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Resonance Scattering Technique and break-up to study nuclear structure

ISOLDE Nuclear Reaction and Nuclear Structure Course

A. Di Pietro

2

Outline of the lecture:

Resonance scattering method in reverse kinematics.

Advantages of the technique.

Resolution. Discrimination of different processes and energy reconstruction.

Resonant break-up

3-body kinematics

3

n

2H1H

3He 4He3H

6Li 7Li

9Be

6He

8Li8He

8Be7Be 10Be9Li

11Be12Be11Li

10B 11B 12B 13B 14B 15B14Be

9B8B

12C 13C 14C 15C 16C 17C 18C 19C 20C17B 19B

11C10C9C8C

14N 15N 16N 17N 18N 19N 20N 21N13N12N11N

12O 13O 14O 15O 16O 17O 18O 19O 20O 21O 22O

core

core

neutron halo

neutron skin

Decoupling of Proton and neutrons

α α

α α

molecular

α

αα

dilute gas

αα α

0+2 in 12C

6He,11Li,11Be

8He,CBe isotopes

10C, 16C

3-2 in 14C

triangle

excited states

HeLiBe

BC

H

Exotic structures in light nuclei

vanishing of magic number

From Y. Kanada En’yo

44

Cluster structure is a well established feature of many light NZ nuclei both in their ground and excited states.

1. Clusters are formed by tightly bound nucleons (cluster is stiff, i.e. not easy to excite);

2. Weakly coupled inter-cluster motion is considered.

Threshold rule: i.e. these states appear close to the threshold for breaking-up into the cluster constituents.

Ikeda diagram

Ex. Hoyle state in 12C

Weak coupling picture:

Conventional cluster structure

K. Ikeda et al. Supp.Progr.Theo.Phys. 68(1980)1

5

Possible ways to study cluster structures: transfer and decay into the constituents

Resonant elastic scattering 2-body process

Experimental signature:

large reduced width for cluster decay

rotational bands with band head around the threshold for cluster decay (measurement of Eexc and Jπ moment of inertia)

inelastic scattering followed by break up

3-body processes

Ex: 10Be+9Be->15C*+a->11Be+a+a

Ex: 10Be+a->14C*->10Be+aEx: 10Be+b->6He+a+b

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Resonant scattering method (RSM) in invese kinematicsK.P.Artemov et al. Sov.J.Nucl.Phys. 52(1990)408

Elastic scattering of heavy projectiles B on a light targets b (protons or as) in order to study properties of the compound nucleus C resulting from

B+b C B+b

Excitation function measured at qcm180º enhanced visibility of resonances with respect to potential and Coulomb scattering.

Used in the last ten years to measure excitation functions with radioactive beams.

thick solid or gasous target

gaseous target (H, He)

easy to change target thickness (changing gas pressure)

more homogeneous target

7

Allows to measure excitation function in a wide energy range without changing beam energy reduces running time of the experiment

Allows to measure recoil particles around q c.m.~180°

Allows precise measurement of resonance properties: Er, Jp, Gtot, Gp, Ga

Very useful in experiments with low intensity beams (104 ÷ 106 pps).

heavy beamlight

recolil particle

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Advantages of using inverse kinematics

E0 e T0 = laboratory projectile energy in direct and reverse kinematics respectively

E0' e T0' = c.m. energy in direct and reverse kinematics respectively

Θ =laboratory scattering angle of light particle

E3 e T3 = light particle laboratory energy in direct and reverse kinematics respectively

E0

Inverse kinematics

QT0

Direct kinematics

Q

T3 E3

9

MmMTT+

0'

0 MmmEE+

0'0

direct inverse

kmM

TE

0

0

22

03 )1( +

+ k

MmmTT

203 4Mm

mMEE+

Some trivial equations (see previous lecture)

For the same c.m. energy:

T0' = E0'

For: θlab = 0° (= 180° in the c.m.) light particle enrgy is:

10

V1L

V2L

V1B

V2B

VBL

In the current notation :

E3=E2L recoil energy in the Lab systemE1L=E0 projectile energy

LLBLLBLcm

Lcm

BLBL

BLBLBBLLL

EMm

mMEEMm

mMmVEMmmV

MmmME

EmM

mE

mVVm

VVVVmmVEE

123122

12

1

22

122

222

223

)(4

)(21

21

2144

21

)cos2(21

21

+

+

+

+

+

-+ q

at q1B=180°

11

€

Eex = Ec.m. +Q = E0m

M +m+Q

QEM

mMElab

ex ++

32 )(cos4 q

Excitation function from measured recoil energy:

B+b C*B+b

12

2

2

4 ZzE

dxdEdxdE

E

HI

li

∆E=beam energy straggling in the laboratory

(dE/dx)li= stopping power for light particles

(dE/dx)HI= stopping power for beam particles

z= charge of light recoil particles

Z=charge of beam particles

Laboratory energy resolution for light recoil particles in inverse kinematics.

