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Evaluation of optical potential for (n,2n) cross section reactions and yields for spherical zirconium isotopes.

INTRODUCTION

In the Nuclear Data Center of International Atomic Energy Agency (IAEA) [I], Nuclear Data Library (EXFOR) is emphasis on the improvement of cross section data for innovative reactor designs and nuclear transmutation analyses. Naturally Zirconium is composed of five isotopes 90, 91, 92, 94, 96Zr with the abundances of 51.45% (90Zr), 11.22% or 11.32% (91Zr), 17.15% or 17.19% (92Zr), 17.38% or 17.28% (94Zr), and 2.80% or 2.76% (96Zr). These isotopes are produced close to the light mass yield peak in the neutron-induced fission. Moreover, Zirconium is important as a structural element in reactor systems. Zirconium alloys are used for fuel rod cladding in fission reactors owing to their small absorption cross section for neutrons. It is pointed out that the isotope 93Zr, being a long-lived fission product with the half-life [T.sub.1/2] = 1.53E+[10.sup.6] years, is important for a nuclear transmutation study. We did not calculate the 93Zr data for lack of experimental data [2,3]. Many authors have reviewed different studies on Zirconium isotopes [4,5,6,7,8,9].

The cross sections of 90Zr(n,2n)89Zr and 96Zr(n,2n)95Zr reactions in the neutron energy range 14.5MeV was measured by the activation technique. Activity of the reaction product was determined by measuring the gamma counts of the product nuclei using high resolution HPGe detector gamma ray spectrometry system [10]. In the present work, we carried out theoretical calculations of recommended cross section for 90,96[Z.sub.r] toward EXFOR. The excitation functions of induced neutron nuclear reactions (n,2n) are measured for Zr (A=90, and 96) with the aid of EXFOR library [11]. The cross sections for these reactions have been evaluated in the present work for the exact estimation of the computed recommended cross sections among different authors for the incident neutron energy range 8.2-20.6MeV by using the statistical model. The obtained cross sections were compared with available experimental data for (n,2n).

This paper describes the standard optical model potential analyses of the spherical zirconium target elements up to 20MeV. The present paper also describes the background of the References Input Parameter Library (RIPL) used for input parameters. These data are used in the real and imaginary part of optical model potential-special emphasis is placed in this study on the isotope dependence of the optical model potential. The objectives of the present work are to provide new recommended cross section from experimental data employing the associated counting method for the neutron flux determination, to validate the current evaluated cross sections of interest at an energy range and to assure a number of cross section data obtained relative to the standard cross section. The accuracy of the neutron flux a key factor for the measurement of the neutron cross section with a reasonably small error.

1. Recommended Cross Section:

The available measured data from EXFOR library for the cross section (n,p) and (n,[alpha]), measured for Zr (A=90 and 96) have been plotted interpolated and recalculated in different fine steps and for different energy range of incident neutron by using Matlab-8.0 in order to calculate the recommended cross section for each mentioned reactions. The interpolation for the nearest data for each energy interval as a function of cross sections and their corresponding errors have been done using Matlab-8.0.

1--The sets of experimental cross sections data are collected for different authors and with different energy intervals. The cross sections with their corresponding errors for each value are rearranged according to the energy interval 0.01 MeV for available different energy range for each author.

2--The normalization for the statistical distribution of cross sections errors to the corresponding cross section values for each author has been done.

3--The interpolated values are calculated to obtain the adopted cross section which is based on the weighted average calculation according to the following expressions [10]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Where the standard deviation error is:

S.D. = 1/[square root of ([N.summation over (i=1)]1/[([DELTA][[sigma].sub.i]).sup.2]) (2)

Where [[sigma].sub.i] : is the cross section value. [DELTA] [[sigma].sub.i] : is the corresponding error for each cross section value.

2. Background of (RIPL):

The Reference Input Parameter Library (RIPL) is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The practical use of nuclear reactions requires a considerable numerical input that describes properties of the nuclei and interactions involved. The (RIPL) represents a fairly comprehensive set of such parameters, collected and selected from sources all over the world. The (RIPL) contains input parameters for theoretical calculations of nuclear reaction cross sections. The library is targeted at users of nuclear reaction interested in nuclear applications. The main recommended optical model parameters files in the (RIPL) are Los Alamos (U.S.A.), and Jaeri (Japan) files [12,13].

