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Quasi-free scattering with exotic nuclei. . collaboration meeting. R3B/EXL. L.V. Chulkov October 16 2007. Study of deep-hole states (s 1/2 ). M. Yosoi et al., Phys. Let. B 551, 255 (2003). M. Yosoi, PhD Thesis, 2003, Kyoto University. Quasi-free scattering.

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Quasi free scattering with exotic nuclei

Quasi-free scattering with exotic nuclei


collaboration meeting


L.V. Chulkov

October 16 2007

Quasi free scattering

Study of deep-hole states (s1/2)

M. Yosoi et al., Phys. Let. B 551, 255 (2003).

M. Yosoi, PhD Thesis, 2003, Kyoto University

Quasi-free scattering.

Owen Chamberlain, Emilio Segre,

Berkeley, Li(p,2p),

350 MeV, 1952

Cross section


distorted proton





free n-n


Cross section

Feynman diagram for quasi-free scattering in the impulse approximation. Vertex 1 corresponds to the reaction P →Q + pewith particle P and Q on their respective mass shells, and the vertex 2 describes the reaction p0 + p1 → q0 + q1 in which p0, q0, and q1 have their physical masses.

Three particles in the final state:

+ 9 kinematical variables.

Momentum and energy conservation:

- 4 kinematical variables.

Cross section generally depends on

9-4=5 variables.








free NN

cross section

Impulse approximation how good it is
Impulse approximation. How good it is?

  • Problems:

  • Results are model dependent.

  • In particular, sensitivity to the wave function.

  • Final state interactions

  • Passage of the probe and knocked out particle through nuclear matter. .

  • Recipe:

  • Choose proper energy - 200-500 MeV.

  • Decrease amount of nuclear matter- light nuclei.

  • Use only in-plane evens

P 2p separation energies widths and angular momentum assignment
(p,2p). Separation energies, widths and angular momentum assignment.

G. Jacobs and Th. Maris, RMP 45 (1973) 6.





Core + valence

nucleons model ??

Distorted momentum distributions of the knocked out particle
Distorted momentum distributions of the knocked out particle.



G. Jacobs and Th. Maris, RMP 45 (1973) 6.

Spectroscopic factors.Experiment in comparison with the Independent-Particle Model and Large-Basis Shell Model.

M.B. Tsang et al.,

PRL 95(2005)222501

Comparison of experimental

spectroscopic factors to predictions from IPM (left) and LB-SM (right). Open and closed symbols denote elements with odd and even Z, respec-tively. The solid line indicate perfect agreement. The two dashed lines indicate ±20% deviation from the solid line.

Conventional and inverse kinematics momentum transfer
Conventional and inverse kinematics.Momentum transfer.

Comparison of conventional and inverse kinematics for

12C+1H → p+p+11B

at 400 MeV/nucleon. Proton detectors are at 430 at both sides if the beam.

Proton elastic scattering on hydrogen

and helium.

The task is the investigation of 8 he structure by quasi free scattering on protons
The task is the investigation of 8He structure by quasi-free scattering on protons.

8He (0+)

M.V.Zhukov et al., PRC 50 (1994) R1

Sounds simple... But how to see structures inside the nucleus?

Experiment with 4 he 6 he and 8 he beams
Experiment with 4He, 6He and 8He beams.

Confirmations of the jj based structure:


I.Tanihata +, Phys.Rev.Let. 55(1985) 2676

A.A.Korsheninnikov+,Phys.Rev.Let. 90(2003) 082501

F.Skaza+,Phys.Rev. C73(2006)044301


Y.Suzuki +, Phys.Rev. C41(1990) 736

M.V.Zhukov+, Phys.Rev.C50(1994)R1

not in agreement with K.Markenroth+, Nucl.Phys. A679 (2001) 462 experiment

Liquid hydrogen target and 4 he 6 he 8 he beams
Liquid hydrogen target and 4He, 6He, 8He beams.

18O 820 MeV/A +9Be target →

→ 6,8He (~700 MeV/A)

GSI, Darmstadt


Neutron and cluster knockout channels can be disentangled .

Cross section impulse approximation
Cross section. Impulse approximation.

Relativistic invariant expressions:

Conventional formalism

A.W.Stetz, Phys.Rev. C21 (1980) 1979.

CM system of participants

Convenient to use when solid angles of the detectors are small. Can not be used when solid angles are big.

1. Φ - dependence is trivial.

2. Treiman-Yang criteria →Ψ dependence is vanished

3. s – appears only in kinematical factor.

4. Why not integrate on Q?

We can not reduce the usual fivefold differential cross section even to a threefold differential.

