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irodov problems in atomic and nuclear physics

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a-particle and its angle of scattering described
by a non-single-valued function? Find the greatest possible angle
of scattering of the a-particle for each of these three cases.
13.5. Find the fraction of the kinetic energy lost by a n~n-rela-
tivistic a-particle due to elastic scattering at an angle '6. = 60°
(in the C frame) by a stationary 12C nucleus.
13.6. A proton with a kinetic energy of 0.90 l\1eV sustains an
elastic head-on collision with a stationary deuteron. Find the pro-
ton's kinetic energy after the collision.
13.7. A non-relativistic neutron is scattered elastically through
the angle 'frn by a stationary 4He nucleus so that the latter is ejected
at an angle of 600 to the direction of motion of the incoming neutron.
Determine the angle 'frn •
13.8. A non-relativistic a-particle is elastically scattered by a 6Li.
Determine the angle of scattering of the a-particle: (a) in the L
frame provided that in the C frame {ta == 30°; (b) in the C frame
provided that in the L frame ita = 45°.
101
13.9. Deuterons with a kinetic energy of 0.30 lVleV are elastically
scattered by protons. Find the kinetic energy of the deuterons scat-
tered through the greatest possible angle in the L frame. What is the
magnitude of the angle?
13.10. Find the energy of the reaction 7Li(p, a)4He if the mean
binding energies per nucleon in 7Li and 4He nuclei are known to
be equal to 5.60 and 7.06 l\IeV respectively.
13.11. Determine the energies of the following reactions:
(a) 3H(p, y)4He; (b) 14N(a, d)160; (c) 12C(a, d)14N; (d) 6Li(d, na)3He.
13.12. Using the tables, calculate the mass of 17N atom, if the
energy of the reaction 170(n, p)17N is known to be Q = -7.89l\tleV.
13.13. Find the velocity with which the products of the reaction
lOB(n, a)7Li come apart; the reaction proceeds due to interaction
of slow neutrons with stationary boron nuclei.
13.14. Find the energy of neutrons produced due to photodisin-
tegration of beryllium according to the reaction 9Be(y, n)8Be by
.,-quanta with an energy of tu» = 1.78 MeV. The energy of the reac-
tion is Q = -1.65 MeV.
13.15. A deuterium target irradiated by v-quanta with an energy
of lu» = 2.62 lVIeV emits photoprotons for which Bp = 63.7 kG-cm.
Ignoring the difference in the masses of a neutron and a proton, find
the binding energy of a deuteron.
13.16. Calculate the energies of the following reactions:
(a) 2H(d, p)3H, if the energy of the incoming deuterons T d =
== 1.20 MeV and the proton, outgoing at right angles to the direction
of the deuteron's motion, has an energy T p = 3.30 MeV;
(b) 14N(a, p)170, if the energy of the incoming a-particles T a =
= 4.00 ~leV and the proton, outgoing at an angle '6' == 60° to the
direction of motion of a-particles, has an energy of T p == 2.08 MeV.
13.17. Determine the kinetic energy of protons activating the
reaction 9Be(p, a)6Li + 2.13 lVleV, if the range of a-particles, out-
going at right angles to the direction of motion of the protons, is
equal to 2.5 em in air at NTP.
13.18. Deuterons with a kinetic energy of T d = 10.0 MeV collide
with carbon nuclei and initiate the reaction 13C(d, a)11B, Q =
= +5.16 MeV. Determine the angle between the directions in which
the products of the reaction are ejected, if: (a) the produced nuclei
diverge in a symmetric pattern; (b) the a-particle is ejected at
right angles to the deuteron beam.
13.19. Derive formula (13.1).
13.20. Calculate the threshold kinetic energies of a-particles
and neutrons in the following reactions:
(a) a+ 7L i -+ 10B + n; (b) a+12C~14N+d;
(c) n+ 12C-+ 9Be + a ; (d) n+t70-+1~C+a.
13.21. Calculate the threshold kinetic energy of an incoming
particle in the reaction p + 3H ~ 3He + n, for the cases when that
particle is: (a) a proton; (b) a tritium nucleus.
102
13.22. Determine the kinetic energies of 7Be and 15 0 nuclei pro-
duced in the reactions:
(a) p-t-7Li~7Be+n, Q= -1.65lVleV;
(b) n+19F-+150+p+4n, Q= -35.8MeV
for the threshold value of energy of the proton and neutron.