1313

Energy resolution depends also from:

Beam spot size

Detector energy resolution

Detector angular resolution

Kinematical spread within dq Beam angular straggling

Recoil angular straggling (small)

Estraggx

x

Due to energy straggling, to the same Ec.m. correspond different Edet. due to different paths. Effect larger at q>00 due to additional contribution of different scattering angles.

Dependence of energy resolution from energy straggling

q=00

q>00

32S+aG. Rogachev Ph.D thesis. Moscow1999

14

Problems of using this technique:

Sources of background inelastic scattering events

Precise knowledge of stopping power to extract correctly the resonance parameters

Need to measure de/dx with radioactive beams (but not only!)

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In experiment with a gasous extended target is possible to discriminate elastic from inelastic from time of flight measurement or tracking (active targets).

How to discriminate elastic from inelastic scattering events?

From a or p spectrum no possibilities to discriminate the process which produces recoil particles.

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Calculated TtOF- ∆E 2d-spectrum

Example: 9Be + 4He

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9Beg

s

9Be*

Projecting on time axis

Time resolution ΔT~1 ns

Inelastic

Elastic

Experimental Ttof-∆E 2d-spectrum

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Excitation function 9Be + α with RSM on infinite target and energy loss calculated using Monte Carlo code SRIM M. Zadro et al, NIM B259 (2007).

— Excitation function α+9Be measured with thin target method varying beam energy at small streps J. Liu [NIM B 108,(1996) 247] , J.D. Goss [PRC 7,(1973) 247]

Excitation function 9Be+4He at Ecm<4.5MeV

Different energy resonance with the two techniques !

Problems with stopping power calculations.

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Using measured energy loss data

Note: changing stopping power date changes also extracted resonance cross-section

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Excitation function 9Be+a at Ecm>4.5 MeV

Excitation function 9Be + α with RSM on infinite target M. Zadro et al, NIM B259 (2007).

— Excitation function α+9Be measured with thin target method varying beam energy at small streps R.B.Taylor [NP 65,(1965) 318]

Using measured energy loss data

Need to measure stopping power with RIBs but not only!

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Some example of experiments performed using RIBs and RSM technique.

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RSM on thick target

Curtsy of C. Angulo

Level scheme of p-rich nuclei unknown for many species.

By bombarding a 1H enriched target with a p-rich radioactive beam possibility to study levels in the p-rich compound nucleus which are proton unbound.

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18Ne+p @ Elab=21, 23.5 and 28 MeV

Experiment performed at CRC Louvain-la Neuve

Average beam intensity ~4 106 ppsTarget 0.5 mg/cm2 polyethylene

Detection set-up

b background

C. Angulo et al. Nucl. Phys. A 716(2003)211

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Very large Coulomb shift (~0.73 MeV) typical of deformed states in nuclei near the drip-line.

R-matrix analysisLevel scheme

2525

Beam profile

E8Li=30.6 MeV I≈5x104pps

P=700 mbarT=295 K

aΔE : quadrants 50x50 mm2 quadrants Si detectors 50 μm thick.

E Double Sided Silicon Strip Detectors, 50x50 mm2 16+16 strip, 1000 μm

50 mm

50 mm

MCP Detectorgas target

Entrance window

ΔE + DSSSDdetectors

Stopping power detectors

beam

8Li+4He12B

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ΔE Eres

Elastic scattering α particle discrimination

3 H

Background: 8Li (β-)→ 8Be*→ 2 α

α - particle punch through

Background a spectrum: 8Li (β-)→ 8Be*→ 2 α

α

2727

Comparison with literature

E MeV Err keV Width keV Jπ;T reazione

13.33 30 50±20 9Be(7Li,α)

13.40 100 Broad 10B(t,p)

13.4 9Be(7Li,2α)

14.1 9Be(7Li,2α)

14.80 100 <200 2+;2 14C(p,3He)

15.50 9Be(7Li, α)

15.7 9Be(7Li,2α)

17.7 9Be(7Li,2α)

13.5

15.8

14.4

12B states. a particle threshold 10.0 MeV

9Be+7Li → 2α+8Li

Soic N., Europhys. Lett.,63 (2003), 524

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Resonant particle spectroscopy: transfer and decay into the constituents

Ex: 10Be+b->6He+a+b

inelastic scattering followed by break up

3-body processes

Ex: 10Be+9Be->15C*+a

Resonant particle spectroscopy

Ex: A+B->C*+a

M. Milin at al. EPJ A41(2009)335

The detection of break-up products select states with large partial widths for decaying into a chosen channel thus enabling the selection of states with well-developed cluster structure. High segmentation of the detection system allows for high resolution measurement.