3. Optical Model Potential:

The Zr isotopes, occurring near the double magic numbers, were assumed to be spherical. The local and global optical model potentials (OMPs) developed by Koning and Delarochel (2003) [13] were used for neutrons and protons. In the frame of the optical model, all the interactions between the nucleons of the projectile and the nucleons of the target are replaced by an average and central interaction V(r) between the projectile and the target in their ground states. The nuclear optical model used to describe the interaction between two nuclei is inspired by the optical phenomenon. The nuclear medium diffracts one part of the incident wave which models the incident particle and another part of the wave is refracted [14].

As the nucleon-nucleon interaction is a short range interaction, the potential [V.sub.v] x [f.sub.r] (r,[r.sub.r],[a.sub.r]) which is approximately the sum of nucleon-nucleon interactions, has the same behavior. The nucleons in the core of the nucleus undergo only the interaction with their closest neighbors. Due to this saturation of the nuclear forces, [V.sub.v] x [f.sub.r] (r,[r.sub.r],[a.sub.r]) is uniform inside the nucleus and then decreases exponentially in the surface region

[15]. The present evaluation are based mainly on the calculations the optical model potential. A standard form of the optical model potential and relevant parameters used in the present work contains volume, surface, and spinorbit parts, each having real and imaginary components. This potential can be written as follows [12,16,17]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In equation (3) [V.sub.v] and [W.sub.v] are the real and imaginary volume potential well depths, [W.sub.s] is the well depth for the surface derivative term, [W.sub.g] is the well depth for the global nucleon-nucleon optical potential, [V.sub.so] and [W.sub.so] are the real and imaginary well depths for the spin-orbit potential, and [[lambda].sup.2.sub.[pi]] is the pion Compton wavelength squared ([congruent to] = 2). The quantity [??]. [??] is the scalar product of the orbital and intrinsic angular momentum operators and is given by [17]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

The [f.sub.i] (r,[r.sub.i],[a.sub.i]) is radial-dependent form factors. The real potential, imaginary potential and form factors are defined below [17]:

a. Real Potential:

[V.sub.v], [V.sub.so] are the depth parameters of real potential in (MeV) taken from (RIPL-3). The parameters were adjusted from their original values as shows in table 3 (Hint: We select the energy at maximum cross section for different reactions for selected isotopes).

b. Imaginary Potential:

[W.sub.s], [W.sub.v], [W.sub.g], [W.sub.so] are the depth parameters of imaginary potential in (MeV) taken from (RIPL- 3), as shown in table 3.

c. Form Factor:

Wood--Saxon form factors is permitted for [f.sub.i] (r, [r.sub.i], [a.sub.i]) terms in equation (3), is as follows:

[f.sub.i](r, [r.sub.i], [r.sub.i], [a.sub.i]) = 1/[1 + exp([X.sub.i])] ; With i - v, s, g, so (Wood-Saxon form factor) (6)

Where [X.sub.i] = (r - [R.sub.i]) / [a.sub.i] ; With i = v, s, g, so (7)

r is the radial distance in (fm) and [a.sub.i] is the diffuseness. The nuclear radius [R.sub.i] is given by:

[R.sub.i] = [r.sub.i] x [A.sup.1/3] + [r.sub.c] (8)

Where: [r.sub.c] is the coulomb radius; [r.sub.v], [r.sub.ws], [r.sub.wv], [r.sub.vso] and [r.sub.wso] are the geometry parameters of real potential in (fm) taken from (RIPL-3). The optical poten.m program has been built in the present work using Matlab-8.0. The aim of this program is to calculate the real and imaginary optical potential as a function of radial distance and the energy of induced neutron for spherical Zr (A=90 and 96) target elements.

4. Activity Yield:

The activity of a certain sample is the number of radioactive disintegrations per sec for the sample as a whole. The specific activity, on the other hand, is defined as the number of disintegrations per sec per unit weight or volume of sample. The unit of activity is the Becquerel (Bq), which is defined as a decay rate of one disintegration per second (dps). The fundamental equation to calculate the activity produced in a target is described by a first order differential equation [18,19] :

dN/dt = [N.sub.tot][phi][sigma]act - [lambda]N (9)

Where:

dN/dt : is the production rate per second.

N : is the number of activated atoms.

[N.sub.tot] : is the total number of target atoms.

