Statick

1

• Statické momenty jader metody jejich merení

2
Merení statických momentu jader

• Static moments of nuclei are measured via
  interaction of the nuclear charge distribution
  and magnetism with electromagnetic fields in its
  immediate surroundings. This can be the
  electromagnetic fields induced by the atomic
  electrons or the fields induced by the bulk
  electrons and first neighboring nuclei for nuclei
  implanted in a crystal, usually in combination
  with an external magnetic field.

3
Atomic hyperfine structure

• Not only the radial distribution of the nuclear
  charge (monopole moment) but also the higher
  multipole electromagnetic moments of nuclei with
  a spin I ? 0 influence the atomic energy levels.
  By interacting with the multipole fields of the
  shell electrons they cause an additional
  splitting called hyperfine structure. For all
  practical purposes it is sufficient to consider
  only the magnetic dipole and the electric
  quadrupole interaction of the nucleus with the
  shell electrons.
• The shell electrons in states with a total
  angular momentum J ? 0 produce a magnetic field
  at the site of the nucleus. This gives a dipole
  interaction energy E -µ B. The spectroscopic
  quadrupole moment of a nucleus with I 1
  interacts with an electric field gradient
  produced by the shell electrons in a state with J
  1 according to E eQ (?2V/?z2).

4
Externally applied EM fields

• When a nucleus with spin I is implanted into a
  solid (or liquid) material, the interaction
  between the nuclear spin and its environment is
  no longer governed by the atomic electrons. For
  an atom imbedded in a dense medium, the
  interaction of the atomic nucleus with the
  electromagnetic fields induced by the medium is
  much stronger than the interaction with its
  atomic electrons.
• The lattice structure of the medium now plays a
  determining role. This hyperfine interaction is
  observed in the response of the nuclear spin
  system to the internal electromagnetic fields of
  the medium, often in combination with externally
  applied (static or radio-frequency) magnetic
  fields.

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Interakce jádra s vnejšími aplikovanými poli

• Experimental techniques based on measuring the
  angular distribution of the radioactive decay are
  often more sensitive than the atomic HF methods,
  and in some cases also allow more precise
  measurements of the nuclear g factor and
  quadrupole moment. This angular distribution is
  influenced by the interaction of the nuclear
  moments with externally applied magnetic fields
  and/or electric field gradients after
  implantation into a crystal
• The radioactive decay intensity is measured as a
  function of time (TDPAD) or as a function of an
  external variable, e.g., a static magnetic field
  or the frequency of an applied radio-frequency
  magnetic field (b-NMR). The former are called
  time differential measurements and the latter
  time integrated measurements.

6
Metody

• Mößbaueruv jev
• Omezeno jen na izotopy a hladiny meritelné pomocí
  Mossbauera
• PAC (Time-Differential Perturbed Angular
  Distribution - TDPAD)
• NMR
• ß-NMR pro hladiny s krátkou dobou života
• Nízkoteplotní orientace

• Velikost hyperjemného pole nezávisí pro daný
  prvek na izotopu
• Lze zmerit pole pomocí jednoho izotopu a pak
  merit momenty u dalších izotopu

7
TDPAD

• Spin-oriented isomeric states implanted into a
  suitable host will exhibit a non-isotropic
  angular distribution pattern, provided the
  isomeric ensemble orientation is maintained
  during its lifetime. If an electric field
  gradient (EFG) is present at the implantation
  site of the nucleus, the nuclear quadrupole
  interaction will reduce the spin orientation and
  thus the measured anisotropy.
• If the implantation host is placed into a strong
  static magnetic field (order of 0.11 Tesla), the
  anisotropy is maintained. If the field is applied
  parallel to the symmetry axis of the spin
  orientation, the reaction-induced spin
  orientation can be measured.
• If a static magnetic field is placed
  perpendicular to the axial symmetry axis of the
  spin orientation, the Larmor precession of the
  isomeric spins in the applied field can be
  observed as a function of time 93, provided
  that the precession period is of the same order
  as the isomeric lifetime (or shorter).
• Can also be used to measure the quadrupole
  moments of these isomeric states, by implantation
  into a single crystal or a polycrystalline
  material with a non-cubic lattice structure
  providing a static electric field gradient.

8
Príklady

• TDPAD spectra for the ?-decay of the Ip 29/2-,
  t1/2 9 ns isomeric rotational bandhead in
  193Pb, implanted respectively in a lead foil to
  measure its magnetic interaction (MI) and in
  cooled polycrystalline mercury to measure its
  quadrupole interaction (QI).

• Detectors are placed in a plane perpendicular to
  the magnetic field direction (? 90?) and at
  nearly 90 ? with respect to each other (f1 f2
  90), the R(t) function in which the Larmor
  precession is reflected, is given by

9
Príklady

• R(t) curves obtained in the study of g-factors of
  Ip 9/2 isomers in neutron-rich isotopes of
  nickel and iron. The isomers, with lifetimes of
  13.3 µs and 250 ns, respectively, have been
  produced in a projectile fragmentation reaction
  at the LISE high-resolution in-flight separator
  at GANIL.

