fragmentation

素粒子原子核物理学特別講義IV / 原子核物理学特殊講義 VIII, 東北大学
中性子過剰核の核分光研究
Y.Satou
Department of Physics and astronomy
Seoul National University
Contents
1. 不安定核物理研究の概観
2. 重イオン核種の分離方法
– 二次ビームの分離生成（入射核破砕法）
– 反応核種の分離（双極電磁石を用いる方法）
3. 二次ビームを用いた逆運動学散乱実験
4. 散乱データの解析
1. 不安定核物理研究の概観
Challenges of Physics of Exotic Nuclei
• Physics of Nuclei
– Exotic nuclear structure of nuclei far from stability
– Limit of existence of nuclei
– Nature of nuclear force that binds protons and neutrons into a nucleus
• Nuclear Astrophysics
– Nuclear processes that take place in the universe
Energy generation, Nucleosynthesis of elements
– Properties of the nuclear equation-of-state (EOS)
Mechanism of the supernova explosion
• Applications
– The basis for applied science which strives to solve practical problems
relevant to the society
Medical imaging/diagnostics technique (X-ray CT, MRI, PET, Gamma
Camera) and therapy, Energy generation, Transmutation of
nuclear waste, geology, archaeology etc.
Introduction
•Disappearance of magicity at N=20
T.Motobayashi et al., PLB346(1995)9.
2007@MUS
O.Tarasov et al., PRC75(2007)064613.
T.Baumann et al., Nature 449(2007)1022.
•Disappearance of
magicity at N=8
H.Iwasaki et al., PLB491(2000)8.
2002@RIKEN/GANIL
M.Notani et al., PLB542(2002)49.
S.M.Lukyanov et al.,
J.Phys.G28(2002)L41.
Neutron
drip-line
•Neutron halos
Challenges in nuclear physics
•
•
I.Tanihata et al.,
PRL55(1985)2676.
1999@RIKEN
H.Sakurai et al., PLB448(1999)180.
•New isotopes
•New magic number N=16
A.Ozawa et al., PRL84(2000)5493.
To establish the drip-line
To accumulate spectroscopic information and find new phenomena
Mass, radius,
half-life,mass
electromagnetic
moment,
andscattering
spectruminofinverse
excitedkinematics
states
The invariant
method utilizing
nucleon
Anomalously large matter radius for 11Li from interaction
cross section measurement => neutron halo structure
𝐼0 I0
x
I
𝐼
Valence
neutrons
core
𝑑𝑃 =
𝑁𝜋𝑅2
𝐿2
= 𝜎𝑛𝑑𝑧, 𝜎 = 𝜋𝑅2
𝑁
𝑛 = 𝐿2𝑑𝑧
𝐼 = 𝐼0 exp(−𝜎𝑛𝑧)
Valence neutrons have extended
spatial distribution outside of the
core where neutrons and protons
are equally distributed.
First indication that some neutrons
can be decoupled from protons in
spite of the strong p-n interaction.
I.Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676.
Neutron halo
structure
Es=0.185
Es=8.000
R
11Li
Neutron halo WF
2  
Borromean nucleus
(any sub pairs are unbound)
    dr  0.8
2
0 0 R
Narrow momentum distribution of valence neutrons
supports the neutron halo structure of 11Li
9Li
11Li
C target
11Li
+ C → 9Li + X
0.79 GeV/nucleon
Es=0.185 MeV -> k ～ 20 MeV/c
Observed narrow component in the
momentum distribution of valence
neutrons provides a further
support of the halo structure of 11Li.
T.Kobayashi et al., Phys. Rev. Lett. 60 (1988) 2599.
Electric dipole response in a break-up reaction of a Halo
nucleus
Pb target
11Be
10Be
γ
11Be
neutron
+ 208Pb → 10Be + n
Virtual photon number
208Pb
11Be
T.Aumann, Nucl. Phys. A 805 (2008) 198c.
β-NMR/NQR technique with polarized RI beam
Small electric quadrupole
moments measure for 15B
and 17B might be related to
the decoupling of core and
valence neutrons.
𝑄=
1
𝑉
𝑑 3 𝑟 3𝑧 2 − 𝑟 2 𝜌(𝑟)
H.Ueno et al., Nucl. Phys. A738 (2004) 211.
