#
Specific Radioactivity of Neutron Induced Radioisotopes: Assessment Methods and Application for Medically Useful ^{177}Lu Production as a Case

## Abstract

**:**

^{177}Lu produced based on two different reactions,

^{176}Lu (n,γ)

^{177}Lu and

^{176}Yb (n,γ)

^{177}Yb (β

^{-}decay)

^{177}Lu, were performed. The irradiation time required for achieving a maximum yield and maximum SA value was evaluated for production based on the

^{176}Lu (n,γ)

^{177}Lu reaction. The effect of several factors (such as elemental Lu and isotopic impurities) on the

^{177}Lu SA degradation was evaluated for production based on the

^{176}Yb (n,γ)

^{177}Yb (β

^{-}decay)

^{177}Lu reaction. The method of SA assessment of a mixture of several radioactive sources was developed for the radioisotope produced in a reactor from different targets.

## 1. Introduction

^{99}Mo/

^{99m}Tc for diagnostic imaging and

^{131}I,

^{32}P,

^{192}Ir and

^{60}Co for radiotherapy. The high SA requirement for these radioisotopes was not critically considered with respect to their effective utilization in nuclear medicine, except for

^{99}Mo. The current wide expansion of targeting endo-radiotherapy depends very much on the availability of high SA radionuclides which can be produced from nuclear research reactor such as

^{153}Sm,

^{188}W/

^{188}Re,

^{90}Y and

^{177}Lu. As an example, as high as 20 Ci per mg SA

^{177}Lu is a prerequisite to formulate radiopharmaceuticals targeting tumors in different cancer treatments [1,2].

^{60}Co and

^{192}Ir, used in industry and radiotherapy. In spite of the target burn-up parameter present in the formula of reaction yield calculation to describe the impact of target depression, the SA assessment using the reaction yield was so significantly simplified that the target mass was assumed to be an invariable value during the reactor activation. Critically, this simplification was only favored by virtue of an inherent advantageous combination of the low neutron capture cross section (37 barns) of the target nuclide

^{59}Co and the long half-life of

^{60}Co (which keeps the amount of elemental Co unchanged during neutron bombardment) [4].

^{177}Lu radioisotope production is presented in this paper. This assessment can also play a complementary or even substantial role in the quality management regarding certifying the SA of the product, when it may be experimentally unfeasible due to radiation protection and instrumentation difficulties in the practical measurement of very low elemental content in a small volume solution of high radioactivity content.

^{176}Lu (n, γ)

^{177}Lu reaction (б = 2,300 barns).

^{177}Lu is a radioisotope of choice for endo-radiotherapy because of its favorable decay characteristics, such as a low energy beta decay of 497 keV (78.6%) and half-life of 6.71 day. It also emits gamma rays of 113 keV (6.4%) and 208 keV (11%) which make it useful for imaging in-vivo localization with a gamma camera.

^{177}Lu can be produced by two different routes, a direct route with the

^{176}Lu (n, γ)

^{177}Lu reaction and an indirect route via the

^{176}Yb (n, γ)

^{177}Yb (β

^{-}decay)

^{177}Lu nuclear reaction-transformation. The direct route could be successfully performed in high neutron flux nuclear reactors but these are available in only a handful of countries in the world. Additionally, large burn-up of the target nuclide during high neutron flux irradiation may cause a degradation of the SA value of the produced nuclide if the target contains isotopic impurities. No-carrier-added (n.c.a) radioisotopes of higher SA can be produced via an indirect route with a nuclear reaction- followed –by- radioactive transformation process, such as in the process of neutron capture-followed-by- β

^{-}decay ,

^{176}Yb (n, γ)

^{177}Yb (β

^{-}decay)

^{177}Lu. In this case, the same reduction in SA is also be experienced if the target contains isotopic and/or elemental Lu impurities.

^{177}Lu production has been reported in many publications [5,6,7,8,9], but until now the product quality, especially the evaluation of

^{177}Lu specific radioactivity in the product, has not been sufficiently analyzed. Based on the theoretical SA assessment results obtained in this report, the optimal conditions for the

^{177}Lu production were set up to produce

^{177}Lu product suitable for radiopharmaceutical preparations for targeting endo-radiotherapy.

#### 1.1. Units of specific radioactivity, their conversion and SA of carrier-free radionuclide

_{Ri(A)}is the hot atom numbers of radioisotope R

_{i}of the chemical element A and λ

_{Ri}

_{(A)}, its decay constant. N

_{A}is the atom numbers of the chemical element A and T

_{1/2}(sec) the half-life of radioisotope R

_{i}.

_{iA}is the atomic weight of the target or radioactive material of given isotopic composition of the chemical element A.

_{n,A}, respectively. The specific radioactivity of the carrier-free radioisotope R

_{i}is calculated as below:

_{iA}as the atomic weight of the concerned radioisotope), it is clear that the SA of a carrier-free radionuclide in unit atom % is 100%.

## 2. Theoretical Approach and Assessment Methods

^{−}decay of this isotope during target activation results in a decrease in both the reaction yield and atom numbers of the target chemical element. The second reaction is the thermal neutron capture followed by radioactive transformation S (n, γ) R

_{x}(β

^{−}decay) R

_{i}. This reaction leads to a carrier-free radioisotope of another chemical element than the target chemical element.

_{x}(β

^{−}decay) R

_{i}which could result in the isotopic impurities for the radioisotope intended to be produced using the first reaction. In this case the SA assessment in (n, γ) reaction based production process can be simplified by investigation of the SA degrading effect of target nuclide burn-up, chemical element depression due to radioactive decay and isotopic impurities present in the target.

_{x}(β

^{-}decay) R

_{i}reaction based isotope production requires an analysis of the combined reaction system. This system is influenced by both (n, γ) reaction and neutron-capture- followed-by-radioactive transformation S (n, γ) R

_{x}(β

^{-}decay) R

_{i}. So the effect of side nuclear reactions in this target system will be assessed in addition to the three above mentioned factors that are involved in the simple target system. In this case the SA assessment is best resolved by a method of SA calculation used for the mixture of several radioactive sources of variable SA, which is referred to as a radioisotope dilution process.

_{i}in the two above mentioned reactions, the following reaction schemes are used for further discussion.

- S
_{1,A}is the target stable isotope of element A in the target; S_{g,A}(with g ≥ 2) is the impure stable isotope of element A originally presented or produced in the target. - S
_{1,B}is the target stable isotope of element B in the target; S_{2,B}is the stable isotope of element B in the target. - R
_{i,A}or R_{i}is the wanted radioisotope of element A produced in the target from stable isotope S_{1,A}. - R
_{x}and R_{y}are the radioisotopes of element B produced in the target. - The particle emitted from reaction (n, particle) may be proton or alpha.
- σ
_{(th)}, σ_{(epi)}and σ_{(fast)}are reaction cross sections for thermal, epi-thermal and fast neutrons, respectively. - σ
_{1,i(th)}, σ_{2,x(th)}, σ_{2,y(th)},. are cross sections of thermal neutrons for the formation of isotopes i, x, y,. from stable isotope 1, 2, 2, respectively. - λ is the decay constant.