10
ß-NMR

• Time-differential measurements are only suited
  for short-lived nuclear states, mainly because of
  relaxation effects causing a dephasing of the
  Larmor precession frequencies with time
  (typically in less than 100 µs). To measure
  nuclear moments of longer-lived isomeric states
  and also for ground states, a time-integrated
  measurement is required. Time integration of
  R(t), taking into account the nuclear decay time,
  will lead to a constant anisotropy.
• Therefore, a time-integrated measurement of the
  angular distribution of this system will not
  allow one to deduce information on the nuclear
  moments. Hence a second interaction, which breaks
  the axial symmetry of the Hamiltonian, needs to
  be added to the system.
• One possibility to introduce a symmetry breaking
  in the system, is by adding a radio-frequency
  (rf) magnetic field perpendicular to the static
  magnetic field (and to the spin-orientation
  axis).
• If the nuclei are implanted into a crystal with a
  cubic lattice symmetry or with a noncubic crystal
  structure inducing an electric field gradient,
  respectively, one can deduce the nuclear g-factor
  or the quadrupole moment from the resonances
  induced by the applied rf field between the
  nuclear hyperfine levels.

11
ß-NMR

• Consider an ensemble of nuclei submitted to a
  static magnetic field B0 and
• an rf magnetic field with frequency ? and rf
  field strength B1. If the applied rf frequency
  matches the Larmor frequency the orientation of
  an initially spin-oriented ensemble will be
  resonantly destroyed by the rf field. For
  ß-decaying nuclei that are initially polarized,
  this resonant destruction of the polarization can
  be measured via the change in the asymmetry of
  the ß-decay.
• For an ensemble of nuclei with the polarization
  axis parallel to the static field direction, the
  angular distribution for allowed ß-decay can be
  written as

• with the NMR perturbation factor G1011 describing
  the NMR as a function of the rf frequency or as a
  function of the static field strength. At
  resonance, the initial asymmetry is fully
  destroyed if sufficient rf power is applied,
  which corresponds to G1011 0. Out of resonance
  we observe the full initial asymmetry and G1011
  1.

12
ß-NMR

• All forms of magnetic resonance require
  generation of nuclear spin polarization out of
  equilibrium followed by a detection of how that
  polarization evolves in time.

• In conventional NMR a relatively small nuclear
  polarization is generated by applying a large
  magnetic field after which it is tilted with a
  small RF magnetic field. An inductive pickup coil
  is used to detect the resulting precession of the
  nuclear magnetization. Typically one needs about
  1018 nuclear spins to generate a good NMR signal
  with stable nuclei. Consequently conventional NMR
  is mostly a bulk probe of matter. On the other
  hand, in related nuclear methods such as muon
  spin rotation (µSR) or ß-detected NMR (ß-NMR) a
  beam of highly polarized radioactive nuclei (or
  muons) is generated and then implanted into the
  material. The polarization tends to be much
  higher between 10 and 100. Most importantly,
  the time evolution of the spin polarization is
  monitored through the anisotropic decay
  properties of the nucleus or muon which requires
  about 10 orders of magnitude fewer spins. For
  this reason nuclear methods are well suited to
  studies of dilute impurities, small structures or
  interfaces where there are few nuclear spins.

13
Príklad

• NMR curve for 11Be implanted in metallic Be at T
  50K. At this temperature the spin-lattice
  relaxation time T1 is of the order of the nuclear
  lifetime t 20 s.

14
Príklad

• Nuclear magnetic resonances for 8Li (I 2)
  implanted into different non-cubic crystals. This
  illustrates the influence of the implantation
  host on the quadrupole frequency as well as on
  the resonance line widths. The nuclear level
  splitting for a nucleus with spin I 2,
  submitted to a magnetic field and an EFG, and the
  corresponding transition frequencies are shown
  for one- and two-photon transitions. The five
  levels are non-equidistant, resulting in four
  equidistant one-photon resonances in the NMR
  spectrum

15
ß-NMR

• At radioactive ion beam facilities such as ISOLDE
  and ISAC it is possible to generate intense
  (gt108/s) highly polarized (80) beams of low
  energy radioactive nuclei.
• Furthermore one has the added possibility to
  control the depth of implantation on an
  interesting length scale (6400 nm).

• Although in principle any beta emitting isotope
  can be studied with ß-NMR the number of isotopes
  suitable for use as a probe in condensed matter
  is much smaller. The most essential requirements
  are
• (1) a high production efficiency
• (2) a method to efficiently polarize the nuclear
  spins and
• (3) a high ß decay asymmetry.
• Other desirable features are
• (4) small Z to reduce radiation damage on
  implantation,
• (5) a small value of spin so that the ß-NMR
  spectra are relatively simple and
• (6) a radioactive lifetime that is not much
  longer than a few seconds.