[phi] : is the neutron flux (number of neutrons per [cm.sup.2]per second).

[sigma]: is the activation cross section (1barns=[10.sup.-24][cm.sup.2]) refers to the production of the particular radioactive

species.

[lambda]: Decay constant.

The activity of radionuclide formed at any time during or at the end of irradiation is obtained by integration of equation [18,19]:

A = [lambda]N = [N.sub.tot][phi][[sigma].sub.act](1-[e.sup.-[lambda]t])

Where:

[N.sub.tot] = m[N.sub.av]a/M (11)

Therefore, the specific activity is:

[A.sub.SP.act.] = [N.sub.av][phi]a[[sigma].sub.act](1-[e.sup.-[lambda]t]) (12)

m : Mass of the target material in grams.

Nv : Avogadro's number (6.023x[10.sup.23] atom/mole).

a : Isotopic abundance of the target isotope.

M : Atomic mass of target material in atomic mass unit.

t : Time of irradiation in sec.

The nuclear reaction cross sections are of considerable importance in optimizing the production process of a radioisotope. In principle, the well known activation equation is applicable to all activation processes, induced by neutron. The calculation of the production yields of Zr (A=90 and 96) target elements by neutron irradiation is selected at 1x[10.sup.9] (n/[cm.sup.2].s) fast neutron flux [20].

RESULTS AND DISCUSSION

Table 1 tabulated available measuring energy with different ranges for different authors [21-31] with corresponding cross section and their errors are recorded in EXFOR library for fast neutron collected for Zr(A=90 and 96) target elements for (n,2n) reaction. The present uncertainties in the cross section values include both systematic and statistical errors. This table also includes the energy at maximum cross section which is selected in the present work for the calculations of optical potential. The measured cross sections including errors obtained for the present investigated 90Zr(n,2n)89Zr and 96Zr(n,2n)95Zr reactions in the neutron energy range 14.00 to 14.78MeV are included in table 1 from within the total evaluated range except that for IbnMajah and Qaim (1990) [28] and Raics et al. (1990) [30]. In this regard, these reactions with high threshold energy are assumed attractive from the appropriate decay half-live of the product especially for 95Zr to be used a substandard for the 14MeV neutron flux determination. Extensive efforts have been devoted by different authors to the evaluations in order to provide comprehensive data. The referred data, however, had been changed author by author, so that always there must be certain systematic errors depending on the referred data. In this view, it is worthwhile to calculate recommended values simultaneously for those cross sections of particular importance as the standard by an absolute measurement technique.

Figure 1 illustrate the recommended cross sections for the above mentioned reactions as calculated in the present work compared with EXFOR library. It can be seen that than in the footnote of each figure, the refry of authors name are arrange according to the year of measured data are listed with the present calculated recommended cross section. The results are in good agreement with the measured data. Activation technique has been used for the maintained nuclear reactions leading to radioisotope production yield with Van de Graaff, Cyclotron, Cock-croft-Walton or fusion neutron source using deuteron-tritium or deuteron-deuterium source as shown in table 2.

A limited number of parameters for spherical potential are included for incident neutron particles. The energy dependence of the neutron potential based on the Zirconium isotopes (A= 90 and 96) is E=8.2-20.6MeV for Zirconium nuclei. Which are included in the present calculations to cover the same energy range for the same target charge and mass. The optical model potential (OMP) parameters used in this work are including in the (RIPL) and tabulated in table 3 for Zr (A=90 and 96) target elements [32,33]. The global potentials are calculated for systematics utilization of nuclear radial distance r =1 to 20fm as well as real and imaginary potential. This model represents the scattering in terms of a complex potential V(r,E), see equation (3), where the functions V and W are selected to give the potential its proper radial dependence. The real part, V, is responsible for the elastic scattering it describes the ordinary nuclear interaction between target and projectile and may therefore be very similar to a shell model potential. The imaginary part, W, is responsible for the absorption. The radial distance is to be at most of the order of the r= 1:20fm and the energy of incident neutrons have been taken at maximum cross section. All parameters used in this work for optical model potential have been taken from (RIPL) library [12].

Figure 2 shows the optical model potential for zirconium target element Zr (A=90 and 96) induced by neutron, in which absorption W is relatively weaker than elastic scattering V. The absorptive part, W, at low energies must have a very different form. It is clear from these figures that for spherical structure both absorption and scattering depth parameters for Zr (A=90 and 96) since the well depth depend on the mass number of the target element.

