Neutron Spectroscopy

(also neutron spectrometry), a branch of nuclear physics that deals with the dependence of the effective cross section for the interaction of neutrons and atomic nuclei on the energy of the neutrons.

The existence of neutron resonances—abrupt increases (by a factor of 10–10⁵) in neutron absorption and scattering near certain energies (Figure 1)—is characteristic of the energy dependence of the cross section σ for the interaction of slow neutrons and nuclei. The selective (resonance) absorption of neutrons of certain energies was first detected by E. Fermi and his colleagues in 1934. Fermi and his co-workers also showed that the capacity for absorbing slow neutrons varies sharply from nucleus to nucleus.

The highly excited (resonance) state of the nucleus that is formed after the capture of a neutron is unstable, with a lifetime of ≃10^-15 sec. The nucleus decays, emitting a neutron (resonance scattering of neutrons) or a gamma quantum (radiative capture); much less frequently, an alpha particle or proton is emitted. Also, the fission of the excited nucleus into two or, less frequently, into three fragments occurs for certain very heavy nuclei, such as uranium or plutonium.

The probabilities of different types of decay of a resonance state of a nucleus are characterized by resonance widths, such as the neutron resonance width Γ_n, the gamma radiation width Γ_γ, the fission width Γ_f, and the alpha width Γ_α. These widths appear as parameters in the Breit-Wigner formula, which describes the dependence of the effective cross section for the interaction of a neutron and a nucleus on the neutron energy ℰ near the resonance energy ℰ_o. For each type (i) of decay, the Breit-Wigner formula may be written in the approximate form

Here, Γ = Γη + Γ_n + Γ_α + ...is the total neutron resonance width, which is equal to the width of the resonance peak at half-maximum, and g is a statistical factor that depends on the spin and parity of the resonance state of the nucleus.

Effective cross sections are measured by a neutron spectrometer, whose principal elements are a source (S) of monoenergetic neutrons with continuously variable energy and a detector (D) of neutrons or secondary radiation. The total cross section Γ is determined from the ratio of the readings of the neutron detector D taken with the target T placed first in the path of the beam and then outside the beam (Figure 2,a).

Figure 2. Diagrams of neutron spectrometers: (a) with mono-energetic source S and (b) with crystal monochromator in a channel of a nuclear reactor; (D) neutron detector, (T) absorbing or scattering target, (C) collimator

In the measurement of partial cross sections, secondary radiation from the target, such as gamma rays, secondary neutrons, and fission fragments, is recorded with the target placed in the path of the neutrons. For energies up to 10 electron volts (eV), crystal neutron monochromators, which are placed in a channel of a nuclear reactor and which select neutron beams of a given energy (Figure 2,b), are sometimes used as neutron sources. The energy of the neutrons can be varied by rotating the crystal. For energies greater than about 30 keV, van de Graaff generators, in which monoenergetic neutrons are produced by nuclear reactions of the type ⁷Li (p,n) ⁷Be, are normally used. By changing the energy of the protons, the energy of the emerging neutrons is varied; the energy spread is Δℰ ≃ 1 keV.

A more widely used method in neutron spectroscopy is the time-of-flight method, in which neutron sources that have a broad energy spectrum and that emit neutrons in the form of short bursts with a duration τ are used. A special electronic device, called a time-delay analyzer, records the time interval t between a neutron burst and the time at which the neutrons strike the detector—that is, the time of flight of the neutrons over the distance L from the source to the detector. The neutron energy ℰ (in eV) is related to the time t (in μsec) by the equation

(2) ℰ = (72.3L)²/t²

The detector is placed close to the target in the measurement of partial cross sections by the time-of-flight method. Since a secondary particle is emitted virtually simultaneously with the capture of a neutron, the time of capture of the neutron by the nucleus is recorded, and the neutron energy is then determined from the time of flight t. The energy resolution Δ ℰ of a time-of-flight neutron spectrometer can be represented in the approximate form

(3) Δℰ/ℰ = 2τ/t

Charged-particle accelerators or steady-state nuclear reactors with mechanical choppers that periodically pass neutrons for a period of time τ ≃ 1 μsec are normally used as pulsed neutron sources. One of the best neutron time-of-flight spectrometers was developed in the USA at Oak Ridge, Tenn. It contains a linear electron accelerator for electrons with an energy of 140 MeV. Because of bremsstrahlung gamma radiation, the electrons dislodge 10₁₁ neutrons from the target during an electron pulse (τ = 10^-8 sec) with a repetition rate of up to 1,000 pulses/sec. The resolution Δℰ of this spectrometer for L = 100 m and ℰ = 100 eV is 3 × 10^-3 eV. Detectors that generate a signal whose magnitude is proportional to the energy of the particle being recorded are frequently used in neutron spectroscopy. They enable the energy spectrum of the secondary particles that emerge from the target to be measured, thus significantly increasing our knowledge of the excited states of nuclei, the mechanisms of various nuclear transitions, and other factors.