16
Isotope Spin Quadrupole moment (mb) T1/2 (s) ? (MHz/T) beta-Decay asymmetry (A) production rate (s-1)
µ 1/2 2.2x10-6 135.5 0.33 75
8Li 2 32 0.842 6.3018 0.33 108
11Be 1/2 13.8 22 0.33 107
15O 1/2 122 10.8 .7 108
17Ne 1/2 0.1 .33 106

• Table gives a short list of the isotopes we have
  identified as suitable for development at ISAC.
  Production rates of 106/s are easily obtainable
  at ISAC. 8Li is the easiest to polarize and
  therefore was selected as the first one to
  develop as a probe at ISAC

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19
LMR

• Another possibility to NMR is Beta-Ray Detected
  Level Mixing Resonance (b-LMR)
• Here, the axial symmetry is broken via combining
  a quadrupole and a dipole interaction with their
  symmetry axes non-collinear. This gives rise to
  resonant changes in the angular distribution at
  the magnetic field values where the nuclear
  hyperfine levels are mixing.
• The resonances observed in a LMR experiment are
  not induced by the interaction with a rf field,
  but by misaligning the magnetic dipole and
  electric quadrupole interactions. This
  experimental technique does not need an
  additional rf field to induce changes of the spin
  orientation. The change of the spin orientation
  is induced by the quantum mechanical
  anti-crossing or mixing of levels, which occurs
  in quantum ensembles where the axial symmetry is
  broken.

20

• Nuclear HF levels of a nucleus with spin I 3/2
  submitted to a combined static magnetic
  interaction and an axially symmetric quadrupole
  interaction
• (a) for collinear interactions, ß 0?
• (b) and (c) for non-collinear interactions with ß
  5? and ß 20?, respectively.

• Crossing or mixing of hyperfine levels occurs at
  well-defined values for the ratio of the involved
  interactions frequencies, if
• (d) At these positions, resonances are observed
  in the decay angular distribution of oriented
  radioactive nuclei, from which the nuclear spin
  and moments can be deduced

21
Atomic hyperfine structure

• For a particular atomic level characterized by
  the angular momentum J, the coupling with the
  nuclear spin I gives a new total angular momentum
  F, F I J, I - J F I J. The HF
  interaction removes the degeneracy of the
  different F levels and produces a splitting into
  2J 1 or 2I1 hyperfine structure levels for J lt
  I and J gt I, respectively.

• Example of the atomic fine and hyperfine
  structure of 8Li. For free atoms the electron
  angular momentum J couples to the nuclear spin I,
  giving rise to the HF structure levels F. The
  atomic transitions between the 2S1/2 ground state
  to the first excited 2P states of the Li atom are
  called the D1 and D2 lines

22

• Using vector coupling rules the HF structure
  energies of all F levels

• The determination of nuclear moments from
  hyperfine structure is particularly appropriate
  for radioactive isotopes, because the electronic
  parts Be(0) and Vzz(0) are usually known from
  independent measurements of moments and hyperfine
  structure on the stable isotope(s) of the same
  element.

23
Optical pumping

• Polarization of a fast beam by optical pumping
  was introduced for the ß-asymmetry detection of
  optical resonance in collinear laser
  spectroscopy.
• Most applications took advantage of the
  additional option to perform nuclear magnetic
  resonance spectroscopy with ß-asymmetry detection
  (ß-NMR) on a sample obtained by implantation of
  the polarized beam into a suitable crystal
  lattice. Whatever is the particular goal of such
  an experiment, it is important to achieve a high
  degree of nuclear polarization.

• Repeated absorption and spontaneous emission of
  photons results in an accumulation of the atoms
  in one of the extreme MF states for which the
  total angular momentum F J I, for an S state
  just composed of the electron spin and the
  nuclear spin, is polarized.

• Optical pumping within the hyperfine structure
  Zeeman levels for polarization of the nuclear
  spin. The example shows the case of I 1 for the
  case of 28Na

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25
Optical pumping

• If a weak magnetic field defines the quantization
  axis in the direction of the atomic and the laser
  beam, each absorption of a circularly polarized
  photon introduces one unit of angular momentum in
  the atomic system. This can be expressed by the
  selection rule ?MF 1 for s light, with s and
  s- being the conventional notations for the
  circular polarization of the light with respect
  to the direction of the magnetic field.

• Repeated absorption and spontaneous emission of
  photons results in an accumulation of the atoms
  in one of the extreme MF states for which the
  total angular momentum F J I, for an S state
  just composed of the electron spin and the
  nuclear spin, is polarized.

26
Collinear Laser Spectroscopy
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28
Merení rozmeru (polomeru) atomových jader
29
Measurement of nuclear radius

• Distribution of charge can not be the same as
  distribution of matter
• Four methods outlined for charge matter radius
• Diffraction (electron) scattering (form factor)
• Atomic x-rays
• Muonic x-rays
• Mirror Nuclides
• Three methods outlined for nuclear matter radius
• Rutherford scattering (via strong interaction)
• Alpha particle decay
• ?-mesic x-rays
• (cross section of fast neutrons)

30
Diffraction scattering
q momentum transfer

• Measure the scattering intensity as a function
  of ? to infer the distribution of charge in the
  nucleus,

31
Diffraction scattering
.

• Density of electric charge in the nucleus is
  almost constant
• The charge distribution does not have a sharp
  boundary
• Edge of nucleus is diffuse - skin
• Depth of the skin 2.3 fm
• RMS radius is calculated from the charge
  distribution and, neglecting the skin, it can be
  shown

Modulus squared of charge form factors (a)
calculated by solving the Dirac equation with
HFBCS proton densities (b)
32
Atomic X-rays

• Assume the nucleus is uniform charged sphere.
• Potential V is obtained in two regions
• Inside the sphere
• Outside the sphere

• For an electron in a given state, its energy
  depends on
• Assume does not change appreciably if Vpt?
  Vsphere
• Then, ?E Esphere - Ept
• Assume can be
• ?E between sphere and point nucleus for
• Compare this ?E to measurement and we have R.