_{n}) or velocity (v

_{n}). In the thermal neutron region, the cross-section usually varies linearly as 1/v

_{n}(so called 1/v

_{n}reaction), where v

_{n}is velocity of neutrons. The cross section-versus-velocity function of many nuclides is, however, not linear as 1/v

_{n}in the thermal region (so called non − 1/v

_{n}reaction.). As the energy of neutrons increases to the epithermal region, the cross section shows a sharp variation with energy, with discrete sharp peaks called resonance.

_{0}given for thermal neutrons of E

_{n}= 0.0253 eV and v

_{n}= 2200 m/s and as I

_{0}(infinite dilution resonance integral in the neutron energy region from E

_{Cd}= 0.55 eV to 1.0 MeV) given for epithermal neutrons.

_{th}and σ

_{epi}used in this paper are identified with the thermal neutron activation cross-section σ

_{0}and the infinite dilution resonance integral I

_{0}, respectively, for the case of 1/v

_{n}(n,γ)-reaction carried out with a neutron source of pure 1/E

_{n}epithermal neutron spectrum (Epithermal flux distribution parameter α = 0). Unfortunately, this condition is not useful any more for practical reaction yield and SA calculations.

_{i}presenting as a sum σ

_{1,i(th)}+ R

_{epi.}σ

_{1,i(epi)}in all the equations below has to be replaced by σ

_{eff}

_{(1/v)}for the “1/v

_{n}”- named (n,γ) reaction and by σ

_{eff}

_{(non − 1/v)}for the “non − 1/v

_{n}” - named (n,γ)- reaction. The detailed description of these σ

_{eff}values can be found in the ‘Notes on Formalism’ at the end of this section.

^{7}n.cm

^{−2}.s

^{−1}fast neutron flux compared to >10

^{14}n.cm

^{−2}.s

^{−1}thermal one in the Rigs LE7-01 and HF-01 of OPAL reactor-Australia). Besides, the milli-barn cross-section of (n,γ) ,(n,p) and (n,α) reactions induced by fast neutrons is negligible compared to that of (n,γ) reaction with thermal neutron [11]. So the reaction rate of the fast neutron reactions is negligible. Nevertheless, for the generalization purposes the contribution of the fast neutron reaction is also included in the calculation methods below described. It can be ignored in the practical application of SA assessment without significant error.

#### 2.1. The specific radioactivity of radionuclide R_{i} in the simple target system for the (n, γ) reaction based radioisotope production

#### 2.1.1. Main characteristics of the simple target system

_{i}is intended to be produced from stable isotope S

_{1,A}via a (n, γ) reaction i = 1 as described above in reaction scheme 1. Other stable S

_{g,A}isotopes ( with g ≥ 2) of the target are considered as impure isotopes.

#### 2.1.1.1. The target burn-up for each isotope in simple target system

_{1,A}is the sum of the burn-up caused by different (n,γ) and (n, particle) reactions from reaction i = 1 to i = k, the cross sections of which are different б

_{1,i}values. This total burn up rate could be formulated as follows:

_{1,i(th)}, σ

_{1,i(epi)}and σ

_{1,i(fast)}are the thermal, epithermal and fast neutron cross section of the S

_{1,i}nuclide for the reaction i, respectively. ϕ

_{th}, ϕ

_{epi}and ϕ

_{fast}are the thermal, epithermal and fast neutron flux, respectively. t

_{irr}is the irradiation time. ${N}_{{S}_{1,A}}$ is the atom numbers of the isotope S

_{1,A}. By putting R

_{epi}= ϕ

_{epi}/ϕ

_{th}and R

_{fast}= ϕ

_{fast}/ϕ

_{th}ratios into eq.4, the following is deduced.

_{1,A}at any t

_{irr}values (${N}_{{S}_{1,A}}$) is achieved by the integration of eq.7 with the condition of ${N}_{{S}_{1,A}}={N}_{0,}{}_{{S}_{1,A}}$ at t

_{irr}= 0. The result is:

_{1,A}(${N}_{b,}{}_{{S}_{1,A}}$) is:

_{g,A}.

_{1/2-B}a half of the original atom numbers of the isotope S

_{1,A}are burned. Putting ${N}_{{S}_{1,A}}={N}_{0,}{}_{{S}_{1,A}}/2$ into eq. 8, the T

_{1/2-B}value is achieved as follows:

#### 2.1.1.2. Reaction yield of radioisotope R_{i} in the simple target system

_{1,A}(eq. 8) , the reaction rate of any isotope in reaction scheme 1 will be evaluated as follows. In this reaction process the depression of the atom numbers of radioisotope R

_{i}is caused by beta radioactive decays and (n, γ)/(n, particle) reaction-related destruction. The depression factor ${\mathsf{\Lambda}}_{{R}_{i}}$ of the radioisotope R

_{i}in reaction scheme 1 is formulated as follows:

_{i}= ϕ

_{th}·ΣΩ

_{i}and Ω

_{i}= σ

_{i(th)}+ R

_{epi}·σ

_{i(epi)}+ R

_{fast}·σ

_{i(fast)}

_{i}radioisotope formation rate is the following:

_{Ri}= 0 at t

_{irr}= 0, the yield of radioisotope R

_{i}at the irradiation time t

_{irr}is the following:

_{i}atom numbers (N

_{Ri}):

_{i}isotope radioactivity (A

_{Ri}):

_{i}atom numbers and radioactivity at the post-irradiation time t

_{c}( N

_{Ri,tc}and A

_{Ri,tc}, respectively) are calculated by multiplying eqs.13 and 14 with the factor ${e}^{-{t}_{c}\cdot {\displaystyle \sum _{m=1}^{m=j}{\lambda}_{m,Ri}}}$.

_{i}. At the irradiation time (denoted as t

_{irr-max}) where $\frac{d{A}_{Ri}}{d{t}_{irr}}=0$, R

_{i}radioactivity reaches maximum (A

_{Ri}

_{−max}). By differentiating eq.14 and making it equal to zero:

_{irr-max}is deduced as follows:

_{i}radioisotope of highest yield. By introducing the value t

_{irr-max}into eqs.13 and 14, we achieve the maximum yield of radioisotope R

_{i}( N

_{Ri-max}and A

_{Ri-max}) as follows:

_{Ri-max}is:

_{Ri-max}is:

_{i}is a function of the variable D.

#### 2.1.2. The SA assessment of radionuclide R_{i} in the simple target for (n, γ) reaction based radioisotope production

#### 2.1.2.1. General formula of SA calculation for the simple multi-isotope target

_{i,A}captures neutrons to form the wanted radioisotope R

_{i}and the isotopic impurities in the target don’t get involved in any nuclear reactions whatsoever. The isotopic impurities may participate in some nuclear reactions to generate either stable isotopes of the target element or an insignificant amount of the isotopes of other chemical element than the target one. This simplified calculation process is supported by a careful targetry study regarding minimizing the radioactive isotopic impurities in the radioisotope product. The following is the SA of radioisotope R

_{i}formed in a target composed of different stable isotopes:

_{i}:

_{g,A}and its depression effect will be ignored.