Not suitable for large-acceptance measurements!

Internal momentum distribution of clusters
Internal momentum distribution of clusters.

Laboratory system

6He → α+2n



Curves are obtained from calculated two-body WF: α + 2n, α + 4n and 6He + 2n with corresponding quantum numbers.

6He in 8He

α in 6He

Tetra-neutron in 8He?

α in 8He

Test case 6 he beam neutron and 4 he knock out
Test case: 6He beam – neutron and 4He knock out.

Sα= 0.8±0.1

Sn = 1.7±0.2

6He(p,p n)

6He(p,p 4He)

Solid lines and open points are the relativistic-invariant cross sections for the proton scattering on free neutron (left panel) and 4He (right panel), normalized to the experimental data.

QFS mechanism is confirmed.

8 he neutron knockout 4 he knockout and knockout
8He. Neutron knockout, 4He knockout, and ??? knockout ???

Solid black lines are the cross sections for the proton scattering on a free neutron (top panels) and 4He (bottom panel), normalized to the experimental data.

QFS mechanism is confirmed.







Red line is the elastic cross section for

6He(p,p) with its r.m.s radius 2.4 fm. Line goes far from the data...



6 he knocked out from 8 he
6He knocked out from 8He.

Effective size of a cluster can be determined.

8He(p,p 6He)

8He(p,p 6He)


<r2>1/2 = 1.8 fm

for a 6He cluster.

<r2>1/2 = 2.4 fm

for a free 6He nucleus.

Elastic scattering was calculated in an eikonal

approximation: C.Bertulani +,Nucl.Phys. A588 (1995) 667.

8 he summary
8He. Summary

[1] L.V.Chulkov et al., NuclPhys. A759 (2005) 43, [2][ N.Keeley et al., Phys.Let. B646 (2007) 232.


Y.Kanada-En'yo, preprint nucl-th:0707.2120v1, 2007.

The inclusive n and α -knockout reveals mainly the 4He + 4n structure, while coincidences the knocked out neutron and fragment point out the importance of the 0p1/2 orbit. The knockout of 6He directly demonstrates the dominance of the 6He+2n structure.

As a perspective,

the studies of the nucleon knockout from the s-shell allow to go beyond the 4He +4n structure and to investigate, for example, how the separation energy of the s-shell nucleon changes with the increasing number of neutrons.

Prototype experiment in inverse kinematics with land aladin 12 c p 2p 11 b sep oct 2007
Prototype Experiment in Inverse Kinematics with LAND/ALADIN: 12C(p,2p)11B – Sep/Oct 2007

Beam cocktail

(40Ar primary beam)


Charged fragments

tracking → Br

ToF, x, y, z


& Protons

20O beam



Reaction products after target

Si recoil detector

~20 m

Present Cave C Setup LAND/ALADIN:

Single layer cube of prototype

Si micro-strip detectors installed

inside NaI Crystal Ball

Target recoil protons from

quasi-free scattering reaction

12C(p,2p)11B tracked by Si

energy measured in Crystal Ball

Proposal- S296.

Conventional and inverse kinematics
Conventional and inverse kinematics LAND/ALADIN:

E1 (MeV)

E2 (MeV)

Comparison of conventional and inverse kinematics for

12C+1H → p+p+11B

at 400 MeV/nucleon. Proton detectors are at 430 at both sides if the beam.

Monte-Carlo simulation for for

12C+1H → p+p+11B assuming

Δθ = 3 mrad.

12 c p 2p some simulations
12 LAND/ALADIN: C(p,2p). Some simulations.

knocked out

p - shell

s - shell


Energy versus angle

Angle versus angle


knocked out

500 MeV/A

Q=√-t versus angle


Experiments with radioactive beams LAND/ALADIN:

Radioactive beams and inverse kinematics

Low beam intensities

Extremely large angular acceptance

Experiments with stable beams

Proton beams

Extremely high beam intensities

Very small angular acceptance

Perfect angular and energy resolution


Experiments with radioactive beams can not compete in the achievable resolution with experiments made in 1960-1970 using proton beams impinging a target of stable isotope.

Extremely large angular acceptance requires nonstandard solution of the physical analysis of the experimental data A theoretical model which can be applied to the data analysis should be formulated in Mandelstam variables (relativistic scalars).

Clear physical task should be set for any experiment and original solution should be found for experimental setup in every particular case. Simulations are necessary be done to prove that the experimental goal can be reached with the proposed setup.

The usage of quasi-free scattering in investigations of exotic nuclei is a perspective but difficult task. No universal setup exist and an original solution should be found in every particular case.