Because of the exclusion principle, the tightly bound nucleons in the nuclear interior cannot participate in absorb the relatively low energy carried by the incident particle. The optical potential is thus often has the proper shape of being large only near the surface, as shown in figure 2. At higher energy, where the inner nucleons can also participate in absorption, W, may look more like V. A spin - orbit term is also included in this optical potential. It is also peaked near the surface, because the spin density of the inner nucleons vanishes. A Wood - Saxon form factor is also included. The calculation using the optical model potential, as described in this work, does not deal with where the absorbed particles actually go; they simply disappear from the elastic channel.

Calculated specific radioactivity of Zr (A=90 and 96) target elements by neutron irradiation of targets for (n,2n) reactions at 14.5MeV compared with experimental data given by Erdtmann (1976) [34] are shown in table 4 during different periods of irradiation (1,60.3600.86400,172800) sec until we reach a state of saturation as shown in figure 3 calculated production yields for target elements using matlab-8.0 program activity .m. With respect to cross section measurements, counting was performed only over one day after each irradiation, and attention was paid exclusively to the short-lived Zr isotopes 89Zr and 95Zr the saturated time is 0.5h while for the longer lived product 95Zr the saturated time is one day.

89Zr isotope is attractive for cancer research because its half-life ([T.sub.1/2] = 3.27 days) is well-suited for in vivo targeting of macromolecules and nano-particles to cell surface antigens expressed by cancer cells. Furthermore, 89Zr emits a low-energy positron (E[beta]+,mean = 0.40 MeV), which is favorable for high spatial resolution in PET, with an adequate branching ratio for positron emission (BR = 23%). The demand for 89Zr for research purposes is increasing; however, 89Zr also emits significant gamma radiation ([[GAMMA].sub.15] kev = 6.6 R.cm2/mCi.h) (Yong, 1998) [12].

Unstable 95Zr isotope ([T.sub.1/2] =65.5 days) decay by [beta]-to 95Nb with spin (5/2+) to avoid a neutron capture.

Therefore, 95Zr decays much less than 89Zr to its new desired initial value. The decay mode data used in the gamma ray spectroscopic analysis of the radioisotopes investigated were taken from Ref. [34,35] and are summarized in Table 5. Also Table 5 shows the Q value and half-life of the product nuclei 89Zr and 95Zr are 2.834MeV and 78.4h and 1.121MeV and 65.5d, respectively. The product isotopes give a gamma-ray after beta decay with 99.775 for 89Zr and 51-98% for 95Zr.

Conclusions:

We have evaluated the neutron induced nuclear cross section data of zirconium isotopes for considerable energy range 8.2-20.6MeV. The recommended cross sections are in good agreement with experimental data. The reliability in this work is to estimate the global optical parameters chosen at certain energies available in RIPL library for Zr (A=90 and 96) target elements for neutron induced reactions. The results confirm that the global optical potential parameters are appropriate for these calculations. Hence, the optical model potential is successful in accounting for neutron induced reactions and leads to an understanding of the nucleon-nucleon interactions. The growth of activity in a target under irradiation increases exponentially and reaches a saturation value limited by the fast neutron flux for a given weight of the Zr (A=90 and 96) target elements. The activity products show good agreement for 96Zr rather than 90Zr since the agreement is poor between calculated and experimental cross section at 14.5MeV and the experimental error on cross section is high. Activation provides an accurate yield measurement at neutron induced on 96Zr. In conclusion, re-evaluation is highly recommended by taking into account the present data as well as recent experimental data in the literature.

ACKNOWLEDGMENTS

We wish to express our deep thanks and gratitude to the International Atomic Energy Agency (IAEA) and the References Input Parameter Library (RIPL-3) for their published database.

m: minute; d: day; mb: millibarn; Sat: Saturation

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(1) Iman Tarik Al-Alawy, (2) Khalid A. Ahamed, (3) Waleed Jabbar Mhana

(l,2,3) Al-Mustansiriyah University, Faculty of Science, Department of Physics, Baghdad, Iraq

Received 2 September 2016; Accepted 2 December 2016; Published 31 December 2016

Address For Correspondence:

Iman Tarik Al-Alawy, Al-Mustansiriyah University, Faculty of Science, Department of Physics, Baghdad, Iraq,

Caption: Fig. 1: Excitation functions with energy of incident neutron for (n,2n) reactions of Zr (A=90 and 96) target elements.