_{g,A}doesn’t participate in any nuclear reaction or its neutron capture generates a stable isotope of the target element, then zero value will be given to the parameter ΔS

_{g}

_{,A}of eq.(19).

#### 2.1.2.2. SA of radioisotope R_{i} in the simple two-isotope target

_{i}is the radioisotope expected to be produced from the stable isotope S

_{1,A}. P

_{1}and M

_{1}, the weight percentage and atomic weight of the isotope S

_{1,A}, respectively. P

_{2}and M

_{2}are for the isotope S

_{2,A}, m is the weight of the target.

_{i}in a two isotope target at the end of neutron bombardment, $S{A}_{{R}_{i},{t}_{irr}}$, is the following:

_{c}, $S{A}_{{R}_{i},{t}_{c}}$, is:

_{i}in the simple two-isotope target. Rendering the differential of eq. 21 equal to zero offers the way to calculate the irradiation time at which the SA of nuclide R

_{i}reaches maximum value ($S{A}_{{R}_{i},\mathrm{max}}$):

^{x}gives the value ${t}_{irr,S{A}_{\mathrm{max}}}$. The analysis of the equation 24 and MAPLE-10 calculation results confirmed that the SA of nuclide R

_{i}reaches maximum at a defined characteristic irradiation time ${t}_{irr,S{A}_{\mathrm{max}}}$ except for the case of P

_{2}=0 or very large ${\Delta}_{{S}_{2,A}}$ value, which will be investigated in the following sections.

_{i}in the simple two-isotope target at the maximum reaction yield. Replacing t

_{irr}of eqs.(21) and (22) with the t

_{irr-max}from eq.15 is to calculate SA at the maximum reaction yield $S{A}_{{R}_{i},{t}_{irr,\mathrm{max}}}$ (achieved at the irradiation time t

_{irr-max}):

_{i}in the target which is considered as a simple two-isotope target. It is also a matter of fact that another very commonly used target system contains more than two stable isotopes (simple multi-isotope target system, g ≥ 2). Except S

_{1,A}as shown in reaction scheme 1, all the impure isotopes of the same chemical element in the target don’t get involved in any nuclear reactions or they may participate in with very low rate giving insignificant burn-up (${\Delta}_{{S}_{g,A}}=0$).This system is considered as a special two-isotope target system for which the non-depression of impure isotopes (${\Delta}_{{S}_{g,A}}=0$) and the combined impure isotope percentage (P

_{imp}

_{,A}) and molecular weight (M

_{imp}

_{,A}) are applied. We will have the relevant equations for the calculation of the specific SA value of this target by putting ${\Delta}_{{S}_{2,A}}={\Delta}_{{S}_{g,A}}=0$, ${M}_{2}={M}_{imp,A}=({\displaystyle \sum _{2}^{g}{P}_{{S}_{g,A}}})/{\displaystyle \sum _{2}^{s}({P}_{{S}_{g.A}}}/{M}_{{S}_{g.A}})$ and ${P}_{2}={P}_{imp,A}={\displaystyle \sum _{2}^{g}{P}_{{S}_{g,A}}}$ into eqs. (21)-(25) (${P}_{{S}_{g,A}}$ and ${M}_{{S}_{g,A}}$ are the weight percentage and atomic weight of impure stable isotopes S

_{g,A}, respectively).

#### 2.1.2.3. SA of radioisotope R_{i} in the simple one-isotope target system

_{2}= 0 into eq.(21), the SA of radioisotope R

_{i}in the simple one-isotope target is the following:

_{irr}and gives a correct solution when t

_{irr}value approaches to infinity .When $({\Delta}_{{S}_{1,A}}-{\mathsf{\Lambda}}_{{R}_{i}})=0$ then a = 1 (as shown in eq.25), hence the differential value is not defined, so the specific radioactivity has no maximum value at any time. This means that the SA of nuclide R

_{i}in the stable isotope target of 100% isotopic purity never reaches maximum at any irradiation time.

_{g,A}makes a multi-isotope target system change to a one-isotope target one. So, no maximum SA will be expected with this type of multi-isotope target system too.

_{irr}. This fact teaches us that a compromise between maximum yield achievable at t

_{irr,max}and favorable higher SA at the time t

_{irr>}t

_{irr,max}is subject to the priority of the producer.

#### 2.2. The specific radioactivity of radionuclide R_{i} in a complex target system for the S(n, γ) R_{x} (β^{-} decay) R_{i} reaction based radioisotope production

#### 2.2.1. Main characteristics of the complex target system

_{i}is intended to be produced from stable isotope S

_{1,B}of chemical element B via a S

_{1,B}(n, γ) R

_{x}(β

^{-}decay) R

_{i}reaction i = 1 as described above in reaction scheme 2. Other stable S

_{g,B}isotopes ( with g ≥ 2) of the element B are considered as impure isotopes and they could be transformed into other isotopes (except R

_{i}) of the chemical element A as described above in reaction scheme 3. Besides, the target could contain different isotopes of the element A as impure isotopes which could be involved in different nuclear reactions during target irradiation.

#### 2.2.1.1. The yield of S_{1B}(n, γ) R_{x} (β^{-} decay) R_{i} reaction

_{i}. The SA

_{Ri}value is 100 atom %. As shown in reaction scheme 2, the atom numbers (N

_{Ri}) and the radioactivity (A

_{Ri}) of R

_{i}radioisotope of chemical element A are calculated based on the general Bateman equation[3,12]. This is detailed in the following equation:

_{i}atom numbers ${N}_{{R}_{i,{t}_{c}}}$ present at post-irradiation time t

_{c}is achieved by multiplying the ${N}_{{R}_{i,{t}_{irr}}}$ value with the decay factor ${e}^{-{\displaystyle \sum _{m=1}^{m=j}{\lambda}_{m,{R}_{i\cdot {t}_{c}}}}}$.

_{Ri}value is simply derived by multiplying the N

_{Ri}values with $\sum _{m=1}^{m=j}{\lambda}_{m,{R}_{i}}$

#### 2.2.1.2. SA-degradation effect of impure stable isotope generated from S_{2,B}(n, γ) R_{y}(β^{-} decay) S_{g},_{A}reaction

_{2,B}in the S

_{1,B}target , reaction S

_{2,B}(n, γ) R

_{y}(β

^{-}decay) S

_{g,A}generates an amount of stable isotope S

_{g,A}of the same chemical element to the wanted radionuclide R

_{i,A}. This fact makes the SA of radionuclide R

_{i,A}produced from stable isotope S

_{1,B}lower, so the atom numbers of the stable isotope S

_{g,A}should be evaluated for the purpose of SA assessment. The atom numbers of S

_{g,A}is determined based on the activity of radioisotope R

_{y}. Identifying eqs. (13) and (14) described for reaction scheme 1 with the process of reaction scheme 3, we get the following equations.