33
Atomic X-rays

• In reality, we will need two measurements to get
  R
• Consider a 2p ?1s transition for (Z,A) and (Z,A)
  where
• A (A-1) or (A1) what x-ray does this
  give?
• Assume that the first term will be 0 larger
  radius (smaller influence)
• Then, use ?E1s from previous slide for each E1s
  term

• This x-ray energy difference is called the
  isotope shift
• One can use optical transitions instead of x-ray
  transitions

34
Use for short-lived nuclei

• Let A, A and mA, mA be the mass numbers and
  atomic masses of the isotopes involved. Then for
  an atomic transition i the isotope shift, i.e.
  the difference between the optical transition
  frequencies of both isotopes, is given by

• This means that both the field shift (first term)
  and the mass shift (second term) are factorized
  into an electronic and a nuclear part. The
  knowledge of the electronic factors Fi (field
  shift constant) and Mi (mass shift constant)
  allows one to extract the quantity dr2 of the
  nuclear charge distribution. These atomic
  parameters have to be calculated theoretically or
  semi-empirically.

• For unstable isotopes high-resolution optical
  spectroscopy is a unique approach to get precise
  information on the nuclear charge radii, because
  it is sensitive enough to be performed on the
  minute quantities of (short-lived) radioactive
  atoms produced at accelerator facilities.
• Other techniques are suitable only for stable
  isotopes of which massive targets are available.

35
Use for short-lived nuclei

• Elastic electron scattering even gives details of
  the charge distribution, and X-ray spectroscopy
  on muonic atoms is dealing with systems for which
  the absolute shifts with respect to a point
  nucleus can be calculated. Thus both methods give
  absolute values of r2 and not only differences.
  Eventually, the combination of absolute radii for
  stable isotopes and differences of radii for
  radioactive isotopes provides absolute radii for
  nuclei all over the range that is accessible to
  optical spectroscopy.

36
Muonic X-rays

• Similar to standard X-rays measurement
• Muons are heavier than electrons (106 MeV x 511
  keV) which causes the difference in the radius
  and energy (energy difference)

Prompt X-ray spectra from deuteron The curves
are the results of the fitting and the
components of pµ X-rays and dµ X-rays are also
shown respectively.
37
Coulomb Energy Differences

• Coulomb energy of the charge distribution
• Consider mirror nuclides

• Can be determined from the b-decay of mirror
  nuclides (from maximum electron/positron energy)
  the only difference in mirror nuclides is
  expected due to the Coulomb energy
• Change in the Coulomb energy can be expected to
  depend as A2/3 (from A/R)

38
Coulomb Energy Differences
Maximum energy of b-ray spectrum (MeV)

• From experimental evidence analyzing mirror
  nuclei, we know that nuclear forces are
  symmetrical in neutrons and protons and that
  nuclear binding between two neutrons is the same
  as that between two protons.
• In the figure the fact that the experimental
  values tend to lie on a straight line indicates
  that these nuclei have coulomb energy which
  correspond to a constant-density model RCR0A1/3
• Dotted lines for R01.4 and 1.610-13 cm clearly
  constitute an interval for the Coulomb-energy
  unit radius.

A2/3
39
Measurement of nuclear radius

• Distribution of charge can not be the same as
  distribution of matter
• Four methods outlined for charge matter radius
• Diffraction scattering (form factor)
• Atomic x-rays
• Muonic x-rays
• Mirror Nuclides
• Three methods outlined for nuclear matter radius
• Rutherford scattering
• Alpha particle decay
• ?-mesic x-rays
• (cross section of fast neutrons)

40
a-decay lifetime

• The penetration of a depends very critically on
  the shape and the height of the of the potential
  energy barrier and on the kinetic energy of a
  after penetration. The height of the barrier is
  given by the nuclear radius, since the particle
  is under the influence of the Colomb repulsion
  without any compensating nuclear attraction when
  its distance from the center is larger than R.
  The probability of penetration is closely
  connected with the decay lifetime.
• In principle, the theory of a-decay allows
  determination of the nuclear radius R from the
  decay lifetime and energy of a particle.

Example of influence of the radius on lifetime
simple calculations
41
Cross section of fast neutrons

• In principle could be used, in reality it is
  rather problematic
• According to the elemental theory of scattering
  (QM) the total cross section of a particle s
  sel sreaction 2p(R l)2 ,where l is an
  uncertainty in the position of the incident
  particle (probably equivalent to the
  wavelength of the the particle)
• In the case of fast neutrons, l is very small and
  there is no Coulomb interaction

42
Merení hmot jader
43

• Quantities which can be measured
• Maximum energy of a decay (Q-value) (n,g), b
  decay
• Frequency measurement determination of q/m
• storage rings
• mass spectrometer (ISOLTRAP) ISOL isotope
  separator on line

• For mass measurements on radioactive nuclides,
  the two worlds most prominent instruments today,
  both in terms of the final mass uncertainty
  reached and its sensitivity and the number of
  measurements performed, are the
• experimental storage ring (ESR) at GSI
  (Darmstadt) and
• Penning trap mass spectrometer ISOLTRAP at
  ISOLDE/CERN.