Nuclear chart
• Number of isotopes predicted to exist: 7,000～10,000
• Known isotopes: ～3,000
• Stable isotopes: 256
• New elements are being synthesized
• New isotopes are being discovered
New Element
Cn
protons
112
(Copernicium)
February 2010
neutrons
New Elements
112
Cn
Copernicium
◇Element 112 is Named Copernicium (Cn)
On February 19, 2010, the 537th anniversary of Copernicus' birth,
IUPAC officially accepted the proposed name and symbol.
Cn is not the end of the story !
Every 2.5 years one new element is discovered !
Z=113→
Z=112→
S. Hofmann, Physics 3, 31 (2010).
The Bethe-Weizsacker mass formula and nuclear binding limits
B/A (MeV)
𝐵 𝑍 + 1, 𝑁 − 𝐵(𝑍, 𝑁) ≤ 0 proton drip line
𝐵 𝑍, 𝑁 + 1 − 𝐵 𝑍, 𝑁 ≤ 0 neutron drip line
Surface
Proton drip line
Coulomb
Mass number
Neutron drip line
14
Can Green function Monte
Carlo calculation make a
nucleus in a computer ?
S.C.Pieper et al., Annu. Rev. Nucl. Part. Sci. 2001.51:53-90
Contents
1. 不安定核物理研究の概観
2. 重イオン核種の分離方法
– 二次ビームの分離生成（入射核破砕法）
– 反応核種の分離（双極電磁石を用いる方法）
3. 二次ビームを用いた逆運動学散乱実験
[軽い中性子過剰核19,17C,14Bの不変質量分光]
4. 散乱データの解析
Challenges of Physics of Exotic Nuclei
• Physics of Nuclei
– Exotic nuclear structure of nuclei far from stability
– Limit of existence of nuclei
– Nature of nuclear force that binds protons and neutrons into a nucleus
• Nuclear Astrophysics
– Nuclear processes that take place in the universe
Energy generation, Nucleosynthesis of elements
– Properties of the nuclear equation-of-state (EOS)
Mechanism of the supernova explosion
• Applications
– The basis for applied science which strives to solve practical problems
relevant to the society
Medical imaging/diagnostics technique (X-ray CT, MRI, PET, Gamma
Camera) and therapy, Energy generation, Transmutation of
nuclear waste, geology, archaeology etc.
2. 重イオン核種の分離方法
•
Isotope Separator On-Line (ISOL) Production
• 二次ビームの分離生成（入射核破砕法）
• 反応核種の分離（双極電磁石を用いる方法）
– SAMURAI magnet を例にした具体的考察
Isotope Separator On-Line (ISOL) Production
Michael S.Smith and K.Ernst Rehm,
Annu. Rev. Part. Sci. 51 (2001) 91.
• Advantages:
– The ISOL beams have excellent
beam qualities and high
purities, with reasonable
intensities, up to ～ 108 cps.
• Limitations:
– Only a few radioactive beam
species can be generated.
– The effectiveness of the ISOL technique depends on the
chemistry of the element.
– Beams with short lifetimes (<1s) are difficult to produce.
Projectile Fragmentation Production
• Advantages:
– Production mechanism is
independent from the
chemical properties of
the secondary beams.
– Separation time is very
short (<0.1 -1 μs).
– Clear identification with
respect to mass and charge is possible.
• Limitations:
– Difficult to obtain low energy beams relevant to astrophysical
reactions with energies less than 2 MeV/nucleon.
– Poor beam quality (large emittance and spot size).
– Contamination of the beam of interest with neighboring nuclei.
Projectile Fragmentation Reaction
Projectile
Projectile Fragment
Β> 0.3c
(～ 50 MeV/u)
Vf
Vp
Target
Target fragment
Before collision
Participant
After collision
1. Versatile coverage of unstable isotopes
2. Easiness of the production scheme
3. Beam are given high energies
Goldhaber Model of the projectile fragmentation
A.S.Goldhaber, Phys. Lett. 53B (1974) 306.
• Fermi motion of a nucleon inside a nucleus:
• A(Projectile) → F(Fragment)
p 2  190MeV/c
Momentum width of the fragment:

 p x2  p y2  p z2 
d 3
 p2 

 exp  
 exp  
3
2 
2


dp
2
 2 


  0
K(A  K)
,
A 1
M.Notani et al., PRC76,044605(2007).