_{y}at irradiation time t

_{irr}are calculated in the same manner as in Section 2.1.1.2 above (using eqs. (13) and (14)):

_{2,B}and ${\Delta}_{{S}_{2,B}}={\varphi}_{th}\cdot {\displaystyle \sum _{y=1}^{y=k}{\mathsf{\Omega}}_{2,y}}$

_{y}and ${\mathsf{\Lambda}}_{{R}_{y}}={\displaystyle \sum _{m=1}^{m=j}{\lambda}_{m,{R}_{y}}}+{\Delta}_{Ry}$, where ${\Delta}_{{R}_{y}}={\varphi}_{th}\cdot \sum {\mathsf{\Omega}}_{{R}_{y}}$

_{y}for the formation of S

_{g,A}isotope is denoted as ${A}_{{R}_{y}}\to {S}_{g,A},{t}_{irr}$. This quantity is calculated by either multiplying eq. (30) with a branch decay ratio ${f}_{{S}_{g,A}}$ or using an individual decay constant ${\lambda}_{{R}_{y}}\to {S}_{g,A}$ as follows:

_{g,A}content (${N}_{{S}_{g,A},{t}_{irr}}$) formed during neutron activation of the impure stable isotope S

_{2,B}is calculated by integrating R

_{y}nuclide radioactivity for the neutron irradiation time t

_{irr}as below.

_{irr}= 0, ${N}_{{S}_{g,A},{t}_{irr}}=0$, then $C=\frac{{\mathsf{\Lambda}}_{{R}_{y}}-{\Delta}_{{S}_{2,g}}}{{\Delta}_{{S}_{2,g}}\cdot {\mathsf{\Lambda}}_{{R}_{y}}}$. Putting C value into the above equation we get:

_{c}) R

_{y}radioactivity decreases as below:

_{g,A}during decay time. By integrating this formation rate we get the S

_{g,A}atom numbers (${N}_{{S}_{g,A},{t}_{c}}$) collected at the time t

_{c}. Because the ${A}_{{R}_{y}}\to {S}_{g,A},{t}_{irr}$ of nuclide R

_{y}at the end-of- neutron-bombardment (E.O.B) time t

_{irr}is independent on the variable t

_{c}, we get the following integral:

_{g,A}content (${N}_{{S}_{g,A}}$) formed in the target from the S

_{2,B}impure stable isotope is composed of a partial amount formed during neutron activation (${N}_{{S}_{g,A},{t}_{irr}}$) of isotope S

_{g,A}and its another part formed during post-irradiation decay of R

_{y}induced in the target.

_{i}in the above mentioned target containing both S

_{1,B}and S

_{2,B}(as described in reaction schemes 2 and 3) is calculated using eqs. (28) and (33b) as follows:

#### 2.2.1.3. SA-degradation effect of impure isotopes of the chemical element A

#### 2.2.2. The SA assessment of radionuclide R_{i} in a complex target system

_{i}and its unfavorable stable isotope are generated from different nuclear reactions of both the target isotope and impurities. The complex target system is considered as a mixture of several radioactive sources of variable SA. The method of SA assessment for this mixture is formulated as below.

_{j,Ri}is the SA of R

_{i}in the radioactive source S

_{j}the R

_{i}radioactivity of which is A

_{j,Ri}.The radioactive source S

_{j}is produced in the target from a given nuclear reaction such as S (n, γ) R

_{x}(β

^{-}decay) R

_{i}reaction (reaction scheme 2) or (n, γ) reaction (reaction scheme 1). There are n different radioactive sources S

_{j}(j=1…n) in the target. So the target is a mixture of radioactive sources. The SA of this radioactive source mixture (SA

_{Mix,Ri}) is calculated as follows:

_{i}atom numbers or R

_{i}radioactivity of the relevant radioactive source j.

_{j,Ri}= 0. This situation excludes the unfavorable effect of some (n, γ) reaction which generates a stable brother isotope S

_{g,A}of radioisotope R

_{i}in the target system ( Reaction scheme 3). To solve this problem we have to combine the atom numbers of this stable brother isotope with the atom numbers of one specified radioactive source of the mixture to generate a new radioactive source of SA ≠ 0, e.g. the combination of radioactive sources produced from the reactions in the scheme 2 and 3. This treatment will be detailed in a practical application for the

^{176}Yb target system in the following section.

#### 2.3. Notes on formalism

_{n}” - named (n,γ) reactions the modified Westcott formalism can be used to improve the accuracy of reaction yield calculation and the reaction rate in both thermal and epithermal neutron region for a diluted sample (both the thermal and epithermal neutron self-shielding factors are set equal to 1 or very close to unity) is:

_{n}) + r’S

_{0}(α} and ${\varphi}_{West\text{}\mathrm{cot}\text{}t}=k{\sigma}_{0}$).

_{n}) = 1 the Westcott values are ${\varphi}_{West\text{}\mathrm{cot}\text{}t}={n}_{n}{v}_{0}={\varphi}_{th}\{1+{f}_{H}\xi (\alpha )\}$ and ${\sigma}_{West\text{}\mathrm{cot}\text{}t}={\sigma}_{0}\{1+r\prime {S}_{0}(\alpha )\}$.Under this condition, the reaction rate is:

_{Cd}= 0.55 eV), respectively, while the Westcott neutron flux values ${\varphi}_{West\text{}\mathrm{cot}t}$ and ${\varphi}_{epi,West\text{}\mathrm{cot}\text{}t}$ are not usually available.

_{0}= 0.0253 eV and E

_{Cd}= 0.55 eV and the Hogdahl ratio f

_{H}= 0.02 (Rig LE7-01 of Australian OPAL reactor).

_{n}” - named (n,γ) reaction yield will be around 1% less than the real value if ${\varphi}_{West\text{}\mathrm{cot}\text{}t}={\varphi}_{th,HogdAhl}$ is used in the Westcott formalism based calculation. So the value ${\varphi}_{th}$ can be safely used in placement of ${\varphi}_{West\text{}\mathrm{cot}t}$. This is agreed with calculation performed by other authors [5].

_{n}), so eq. (N.2) can be re-written as follows:

_{n}” - named (n,γ) reactions can be calculated as:

_{n}”- named (n,γ) reactions, the reaction rate in both thermal and epithermal neutron region calculated based on the Hogdahl convention ion is:

_{epi}is used instead i.e f

_{H}= R

_{epi}). Q

_{0}= I

_{0}/σ

_{0}is infinite dilution resonance integral I

_{0}per thermal neutron activation cross-section σ

_{0}at the corresponding energy E

_{0}= 0.0253eV; ${I}_{0}={\displaystyle \underset{Ec}{\overset{1\text{}MeV}{\int}}\frac{\sigma (E)}{E}}dE;\text{}{I}_{0}(\alpha )={Q}_{0}(\alpha ){\sigma}_{0}:$

_{Cd}= 0.55 eV correction,

_{eff}

_{(1/v)}is Hogdahl convention effective cross-section. n

_{n}is total neutron density.

