**3. Calculation results**

An analysis of the dependences of the micro-cross sections of neutron radiative capture by gadolinium isotopes on the neutron energy, presented in [4], indicates a favorable combination of properties of two gadolinium isotopes with mass numbers of 155 and 156, consisting in preferential absorption of neutrons by the light isotope in a rather wide energy range.

The reaction cross section of the neutron radiative capture by Gd155 nuclei exceeds by 3–4 orders of magnitude that for Gd<sup>156</sup> nuclei at neutron energies to 10 eV; the resonance integral for Gd155 nuclei significantly exceeds that for Gd<sup>156</sup> nuclei. The production rate of Gd156m nuclei is significantly higher than their

### *Application of the Gadolinium Isotopes Nuclei Neutron-Induced Excitation Process DOI: http://dx.doi.org/10.5772/intechopen.85596*

"shooting" by neutrons and the rate of their ground-state transition even at flux densities of resonant and thermal neutrons of the order of �10<sup>13</sup> cm�<sup>2</sup> <sup>s</sup> �1 . The further increase in the neutron flux density leads to reducing the time interval after which the excess energy begins to accumulate. As a result, rapid accumulation of excess energy in the metastable state of gadolinium-156 isotope nuclei should be expected at moderate neutron flux densities.

The possibility of pumping the medium formed by hafnium nuclei with gamma-quanta was studied in [5]. External gamma-quantum flow cannot provide conditions for population inversion of metastable nuclei energy levels. To compare the ability to accumulate energy in isomeric conditions at nuclei excitation, according to the scheme presented in **Figure 1**, the stable isotope 72Hf<sup>178</sup> was considered. Metastable nuclei of hafnium-178m2 form from the nuclei of hafnium-178 (stable isotope with 27.28% content in natural mixture). According to contemporary data [6–8], the energy of emitted gamma-quantum is 2.446 MeV at transition to the ground state and the half-life of 31.0 years correspond to metastable nuclei of hafnium-178m2. These parameters are different for metastable nuclei of hafnium-178m3 (higher energy level) and are equal to 2.534 MeV and 68 μs, and 1.147 MeV and 468 μs for metastable nuclei of hafnium-178m1.

The metastable nuclei of hafnium-178m2 form not only at inelastic scattering of fast neutrons on nuclei of hafnium-178, but also at radiation neutron capture by the nuclei of hafnium-177 (stable isotope with 18.6% content in natural mixture). As a result of neutron capture, the main nucleus of hafnium-178\* forms in a very excited state. The excitation energy is equal to the sum of neutron-binding energy in the nucleus and neutron kinetic energy. Lifetime of the compound nucleus in a state of excitement is not more than 10�<sup>13</sup> s, excitation is removed by emission of highenergy gamma-quantum, and the nucleus transfers either to the ground or one of the metastable states.

Inelastic scattering cross section on nuclei of hafnium-178 does not exceed 2.5 barns in a wide range of neutron energies, which leads to impossibility to accumulate considerable amount of energy in isomeric states only by means of inelastic scattering, even if the neutron flux density of <sup>Ф</sup> � <sup>10</sup><sup>14</sup> cm�<sup>2</sup> <sup>s</sup> �1 . The condition *y t*ð Þ *z t*ð Þ <sup>≥</sup>1 due to only inelastic scattering will be achieved in a very big period of time. The balance of hafnium-178 nuclei in the isomeric state **m2** improves, if it is taken into account that they form as a result of radiation neutron capture by nuclei of hafnium-177. Cross section of this process is hundreds of barn for thermal neutrons and is more than 1 barn for neutrons with the energy to 100 eV. The condition *y t*ð Þ *z t*ð Þ <sup>≥</sup>1 can be achieved in a significantly shorter period of time with account of radiation neutron capture, but if it is taken into account that as a result of neutron capture by nuclei of hafnium-178 and its isomers (the cross section of the process for thermal neutrons is tens of barn) all these nuclei disappear, the condition can be not achieved in principle.

To perform the research of excess energy accumulation in Gd, the following system to place Gd2O3 in the reactor core was used (see **Figure 2**).

Gd2O3 is placed in a cylindrical volume made of pure tungsten. Further, the cylinder is placed in the active core of the reactor unit. Uranium-graphite reactor is chosen as a reactor unit for the purpose of investigating the sample in thermal neutrons spectrum [9–13].

