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).

-4 -3 -2 -1 0 1 2 3 4-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Rea

l

EXACTLSCA

-4 -3 -2 -1 0 1 2 3 4-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-4 -3 -2 -1 0 1 2 3 4sr (fm)

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Imag

inar

y

-4 -3 -2 -1 0 1 2 3 4

s (fm)

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

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

50 100 150 200 250 300 35010

-03

10-02

10-01

1000

1001

DD

X (m

b / M

eV sr

)

1+2+3STEP1STEP2STEP3STEPCowley et al.

50 100 150 200 250 300 350

Energy transfer (MeV)

10-03

10-02

10-01

1000

DD

X (m

b / M

eV sr

)

1+2+3STEP1STEP2STEP3STEPCowley et al.

50 100 150 200 250 300 350

Energy transfer (MeV)

10-04

10-03

10-02

10-01

1000

1+2+3STEP1STEP2STEP3STEPCowley et al.

50 100 150 200 250 300 35010

-04

10-03

10-02

10-01

1000

1+2+3STEP1STEP2STEP3STEPCowley et al.

50 100 150 200 250 300 35010

-04

10-03

10-02

10-01

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).