Question 9.1.Q1: Neutrons, like photons, belong to the category of indirectly......

(a) Basic properties of neutrons with emphasis on use in medicine.

(1) Neutron is a subatomic particle in the family of hadrons, composed of three quarks and exhibiting strong interaction with other hadrons.
(2) Ernest Rutherford in 1920 postulated the existence of the neutron and William Chadwick in 1932 discovered it at the University of Cambridge in the U.K.
(3) The symbol for the neutron is n or n^0. It possesses no electric charge and its rest mass m_n is slightly larger than that of the proton.
Rest mass of neutron: m_n = 939.6 MeV/c²; rest mass of proton: m_p = 938.3 MeV/c².
(4) Neutron is stable when it is bound in atomic nucleus; however, a free (extranuclear) neutron is unstable (radioactive) and decays through β^− decay into a proton, electron, and electronic antineutrino \left(\mathrm{n}^0 \rightarrow \mathrm{p}^{+}+\mathrm{e}^{-}+\bar{\nu}_{\mathrm{e}}\right) with a mean lifetime τ ≈ 14.9 min or half-life t_{1/2} = τ ln 2 ≈ 10.3 min. In unstable nuclei that harbor an excess number of neutrons, neutron can also decay through β^− decay, however, the half life of this β^− decay is a characteristic of the decaying nucleus and different from that of the free neutron.
(5) Free neutrons easily pass through atoms, because they have no electrical charge, thereby forming highly penetrating, indirectly ionizing, radiation beams that interact with matter only through direct collisions with nuclei of absorber atoms. Interactions of neutrons with orbital electrons of absorber atoms are generally not of any importance and are thus ignored.
(6) Neutron detection is more complex than detection of directly ionizing charged particles and indirectly ionizing photons. Most common methods for detection of neutrons rely on neutron capture (neutron absorption) by the nucleus of an absorber atom or on elastic scattering of neutrons off nuclei of absorber
(7) The secondary charged particles released by fast neutrons in the absorbing medium produce a dose build-up similar to that that occurs in megavoltage photon beams. The depth of dose maximum z_{max} of a clinical fast neutron beam depends on the energy and spectrum of the beam and for a sourcesurface distance of 100 cm and field size of 10\times 10\ cm^2 is of the order from 0.5 cm to 1.5 cm. Beyond z_{max} there is a continuous quasi-exponential fall-off in the dose with increasing depth in water as a result of:

(i) Attenuation of the neutron beam by absorbing medium (water).
(ii) Increase in distance from the source (inverse square law).

In contrast to megavoltage x-ray beams, the field size of neutron beams has a significant effect on depth dose characteristics because of the high probability for neutron scattering within the neutron beam.
(8) Fast neutron beams are significantly more complex and more expensive to use in radiotherapy than are megavoltage x-ray beams, yet, from a physics pointof-view, they produce no better dose distributions than do megavoltage x-ray beams. However, from a radiobiological point-of-view, fast neutrons offer a distinct advantage over megavoltage x-ray beams because of the so-called oxygen enhancement ratio (OER) which amounts to 3 for x rays while it is much closer to 1 for fast neutron beams.
It turns out that the presence of oxygen in a cell acts as a radiosensitizer, making radiation more damaging for a given delivered dose. Since tumor cells are typically poorly oxygenated (tumor hypoxia) in comparison to normal cells, a given dose of x rays causes more damage to well oxygenated normal cells than to hypoxic tumor cells. Thus, in comparison to normal tissue, the oxygen effect decreases the sensitivity of tumor tissue to megavoltage x rays and decreases the tumor control probability. It is generally believed that fast neutron irradiation overcomes this effect, because the OER of fast neutrons is much smaller than that of megavoltage x rays.
(9) For use in radiotherapy, neutron beams are produced either with a cyclotron or a neutron generator. In a cyclotron protons or deuterons are accelerated to kinetic energies of 50 MeV to 80 MeV and strike a thick beryllium target to produce fast neutrons that are collimated into a clinical neutron beam. The neutron beam produced with a beryllium target has beam penetration and build-up characteristics similar to those of 4 MV to 10 MV megavoltage xray beams. In a neutron generator deuterons (d) are accelerated to 250 keV and strike a tritium (t) target to produce a 14.1 MeV neutron beam with depth dose characteristics similar to those obtained for a cobalt-60 teletherapy γ -ray beam.

(b) Velocity of a neutron with a given kinetic energy E_K and rest energy m_nc^2 = 939.6 MeV is calculated from the classical expression for kinetic energy (T2.5)

E_{\mathrm{K}}=\frac{m_{\mathrm{n}} v^2}{2}=\frac{m_{\mathrm{n}} c^2}{2}\left(\frac{v}{c}\right)^2 \quad \text { or } \quad \frac{v}{c}=\sqrt{\frac{2 E_{\mathrm{K}}}{m_{\mathrm{n}} c^2}}           (9.1)

for relatively slow neutrons with velocity v < 0.01c and from the relativistic expression for E_K (T2.7)

E_{\mathrm{K}}=m_{\mathrm{n}} c^2\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right) \text { or } \frac{v}{c}=\sqrt{1-\frac{1}{\left(1+\frac{E_{\mathrm{K}}}{m_{\mathrm{n}} c^2}\right)^2}}              (9.2)

for fast neutrons with velocity v > 0.01c.
Results of our neutron velocity calculations are displayed in Table 9.1 and plotted in Fig. 9.1 in the form of log v/c against log E_K which appears to follow a power function of exponent 1/2 [classical expression (9.1)], except for saturation occurring at very high (relativistic) kinetic energies where (9.2) must be used and (9.1) is no longer applicable.