Several versions of the tungsten bulb with graphite reflector and without reflector are considered in the work (see **Table 2**). Graphite block serves as a reflector. Isotopic composition of Gd consists of 50% Gd<sup>155</sup> and 50% Gd156.

The neutronic calculation was performed using a WIMSD-5B.12 specialized program (OECD Nuclear Energy Agency). The program WIMS is applied for

To evaluate the possibility of energy accumulation in isomeric nuclei states due to radiation neutron capture in such material, it is required to solve the differential

*dt* <sup>¼</sup> *<sup>σ</sup>*1*x*<sup>Φ</sup> � *<sup>σ</sup>*2*x*<sup>Φ</sup> � *<sup>λ</sup><sup>y</sup>*

Here *x*(*t*), *y*(*t*), *z*(*t*) – Gd155, Gd156m, Gd156 nuclei concentration, respectively; Ф is the neutron flux density; *σ* is the micro-cross section of radiation neutron capture (*σ*1—for Gd<sup>155</sup> nuclei, *σ*2—for Gd156m nuclei, *σ*3—for Gd<sup>156</sup> nuclei), and *λ* is the

Solution of the system of equations gives the formulae to determine the possibility to achieve the condition at which the nuclei concentration in isomeric state *y* (*t*) becomes bigger or equal to the concentration of nuclei in the ground state *z*(*t*)

*z t*ð Þ <sup>≈</sup> *<sup>λ</sup><sup>t</sup>* � ð Þ *<sup>σ</sup>*<sup>1</sup> � *<sup>σ</sup>*<sup>2</sup> <sup>Φ</sup>*<sup>t</sup>*

tion of Gd<sup>156</sup> nuclei. When this ratio becomes greater than 1, that means that, starting from a certain point in time, the concentration of Gd156m nuclei becomes greater than the concentration of Gd<sup>156</sup> nuclei. It is taken into account that the Gd156m nuclei transfer to the ground state with the emission of gamma-quants that

act on the Gd<sup>156</sup> nuclei, transferring them to the excited metastable state.

several tens of seconds. It is explained by almost unique combination of absorbing properties of two isotopes of gadolinium (Gd155 and Gd156) in both thermal and

An analysis of the dependences of the micro-cross sections of neutron radiative capture by gadolinium isotopes on the neutron energy, presented in [4], indicates a favorable combination of properties of two gadolinium isotopes with mass numbers of 155 and 156, consisting in preferential absorption of neutrons by the light isotope

The reaction cross section of the neutron radiative capture by Gd155 nuclei exceeds by 3–4 orders of magnitude that for Gd<sup>156</sup> nuclei at neutron energies to 10 eV; the resonance integral for Gd155 nuclei significantly exceeds that for Gd<sup>156</sup> nuclei. The production rate of Gd156m nuclei is significantly higher than their

ð Þ *<sup>σ</sup>*<sup>1</sup> � *<sup>σ</sup>*<sup>2</sup> <sup>þ</sup> *<sup>σ</sup>*<sup>3</sup> <sup>Φ</sup> <sup>þ</sup> ð Þ *<sup>λ</sup>* � ð Þ *<sup>σ</sup>*<sup>1</sup> � *<sup>σ</sup>*<sup>2</sup> <sup>Φ</sup> ð Þ <sup>1</sup> � *<sup>σ</sup>*3Φ*<sup>t</sup>*

*z t*ð Þ is the ratio of the concentration of Gd156m nuclei to the concentra-

�1 :

*<sup>S</sup><sup>λ</sup> ,* (5)

ð Þ *<sup>σ</sup>*<sup>1</sup> � *<sup>σ</sup>*<sup>2</sup> <sup>þ</sup> *<sup>σ</sup>*<sup>3</sup> <sup>Φ</sup>ð Þ *<sup>λ</sup>* <sup>þ</sup> *<sup>σ</sup>*3<sup>Φ</sup> *:* (6)

�<sup>1</sup> influence the neutrons

*z t*ð Þ <sup>≈</sup>1 is achieved within

(4)

*dt* ¼ �*σ*3*z*<sup>Φ</sup> <sup>þ</sup> *<sup>λ</sup><sup>y</sup>*

*dx*

8 >>>>>><

>>>>>>:

influenced by neutrons with the flux density Ф to 10<sup>16</sup> cm�<sup>2</sup> s

*y t*ð Þ

*<sup>λ</sup>* <sup>þ</sup> *<sup>σ</sup>*3<sup>Φ</sup> � <sup>1</sup> � ð Þ *<sup>σ</sup>*<sup>1</sup> � *<sup>σ</sup>*<sup>2</sup> <sup>þ</sup> <sup>2</sup>*σ*<sup>3</sup> <sup>Φ</sup>*<sup>t</sup>*

When neutrons with the flux density Ф = 1013 cm�<sup>2</sup> s

absorber formed by gadolinium nuclei, the condition *y t*ð Þ

resonant energy regions of neutrons.

