Nuclear Physics (PHY-31) Dr C. M. Cormack 11 Nuclear Physics This Lecture This Lecture We will discuss an important effect in nuclear spectroscopy The Mössbauer Effect and its applications in technology α-β-γ-decay and nuclear spectroscopy This will be the last in the series of lectures investigating properties of nuclear energy levels before we move on to nuclear technologies and applications to other branches of investigation Lecture 11 Nuclear Physics Dr C M Cormack 1
Nuclear Absorption The inverse process of -ray emission is -ray absorption a nucleus in its ground state absorbs a photon of energy E and jumps to an excited state an energy E above the ground state, these are related by the following equation: Eγ Partial Width E = Eγ Γ = Mc As the energy of the excited state is not sharp (as the state is short lived) the absorption will take place when the gamma energy differs somewhat from the resonant value, the measurement of the resonant cross section gives the following σ ( E γ ) σ ( E ) = σ ( Γ ) [ E ( E + )] + ( Γ ) Lecture 11 Nuclear Physics Dr C M Cormack 3 γ E 0 γ Γ E + E R E R Eγ τ Resonant Absorption A schematic of a resonant absorption experiment is shown below: Intensity Nuclei E γ Doppler Width = ln E γ kt Mc Detector At energies far from the resonance, the nuclei are transparent to the radiation and no absorption occurs. At resonance the transmitted intensity reaches a minimum value. In practice it would not be possible to observe the natural line width. This is because the nuclei are not at rest, they are in constant motion due to thermal excitation. If the motion of the nuclei is represented by the usual Maxwell velocity distribution there will be a distribution of energies of the form ( mc / kt )( 1 E γ / E γ ) e Lecture 11 Nuclear Physics Dr C M Cormack 4
Resonant Absorption At room temperature, kt 0.05 ev and for a 100 kev transition in a medium weight nucleus 0.1 ev, which dominates the natural linewidth for most nuclear transitions. Even cooling to low temperatures (eg 4K) reduces the linewidth by only an order of magnitude. To perform absorption experiments it is necessary to have a tunable source of photons. This can only be achieved from a continuous electromagnetic spectrum as obtained from bremsstrahlung or synchrotron radiation. In most cases in a laboratory absorption experiments a source with a downward nuclear transition is used to excite an upward transition. This transition must be within 0.1eV of the desired resonant energy. An example of such a transition is shown in the diagram: Lecture 11 Nuclear Physics Dr C M Cormack 5 Mössbauer Effect The main problem with the previous example is that it is very difficult to overcome the recoil energy. One method to overcome this is to Doppler shift the source by moving it close to the absorber. A more successful technique for over coming the recoil problem is a method know as the Mössbauer effect. Developed by Rudolf Mössbauer. In his original experiment he used a source of 191 Ir(E =19 kev; E R =0.047 ev). The important point about his experiment was that the emitting and absorbing nuclei were bound in a crystal lattice. It was known that typical binding energies of an atom in a lattice are 1-10eV. Consequently the recoil energy of typical nuclear transitions are not sufficient to remove an atom from the lattice. The effect can be thought of in terms of hitting a brick with a cricket bat (the brick will move!) and then hitting the brick whilst it is in a wall (the brick will almost certainly not move!). Lecture 11 Nuclear Physics Dr C M Cormack 6 3
Mössbauer Effect Therefore the mass that appears in the expression for the recoil energy becomes the mass of the entire solid, rather than the mass of one atom. In addition, a certain fraction of the atoms in a lattice are in the vibrational ground state of thermal motion and consequently shows very little thermal Doppler broadening. The result is very narrow, overlapping emission and absorption lines, each characterised by the natural line-width. This has been nicely demonstrated by Doppler shift experiments where one source was moved relative to the other at low speed. If the speed is such that the Doppler shift is greater than the natural line-width the resonance is destroyed. For a resonance of line-width 6x10-6 ev, it is found that the necessary speed is about 15 mm/s! Lecture 11 Nuclear Physics Dr C M Cormack 7 Mössbauer Effect - Uses The most remarkable thing about the Mössbauer effect is its extreme precision for the measurement of relative energies. In some circumstances it is possible to measure shifts in energy of one part in 10 1. Further details of the statistical mechanics of the Mössbauer effect can be obtained from Krane. The reason why I have spent so much time on the Mössbauer effect is that it has applications in an enormous variety of areas. Its main use is in determining the properties of nuclei to high precision. One of its most significant uses however was as a test of Einsteins general theory of relativity, specifically the gravitational red shift. One of the corner stones of Einsteins theory is the principle of equivalence according to which the effects of a local uniform gravitational field cannot be distinguished from those of a uniformly accelerated reference frame. Lecture 11 Nuclear Physics Dr C M Cormack 8 4
