Some note on the correspondence between
nuclear clustering and scattering observables
第5回クラスター階層領域研究会

Kazuyuki Ogata
RCNP, Osaka University / Osaka City University

Knock it out!
K1

KB

K0
K2
KCKB

K2

K0 → K1

KC = K1 + K2 - K0 = - KB
(Fermi motion)

KC = 0 in this toy.

Nuclear clusteringpna, d, and 2n in nuclei are of interest, not in free space.

a clustering• antisymmetrization effecton the a clustering picture

deuteron(-like) pair• fragileness of d• breakup/reformation afteremission

di-neutron pair• not bound• Final State Interaction (FSI)a clustering

20Ne(p,pa) at 101.5 MeV
Tp varied
K. Yoshida+, PRC 100, 044601 (2019).

qp fixed
qa fixedrecoilless

R j (R) (fm-1/2)

s.p. a wave function AMD (20-body calc.)
0.5
0.4
0.3
0.2
0.1
0-0.1
-0.2
-0.3

02

4

68

1012R (fm)Triple-diff. cross section (TDX)Clustering picture of identical particals
Here is an a clustering.

16Oaa
16O

Where is a?

Antisymmetrization effect
0.5
0.4
0.3
0.2
0.1
0-0.1-0.2-0.3

not probed by (p,pa)

AMDR j (R) (fm-1/2)

R j (R) (fm-1/2)

not probed by (p,pa)

Sa= 0.258
02

46R (fm)

8

10

120.5
0.4
0.3
0.2
0.1
0-0.1
-0.2
-0.3

Woods-Saxon(no antisym.)

Sa= 0.388
02

4

68

10

12R (fm)• Because of the absorption, only the surface region (R > 3.5 fm) is found to be probed.
• Using a WS model is ok when we just talk about the surface region (for a knockout).
• Sa (square norm of j) is significantly (~50%) affected by the antisymmetrization.

10Be(p,pa)6He at 250 MeV
M. Lyu, K. Yoshida, Y. Kanada-En'yo, and KO, PRC 97, 044612 (2018).

Gas like

Shell model likeMolecular

12Be(p,pa)8He at 250 MeV
M. Lyu, K. Yoshida, Y. Kanada-En'yo, and KO, PRC 99, 064610 (2019).

weakeneddefault

10Be(p,pa)6He in inverse kinematics
recoilless

qp fixed
qa fixed
10Be• Phase space determines the shape of the TDX.
• For each Tp, there are two solutions for thekinematics of the three particles.
• TDX in inverse kinematics will not be a goodobservable.

d3s / dTpdWpdWa (mb sr-2MeV-1)

Tp varied

10

2
6He: g.s.

10110010-1

10-2

6He: 2+025
Tp (MeV)150

deuteron-like correlation

Experimental fact
C. Samanta+, RRC 26, 1379 (1982).
16O(p,pd)14N
1+(3.95) at 101.3 MeV

C. Samanta+, RRC 34, 1610 (1986).

16O(p,2p)15N
gnd at 101.3 MeV

Remarks on the pn knockout
deuteron breakup/(re)formation during
the emission described by CDCC
pn pair distribution calculated with DFT
in collaboration w/ K. Yoshida (Kyoto)

The elementary process can be either
knockout “d” or breakup the pn pair.

Pairing strength vs. TDX
Y. Chazono, K. Yoshida, K. Yoshida, and KO, arXiv:2007.06771

・The peak height of the TDX clearly reflects the pn pairing strength.
・The deuteron breakup is neglected.
・The elementary process is assumed to be the pd elastic scattering.

Breakup effect of the emitted deuteronY. Chazono, K. Yoshida, and KO, in preparation.
16O(p,pd)14N
1+(3.95) at 101.3 MeV・The deuteron breakup effect is very large.
・A naïve pn single-particle wave functionis adopted.
・The elementary process is assumed to be
the pd elastic scattering.

Remarks on the pn knockout
deuteron breakup/(re)formation during
the emission described by CDCC
pn pair distribution calculated with DFT
in collaboration w/ K. Yoshida (Kyoto)

The elementary process can be either
knockout “d” or breakup the pn pair.
reformation may be very importantdi-neutron correlation

ds/dE [b/MeV]

Y. Kikuchi, T. Myo, K. Kato, and K. Ikeda, PRC 87, 034606 (2013).

We must minimize the effect of the FSI.
(unless we are interested in 2n in free space)

These fragments interact eachother after breakup=Coulomb breakup cross section of 11Li

Our starting point

Final State Interaction (FSI)

E [MeV]
Note: E1 sum rule is free from the FSI.

Proving 2n correlation in 6He via (p,pn) process
Y. Kikuchi, KO, Y. Kubota, M. Sasano, and T. Uesaka, PTEP 2016, 103D03 (2016).

250 A MeV

6HepNuclear “clustering” (future study)
4n and 7H in free space is of interest.

tetra neutron

7H• FSI should be maximized.
• 8He(p,pa) has been measured
at RIBF.
• DWIA+5-body CDCC

• FSI should be maximized.
• 8He(p,2p) has been measured
at RIBF.
• DWIA+6-body CDCC

short-range/tensor corr.

spatial depletion• pickup (exchange) type(p,pd) can be used.
cf. Terashima+, PRL121, 242501

Summary of the notes
I. a cluster structure via (p,pa)
・Antisymmetrization should be kept in mind. Sa will not be a useful measure of the a clustering.
・Triple-differential cross section has an “ill behavior” in inverse kinematics. Conversion of it toforward kinematics will be recommended.

II. deuteron-like correlation
・The final-state interaction (FSI) can not be avoided.
・Even the breakup/reformation process in the final channel will be needed.

III. di-neutron correlation
・(p,pn) for two-neutron halo nuclei is suitable to minimize the FSI.
・Detection of 2n is not a outcome of the di-neutron correlation.

IV. Other related activities
・4n and 7H can be studied by KO reactions with kinematics in which the FSI is maximized.
・Tensor correlation can be studied by pickup-type (p,pd) reactions.

To integrate our knowledge on clustering, an appropriate interpretation of(nuclear) reaction data will be indispensable.