6He+12C4He+14C*4He+4He+10Be

Three body kinematics

Three body kinematics

Center of mass system Sequential decay relative coordinate system

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3

1

2

3

VBL

V1B

V1L

q1L q1B

Reaction: P+T→1+2+3

VBL=(2mPEPL)1/2/(mP+mT)

V1B2=V1L2+VBL2-2V1LVBLcosq1L

E1B=½m1V1L2+m1(mPEPL)/(mP+mT)2-m1V1L(2mPEPL)1/2/(mP+mT)cosq1L

a12

E1B=E1L-2a1E1Lcosq1L+a12

f1B=f1L

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211111

1111

cos2

coscos

aEaE

aE

BBB

BBL

++

+

q

qq f1B=f1L

2111111 cos2 aEaEE BBBL ++ q

21211111

1111

cos2

coscos

aEaE

aE

LLL

LLB

+-

-

q

qq

bLTbL

bB

bLALA

bLbBB

DEE

EmEm

qq

qq

sin/sin

sinsin

If we detect particle one the kinematics is completely determined by the two body (particle 1 and 23) kinematics.

If we detect particle 2 and 3 we have to reconstruct the excitation energy of particle 23.

322313 -- ++

+ EEEmm

mQE LP

TP

TbodyTot

Total energy available in the cener of mass system

m1=mass of particle 1m23=m2+m3= mass of particle 23M=m1+m2+m3

We define the reduced masses:m1-23=m1m23/(m1+m23)=m1(m2+m3)/Mm2-3=m2m3/m2+m3

Ecm

Measured quantities are E1L,q1L,f1L – E2L,q2L,f2L- E3L,q3L,f3L of one, two or even three particles

NB: we note that the velocity vectors are in the 3 dimentional space not in plane and both q and f angles are important.

Eg. One wants to reconstruct excitation energy of particle 23

1

2

3q2L,f2L

q3L,f3L

q1L,f1L

V2L

V3L

V1L

VBL

23

c’ system

€

EαB + E6LiB = Ecm − E6Li* +Q2body(α −6Li)

From two body kinematics one can reconstruct the excitation energy of the intermediate 23 system.See equations for two body kinematics

Reaction p+T→1+23*→1+2+3e.g. : a+6Li→a+6Li*→a+a+d

1

2

3q2L,f2L

q3L,f3L

q1L,f1L

V2L

V3L

V1L

VBL

V23B

V23L

V1B

6Li+a6Li*+aa+d+a

E*(6Li)=2 MeV

E*(6Li)=10 MeV

Reaction p+T→1+23*→1+2+3

Q(23→2+3)E*

23

E 2-3

E2-3=E23*+Q(23→2+3)=1/2mvrel(2-3)2=1/2m(V2L-V3L)2

quantity we want to extract from the experiment

quantities to be measured

1

2

3q2L,f2L

q3L,f3L

q1L,f1L

V2L

V3L

V1L

VBL

V23B

V23L

V1B

V2L→ V2L,q2L,f2L V3L→ V3L,q3L,f3L

V2rel=(V2L –V3L)2= V2L 2+V3L

2-2 V2L● V3L

V2L● V3L = V2L V3L cosqrel=V2Lx V3Lx +V2Ly V3Ly +V2Lz V3Lz=V2Lsinq2Lcosf2L V3Lsinq3Lcosf3L +V2Lsinq2Lsinf2L V3Lsinq3Lsinf3L +V2Lcosq2L V3Lcosq3L

V3Lx= V3Lsinq3Lcosf3L

V3Ly= V3Lsinq3Lsinf3L

V3Lz= V3Lcosq3L

V2Lx= V2Lsinq2Lcosf2L

V2Ly= V2Lsinq2Lsinf2L

V2Lz= V2Lcosq2L

€

V2L =2E2L

m2

€

V3L =2E3L

m3

relLL

rel mE

mEV qcos222

3

3

2

22 -+ 32232

32*

32 21

--- - QVE relm

measured quantities energies and angles

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Summary and conclusions

Cluster structures can be measured in various way.

Resonant elastic scattering gives the possibility to measure the excitation function in a single run without changing beam energy. Particularly useful in RIB experiments.

With this technique only unbound states can be measured and the main limitation is the minimum resonance width that can be measured.

Both single particle and cluster states can be studied with RSM.

Resonant particle spectroscopy is the most commonly used technique to study cluster structure.

Good energy and angular resolution is required.