wolfram korten 1 euroschool leuven – september 2009 coulomb excitation with radioactive ion beams...

Euroschool Leuven – September 2009Wolfram KORTEN 1

Coulomb excitation with radioactive ion beams

• Motivation and introduction • Theoretical aspects of Coulomb excitation• Experimental considerations, set-ups and

analysis techniques• Recent highlights and future perspectives

Lecture given at the Euroschool 2009 in Leuven

Wolfram KORTENCEA Saclay


Shell structure of atomic nucleiprotons

neutrons

82

5028

28

50

82

2082

28

20

126

no 28O !

stable double-magic nuclei4He, 16O, 40Ca, 48Ca, 208Pb

radioactive: 56Ni, 132Sn, magic ? 48Ni, 78Ni, 100Sn

70Ca ?48Ca40Ca

42Si32Mg


protons

neutrons

82

5028

28

50

82

2082

28

20

126

Changes in the nuclear shell structure

110Zr70132Sn82

“drip line”

g9/2

s1/2

d5/2

70

40

h11/2

d3/2

g7/2

f7/2

N/ZN/Z

g9/2

s1/2

d5/2

82

stabil

50

f7/2

h11/2

d3/2

g7/2

p1/2 p1/2

Spin-orbit term of the nuclear int. ?Only observable in heavy nuciei: (Z,N) > 40


Changes in the nuclear shell structure

Example: “Island of inversion” around 32Mg deformed ground state

12 16 20 24 N

4

3

2

1

0

E(2

+)

[MeV

]

12Mg 16S

20Ca

N=20

N/Z

40Ca 38Ar 36S 34Si 32Mg 30Ne

200

400

B(E

2) [

e2 fm

4 ]

N=20

sd

sd+fp

Masses and separation energies

0

5000

1 104

1,5 104

2 104

10 15 20 25 30

Ca

K

Ar

Cl

S

P

Si

Al

Mg

Na

Ne

F

O

N

C

B

S2N

(ke

V)

Neutron number

17B

20C

23N

29F

32Ne 35

Na

37Mg

40Al

42Si

44P

45S

47Cl

48Ar

2016 28

24O

Observables:

Properties of 2+ states


Shapes of atomic nucleiprotons

neutrons

82

5028

28

50

82

2082

28

20

126

The vast majority of all nuclei shows a non-spherical mass distribution

Z, N = magic numbers

Closed shell = spherical shape

DeformedDeformed

SphericalSpherical

8

20

28

50

2

sng

le p

arti

cle

eneg

ies

elongation

Nilssondiagramm

Oblate Prolate


Quadrupole deformation of nuclei

Coulomb excitation can, in principal, map the shape of all atomic nuclei

M. Girod, CEA


Quadrupole deformation of nuclei

M. Girod, CEA

N=Z

Oblate deformed nuclei are far less abundant than prolate nucleiShape coexistence possible for certain regions of N & Z

Prolate

Oblate Pb & Bi

N~ZFission

fragments


Shape variations and intruder orbitalssi

ngle

-par

ticle

ene

rgy

(Wo

ods-

Sax

on)

quadrupole deformation

ND

235U

SD

152Dy

Z=48

HD

108Cd i13/2

(N+1) intruder normal deformed, e.g. 235U

(N+2) super-intruder Superdeformation, e.g. 152Dy, 80Zr

(N+3) hyper-intruder Hyperdeformation in 108Cd, ?

N+2 shell

N+3 shell

N shell

N+1 shell

Fermi level

En

erg

y

Deformation


Exotic shapes and “deformation” parameters

),()(1)( 0 YtaRtR

quadrupole

octupole

hexadecapole

cos220 a sin2

122222 aa

oblate non-collective

prolatecollective

2 : elongation

prolate non-collective

Lundconvention

spherical

oblatecollective

: triaxiality

Generic nuclear shapes can be described

by a development of spherical harmonics

deformation parameters

Tetrahedral Y32 deformation

Dynamic vibration

Static rotation

Triaxial Y22 deformation


Coulomb excitation – an introduction


Rutherford scattering – some reminders

• Elastic scattering of charged particles (point-like monopoles) under the influence of the Coulomb field

FC = Z1Z2e2/r2 with r(t) = |r1(t) – r2(t)| hyperbolic relative motion of the reaction partners

• Rutherford cross section

d/dZ1Z2e2/Ecm2 sin-4(cm/2)

b

projectile

target

r(t)

int2

21c2

TP

TP20cm /ReZZVv

mm

mmvm Eas long as valid

12

2

2

2

b

y

a

x a beam energyb = impact parameter


Coulomb excitation – some basics

Nuclear excitation by the electromagnetic interaction acting between two colliding nuclei.