Based on H.-J. Kluge et al. / Nuclear
Instruments and Methods in Physics Research A 532
(2004) 4855 Klaus Blaum / Physics Reports 425
(2006) 1-78
44
ESR

• At the ESR, two new, complementary techniques,
  Schottky-Mass-Spectrometry (SMS) and
  Isochronous-Mass-Spectrometry (IMS), have been
  developed during the last years and were used in
  several experimental runs for mapping large areas
  of the nuclidic mass surface.
• The target is located at the entrance of the
  FRagment Separator (FRS), a magnetic high
  resolution spectrometer. Depending on the
  operation mode, the FRS can provide cocktail
  beams (a mixture of nuclei, which are
  characterized by similar mass-to-charge ratio) or
  monoisotopic beams. At relativistic velocities
  the reaction products leave the production target
  as highly-charged ions and mainly bare ions
  occur. The ions are injected as a bunch of about
  400 ns pulse length into the ESR. After
  injection, the ESR is used as high-resolution
  mass analyzer, and the masses are determined from
  the precise measurement of their revolution
  frequencies.
• For an unambiguous relation between frequency and
  mass, the second (velocity dependent) term on the
  rhs of the equation on next slide must be
  canceled and two methods apply. For SMS, the ESR
  is operated with gt 2.4, electron cooling is
  applied so that Dv/v ? 0 and the revolution
  frequency is determined from a Schottky-noise
  analysis. For IMS, the ESR is operated in the
  isochronous mode at gt 1.4 Ions are injected
  with a suitable velocity so that their Lorentz
  factor g gt and their revolution frequency is
  determined from their time-of-flight (TOF) for
  each turn.

45
ESR

• When relativistic ions (from heavy ion
  synchrotron - SIS), accelerated to almost the
  velocity of light, collide with a thick target, a
  broad spectrum of nuclei with mass and charge
  numbers below those of the projectile nucleus fly
  onward, close to the velocity of the primary
  beam. An exotic nucleus can be separated from
  this mixture almost free of background. This is
  accomplished by deflecting the ions in
  electromagnetic fields and, in addition, slowing
  them down in thick layers of matter. This is the
  basic principle of the FRS fragment separator at
  GSI.

46
FRSESR mass measurements

• Schematic view of the principle of mass
  measurement in the ESR. The motion of up to four
  different species labeled by (m/q)1...4, is
  indicated. For SMS (left) ions are cooled and
  have the same mean velocity v whereas for IMS
  (right) the ions are hot and have different
  velocities. gt is an ion-optical parameter, which
  characterizes the transition point of the ESR

47
Detection in IMS

• In the IMS mode of the storage ring the
  revolution times of each individual stored ion
  are measured by a destructive time-of-flight
  technique. To this end the ions cross a very
  thin, metallized carbon foil, being typically a
  few g.cm-2 thick, mounted in the ring aperture,
  and eject at each passage -electrons which are
  guided by electric and magnetic fields to a
  suitable detector. In this way, every ion
  produces periodically at each passage a
  time-stamp. With a proper data analysis software
  the fast-sampled sum signal can be assigned to
  individual ions and their mass can be determined
  via the measured time of flight. Due to energy
  loses in the foil only a few hundred to a few
  thousand turns can be observed for one and the
  same ion.

48
Detection in SMS

• The SMS method in a storage ring is based on the
  detection of image charges and provides, as in
  the case of a Penning trap, single-ion
  sensitivity. The revolution frequency of the
  highly charged ions is determined from a
  Schottky-noise analysis, i.e., at each turn the
  induced mirror charges of the circulating ions on
  two electrostatic pick-up electrodes is
  monitored. Typically the 3034th harmonics of the
  signals are picked up by a resonant circuit. The
  signals of both pick-up plates are amplified with
  low-noise amplifiers and then summed. The Fourier
  transformed signal delivers the frequency and
  thus the mass spectrum. At a charge state of q
  30 the detection sensitivity is high enough to
  detect single ions.

49
FRSESR mass measurements

• In the ESR. After cooling, the nuclides are
  sorted according to their mass-to-charge
  ratio in the spectrum (increasing mass-to-charge
  ratio with decreasing revolution frequency). The
  nuclides with known masses (indicated by full
  letters in the Fig. on next slide) are used as
  calibrants of the spectrum and thus the so far
  unknown masses can be obtained. The inset shows
  that low-lying isomeric states can be resolved
  and that the measurement reaches ultimate
  sensitivity, i.e., even single ions can be
  detected and their mass can be determined with a
  precision in the order of 50 keV. This is ideally
  adapted to the requirements of an experiment with
  exotic nuclei, which are produced in tiniest
  amounts, some of them with rates of the order of
  a few ions per day.
• Neutron deficient nuclei were produced by bismuth
  fragmentation.
• Neutron-rich nuclei are of special interest.
  These neutron-rich nuclei can be produced at the
  FRS by fission of high-energy uranium
  projectiles. IMS is used, which has the potential
  to investigate nuclides with half-lives down to
  the microsecond range because no cooling is
  required.