_{n}is neutron velocity and v

_{0}is the most probable neutron velocity at 20 °C (2200 m/s).

_{n}) is Westcott’s g-factor for neutron temperature T

_{n}, g(T

_{n}) ≠ 1 for “non − 1/v

_{n}” reactions.

_{0}is ratio of the modified reduced resonance integral (1/v

_{n}− tail subtracted) to the thermal cross-section σ

_{0},

_{n}” effective cross-section,

## 3. Experimental

#### 3.1. Reagents and materials

^{176}Yb

_{2}O

_{3}and

^{176}Lu

_{2}O

_{3}targets for neutron activation were purchased from Trace-Sciences International Inc.USA [10]. The

^{176}Yb

_{2}O

_{3}target isotopic compositions were

^{176}Yb (97.6%),

^{174}Yb (1.93%),

^{173}Yb (0.18%),

^{172}Yb (0.22%),

^{171}Yb (0.07%),

^{170}Yb (<0.01%) and

^{168}Yb (<0.01%). The main Lanthanide impurities of this target were Er (50 p.p.m), Tm (50 p.p.m) and Lu (50 p.p.m). The

^{176}Lu

_{2}O

_{3}target isotopic compositions were

^{176}Lu (74.1 %),

^{175}Lu (25.9%). The main Lanthanide impurities of this target were La (66 p.p.m), Yb (13 p.pm), Tm (<1 p.p.m), Er (17 p.p.m), Dy (4 p.p.m), Gd (6 p.p.m), Eu (20 p.p.m), Sm (2 p.p.m) and Nd (1 p.p.m).

#### 3.2. Targets, reactor irradiations, chemical separation, elemental analysis and radioactivity calibration

^{177}Lu +

^{175}Yb solutions were obtained by the reactor thermal neutron irradiation of

^{176}Yb

_{2}O

_{3}and/or

^{176}Lu

_{2}O

_{3}targets. A quartz ampoule containing an adequate amount of

^{176}Yb

_{2}O

_{3}or

^{176}Lu

_{2}O

_{3}target was irradiated with a thermal neutron flux in HIFAR reactor (Australia). A 24-hour cooling period was needed to let all

^{177}Yb (T

_{1/2}= 1.911 hours) radionuclides (which formed via

^{176}Yb (n, γ)

^{177}Yb) to be transformed to

^{177}Lu via beta particle decay. The irradiated target was then dissolved in HCl solution and the radiochemical separation of

^{177}Lu from the target solution was performed as reported in our previous papers [8,9]. The radioactivity of the different radioisotopes was calibrated using a CAPINTEC Dose calibrator and gamma-ray spectrometer coupled with ORTEC HP Ge detector. The gamma ray energy and counting efficiency calibration of this analyzer system were performed using a radioactive standard source of

^{152}Eu solution. Lutetium element and other metal content in the completely decayed

^{177}Lu solutions (at least > 10 half-lives) was analyzed using ICP-MS instrument.

## 4. Results and Discussion

^{176}Lu and

^{176}Yb targets.

^{177}Lu produced from these targets is a representative for the state-of-the-art radioisotopes of high specific radioactivity used in targeted endo-radiotherapy.

#### 4.1. The specific radioactivity of ^{177}Lu radioisotope produced via ^{176}Lu (n, γ)^{177}Lu reaction

^{176}Lu enriched target is used for

^{177}Lu production. The main nuclear characteristics and nuclear reactions/ radioactive transformations of the

^{176}Lu and

^{175}Lu isotope are listed in Table 1. The production of

^{177}Lu radioisotope is based on the reaction Lu-1. As shown in this data list, the target composes of two stable isotopes,

^{176}Lu and

^{175}Lu. In the reactions Lu-6 and Lu-3 the neutron captures yield the isotopes of another chemical element, so these reactions may cause a depression in elemental Lu atom numbers of the target during neutron bombardment.

^{176}Lu enriched target and the multi-isotope target system of depression factor Δ

_{S2,A}= 0 as described in Section 2.1.2.2 (Third bullet). So, eqs. 20–25 are adopted for the

^{177}Lu specific radioactivity assessment of the Lu target. For this SA assessment process the relevant parameters should be identified to individualize the selected equations for the above mentioned

^{177}Lu production reaction. These parameters are the following:

_{1,A}is

^{176}Lu and re-denoted as S

_{1,Lu}. S

_{2,A}is

^{175}Lu and re-denoted as S

_{2,Lu}. R

_{i}is

^{177}Lu.

_{1}is the weight percentage of

^{176}Lu. P

_{imp,A}is weight percentage of

^{175}Lu and re-denoted as P

_{imp,Lu}. M

_{1}is atomic weight of

^{176}Lu. M

_{imp,A}is atomic weight of

^{175}Lu and re-denoted as M

_{imp,Lu}. ${\Delta}_{{S}_{1,A}}$ is ${\Delta}_{{S}_{1,Lu}}$ for isotope

^{176}Lu.

^{176}Lu has three neutron capture reactions (i=1, 2, 3) as listed in Tab. 1, the ${\Delta}_{{S}_{1,Lu}}$ value is ${\Delta}_{{S}_{1,Lu}}={\varphi}_{th}\cdot {\displaystyle \sum _{i=1}^{i=3}{\mathsf{\Omega}}_{1,i}}\text{}\mathrm{or}\text{}{\Delta}_{Lu-176}={\varphi}_{th}\cdot {\displaystyle \sum _{}^{}({\sigma}_{1,i(th)}+R.{\sigma}_{1,i(res)})},$

^{176}Lu is a typical non-1/υ

_{n}nuclide, the σ

_{1,i(th)}cross section (of reaction Lu-1 in Table 1), which is tabulated for neutron of E= 0.0253 eV and υ

_{n}= 2,200 m/s, should be multiplied with a so called k-factor which is based on the Westcott convention equation as discussed in Section 2.3 [5,6]. The k values ranging from 1.67 at 10 °C to 1.9 at 40 °C were calculated for the Munich reactor [5]. As generally accepted, we use the value k = 1.74 tabulated in reference [11] for our further calculation.

^{175}Lu and ${\Delta}_{{S}_{2,Lu}}={\varphi}_{th}\cdot {\displaystyle \sum _{y=1}^{y=3}{\mathsf{\Omega}}_{2,y}}\text{}=0\text{}$

^{177}Lu and ${\mathsf{\Lambda}}_{Lu-177}={\lambda}_{Lu-177}+{\Delta}_{Lu-177}$

^{177}Lu specific radioactivities as a function of the target isotopic composition, neutron flux and irradiation time were formulated and calculated (as shown in Figure 1 and Figure 2). The maximum values of

^{177}Lu specific radioactivity and irradiation time were evaluated. These were used as optimal conditions for carrier-containing

^{177}Lu production.

_{irr,Yield-max}) and that for maximum specific radioactivity (t

_{irr,SA-max}) are different. The results presented in Figure 3a state that the higher the

^{176}Lu enrichment of the target, the bigger the difference between values t

_{irr,Yield-max}and t

_{irr,SA-max}. The ratio of these times varies with thermal neutron flux applied and reaches a maximum value at the flux value of around 3·10

^{14}n·cm

^{−2}·s

^{−1}for all the

^{176}Lu enrichment values of the target.

