end at Dec. 31, 2018.・Keyword: high risk and high impact
Reduction and ResourceRecycleofHighLevelRadioactiveWasteswith NuclearTransmutation (PM: ReikoFujita)
Spallation cross section taken at RIBFS. Kawase et al., PTEP2017, 093D03 (2017).93Zr at 100 MeV/nucleon
Problem on 1N process
k (fm1)n
(fm
3 )
r = 8 fm
p in 208Pb
WignerDistribution
INCLLFG(QMD)
A
Cro
ss se
ctio
n (m
b)
137Cs 185MeV on proton
cf. D. Mancusi et al., PRC 91, 034602 (2015).
Outline of the modelKO, arXiv:1801.09994.
Excitation energy distribution0 0
Exci
tatio
n en
ergy
di
strib
utio
n (m
b/M
eV)
Exci
tatio
n en
ergy
di
strib
utio
n (m
b/M
eV)
KO, arXiv:1801.09994.
0 50 100 150 2000
50
100
150
200
250fit@118fit@196Wang et al.
1n
(mb)
107Pd
Ein (MeV)
Incident energy dependence
0 50 100 150 2000
50
100
150calcKawase et al.
1n
(mb)
93Zr
Ein (MeV)
0 50 100 150 20005
101520253035
fit@118fit@196Wang et al.
1p
(mb)
107Pd
Ein (MeV)
0 50 100 150 2000
5
10
15
calcKawase et al.
1p
(mb)
93Zr
Ein (MeV)
The Semi-Classical Distorted Wave model (SCDW) for inclusive QFSprocesses is reviewed.
With SCDW, an intuitive picture of the cascade QFS is derived from DWIA. multistep direct processes up to 3-step are described. spin observables also are calculable. general description of an elementary process inside a nucleus is possible.
Summary
Future plans: application of SCDW to other types of inclusive knockout process better description of the spallation cross sections of LLFP.
This work was funded in part by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).