50
FRSESR mass measurements

• Frequency spectrum of cooled exotic nuclei. The
  inset, which shows ground and isomeric excited
  state of fully stripped 143Sm, demonstrates the
  ultimate sensitivity of SMS to detect single ions.

51
FRSESR mass measurements

• The performance of SMS depends strongly on the
  features of electron cooling. Thus, a large
  cooling force is desired, but a high electron
  current causes rapid beam loss due to charge
  exchange by the capture of electrons from the
  electron cooler.
• Mass precission about 35 keV
• With IMS, where no cooling is required at all.
  There, the ions make only a few thousand
  revolutions before they are lost due to the
  energy loss in the foil of the TOF-detector
• Mass precision of typically 100 keV is achieved

52
The ISOLTRAP experiment

• ISOLTRAP is a triple trap mass spectrometer
  connected to the on-line mass separator ISOLDE.
  There, the radionuclides are produced by
  bombarding a thick target with 1.4 GeV proton.
  The produced nuclides diffuse out of the target
  and are ionized either by surface, plasma or
  resonant laser ionization. The 60 keV ion beam is
  mass separated in a magnetic spectrometer with a
  resolving power of up to 8000 and delivered to
  different experiments.
• ISOLTRAP measures the mass m via the
  determination of the cyclotron frequency nc
  (1/2p)(q/m)B of ions with charge q stored in a
  homogeneous and stable magnetic field B. The main
  components of the ISOLTRAP setup are shown in the
  Fig. on next page. It consists of three traps
  that perform specific tasks (i) the
  radiofrequency quadrupole (RFQ) used as a beam
  conditioning trap in which the 60-keV ISOLDE beam
  is decelerated, cooled, and bunched to adapt the
  beam to the requirements of ISOLTRAP with respect
  to its time structure and emittance (ii) the
  preparation Penning trap, in which contaminant
  ions are removed by a mass-selective buffer gas
  cooling technique and (iii) the precision
  Penning trap for the actual mass measurement.
• A stable alkali reference ion source located
  upstream of the RFQ trap allows testing and
  preparation of the complete setup before
  radioactive-beam experiments.

53
The ISOLTRAP experiment

• Sketch of the triple trap mass spectrometer
  ISOLTRAP at ISOLDE/CERN. Micro-channel plate
  (MCP) detectors are used to monitor the ion
  transfer as well as to record the TOF resonance
  (MCP5) for the determination of the cyclotron
  frequency. The inset shows the cyclotron
  resonance of 33Ar with the fit of a
  theoretically expected curve

54
Penning trap

• An ideal Penning trap consists of a strong
  homogenous magnetic field and a weak quadrupolar
  electrostatic potential.
• As a Paul trap, a Penning trap also consists of
  ring and endcap electrodes. Quite often so-called
  guard or correction electrodes are placed between
  endcaps and the ring to compensate for the
  truncation of the hyperbolical electrodes.
• Two types of geometry configurations are commonly
  used hyperbolic and cylindrical. Both constructs
  have their own benefits although in precision
  experiments usually hyperbolical are favored due
  to better production of quadrupolar electric
  field. On the other hand, cylindrical electrodes
  are easier to manufacture and sometimes more open
  geometry offer other benefits such as better
  conductance of gas.

In contrast to a Paul trap, full confinement is
achieved with static trapping fields (R 1cm).
55
Paul trap

• In a Paul trap the trapping effect is achieved
  solely with electric fields. They consist of a
  ring electrode and two endcap electrodes that in
  ideal case are hyperboles of revolution.
  Confinement of ions is achieved by using both DC
  and AC electric fields. Motion of ions is
  described with Mathieu equations which in short
  describes the suitable combinations of frequency
  and amplitude of the electric field for storing
  ions with certain m/q ratio.

Radio-frequency Paul trap consisting of two end
caps and a ring electrode. (a) Cutaway view
(after G. Kamas, ed., Time and Frequency Users's
Manual, National Bureau of Standards Technical
Note 695, 1977). (b) Cross section, showing the
amplitude of the instantaneous oscillations for
several locations in the trap.
56
Paul trap
From http//mathworld.wolfram.com

• In nuclear physics Paul traps are used mainly for
  storing and cooling ions. Some trap structures
  are prepared so that the center of the trap is
  exposed for example for lasers and particle
  detectors.

57
Penning trap
For the storage of charged particles in a Penning
trap a strong homogeneous magnetic field B for
radial confinement and a weak static electric
field for axial trapping are superposed. The
latter is created by a voltage U0 (or Udc)
applied between the ring electrode and the two
end electrodes.

• An ion with a charge-to-mass ratio q/m stored in
  a pure magnetic field B B(z) in the
  z-direction and with a velocity component v
  perpendicular to the direction of the magnetic
  field will experience a Lorentz force FL qv
  B. This force confines the charged particle in
  the radial direction and the ion performs a
  circular motion with angular frequency wc
  (q/m)B.
• Since there is no binding in the direction of the
  magnetic field lines, i.e. in the axial
  direction, a three-dimensional confinement is
  obtained in the Penning trap by superposing a
  weak static electric quadrupole potential F(z,
  r) (U0/2d2)(z2 - r2/2) given in cylindrical
  coordinates.