_{S1,A}/Λ

_{Ri}) plays an important role in the creation of this maximum value of t

_{irr,Yield-max}and t

_{irr,SA-max}/ t

_{irr,Yield-max}ratio at a specified neutron flux value specific for a given target system.. Although the higher neutron flux irradiation gives the higher SA as shown in Figure 3b, the bigger difference between values t

_{irr,Yield-max}and t

_{irr,SA-max.}makes the outcomes of maximum yield and maximum SA incompatible.

^{177}Lu via

^{176}Lu (n,γ)

^{177}Lu reaction with neutron flux of around 3·10

^{14}n·cm

^{−2}·s

^{−1}could be awkward. Hence the production yield and desired SA should be compromised to achieve a cost effective production of clinically useful

^{177}Lu product. The t

_{irr,SA-max}values increase with the

^{176}Lu enrichment on the target (Figure 2) and the 100% purity

^{176}Lu target showed no-maximum SA value during neutron activation as seen in Figure 1b. This is confirmed by the analysis of differential equation 27, which was described in Section 2.1.2.3 above.

#### 4.2. The specific radioactivity of ^{177}Lu radioisotope produced via neutron- capture- followed- by- radioactive transformation, ^{176}Yb (n, γ) ^{177}Yb (β^{-} decay) ^{177}Lu

^{176}Yb enriched target is used for

^{177}Lu radioisotope production. Based on the isotopic compositions of the elemental Lu -contaminated

^{176}Yb

_{2}O

_{3}target and the possible nuclear reactions listed in Table 1 and Table 2, the total

^{177}Lu radioactivity in this activated

^{176}Yb target composes of one part (denoted as A

_{1-Lu-177}) induced from the

^{176}Yb target nuclide via reaction

^{176}Yb (n, γ)

^{177}Yb (β

^{-}decay)

^{177}Lu and another part (denoted as A

_{2-Lu-177}) from the

^{176}Lu impurity via

^{176}Lu (n, γ)

^{177}Lu reaction. As shown in Table 2, the Lu-free

^{176}Yb target contains

^{174}Yb impure isotope, so the

^{175}Lu induced via reaction

^{174}Yb (n, γ)

^{175}Yb (β

^{-}decay)

^{175}Lu increases the atom numbers of elemental Lu in the target during neutron activation. Especially, due to long-lived

^{175}Yb, the

^{175}Lu generation from beta decay of

^{175}Yb will be continued during post-irradiation processing/cooling of the target. The SA degradation effect of

^{174}Yb and Lu impurities on the carrier-free

^{177}Lu producible from an isotopically pure

^{176}Yb target is demonstrably predictable. The assessment of this effect measure is a showcase example for a complex target system in which a stable brother isotope of radioisotope R

_{i}may be generated from the elemental impurities.

_{Lu-177}achievable in the Lu- and

^{174}Yb-contaminated

^{176}Yb target will be calculated based on “isotopic dilution” equation (35) which is applied for a multi radioactive source system. The

^{176}Yb enriched target discussed in this report is referred to as a system composed of two

^{177}Lu radioactive sources, S

_{1}and S

_{2}. The source S

_{1}refers to the radioisotopes induced in the elementally pure (Lu impurity-free) Yb target, while S

_{2}is the radioactive part produced from the Lu impurity in the target.

#### 4.2.1. ^{177}Lu radioactive source 1 (S_{1}): Radioactivity (A_{1-Lu--177}) and specific radioactivity (SA_{1-Lu--177}) of ^{177}Lu isotope in the elementally pure (Lu impurity-free) Yb target

^{176}Yb and

^{174}Yb are involved in the neutron capture reactions (reactions Yb-1 and Yb-2, respectively) to produce the Lu isotopes (

^{177}Lu and

^{175}Lu). It is obvious that in the elementally pure (Lu impurity-free) Yb target, the

^{177}Lu radioactivity is generated from reaction Yb-1. The elemental Lu atom numbers, however, result from both reactions Yb-1 and Yb-2. The following parameters should be evaluated for the SA assessment of

^{177}Lu isotope in the given Yb target.

^{177}Lu ( A

_{1-Lu—177}) from the reaction Yb-1 in the Lu -free Yb target.

_{c}(A

_{1-Lu-177,tc}) can be calculated using eq.28. The carrier-free

^{177}Lu activity is the following:

_{1,1}for Ω

_{Yb}

_{-176,1}(or Ω

_{Yb}

_{-176,Yb-177}),Ω

_{x}for Ω

_{Yb}

_{-177}and Ω

_{i}for Ω

_{Lu}

_{-177}, these parameters are the following:

_{fast}·σ

_{Yb}

_{-176,1(fast)}, R

_{fast}·σ

_{Yb}

_{-177(fast)}and R

_{fast}·σ

_{Lu}

_{-177(fast)}can be ignored due to the insignificant value of fast neutron flux)

_{0,Yb-176}denotes the atom numbers of

^{176}Yb in the m grams weight target.

_{0,Yb-176}=6.02·10

^{23}·m·P

_{Yb}

_{-176}/(100·176), where P

_{Yb-176}is the weight percentage of

^{176}Yb in the

^{176}Yb enriched target.

_{1-Lu}in the Lu impurity-free

^{176}Yb target. This amount is the sum of the Lu atom numbers of carrier-free

^{177}Lu radioisotope (N

_{1-Lu-177,tc}) from reaction Yb-1 and Lu atom numbers generated from the

^{174}Yb impurity of the target (N

_{1-Lu-175,tc}) from reaction Yb-2.

_{1-Lu-177,tc}is calculated by a quotient of eq.36 and λ

_{Lu}

_{-177}:

^{175}Lu isotope generated from

^{174}Yb, the following is identified.

_{2,B}is stable isotope

^{174}Yb. ${\Delta}_{{S}_{2,B}}$ is re-denoted as ${\Delta}_{Yb-174}$ for isotope

^{174}Yb. Because

^{174}Yb has only one neutron capture reaction (y = 1) as shown in Tab. 2, the ${\Delta}_{Yb-174}$ value is ${\Delta}_{Yb-174}={\varphi}_{th}\cdot {\displaystyle \sum _{y=1}^{y=1}{\mathsf{\Omega}}_{Yb-174,y}}={\varphi}_{th}\cdot {\mathsf{\Omega}}_{Yb-174,1}$, where ${\mathsf{\Omega}}_{Yb-174,y}={\sigma}_{Yb-174,y(th)}+{R}_{epi}\cdot {\sigma}_{Yb-174,y(epi)}+{R}_{fast}\cdot {\sigma}_{Yb-174,y(fast)}$. (The items ${R}_{fast}\cdot {\sigma}_{Yb-174,y(fast)}$ can be ignored due to the insignificant value of fast neutron flux).