9Be(40Ar,X)
 0  90MeV/c
Projectile
Beam particle
fragment
in its rest frame
A
K
PKA   pii  0?
ii11
100 MeV/u
Secondary beam facilities in the world
TRIUMF-ISAC
GSI
Louvain
RIKEN
RIBF
MSU
GANIL
ORNL
CERN
ISOLDE
Projectile fragmentation facility
ISOL (Isotope Separator On-Line) facility
Isotope Separator On-Line (ISOL) Production
•Surface ion source
•Plasma ion source
•Laser ion source
Mass analysis
M
v2

 qvB

B 
M
v
q
With other types of ion sources (surface and plasma
ion sources) more than 600 isotopes of more than
60 elements have been produced
Laser ion source
Step-wise resonance
photo-ionization
RILIS: the Resonance Ionization Laser Ion Source
Fast RI beams
- RIPS (1990-)
v~0.3c
RI Beam Factory (RIBF)
350 MeV/nucleon
for d-U
SHE (Z=110, 111, 112, 113) - GARIS
~5 MeV/nucleon
pol. d beams
Nov. 2008
v~0.6c
Mar. 2007
135 MeV/nucleon
for light nuclei (1986-)
RI beams (<5 AMeV)
CRIB CNS
v~0.1c
350 MeV/nucleon
up to U
•1st beam: Dec. 2006
•U beam/RI beams with
•U-fission: Mar. 2007
•RI beams with 48Cafragmentation: Dec. 2008
to
be
built
RIBF new facility
• Intense RI beams from in-flight
methods (PF, fission)
a few 100 MeV/nucleon (v~0.6c)
whole range of atomic masses
Fragment separators
• First generation 1985Separator @ LBL BEVALAC (USA)
LISE@GANIL (France)
～ GeV/nucleon
～ 50 MeV/nucleon
• Second generation 1990RIPS@RIKEN (Japan)
～ 50-100 MeV/nucleon
A1200@MSU (USA)
～ 50-100 MeV/nucleon
FRS@GSI (Germany)
～ GeV/nucleon
LISE3,alpha-SISSI@GANIL (France)
～ 50-100 MeV/nucleon
• 2.5 generation 2000A1900@MUS (USA)
• Third generation 2007RIBF@RINEK (Japan)
Super-FRS@GSI FAIR (Germany)
～ 100-400 MeV/nucleon
～ GeV-10 GeV/nucleon
• Fourth generation
FRIB@MUS (USA)
KoRIA(Korea)
～ 200 MeV/nucleon
～ 200 MeV/nucleon
Projectile Fragmentation Production
<Two-stage separation>
Target
Heavy ion beam
First stage
Separation with magnetic rigidity:
A
B1  v
Z
Second stage
Separation with range differences among
different species in the energy degrader:
 A2.5 
B 2～　f  1.5 
Z 
Small Z
Large Z
Secondary beam
Isotope separation using the Fragment separator
J.P.Dufour et al.
Nuclear Instruments and Methods
in Physics Research A248 (1986) 267-281.
A/Z
A2.5/Z1.5
LISE spectrometer at GANIL (France)
SAMURAI
Superconducting Analyser for MUlti-particles from RAdio-Isotope Beam
Large gap (80 cm)
Superconducting
Magnet
Bending Power : BL=7
Tm (B=3T, 60 deg
bending)
Spokesperson
T.Kobayashi
Vacuum chamber
neutron
target
Large gap (80 cm) to let
neutrons pass through
Sweep Beams and Charged
Fragments
Neutron detector array
Focal plane detectors
proton
Charged fragments
Good Mass Resolution for
PID @A ～ 100
Construction underway: 2008 - 2012
A consideration on the mass
resolution of SAMURAI
http://rarfaxp.riken.jp/~ysatou/samurai/mass_res.pdf
A
B1  v
Z
𝑥0 , 𝜃0
𝑥1 , 𝜃1
Fragment mass identification
• The momentum: P
𝐵𝜌 Tm =
𝑃 = 𝑃0 1 + 𝛿
𝑑𝑃
𝛿=
𝑃0
• Ion optical transfer matrix
𝑥1
𝑐11
𝜃1 = 𝑐21
0
𝛿
𝑐12
𝑐22
0
𝑐13
𝑐23
1
𝑥0
𝜃0
𝛿
• 𝛿 values
1
𝑐11
𝑐12
𝑥1 −
𝑥0 −
𝜃0
𝑐13
𝑐13
𝑐13
1
𝑐21
𝑐22
𝛿=
𝜃 −
𝑥 −
𝜃
𝑐23 1
𝑐23 0
𝑐23 0
𝛿=
𝑝𝑐[MeV]
299.793 m s ∙ 𝑍[eC]
Transfer Matrix Elements
Ion optical
calculation code:
OPTRACE
S.Morinobu
Fragment mass resolution
• The mass of a particle:M
𝑀 = 𝑃 𝛾𝛽
• The mass resolution
∆𝑀
=
𝑀
∆𝑃0
𝑃0
2
∆𝛽
2
+ ∆𝛿 +
𝛽
∆𝛿 𝑥1 =
∆𝑥1
𝑐13
2
2
∆𝛿 𝜃1 =
∆𝜃1
𝑐23
2
1 + 𝛾 4 𝛽4
𝑐11 ∆𝑥0
+
𝑐13
2
𝑐12 ∆𝜃0
+
𝑐13
2
𝑐21 ∆𝑥0
+
𝑐23
2
𝑐22 ∆𝜃0
+
𝑐23
2
Fragment mass resolution
• Coulomb multiple scattering effect in Counter gas, He
bags, window materials
𝜃mul
13.6 MeV
=
𝑧 𝑥 𝑋0 1 + 0.038ln 𝑥 𝑋0
𝛽𝑐𝑝
• Estimated mass resolution
𝑀 = 100
∆𝑀~0.15
1 ∆𝑀~7
Enough separation by more than 5𝜎
in mass for neighboring isotopes !