58
Penning trap
For an ideal electric quadrupole field there are
three eigenfrequencies of the ion motion
In order that the motion be bounded, the roots in
Eqs. must be real, leading to the trapping
condition

• Schematic trajectory (three-dimensional and
  projection onto the xy-plane) with ideally three
  independent eigenmotions of an ion in a Penning
  trap a harmonic oscillation in the axial
  direction (axial motion with frequency wz), and
  a radial motion that is a superposition of the
  modified cyclotron motion with frequency w and
  the magnetron motion with frequency w-

59
Cooling of ions in the RFQ trap

• The operating principle of a linear RFQ is based
  on the radial confinement of ions in the
  quadrupolar field of a four-rod structure. The
  time-averaged radial centering force can be
  described as a harmonic pseudo-potential well.
  The ISOLTRAP RFQ is in addition filled with He as
  buffer gas, thus ions are not only radially
  confined but also cooled by collisions with
  buffer gas atoms, and the four rods are 26-fold
  segmented and an axial DC potential is applied in
  order to allow the accumulation of a number of
  ions in cooled bunches.
• The total length of the RFQ is about 1m and the
  trap is operated at gas pressures of about 1 Pa,
  at a radiofrequency of typically 1 MHz, and at
  peak-to-peak RF amplitudes of up to 250 V,
  depending on the ion mass. After an accumulation
  period of about 510 ms the ions are ejected
  towards the preparation trap through a pulsed
  drift tube in which their energy is adapted to
  ground potential.

Left Radiofrequency quadrupole mass filter
electrodes having hyperbolic cross-section.
Right Equipotential lines for a quadrupole field
generated with the electrode structure shown left.
electrodes of a linear paul trap (RFQ)
60
Cooling in a Penning trap

• In ISOLTRAPs preparation Penning trap a
  combination of He buffer gas collisions and
  application of a resonant azimuthal quadrupole
  radiofrequency excitation at the true cyclotron
  frequency nc is used. Both, cyclotron and axial
  oscillations are damped by buffer gas collisions.
  Due to the potential energy loss by collisions
  with the buffer gas atoms the magnetron radius
  increases. A mass selective recentering of the
  ions by a radiofrequency field that couples the
  modified cyclotron and the magnetron motion
  avoids ion loses.
• This mass selective technique allows ions to be
  cooled to a temperature equivalent to that of the
  buffer gas and to eliminate at the same time
  contaminant ions of other masses present in the
  trap. Using this technique, a mass resolving
  power of 105 could be demonstrated with 100 ms
  cooling time.

61
Mass determination in Penning trap

• Two methods are used for measuring cyclotron
  frequencies in high-accuracy mass spectrometry
  with ion traps
• manipulation of the ion motion by radiofrequency
  fields and measurement of the time of flight
  (TOF) of the ions from the ion trap after
  ejection to an ion detector placed outside the
  magnetic field and
• broad-/ narrow-band observation of the
  oscillating image currents induced by the motion
  of the ion in the trap electrodes (detection by
  image charges).

62
TOF measurement in a Penning trap

• The ions cyclotron frequency nc is probed by
  excitation of the ions motion by a radiofrequency
  signal and measurement of the TOF to the
  micro-channel-plate (MCP) detector. The cyclotron
  resonance is determined by repetition of this
  sequence and measurement of the TOF as a function
  of the frequency of the applied signal. The value
  of the magnetic field B is measured by a
  determination of the cyclotron frequency of a
  reference ion with well-known mass both before
  and after the measurements of the cyclotron
  frequency of the ion of interest.

An example for 33Ar is shown. A fit of the
resonance curve to the theoretical function
yields the cyclotron frequency nc.
63
TOF measurement in a Penning trap from
different paper

• In the time-of-flight ioncyclotron resonance
  (TOF-ICR) detection technique the ions are first
  prepared at a well-defined radius of the
  magnetron motion. Here, the orbital frequency
  and, therefore, the orbital magnetic moment m as
  well as the associated energy E m.B , are
  small. By application of a resonant quadrupolar
  excitation, with an appropriate choice of
  amplitude and excitation time, the magnetron
  motion is completely converted into the
  (modified) cyclotron motion while the radial
  radius remains constant.
• When the ions are ejected from the trap after one
  full conversion (by lowering the trapping
  potential of the downstream end electrode) at
  initially low axial velocity they drift along the
  axis out of the magnetic field. In passing
  through the magnetic field gradient the ions get
  accelerated due to the gradient force and thus
  the axial velocity of the ions increases.
• In each of several experimental cycles, different
  excitation frequencies are applied. Since the
  magnetic moment and the radial energy of the ions
  are larger in resonance due to the higher
  frequency of the cyclotron motion as compared to
  the magnetron frequency, the resonantly excited
  ions arrive earlier at the detector than those
  ions that have been excited non-resonantly.

• A variation of the quadrupole frequency rf
  results in a characteristic time-of-flight
  cyclotron resonance curve. The theoretically
  expected line shape for such a resonance is
  mainly determined by the Fourier transformation
  of the rectangular time excitation profile and is
  similar to the absolute value of the so called
  sinc(x)-function f(x)sin(ax)/(ax).

