262 pág.

## Pré-visualização | Página 33 de 50

Breit-Wigner formula, identify the conditions under which the cross-section of radiative capture of neutrons obeys the llv law. 14.31. On irradiation of a magnesium target with neutrons (2.5 MeV), it was observed that in addition to elastically scattered neutrons there is a group of inelastically scattered neutrons whose energy corresponds to a certain excited level of transitional nuclei (1.3 MeV). Determine the relative width of the given level for inelas- tic scattering, if it is known that the total cross-section of the process Otot = 2.2 h and the elastic scattering cross-section <leI = 1.6 b, 44 % of which represents potential scattering. 8-0339 113 PROPAGATION OF NEUTRONS THROUGH MATTER 14.32. What must the thickness of cadmium plate be to reduce the flux of thermal neutrons 100-fold after passing through it? 14.33. How many times will a narrow beam of thermal neutrons be attenuated after passing through a layer of heavy water 1.0 em in thickness? 14.34. Evaluate in what proportion a narrow beam of fast neu- trons with an energy of 10 l\IeV attenuates on passing through a lead plate 4.0 em in thickness. The effective nuclear cross-section is assumed to be (J = 2n (R + t. )2; R is the radius of the nucleus; ~ is the neutron wavelength. 14.35. In the centre of a spherical graphite layer whose inside and outside radii are r1 = 1.0 em and r 2 == 10.0 cm a point source of monochromatic neutrons is located, emitting 1 0 = 2.0.104 neu- trons/s with an energy of 2.0 Mev , The interaction of neutrons of such an energy with carbon nuclei is characterized by a cross-section (J = 1.6 b. Determine the neutron flux density at the outside surface of the layer, counting only neutrons that penetrated the layer with- out collisions. 14.36. The intensity of a narrow beam of slow monochromatic neutrons diminishes 20-fold on passing through a plate of natural boron with a mass thickness of 1.0 g/cm'', Determine the energy of neutrons, taking into account that the 1/u law is valid in this case. 14.37. A narrow beam of neutrons with an energy of 10.0 eV passes a distance l = 15.0 em along the axis of a counter filled up with BF 3 at NTP (natural boron is used). Determine the counter efficiency provided that the cross-section of the reaction (n, ex) is known to obey the llv law. 14.38. In a neutron counter with LiI crystal sensor the reaction (n, ex) in 6Li nuclei is used. Determine the efficiency of the counter for a thermal neutron beam, if the thickness of the crystal is known to be 2.0 em and density 4.0 g/cm3 (natural lithium is used). The scattering of neutrons is to be neglected. 14.39. Find the decrease in efficiency (%) of a neutron detector, a thin lOB layer, that was irradiated for a week by a plane flux of thermal neutrons with a density J == 1.00-1013 neutrons/Icm--s). 14.40. A non-monochromatic beam of slow neutrons falls on a thin target activating a nuclear reaction whose cross-section is (J ex: 11v. Demonstrate that in this case the mean cross-section of the reaction (averaged over all neutron velocities) (0" (v) = (J ( (v»). 14.41. A beam of neutrons with energies falling within the inter- val, in which the cross-section of the reaction (n, ex) is proportional to llv, passes through a thin 6Li foil 10 mg/cm'' in thickness. What is the mean velocity of the neutrons, if the yield of the reaction (n, a) is known to be 0.40 in this case? 14.42. A neutron counter with a volume of 100 cm'' filled up with BF 3 gas at NTP is placed in the uniform field of slow neutrons (boron 114 :# of natural isotopic composition is used). Assuming that the reaction cross-section ana oc 1lv, determine: (a) the volume density of neu- trons if 1.0.1012 reactions occur in the counter per one second; (b) the number of reactions occurring in the counter per one second if <D === 1.1.1010 neutrons/Icmv- s) and the neutron temperature is 300 K. 14.43. Demonstrate that in a thin target exposed to an isotropic field of neutrons the reaction rate is twice that in the case when a par allel flux of neutrons with the same energy spectrum falls normally on the target's surface. The number of neutrons hitting the target is the same in both cases. 14.44. How long does it take to irradiate a thin layer of lOB nuclide in a field of thermal neutrons with a volume density n = === 4.0.108 neutrons/em" to decrease the number of lOB nuclei by 50 percent? I t is known that the reaction cross-section ana ex: 1lu. 14.45. A thin sample of metallic sod ium of 0.40 g mass was placed in an isotropic field of thermal neutrons with <D === 1.0 X X 1010 neutrons/(cm2·s). Assuming the 24Na radionuclide production rate constant, determine: (a) the activity of the saturated sample and the fraction of 24Na nuclei accumulated in such a sample; (b) the irradiation time required to raise the sample's activity up to 75% of its saturation activity. 14.46. The specific activity of a neutron-activated golden foil equals A == 1.1.108 dis/Is-g) == 3.0 mCi/g. For how long has this foil to be additionally exposed to the field of thermal neutrons with $ === 1.0.1010 neutrons/Icmv-s) to increase its activity by a factor of YI == 10? 14.47. A thin copper plate is exposed to the isotropic field of thermal neutrons with <1> == 0.9.1012 neutrons/fcm--s). Determine the specific activity of the plate t == 2.0 h after the beginning of the exposure. 14.48. A thin 1151n foil of mass 0.20 g was exposed to an isotropic thermal neutron flux for 't == 2.0 h. In t == 0.50 h after the exposure- was discontinued, the foil activity turned out to be A === 0.07 meL Determine the neutron flux density <D. 14.49. A 51V sample of mass 0.50 g is activated up to saturation in a thermal neutron field. During 't = 5.0 min immediately after' completion of irradiation, N == 0.8-109 pulses were registered, the .. count efficiency being ~ == 0.010. Determine the volume density' of neutrons, assuming the activation cross-section to obey the 1/w law in this case. 14.50. An 1151n foil whose both sides are covered with thin layers of cadmium was exposed to an isotropic neutron field. Taking into account that the cross-section of indium activation obeys the 1llJ law in the case of thermal neutrons, determine the specific saturation activity of the foil, if the volume density of thermal neutrons n =' == 3.1 .10 4 cm -3 and a cadmium ratio of Red = 20. Cadmium is s* 115 supposed to absorb all thermal neutrons and let through above- thermal ones. N ate. Red is the ratio of saturation activities of the naked foil and cadmium-coated one. MODERATION AND DIFFUSION OF NEUTRONS 14.51. What fraction of its kinetic energy does a neutron lose in: (a) an elastic head-on collision with initially stationary nuclei 2H, 12C, and 238U; (b) an elastic scattering through the angle 'ft by an initially stationary deuteron, if the angle -fr is equal to 30, 90, and 150°? 14.52. Neutrons with the kinetic energy To are elastically scat- tered by nuclei with the mass number~. Determine: (a) the energy of neutrons scattered through the angle {} in the C frame; (b) the frac- tion of neutrons that after single scattering possess a kinetic energy whose value falls within the interval (T, T + dT) provided the scattering in the C frame is isotropic. Plot the distribution of scat- tered neutrons in terms of energy. 14.53. Neutrons with a kinetic energy of To = 1.00 MeV are elastically scattered by initially stationary 4He nuclei. Determine the mean energy value of singly scattered neutrons, assuming the scattering in the C frame to be isotropic. 14.54. Determine the probability that after a single elastic scat- tering of a neutron by a deuteron the neutron energy becomes less . than half the initial value; the scattering in the C frame is isotropic. 14.55. Neutrons are scattered by initially stationary protons. Assuming this scattering