Mössbauer Effect Gravitational Redshift If we were to observe the emission and absorption of radiation in an accelerated reference frame, in which H is the distance between the source and absorber, then the time H/c necessary for radiation to travel from the source to the absorber, the absorber would require a velocity gh/c, where g is the acceleration. The radiation photons are therefore Doppler shifted according to E E v = = c gh c This amounts to about 1x10-16 per meter in the Earth s gravitational field Lecture 11 Nuclear Physics Dr C M Cormack 9 Mössbauer Effect Gravitational Redshift In the original experiment of Pound and Rebka (Phys. Rev. Lett. 4 337 (1960)), 57 Fe was used and the 14.4 kev photons were allowed to travel.5 m of the Jefferson Physical Laboratory at Harvard. The effect was expected to be of order x10-15. This required a considerable amount of scientific expertise as the sensitivity of 57 Fe of roughly 3x10-13. To observe the small shift (about 10 - of the resonance width) they concentrated on portions of the side of the resonance curve with the greatest slope. To reduce systematic effects the source and absorber were held at a constant temperature. Krane p368 fig 10.8 Lecture 11 Nuclear Physics Dr C M Cormack 10 5
Mössbauer Effect Gravitational Redshift After 4 months of experiments, the result was E/E = (4.90±0.041) x10-15 compared with the expected value 4.905 x10-15. This experiment represents one of the most precise tests of the General Theory of Relativity Lecture 11 Nuclear Physics Dr C M Cormack 11 Other uses of the Mössbauer Effect The primary application of the Mössbauer effect has been in the study of the interaction of nuclei with their physical and chemical environments. One example is the study of the effect of the penetration of the atomic wave function into the nuclear volume this is known as the study of hyperfine interactions. As the nucleus is not a point object, but a distribution of charge this shifts the energy of the atomic electrons by an amount E. However from conservation of energy arguments the energy levels of the nucleus are shifted by an equal but opposite amount. This gives rise to a transition energy change of: E = ( E + E ) ( E + E ) e g g Lecture 11 Nuclear Physics Dr C M Cormack 1 6
Mössbauer Effect Isomer Shift If the source and absorber in a Mössbauer experiment had the same chemical environment, the resonance would not be affected, but if the source and absorber are different, then the transition energies are slightly different. The effect is shown in the figure below: Excited State δe E S E S E 0 E 0 Ground State Source Absorber The isomer shift. In different materials, the ground state and the excited states show different shifts. The effect on this experiment is to shift the resonance away. In this experiment the energy shift is achieved by Doppler shifting the source the velocity of the shift is shown in the figure Lecture 11 Nuclear Physics Dr C M Cormack 13 Mössbauer Zeeman Effect Another kind of hyperfine coupling is the study of the splitting of the nuclear levels in a magnetic field known as the Zeeman effect. The equivalent process in atomic physics results in the removal of the spin degeneracy levels (m-degeneracy) of a level of angular momentum I, the field splits into I+1 equally spaced sublevels. The atomic effect shifts the energies by 1 part in 10 4. The nuclear effect however is 1 part in 10 1. This effect is shown in the figure below: E M = µ Hm I I + 3 + 1 m I 3 1 3 1 1 Isomer Shift + 1 Magnetic Dipole Splitting Lecture 11 Nuclear Physics Dr C M Cormack 14 7
Nuclear Magnetic Resonance µb >> A When the external magnetic field is increased the quantum numbers F are no longer good quantum numbers. The large field breaks the coupling of I and J, instead the good quantum numbers are I, m i and J, m J. The perturbed energies are: E = Am m g µ B m g µ B I J J B ext J I N ext m I The high field splitting of our example becomes: F = 3 + 1 High field splitting P3 F = 1 F =1 F = 0 + 3 Lecture 11 Nuclear Physics Dr C M Cormack 15 Mössbauer Electric Quadrupole The nuclear quadrupole moment can interact with an electric field gradient to give an electric quadrupole splitting. This splitting is proportional to m, thus m and m are shifted equally in the same direction. The figure below shows the shift with 57 Fe m I I 3 ± 3 E Q ± 1 3 Isomer Shift 3mI I( I + 1) EQ ( mi ) = eqq 4I(I 1) Quadrupole Splitting ± 1 Lecture 11 Nuclear Physics Dr C M Cormack 16 8
Mössbauer - Summary 1. Mössbauer spectroscopy has been shown to be a very powerful technique in determining with high precision the energy levels within a nucleus.. It has played an important role in determining the effects on these energy levels due to magnetic and electric fields. 3. Its ability to make high precision measurements has allowed the most accurate tests of Einstein s general theory of relativity. 4. Mössbauer spectroscopy has also found uses in medical diagnosis, in tests for certain blood diseases (by exploiting the presence of Iron in blood cells) This section wraps up much of the introduction to nuclear physics theories and techniques, the rest of the lecture course will be devoted to applications of these techniques to technology, astro-physics and cosmology. We will return towards the end of the course to look at nuclear interactions and summarise what we know about fundamental forces in terms of particle physics Lecture 11 Nuclear Physics Dr C M Cormack 17 Neutron Physics The uncharged member of the nucleon pair, the neutron plays an important role in the study of nuclear forces. Unaffected by the Coulomb barrier neutrons of even very low energy (~1 ev or less) can penetrate the nucleus and initiate nuclear reactions. The lack of charge also posses a problem for detection of neutrons, it also posses a problem for energy selection and focussing. The first experimental observation of the neutron was in 1930 when Bothe and Becker bombarded beryllium with -particles, however the form of the radiation emitted was not understood until 193 when Chadwick provided the correct hypothesis for the radiation he is generally credited with being the discoverer of the neutron. Neutron physics today provides many tests of fundamental theories, including tests of Grand Unified Theories and recently tests of the quantisation of gravity. Lecture 11 Nuclear Physics Dr C M Cormack 18 9