From the analysis of the experimental data it is possible to determine such characteristics of the resonance as the energy So, the total width Γ, and the partial widths, as well as the spin and parity of the resonance states of nuclei. For most stable nuclei, these characteristics (at least ℰ and Γ_n) are known for tens and sometimes hundreds of resonances. For neutrons of higher energies, the resolving power of neutron spectrometers is not high enough to separate individual resonances. In this case, averaged total and partial cross sections, which give information on the average characteristics of the resonances, are studied.

The magnitudes of the energy intervals D between adjacent resonances of a nucleus vary. The average value can change sharply from nucleus to nucleus. A general feature is a decrease in with increasing mass number A, from 10⁴ eV for A = 30 to 1 eV for uranium and heavier nuclei. There is a sharp increase in in going from nuclei with odd A to the neighboring nuclei with even A; this increase is related to the change in the binding energy of the captured neutron. The neutron resonance widths Γ_n also vary from resonance to resonance for a given nucleus. Moreover, on the average, Γ_η increases in proportion to ε₀½ therefore, reduced neutron widths Γ_η⁰ = Γ_ηn/ε₀^½ are normally used. The mean values of the neutron resonance widths Γ_η correlate with the values of <D>. Each of these may differ by a factor of 10³-10⁴ for different nuclei, but the ratio S_o = n/ℰ>/, which is called the force function, shows a slight but gradual variation from nucleus to nucleus. The dependence of S_o on A can be satisfactorily explained by using the optical model of the nucleus.

After capturing a neutron, the nucleus is raised to a highly excited state, below which a large number of other states normally lie. The nucleus can decay in many different ways through various intermediate levels, with the emission of gamma quanta. This leads to a situation in which the total radiation width Γ _γfor each resonance is averaged over a large number of decay paths and consequently changes little from resonance to resonance and changes smoothly from nucleus to nucleus. Generally speaking, the total radiation width in going from intermediate nuclei (A≈50) to heavy nuclei (A≈ 250) changes approximately from 0.5 eV to 0.02 eV. At the same time, the radiation widths that characterize the probability of a gamma transition to a given intermediate level vary greatly from resonance to resonance, just as the neutron widths do. The gamma-ray spectrum of neutron resonance decays gives data on the decaying state, including spin, parity, and a set of partial widths. Moreover, from the energies of the different gamma transitions it is possible to determine the energies of lower levels, and from the intensities of the gamma transitions it is possible to determine the spin and parity and, sometimes, the nature of the level as well.

The fission widths Γf also vary significantly from resonance to resonance. Gamma quanta and secondary neutrons, as well as fragments, are emitted during the fission of nuclei bombarded with neutrons. The number of neutrons is two or three per fission event and remains virtually unchanged from resonance to resonance. This quantity and the ratio of the probabilities of radiative capture and fission play an important role in nuclear reactor design.

The emission of alpha particles after the capture of slow neutrons has been observed in some 15 nuclei. This process is predominant in light nuclei, such as boron and lithium. In intermediate and heavy nuclei, however, the process is hampered by the Coulomb barrier of the nucleus and even in the most favorable cases, Γα is 10⁴ -10⁹ times smaller than Γ_γ. Here, neutron spectroscopy provides information on highly excited states of nuclei and on the mechanism of alpha decay.

Neutron spectroscopic data are important not only for nuclear physics. Reactor engineering requires precise data on the interaction of neutrons with fissile materials and with the structural and shielding materials used in reactors. Neutron spectroscopic data are used for the nondestructive determination of the elemental and isotopic composition of specimens (seeACTIVATION ANALYSIS). In astrophysics, these data are essential for understanding the relative abundance of elements in the universe.

Neutron spectroscopic techniques have found extensive application in studies of the structure of solids and liquids and of the dynamics of various processes, such as the vibrations of the crystal lattice.