^{175}Yb and ${\Delta}_{Yb-175}={\varphi}_{th}\cdot {\displaystyle \sum {\mathsf{\Omega}}_{Yb=175}}$.

_{175}and ${\mathsf{\Lambda}}_{Yb-175}={\displaystyle \sum _{m=1}^{m=j}{\lambda}_{m,Yb-175}}+{\Delta}_{Yb-175}$. For simplification, $\sum _{m=1}^{m=j}{\lambda}_{m,Yb-175}}={\lambda}_{Yb-175\to Lu-175$ is applied and value ${\Delta}_{Yb-175}$ is ignored due to unavailability of $\sum {\Omega}_{Yb-175}$ value. So we get ${\mathsf{\Lambda}}_{Yb-175}={\lambda}_{Yb-175\to Lu-175}={\lambda}_{Yb-175}$. ${N}_{0,{S}_{2,B}}$ is the initial

^{174}Yb atom numbers ${N}_{0,Yb-174}$. This quantity is ${N}_{0,Yb-174}=6.02\cdot {10}^{23}\cdot m\cdot {P}_{Yb-174}/(100\cdot 174)$. P

_{Yb-174}is the weight percentage of

^{174}Yb impurity in the

^{176}Y target.

^{177}Lu specific radioactivity of the Lu impurity-free

^{176}Yb target. The specific radioactivity of

^{177}Lu source (the

^{177}Lu radioactive source 1) generated from the elemental Lu impurity-free

^{176}Yb target is the following:

#### 4.2.2. ^{177}Lu radioactive source 2 (S_{2}): Radioactivity A_{2-Lu-177)} and specific radioactivity SA_{2-Lu-177} of ^{177}Lu generated from ^{176}Lu (n, γ) ^{177}Lu reaction of the elemental Lu-impurity in the Lu-contaminated ^{176}Yb target

_{2-Lu-177}of

^{177}Lu radioisotope produced in this target is calculated using the same process as described in the previous Section 4.1 ‘The specific radioactivity of

^{177}Lu radioisotope produced via

^{176}Lu (n, γ)

^{177}Lu reaction’ of Results and Discussion. In this case the impure Lu content in the

^{176}Yb target is assumed to have natural abundance, so the values P

_{1}= 2.59% for

^{176}Lu and P

_{imp,Lu-175}= 97.41% for

^{175}Lu are put into calculation.

^{177}Lu from the elemental Lu impurity in the

^{176}Yb target at post-irradiation time t

_{c}is calculated using eq. (14):

_{1}=2.59 % is natural abundance of

^{176}Lu. m is the weight of elemental Lu impurity in the

^{176}Y target.

#### 4.2.3. ^{177}Lu specific radioactivity SA_{Lu}_{-177} and ^{177}Lu radioactivity A_{Lu}_{-177} in the Lu-contaminated ^{176}Yb target as a combination of ^{177}Lu radioactive source S_{1} and S_{2}

^{177}Lu specific radioactivity SA

_{Lu}

_{-177}. The method of SA assessment of the mixture of several radioactive sources (referred to Section 2.2.2) is used for the SA calculation. The

^{177}Lu specific radioactivity SA

_{Lu}

_{-177}in the Lu-contaminated

^{176}Yb target is calculated using eq. (35) with relevant parameters of the mixture of two

^{177}Lu radioactive sources S

_{1}and S

_{2}as described above,

^{177}Lu radioactivity. Total

^{177}Lu radioactivity in the target is A

_{Lu}

_{-177}= A

_{1-Lu-177}+ A

_{2-Lu-177}.

^{175}Lu isotope generated from

^{174}Yb (n, γ)

^{175}Yb (β

^{-}decay)

^{175}Lu process and elemental Lu impurities remaining in the

^{177}Lu product (which is chemically separated from

^{176}Yb target) makes the SA value of

^{177}Lu strongly decreased.

^{177}Lu reaches maximum value (SA

_{Lu}

_{-177,max}). The maximum SA is predicted based on the opposite tendency of SA variation of elementally pure and Lu-contaminated Yb targets. This argument is supported by the results obtained below.

^{177}Lu radioisotope produced by the

^{176}Yb (n, γ)

^{177}Yb (β

^{-}decay)

^{177}Lu process as a function of the elemental and isotopic impurities of the

^{176}Yb enriched target and the times t

_{irr}and t

_{c}is shown in Figure 4 and Figure 5. The experimental results reported in our previous publications agree well with the theoretical calculation results shown in Figure 5. The maximum SA value present on the curve D of Figure 4 shows a combined effect of

^{174}Yb- and elemental Lu- impurities on the SA degradation. This tells us that the irradiation time should be optimized to obtain the highest SA for

^{177}Lu produced via

^{176}Yb (n, γ)

^{177}Yb (β

^{-}decay)

^{177}Lu reaction. While being the best theoretical way to produce carrier-free

^{177}Lu, with this reaction we always obtain a

^{177}Lu product of much lower SA due to the use of an isotopically/elementally impure target. The maximum SA value mentioned above is characterized for a specific target composition and its neutron irradiation conditions, so the theoretical assessment of SA developed in this paper is important before starting the neutron activation process. This avoids over-bombardment destroying the SA of

^{177}Lu product and wasting expensive reactor operation time. Moreover, the post-irradiation processing time should be minimized to keep the SA as high as possible, the effect of which is shown in Figure 5.

## 5. Conclusions

^{177}Lu,

^{153}Sm,

^{169}Yb,

^{165}Dy,

^{153}Gd... This evaluation plays a complementary or even substantial role in the quality management system regarding certifying the SA of the product which may be experimentally inaccessible due to radiation protection and instrumentation difficulties in the practical measurement of very low elemental content (<0.01 μg/mCi·μL) of a radioactive solution of very high specific volume and specific radioactivity.

## Acknowledgments

## References

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Sample Availability: Not available. |

**Figure 1.**

**a-**

^{176}Lu target nuclide depression,

^{177}Lu build-up and

^{177}Lu specific radioactivity in the

^{176}Lu enriched target vs. irradiation time (Thermal neutron flux: 2.5·10

^{14}n·cm

^{−2}·s

^{−1}; Target composition: 74.1%

^{176}Lu + 25.9%

^{175}Lu; Target weight: 1.0 mg), $\u2022-\u2022-\u2022$: Specific radioactivity of

^{177}Lu; Δ–Δ–Δ: Atom numbers of

^{177}Lu; ◊-◊-◊: Atom numbers

^{176}Lu target nuclide.

**b-**

^{177}Lu specific radioactivity in the

^{176}Lu enriched target vs. irradiation time and

^{176}Lu enrichment of the target (Thermal neutron flux: 2.5·10

^{14}n·cm

^{−2}·s

^{−1}), ♦-♦-♦: 100% purity

^{176}Lu target; ◊-◊-◊: Target composition: 74.1%

^{176}Lu + 25.9 %

^{175}Lu.

**Figure 2.**

^{177}Lu specific radioactivity as a function of irradiation time and

^{176}Lu isotopic purity in the target (Thermal neutron flux of 1.7·10

^{14}n·cm

^{−2}·s

^{−1}was applied. Nuclear data was extracted from literatures [11]).