b

projectile

target

Target and projectile excitation possibleoften heavy, magic nucleus (e.g. 208Pb) as projectile target Coulomb excitation as target projectile Coulomb excitation(important technique for radioactive beams)

small impact parameter back scattering close approach strong EM field

large impact parameter forward scattering large distance weak EM field

Coulomb trajectories only if the colliding nuclei do not reach the “Coulomb barrier” purely electromagnetic process, no nuclear interaction, calculable with high precision


Reactions below the Coulomb barrierVC= Z1Z2e2/rb (1-a/rb)rb = 1.07(A1

1/3+A21/3) + 2.72 fm

a=0.63 fm (surface diffuseness)

Beam energy per nucleon (EB/A) rather constant, e.g. for 208Pb target 5.6 to 6 A.MeV

exp

/R

uth

Pure Coulomb excitation requires amuch larger distance between the nuclei”safe energy” requirement

Inelastic scattering (e.m/nucl.) Transfer reactions Fusion


„Safe“ energy requirement

• Rutherford scattering only if the distance of closest approach is large compared to nuclear radii + surfaces:„Simple“ approach using the liquid-drop model

Dmin rs = [1.25 (A11/3 + A2

1/3) + 5] fm

• More realistic approach using the half-density radius of a Fermi mass distribution of the nuclei :

Ci = Ri(1-Ri-2) with R = 1.28 A1/3 - 0.76 + 0.8 A-1/3

Dmin rs = [ C1 + C2 + S ] fm

b

projectile

target

Dmin

min

2TP

cm D

eZZE


Empirical data on surface distance S as function of half-density radii C i

require distance of closest approach S > 5 - 8 fm choose adequate beam energy (D > Dmin for all ) low-energy Coulomb excitation limit scattering angle, i.e. select impact parameter b > Dmin, high-energy Coulomb excitation

„Safe“ energy requirement e

xp/

Rut

h

Dmin


He

O

Pb

Ar

Validity of classical Coulomb trajectories

b=0

projectile target

Sommerfeld parameter

>> 1 requirement for a semi classical

treatment of equations of motion measures the strength of the

monopole-monopole interaction equivalent to the number of

exchanged photons needed to force

the nuclei on a hyperbolic orbit

1v

eZZaη

2TP

D=2a


Coulomb trajectories – some more definitions

distance of closest approach (for w=0):

impact parameter:

angular momentum :

Principal assumption >>1 classical description of the relative motion of the center-of-mass of the two nuclei hyperbolic trajectories

r (w) = a (sinh w + 1)t (w) = a/v (cosh w + w) a = Zp Zt e2 E-1

2cot12 cmL

2

θsin1a ) ε(1a )(θ D

1

cmcm

2

θcot a 2aD- D b cm2

b

projectile

target

D()


Coulomb excitation – the principal process

b

projectile

target

vi

vf

TP

TP0

2f

2i02

1fi mm

mmm withvvmEEΔE

Inelastic scattering: kinetic energy is transformed into nuclear excitation energy

e.g. rotation vibration

Excitation probability (or

cross section) is a measure

of the collectivity of the

nuclear state of interest

complementary to, e.g.,

transfer reactions


Coulomb excitation – “sudden impact”

Excitation occurs only if nuclear time scale is long compared to the collision time:„sudden impact“ if nucl >> coll ~ a/v 10 fm / 0.1c 2-310-22 s

coll ~ nucl ~ ћ/E adiabatic limit for (single-step) excitations

v

1

v

1eZZ

v

aΔEτ

ΔEξ

if

221

coll

: adiabacity paramater sometimes also () with D() instead of a

a

v1)(ξΔEmax

Limitation in the excitation energy E

for single-step excitations in particular for low-energy reactions (v<c)


Coulomb excitation – first conclusions

Maximal transferable excitation energy and spin in heavy-ion collisions

1 /cfor v c

v

a

c1)(ξΔE i

imax

βγ a

1)(ξΔEmax

c cCM

grmax V E

2

θηcotL

=1

)cosθ(1Dv

QeZL cm2

rot2

1max


Coulomb excitation – the different energy regimes

MeV2εa

vΔEmax

Low-energy regime (< 5 MeV/u)

High-energy regime (>>5 MeV/u)

Energy cut-off 0.4)10MeV(βεa

γβ cΔEmax

Spin cut-off: L up to 30ћ L~ n with n~1


Summary

• Coulomb excitation is a purely electro-magnetic excitation process of nuclear states due to the Coulomb field of two colliding nuclei.

• Coulomb excitation is a very precise tool to measure the collectivity of nuclear excitations and in particular nuclear shapes.

• Coulomb excitation appears in all nuclear reactions (at least in the incoming channel) and can lead to doorway states for other excitations.

• Pure electro-magnetic interaction (which can be readily calculated without the knowledge of optical potentials etc.) requires “safe” distance between the partners at all times.

wolfram korten 1 euroschool leuven – september 2009 coulomb excitation with radioactive ion beams...

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