**3. Calculation results**

in a rather wide energy range.

**70**

decay constant of isomers nuclei Gd156m.

*dy*

*dz*

*dt* ¼ �*σ*1*x*<sup>Φ</sup>

equations system:

*Rare Earth Elements and Their Minerals*

where

*<sup>S</sup>* <sup>¼</sup> <sup>1</sup> � ð Þ *<sup>λ</sup>* <sup>þ</sup> <sup>2</sup>*σ*3<sup>Φ</sup> *<sup>t</sup>*

The ratio *y t*ð Þ

calculation of thermal and fast reactors. It is also successfully used for designing reactors and calculation and analysis of various effects in current reactor units. At present, the program uses the universal 69-group library of constants made on the basis of the evaluated neutron data files (ENDF, JEF, JENDL и т.д.) [11–18].

reactor's neutron spectrum at the location of a cylinder made of Gd2O3 suggest that the rate of "production" of metastable Gd156m nuclei will significantly exceed their "burnout" rate in the neutron field. Simultaneous fulfillment of the condition *y t*ð Þ

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

will lead to the generation in the Gd2O3 volume of radiation with a wavelength of

0.0006 nm.

**Figure 4.**

**Figure 5.**

**Figure 6.**

**73**

*The spectrum in the energy range from 0 to 30 eV.*

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

*The spectrum in the energy range from 0 to 200 eV.*

*The spectrum in the energy range from 0 to 1000 eV.*

*z t*ð Þ >1

The calculation was performed for all variants of the placed sample. To compare and analyze the obtained results a preliminary calculation of the *initial spectrum* in the placement region of the sample in the reactor active core. The spectrum calculation results in the placed sample are presented in **Figures 3–7**. Changes in the

### **Figure 2.**

*The scheme of tungsten bulb placement in the reactor unit: (а) without the reflector and (b) with the reflector.*


### **Table 2.**

*Geometrical characteristics of the tungsten bulb with Gd2O3.*

**Figure 3.** *The spectrum in the energy range from 0 to 5 eV.*

*Application of the Gadolinium Isotopes Nuclei Neutron-Induced Excitation Process DOI: http://dx.doi.org/10.5772/intechopen.85596*

reactor's neutron spectrum at the location of a cylinder made of Gd2O3 suggest that the rate of "production" of metastable Gd156m nuclei will significantly exceed their "burnout" rate in the neutron field. Simultaneous fulfillment of the condition *y t*ð Þ *z t*ð Þ >1 will lead to the generation in the Gd2O3 volume of radiation with a wavelength of 0.0006 nm.

**Figure 4.**

calculation of thermal and fast reactors. It is also successfully used for designing reactors and calculation and analysis of various effects in current reactor units. At present, the program uses the universal 69-group library of constants made on the basis of the evaluated neutron data files (ENDF, JEF, JENDL и т.д.) [11–18].

*Rare Earth Elements and Their Minerals*

**Figure 2.**

**Table 2.**

**Figure 3.**

**72**

Without reflector

With the reflector

*Geometrical characteristics of the tungsten bulb with Gd2O3.*

*The spectrum in the energy range from 0 to 5 eV.*

The calculation was performed for all variants of the placed sample. To compare and analyze the obtained results a preliminary calculation of the *initial spectrum* in the placement region of the sample in the reactor active core. The spectrum calculation results in the placed sample are presented in **Figures 3–7**. Changes in the

*The scheme of tungsten bulb placement in the reactor unit: (а) without the reflector and (b) with the reflector.*

5\_get 5 7 — 30 31 10\_get 10 12 — 30 31

5\_get+С 5 7 30 30 31 10\_get+С 10 12 30 30 31

**d1, cm d2, cm d3, cm h1, cm h2, cm**

*The spectrum in the energy range from 0 to 30 eV.*

### **Figure 5.**

*The spectrum in the energy range from 0 to 200 eV.*

**Figure 6.** *The spectrum in the energy range from 0 to 1000 eV.*

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

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kinetics involving hafnium and

**Figure 7.** *Total neutron spectrum.*