13.23. A lithium target is irradiated with a beam of protons whose
kinetic energy exceeds the threshold value 1.50 times. Find the
energy of neutrons ejected as a result of the reaction 7Li(p, n)7Be -
- 1.65 MeV at an angle of 90° to the proton beam.
13.24. Evaluate the lowest kinetic energy an incoming a-par-
ticle requires to overcome the Coulomb potential barrier of a 7Li
nucleus. Will this amount of energy he sufficient for the a-particle
to activate the reaction 7Li(a, n)I°B?
13.25. Neutrons with the kinetic energy T === 10.0 l\leV activate
the reaction lOB(n, d)9Be for which Tth = 4.8 MeV. Find the kinetic
energy of deuterons for the reverse reaction under assumption that
the total energies of interacting particles are equal for both processes
in the C frame.
13.26. Derive the expression for the momentum p of particles
produced by the reaction M (m, m') M' + Q in the C frame, if the
kinetic energy of an incoming particle in the L frame is equal to T m-
13.27. Determine the kinetic energy of oxygen nuclei ejected
following the reaction 14N(p, n)140 - 5.9 MeV at an angle of 300
to the direction of motion of the striking protons whose kinetic
energy is 10.0 MaV. Obtain the solution, using the vector diagram
of momenta drawn to scale.
13.28. Find the highest kinetic energy of a-particles produced
by the reaction 160(d, a)14N + 3.1 MeV, if the energy of the striking
deuterons is 2.0 ~IeV.
13.29.. Find the width of the energy spectrum of neutrons pro-
duced by the reaction IlB(a, n)14N + 0.30 MeV, if the kinetic
energy of striking a-particles is equal to 5.0 MeV.
13.30. A lithium target is bombarded with a-particles with the
kinetic energy T a. As a result of the reaction 7Li(a, n)lOB, Q =
== -2.79 MeV, the target emits neutrons. Find:
(a) the kinetic energies of neutrons ejected at the angles 0, 90,
and 1800 to the direction of motion of the striking a-particles, if
T a == 10.0 MeV;
(b) at what values of T ex. the neutrons will be emitted into the
front hemisphere only ('0' ~ 90°).
13.31. To obtain high-intensity fluxes of fast neutrons, lithium
deuteride LiD is placed into a reactor, so that slow neutrons activate
the reaction "Li(», a)3H + 4.80 MeV. The generated tritium nuclei
in its turn activate the reactions: (a) D(t, n)4He + 17.6 MeV and
(b) 'Li(t, n)9Be + 10.4 MeV, providing fast neutrons. Find the
highest energies of these neutrons.
103
13.32. Neutrons with an energy of 1.50 ~IeV strike a target pos-
sessing the nuclides 6Li and 2H. Using the vector diagram of momenta,
determine the width of energy spectrum of neutrons appearing
after the following successive transformations:
n + 6Li-+- 4He+ 3H; 3H -t- 2H~ 4He+ n,
13.33. Find the greatest possible angles (in the L frame) at which
the products of the following reactions move:
(a) 9Be(p, n)9B-1.84l\tIeV, if T p==4.00MeV;
(b) 4He (n, d)3H -17.5 MeV, if T'; = 24.0 MeV.
Here T is the kinetic energy of a striking particle.
13.34. A beam of neutrons with an energy of 7.5 l\leV activates
the reaction 12C(n, ex)9Be - 5.70 MeV in a carbon target. Find:
(a) the fraction of ex-particles ejected into the front hemisphere
(tl'a ~ 90°), assuming the angular distribution of the reaction prod-
ucts to be isotropic in the C frame; (b) the angle at which the
ex-particle is ejected in the C frame, if the corresponding angle in
the L frame is equal to '6'a = 30°.
13.35. Find the threshold energy of a v-quantum sufficient to
activate the endoergic photodisintegration of a stationary nucleus
of mass M, if the reaction yield is equal to Q.
13.36. Calculate the kinetic energies of neutrons in the following
disintegration reactions: (a) y + d ~ n + p; (b) y + 7Li -+ n +
+ 6Li, if the y-quanta possess the threshold values of energy.
13.37. Demonstrate that in a nuclear photodisintegration reaction
l' + M -+ m, + m2 , when the products of the