More refined treatments and future
investigations
• Energy straggling
• Charge states
• Thorough geometry
– Detector configuration
– Vacuum chambers
• Examination of the momentum and bending
angle dependences of the mass resolution
• Experimental verification
３．二次ビームを用いた
逆運動学散乱実験
Introduction
• The secondary radioactive beam using projectile
fragmentation has continuously developed to open up a new
regime of spectroscopy on unstable nuclei.
• Two of the major subjects intensively pursued are
(1) exotic nuclear structure of nuclei very far from the valley
of stability and
(2) determination of key cross sections relevant to
astrophysical phenomena.
Advantage of the fragment beam
• Versatile coverage of unstable isotopes
– Beams of very broad range of isotopes can be obtained almost
independently of elements or lifetimes.
• Easiness of the production scheme
– The beam is directory obtained from the simple bombarding process
without involving any sophisticated treatment.
• Beams are given high energies
Projectile
Projectile Fragment
Vp
Vf
Participant
Target
Before collision
Target fragment
After collision
Drawbacks of the fragment beam
• Low beam intensity
• Large emittance for the fragment ions
• Scattering experiments must be done under the inverse
kinematics condition
Decay particle
Projectile
Ejectile
(Beam of
fragment ion)
Fragment
γ-ray
Target
Low intensities of RI beams
• Radioactive beam experiments using projectile fragments
often suffer from low statistics due to limited intensity.
(c.f. 1 nA～6×109 /s)
• Types of feasible experiment strongly depend on the available
beam intensity.
– ～ 1 particle per second (pps)
◇Synthesis of unknown isotopes
◇Measurement of observables such as T1/2, mean radius of nuclei
– ～100s pps
◇A variety of direct reactions can be feasible as a spectroscopic
means.
Direct reaction spectroscopy
• The family of reaction processes referred to as “direct
reactions” involves such processes as
(1) inelastic scattering, (2) charge-exchange reactions,
(3) transfer reactions, (4) Coulomb excitation,
(5) knockout reactions (e.g., (p,2p) reactions)
• These reactions have been a subject of extensive investigation
using stable beams. => well established theoretical treatment
• The direct reaction has a stringent selectivity for states to be
excited, favoring particular modes of nuclear excitation.
The direct reaction offers a versatile spectroscopy with good
selectivity and enhanced sensitivity.
Nuclear structure of very neutron rich
nuclei
• Very neutron rich nuclei have been a subject of intensive investigations;
various exotic properties might be induced due to the large excess of
neutrons and weak binding of valence neutrons.
1. Isospin inhomogeneity
2. Neutron halo structure and cluster formation
3. Changes in the shell structure and deformability of nuclei
4. Modification in the effects of Pauli blocking and enhancement
of the coupling with continuum state.
• Direct-reaction spectroscopy is expected
to be highly effective in exploring these
features of neutron rich nuclei.
Inverse kinematics using secondary beams
• In direct reaction spectroscopy on unstable nuclei, one observe the
reaction in inverse kinematics, where an RI beam impinges on a target to
be excited and scattered to a forward direction.
Decay particle
A large emittance
and a large energy
spread
Projectile
Ejectile
(Beam of
fragment ion)
Fragment
γ-ray
Target
Focused along
the beam
direction with
beam like
velocities
Emitted in a broader range of
angles and energies
• Establishment of a workable scheme to cope with difficulties associated
with secondary beams is important.
