Upload
gary-cummings
View
223
Download
1
Embed Size (px)
Citation preview
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
Euroschool Leuven – September 2009Wolfram KORTEN 2
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
Euroschool Leuven – September 2009Wolfram KORTEN 3
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
Euroschool Leuven – September 2009Wolfram KORTEN 4
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
Euroschool Leuven – September 2009Wolfram KORTEN 5
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
Euroschool Leuven – September 2009Wolfram KORTEN 6
Quadrupole deformation of nuclei
Coulomb excitation can, in principal, map the shape of all atomic nuclei
M. Girod, CEA
Euroschool Leuven – September 2009Wolfram KORTEN 7
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
Euroschool Leuven – September 2009Wolfram KORTEN 8
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
Euroschool Leuven – September 2009Wolfram KORTEN 9
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
Euroschool Leuven – September 2009Wolfram KORTEN 10
Coulomb excitation – an introduction
Euroschool Leuven – September 2009Wolfram KORTEN 11
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
Euroschool Leuven – September 2009Wolfram KORTEN 12
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
Euroschool Leuven – September 2009Wolfram KORTEN 13
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
Euroschool Leuven – September 2009Wolfram KORTEN 14
„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
Euroschool Leuven – September 2009Wolfram KORTEN 15
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
Euroschool Leuven – September 2009Wolfram KORTEN 16
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
Euroschool Leuven – September 2009Wolfram KORTEN 17
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()
Euroschool Leuven – September 2009Wolfram KORTEN 18
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
Euroschool Leuven – September 2009Wolfram KORTEN 19
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)
Euroschool Leuven – September 2009Wolfram KORTEN 20
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
Euroschool Leuven – September 2009Wolfram KORTEN 21
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
Euroschool Leuven – September 2009Wolfram KORTEN 22
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.