64
Image charges detection

• With the detection of the image charges a full
  resonance spectrum after one experimental cycle
  can be obtained instead of repeated probing of
  the expected cyclotron frequency.
• The signal of the charged particle stored in a
  Penning trap is picked up by means of an attached
  narrow-band electronic resonance circuit working
  under cryogenic conditions (T 4.2K). It enables
  the detection of a single ion as well as further
  successive measurements with the same ion.
• Generally the axial oscillation is monitored.

Experimental setup for a sensitive, narrow-band
detection of a single stored ion. Due to a tuned
resonance circuit with a high quality factor Q an
improved detection sensitivity is reached.
65
The ISOLTRAP experiment

• ISOLTRAP looks back on a highly successful
  physics program. In total the masses of 271
  radionuclides throughout the entire nuclear chart
  of the nuclides have been determined since its
  installation at the original ISOLDE facility in
  1992. The
• relative uncertainty is typically dm/m 10-7 and
  even almost up to one order of magnitude better
  in some special cases

66
Micro-channel plate detector

• A micro-channel plate is a slab made from highly
  resistive material of typically 2 mm thickness
  with a regular array of tiny tubes or slots
  (microchannels) leading from one face to the
  opposite, densely distributed over the whole
  surface. The microchannels are typically
  approximately 10 mm in diameter (6 mm in high
  resolution MCPs) and spaced apart by
  approximately 15 mm they are parallel to each
  other and often enter the plate at a small angle
  to the surface (8).

• A single x-ray interacting in a channel of the
  MCP produces a charge pulse of about 1000
  electrons that emerge from the rear of the plate.
  Since the individual tubes confine the pulse, the
  spatial pattern of electron pulses at the rear of
  the plate preserve the pattern (image) of x-rays
  incident on the front surface. When coupled to an
  additional MCP and an electronic readout and
  display the MCP becomes an x-ray image
  intensifier.
• a small photomultiplier

67

• THE END
• zazvonil zvonec a pohádek je konec

68
Merení hmot jader

• An ideal Penning trap consists of a strong
  homogenous magnetic field and a weak quadrupolar
  electrostatic potential. In contrast to a Paul
  trap, full confinement is achieved with static
  trapping fields. As a Paul trap, a Penning trap
  also consists of ring and endcap electrodes.
  Quite often so-called guard or correction
  electrodes are placed between endcaps and the
  ring to compensate for the truncation of the
  hyperbolical electrodes. Two types of geometry
  configurations are commonly used hyperbolic and
  cylindrical. Both constructs have their own
  benefits although in precision experiments
  usually hyperbolical are favored due to better
  production of quadrupolar electric field. On the
  other hand, cylindrical electrodes are easier to
  manufacture and sometimes more open geometry
  offer other benefits such as better conductance
  of gas.

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On-Line NMR/ON

• Nuclear Magnetic Resonance on Oriented Nuclei is
  done at 10 mK temperatures.
• Polarised radioactive nuclei are exposed to an RF
  field of variable frequency.
• When the Zeeman splitting frequency is found
  resonant absorption changes the
• sublevel populations and hence also the observed
  anisotropy a resonance in the
• anisotropy versus frequency plot.

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• COLlinear LAser SPectroscopy

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On-Line Laser spectroscopy Collinear and
In-Source Methods Atomic
Hyperfine Structure splitting
In Source, Doppler width resolution 250
MHz Collinear Concept - add constant energy to
ions
68Cu
?Econstd(1/2mv2)mvdv

Resolution 1 MHz, resulting from the velocity
compression of the line shape through energy
increase.
In Cu ion, electron states involved are s1/2 and
p1/2.

With nuclear spin I these each form a doublet
with F ( I J) I 1/2 and I -
1/2. Transitions between these doublets give four
lines in two pairs with related splittings. -
poor resolution (In Source) only for the A
(large magnetic dipole) splitting - good
resolution (Collinear) for both A and B (smaller
electric quadrupole splitting)

81
The NSCL Fragment Separator, MSU
Fragmentation b-NMR Fragments are polarised in
their creation. Implanted in cubic materials,
their polarisation can be detected by measurement
of the asymmetry of their beta decay. Application
of a magnetic field creates a Zeeman splitting
which is deduced from resonant destruction of the
asymmetry, yielding the nuclear g-factor.
82

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• The spectroscopic quadrupole moment can be
  related to an intrinsic quadrupole moment Q0
  reflecting the nuclear deformation ß, only if
  certain assumptions about the nuclear structure
  are made. An assumption that is often made (but
  is not always valid!), is that the nuclear
  deformation is axially symmetric with the nuclear
  spin having a well-defined direction with respect
  to the symmetry axis of the deformation (strong
  coupling). In this case, the intrinsic and the
  spectroscopic quadrupole moment are related as
  follows

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• SCATTERING OF HIGH-ENERGY NEUTRONS BY NUCLEI
• cross section of the very fast neutrons (usually
  14 and 25 MeV neutrons used) reaches the value
  2pR2
• THE YIELD OF NUCLEAR REACTIONS INITIATED BY
  PROTONS OR a-PARTICLES
• Comparison of excitation functions with theory
  can give information about nuclear radius

• Scattering of e- of high energy (200 MeV)
• Diffraction pattern is expected if the charge is
  expected to be uniformly distributed around the
  nucleus (not point-like)
• Assuming different values of R and b, one can try
  to find the best fit observed angular distribution

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