**1. Introduction**

Active medium is considered to be some matter in which it is possible to create the nucleus energy level population inversion due to radiation capture reaction and inelastic neutron scattering by the nuclei present in the matter.

The combination of nuclear transformations occurring in the matter under the influence of the neutron flux is called nuclide kinetics. Differential and integral characteristics of nuclide kinetics determine isotopic composition of the matter which was or is in the neutron field. At present, the nuclide kinetics investigation results are applied mainly in physics and nuclear reactors engineering [1] and in

particular their nuclear safety. The possibility of accumulation and uncontrolled release of excess energy in neutron-absorbing materials because of potential accumulation of excess energy in isomeric states of atomic nuclei (for example, hafnium or gadolinium) comprising some of them was paid attention to [2].

magnitude longer than the nuclear interaction time. Therefore, the nucleus in the excited state can gain and conserve energy ΔE transferred to it as a result of neutron scattering on it. Energy supplied to the nucleus when the neutron dissipates on it depends on the nucleus mass—the less the nucleus mass is, the bigger energy the neutron gives to it during dissipation. In the ideal case, energy Δ*E* transferred at dissipation is the value equal to the difference between the energy of metastable state and energy of excitation. For the given value of the neutron energy *E*n, the value of the energy Δ*E* transferred at inelastic scattering on the nucleus can be

*Application of the Gadolinium Isotopes Nuclei Neutron-Induced Excitation Process*

determined from the transcendent equation:

*DOI: http://dx.doi.org/10.5772/intechopen.85596*

@

of the nucleus to the corresponding excitation level.

active medium is determined by the following relation:

where <sup>υ</sup> is the neutron velocity (*<sup>υ</sup>* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffi

*A* þ 1 2 � *ΔEi En*

0 s

� <sup>0</sup>*:*07*A*2*=*<sup>3</sup>

where *A* is the nucleus mass number. The equation is obtained on the assumption that the transferred energy Δ*E* is equal to the energy of nucleus excitation from the ground state. If the nucleus has several excitation levels (i = 1, 2, 3…), the equation allows determining the value of the neutron energy *En*, providing transfer

The number of collisions (dissipations) of the neutrons with the nuclei of active medium occurring in the medium volume unit per time unit can be determined by

where Ф is the neutron flux density, σ is the microscopic cross section of inelastic neutron scattering on the nuclei, and nnuc is the number of nuclei per medium volume unit. In this case, the scattering frequency experienced by neutrons in the

2*E=m* p ). For example, to transfer nuclei of 54Xe<sup>130</sup> isotope from the ground state to the excited state, taking into account that they have three excitation levels (0.54, 1.21, and 1.95 MeV), the presence of neutrons with the energies of 0.709, 1.285, and 2.005 MeV, correspondingly, is required in the flux. To transfer nuclei of 10Ne<sup>22</sup> isotope from the ground state to the excited state, which also has three excitation levels, the presence of neutrons with the energies of 2.075, 3.747, and 4.859 MeV is required in the flux. The average neutron energy of the fission spectrum is 2 MeV. The average neutron spectrum energy of the nuclear reactor (even fast neutron reactors) is significantly lower. Besides, to transfer isotope nuclei to the excited state by direct scattering of neutrons on nuclei, it is necessary to "choose" isotopes not only with bigger specific binding energy of nucleons in the nucleus but also with small value of the neutron absorption cross section. Therefore, to accumulate nuclei in the excited state, it is reasonable to obtain them as a product of the reaction of neutron radiative capture by nuclei with a mass number smaller by one unity. The daughter nucleus is formed in the excited state and, if required, gains an additional energy due to neutron scattering on it. As a result, the daughter nucleus appears in

*En*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � *<sup>A</sup>* <sup>þ</sup> <sup>1</sup> *A* �

Φ*σnnuc,* (2)

*υσnnuc,* (3)

*ΔEi En*

1

A*,* (1)

ð Þ *<sup>A</sup>* <sup>þ</sup> <sup>1</sup> <sup>2</sup> <sup>1</sup> <sup>þ</sup>

*ΔEi En*

<sup>¼</sup> <sup>2</sup>*<sup>A</sup>*

the following relation:

the metastable state.

**69**