Neutron Sources For the remainder of this lecture we will consider some of the applications of neutrons in nuclear reactions and other areas of physics such as crystallography. Sources Beams of neutrons can be produced from a variety of nuclear reactions. We cannot accelerate neutrons as we can charged particles, but we can start with high energy neutrons and reduce their energy through collisions with atoms. This process of slowing is called moderating. The energy range of neutrons is given below. o Thermal E 0.05 ev o Epithermal E 1.0 ev o Slow E 1.0 kev o Fast E 100keV 10MeV Lecture 11 Nuclear Physics Dr C M Cormack 19 Neutron Sources One of the main sources of neutrons for use in the laboratory comes from -Beryllium sources, 9 Be has a relatively loosely bound neutron. If a typical -particle from a radioactive decay (5-6MeV) strikes a 9 Be nucleus a neutron can be released: 4 9 1 He + Be C + n Photoneutron Sources In a process similar to the one above it is possible to use photons to produce neutrons. The advantage of this method is that it is possible to produce nearly monoenergetic sources such a reaction is shown below: 9 8 γ + Be Be + n Another very common source of neutrons are from Reactors. We will discuss this in later lectures. Lecture 11 Nuclear Physics Dr C M Cormack 0 10
Absorption and Moderation of Neutrons The importance of this topic will be revealed when we come to discuss reactor physics As a beam of neutrons travels through bulk matter, the intensity will decrease as neutrons are removed from the beam by nuclear interactions. For fast neutrons many interactions are possible (n,p) (n, ) or (n,n), but for slow or thermal neutrons the primary cause for their disappearance is capture. Often the cross sections for these capture reactions are dominated by one or more resonances where the cross section becomes very large. Off resonance, the cross section decreases with increasing velocity like v -1. The loss in intensity of neutrons traversing a given material of thickness dx, the neutrons will encounter ndx atoms per unit surface area, where n is the number of atoms per unit volume of the material. If t is the total cross section, the loss in intensity is: σ tnx di = Iσ ndx I = I e Lecture 11 Nuclear Physics Dr C M Cormack 1 t 0 Neutron Collisions For an elastic collision between a neutron of initial energy E and velocity v with a target atom of mass A (at rest) gives the following ratio between the final neutron energy E. E A = E + 1+ Acosθ ( A + 1) Where is the scattering angle in the centre-of-mass frame. For no scattering =0 0 the ratio is 1! The maximum energy loss occurs for a head on collision E E = A 1 A + min 1 Lecture 11 Nuclear Physics Dr C M Cormack 11
Neutron Collisions For scattering of neutron energies below 10 MeV and below, the scattering is mostly s-wave and is thus independent of. The results of multiple scattering of neutrons in a medium is shown in the figure below. After many scatterings the neutron distribution will approach the Maxwellian energy distribution shown below: Lecture 11 Nuclear Physics Dr C M Cormack 3 Neutron Detectors As neutrons produce no direct ionisation, neutron detectors must be based on detecting the secondary events produced by nuclear reactions such as (n,p), (n,α), (n,γ) or (n, fission). For slow and thermal neutrons, detectors based on the (n,p) and (n,α) reactions provide a direct means for observing neutrons, from the ionisation signal from the energetic p or α. 10 B is commonly used by producing an ionisation chamber, the reaction is: 10 7 B + n Li +α For thermal neutrons the cross section has a very high value of 3840b and the cross section follows the 1/v law up to about 100 kev (the cross-section is featureless as there are no resonances present). Neutron detection and absorption has some Important applications in crystallography. Lecture 11 Nuclear Physics Dr C M Cormack 4 * 1
Neutron Velocity Selection Early devices used for determining neutron energies were mechanical devices called selectors (shown below). This were basically rotating shutters made of highly absorbing materials such as Cadmium (Cd). Lecture 11 Nuclear Physics Dr C M Cormack 5 Neutron Diffraction Another way of measuring the energy of neutrons in the thermal region is by using crystal diffraction. Thermal neutrons have a de Broglie wavelength of about 0.1 nm, about the same as the spacing between atoms in a crystal lattice. If a beam of thermal neutrons is incident on a crystal it is possible to select wavelengths from interference maxima from the Bragg condition. n λ = d sinθ Lecture 11 Nuclear Physics Dr C M Cormack 6 13
Nuclear Physics Next Lecture Summary This concludes much of the technical introduction to nuclear physics. We have seen that the Mössbauer effect can provide extremely high resolution measurements of nuclear states. It is also important uses in testing other physical theories such as General Relativity Use of Neutrons has been discussed, they have many applications in crystallography, but their most significant use is in Nuclear Fission. Next Lecture Nuclear Fission 1. Theory. Applications Reactors Lecture 11 Nuclear Physics Dr C M Cormack 7 14