**Figure 3.**

**a**- Irradiation time ratio (t

_{irr,SA-max}/ t

_{irr,Yield-max}) vs. thermal neutron flux and target composition.

**b**- Maximum specific radioactivity of

^{177}Lu vs. thermal neutron flux and target composition.

**Figure 4.**Specific radioactivity of

^{177}Lu radioisotope in the

^{176}Yb target vs. irradiation time and content of

^{174}Yb- and elemental Lu- impurities.(Thermal neutron flux: 5·10

^{13}n·cm

^{−2}·s

^{−1}, Nuclear data extracted from literatures [11]).

^{177}Lu isotope in impurity-free

^{176}Yb target; b: Specific radioactivity of

^{177}Lu isotope in the

^{176}Yb target containing 1.93%

^{174}Yb; c: Specific radioactivity of

^{177}Lu isotope in the

^{176}Yb target containing 50 p.p.m Lu element impurities; d: Specific radioactivity of

^{177}Lu isotope in the

^{176}Yb target containing 1.93%

^{174}Yb and 50 p.p.m Lu element impurity.

**Figure 5.**Specific radioactivity of

^{177}Lu in the

^{176}Yb target vs. post-irradiation time and content of

^{174}Yb and elemental Lu impurities. (Thermal neutron flux: 5·10

^{13}n·cm

^{−2}·s

^{−1}; Irradiation time: 240 hours; Nuclear data extracted from literatures [11]).

^{177}Lu isotope in the impurity-free

^{176}Yb target; b: SA of

^{177}Lu isotope in the

^{176}Yb target containing 1.93%

^{174}Yb; c: SA of

^{177}Lu isotope in the

^{176}Yb target containing 50 p.p.m Lu element impurities; d: SA of

^{177}Lu isotope in the target containing 1.93%

^{174}Yb and 50 p.p.m Lu element impurity. (*) is the experimental measurement result for this type of target.

**Table 1.**Nuclear characteristics of the radionuclides produced in the

^{176}Lu enriched target [11].

Target Stable Isotope (Denoted) | Conc. in target | Cross Sections, Barn | Nuclear reaction and product (T_{1/2}) | Reaction No. (Reaction branch) | |
---|---|---|---|---|---|

σ_{th or} σ_{0} | σ_{epi or} I_{0} | ||||

^{176}Lu (S_{1,Lu}) | P_{1} =74.1 % | 2300 | 1200 | ^{176}Lu (n,γ)^{177}Lu (6.7d)^{(*)} $\underrightarrow{\mathsf{\beta}\u2013177}$Hf (stable) | Lu-1 (i = 1) |

2 | 3 | ^{176}Lu (n,γ)^{177m}Lu(160.7d) $\underrightarrow{\mathrm{IT}\u2013177}$Lu(6.7d) $\underrightarrow{\mathsf{\beta}\u2013177}$Hf(s) | Lu-2 (i = 2) | ||

<2.10^{−3} | - | ^{176}Lu (n,α) ^{173}Tm (8.2h) $\underrightarrow{\mathsf{\beta}\u2013173}$Yb ( Stable) | Lu-3 (i = 3) | ||

^{175}Lu(S_{2,Lu}) | P_{imp,Lu} =25.9 % | 16 | 550 | ^{175}Lu (n,γ) ^{176m}Lu (3.7h) $\underrightarrow{\mathrm{IT}\u2013176}$Lu ( Stable) | Lu-4 (y = 1) |

9 | 300 | ^{175}Lu (n,γ) ^{176}Lu ( Stable) | Lu-5 (y = 2) | ||

<10^{−5} | ^{175}Lu (n,α) ^{172}Tm (2.6d ) $\underrightarrow{\mathsf{\beta}\u2013172}$Yb (Stable) | Lu-6 (y = 3) |

^{177}Lu depression caused by possible (n, γ) and/or (n, p) reactions is ignored compared to radioactive decay rate of

^{177}Lu isotope.

Stable Isotope (Denoted) | Conc. in target(%) | Cross Section, Barns | Nuclear reactions and products (T_{1/2}) | Reaction No. (Reaction branch) | |
---|---|---|---|---|---|

σ_{th or} σ_{o} | σ_{epi or Io} | ||||

^{176}Yb (S_{1,B}) | 97.6 | 3.0 | 8 | ^{176}Yb(n,γ) ^{177}Yb (1.9h) $\underrightarrow{\mathsf{\beta}\u2013177}$Lu (6.7d) $\underrightarrow{\mathsf{\beta}\u2013177}$Hf (stable) | Yb-1 (x = 1) |

^{174}Yb (S_{2,B}) | 1.93 | 63.0 | 60 | ^{174}Yb (n,γ) ^{175}Yb (4.2d) $\underrightarrow{\mathsf{\beta}\u2013175}$Lu (Stable) | Yb-2 (y = 1) |

^{173}Yb (S_{3,B}) | 0.18 | 17.4 | 400 | ^{173}Yb (n,γ) ^{174}Yb (Stable) | Yb-3 (z = 1) |

^{172}Yb (S_{4,B}) | 0.22 | 1.3 | 25 | ^{172}Yb (n,γ) ^{173}Yb (Stable) | Yb-4 (p = 1) |

^{171}Yb (S_{5,B}) | 0.07 | 50.0 | 320 | ^{171}Yb (n,γ) ^{172}Yb (Stable) | Yb-5 (q = 1) |

^{170}Yb (S_{6,B}) | <0.01 | 10.0 | 300 | ^{170}Yb (n,γ) ^{171}Yb (Stable) | Yb-6 (v = 1) |

^{168}Yb (S_{7,B}) | <0.01 | 2300 | 2100 | ^{168}Yb(n,γ) ^{169}Yb (32d) $\underrightarrow{\left(\mathrm{EC}\right)169}$Tm (Stable) | Yb-7 (w = 1) |

Lu ^{(*)} | 5.10^{-3} | Nuclear reactions and characteristics referred to Table 1 |

^{176}Yb target is assumed, i.e. 97.41 %

^{175}Lu and 2.59 %

^{176}Lu.

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**MDPI and ACS Style**

Le, V.S.
Specific Radioactivity of Neutron Induced Radioisotopes: Assessment Methods and Application for Medically Useful ^{177}Lu Production as a Case. *Molecules* **2011**, *16*, 818-846.
https://doi.org/10.3390/molecules16010818

**AMA Style**

Le VS.
Specific Radioactivity of Neutron Induced Radioisotopes: Assessment Methods and Application for Medically Useful ^{177}Lu Production as a Case. *Molecules*. 2011; 16(1):818-846.
https://doi.org/10.3390/molecules16010818

**Chicago/Turabian Style**

Le, Van So.
2011. "Specific Radioactivity of Neutron Induced Radioisotopes: Assessment Methods and Application for Medically Useful ^{177}Lu Production as a Case" *Molecules* 16, no. 1: 818-846.
https://doi.org/10.3390/molecules16010818