Thicker target
A detector assembly with a broad angle coverage
Relatively easily realized
for projectile-like particles
On the energy resolution
• In performing direct-reaction spectroscopy a good energy
resolution (less than a few 100s keV) for excitation energy is
essential to separate and identify individual final states.
– Resolution of fragment beam is typically a few %.
ΔE= a few 10s MeV for 100 A MeV 11Li beam
– Use of a thicker target deteriorates the resolution of outcoming
particles.
For the 100 A MeV 11Li, energy loss amount to 6 MeV across a 12C target of 100 mg/cm2
• “The missing mass method” in which one measures energies
of incident and outcoming particles to determine the
excitation energy from their difference, is impractical if a thick
target is demanded.
Workable schemes
• Gamma-ray detection
– Applicable to bound excited states
– Ge or scintillation crystal such as NaI
– Energy resolution ～ a few keV to some 10s keV
• Invariant mass method
Excitation energy
– Applicable to unbound excited states
MeV
n
Sn
γ
0.0
⇒ particle decay spectroscopy
⇒ γ-ray spectroscopy
Access to unbound states is
particularly important in the
study of neutron rich nuclei
near the drip line, because in
such nuclei most of the states
are unbound against particle
emissions.
Invariant mass method in inverse kinematics
•
•
Once an unbound state is formed it decays by emitting neutrons and/or charged
particles leading to 2-body or more-body final channels.
In a geometry of inverse kinematics these particles will fly to forward directions.
Kinematical complete measurement implies detection of all these decay particles
in coincidence and their momentum vectors are to be registered.
－
• No need for the incident beam momentum
• 10Be+n at Ei(i=1,2)=50 AMeV, ΔPi/Pi=0.01
=> ΔErel=0.1 MeV at Erel=1 MeV
c.f.) ΔE～10 MeV for 10Be, ΔE～1 MeV for n
• The drastic gain in the Erel resolution validates use
of the invariant mass method for spectroscopy.
Excitation energy
•
MeV
Erel n
Sn
0.0
Projectile
Ejectile
(E2,P2)
Target
θ
Erel
Neutron
(E1,P1)
summary
• The kinematically complete measurement facilitates an
efficient and powerful spectroscopy on unbound final states.
• It is rich with spectroscopic information, providing
information of the energy spectrum of excited states, angular
distribution (differential cross section) of the reaction, and so
on.
• The kinematically complete measurement does not cost the
experiment a significant loss of efficiency as far as the forward
angle detector arrays are properly set for the decay particles.
• An incident beam intensity of several 100s pps (particles per
second) often suffices for the measurement.
レポート提出先：総合棟６４１号外の箱（小林あて）
締め切り：１月３１日（月）夕方
問題１：授業で取り上げた磁器分析系をモデル化した下記の磁器分析系について、一次のトランスファー行列を求めよ。結果を、次の、
数値計算値と比較せよ。
𝜌=190 [cm]
𝑥1
−1.217 −0.052 3.580 𝑥0
𝐿1 =290 「ｃｍ」 𝛼(bending angle)=60°
𝜃1 = −5.063 −1.032 8.171 𝜃0
𝛿
𝛿
0
0
1
始点
単位: x [cm], 𝜃 mrad , 𝛿 [%]
𝐿2 =330 [cm]
終点
問題２：中性子数N=50の陽子ドリップライン原子核、および、陽子数Z=50の中性子ドリップライン原子核を、Bethe-Weizsacker の質量公
式に基づいて評価せよ。
問題３：N個の中性子とZ個の陽子から構成されるフェルミガスを考える。全エネルギーは次で与えられる。
2/3
2/3
3
2𝑁
2𝑍
𝐸 = 𝜀𝐹 𝑁
+𝑍
.
5
𝐴
𝐴
ℏ2
1
2/3
∆2
ここで𝜀F = 2𝑚 3𝜋 2 2 𝑛0
,𝑛0 ~0.15 fm−3 （核子密度）である。この表現を中性子過剰度∆= 𝑁 − 𝑍で展開すると、 𝐴
の一次のオーダーで次が得られることを証明せよ。
3
𝜀𝐹 𝑁 − 𝑍 2
E = 𝜀𝐹 𝐴 +
.
5
3
𝐴
この式よりBethe-Weizsacker 質量公式の非対称エネルギー項の係数を求めよ。

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