Caption: Fig. 2: The Optical Model Potential of neutron reaction on spherical Zr (A=90 and 96) calculated in the present work as a function of radial distance. Typical parameters chosen are taken for energy range 8.220.6MeV (Riple3 Library).

Caption: Fig. 3: Calculated and experimental (Erdtmann, 1976) [34] activation for the production yields of Zr (A=90 and 96) target elements by neutron irradiation of targets as a function of irradiation time at 1x[10.sup.9] fast neutron flux (n/[cm.sup.2].s) with 1 microgram of target element.
Table 1: Available measuring energy and cross section data in EXFOR
library for fast neutron collected for Zr(A=90 and 96) target elements
for (n,2n) reaction.
                                                    energy (MeV) at
                                    Energy Range    Maximum cross
Target            Reaction          (MeV)           section(mb)

[sup.90.sub.40]   [sup.90.sub.40]   12.3-19.76      19.76(1173)
[Zr.sub.50]       [Zr.sub.50]       13.57-18.18     18.18(1385.8)
                  (n,2n)            12.335-19.525   19.525(1219)
                  [sup.89.sub.40]   12.37-18.24     18.24(1216)
                  [Zr.sub.49]       13.64-14.83     14.83(810)
                                    13.2-20.6       19.1(1240)
[sup.96.sub.40]   [sup.96.sub.40]   13.33-14.92     14.43(1550)
[Zr.sub.56]       [Zr.sub.56]       8.215-10.614    10.614(1618)
                  (n,2n)            12.82-17.69     14.8(1594)
                  [sup.95.sub.40]   8.2-12.25       10.23(1233)
                  [Zr.sub.55]       13.64-14.83     14.83(1604)
                                    13.56-14.78     14.42(1627)

Target            Ref.

[sup.90.sub.40]   Prestwood and Bayhurst (1961)[21]
[Zr.sub.50]       Abboud et al. (1969) [22]
                  Pavli et al. (1982) [23]
                  ZhaoWenrong et al. (1984) [24]
                  Molla et al. (1991) [25]
                  Semkova et al. (2010) [26]
[sup.96.sub.40]   Ikeda et al. (1988) [27]
[Zr.sub.56]       IbnMajah and Qaim (1990) [28]
                  LuHanlin et al. (1990) [29]
                  Raics et al. (1990) [30]
                  Molla et al. (1991) [25]
                  Filatenkov et al. (1999) [31]

Table 2 Measured (n,2n) reactions using neutron activation method
explaining the detector, source, and accelerator used for Zirconium
target element.

Reaction         Detector        Source          Accelerator

[sup.90.sub.40]     Deuteron-             ...            ...
[Zr.sub.50]           Tritium
(n,2n)              Deuteron-    Sodium-Iodide       Van de
[sup.89.sub.40]       Tritium         crystal        Graaff
[Zr.sub.49]         Deuteron-    Sodium-Iodide   Cockcroft-
                      Tritium         crystal        Walton
                 Sodium-Iodide      Deuteron-        Van de
                      crystal         Tritium        Graaff
                    Hyperpure       Deuteron-        Van de
                    Germanium         Tritium        Graaff
                    Hyperpure       Deuteron-       Neutron
                    Germanium         Tritium     generator
                    Germanium       Deuteron-        Van de
                      Lithium         Tritium        Graaff

[sup.96.sub.40]    Germanium-       Deuteron-        Fusion
[Zr.sub.56]           Lithium         Tritium       neutron
[Zr.sub.56]                                          source
[sup.95.sub.40]    Germanium-       Deuteron-     Cyclotron
[Zr.sub.55]           Lithium       Deuterium          CV28
                 55 Germanium-      Deuteron-        Van de
                      Lithium         Tritium        Graaff
                   Germanium-       Deuteron-     Cyclotron
                      Lithium       Deuterium
                    Hyperpure       Deuteron-       Neutron
                    Germanium         Tritium     generator
                 Scintillation      Deuteron-    Cockcroft-
                                      Tritium        Walton

Reaction         Ref.

[sup.90.sub.40]  Prestwood & Bayhurst
[Zr.sub.50]               (1961)[21]
(n,2n)                 Abboud et al.
[sup.89.sub.40]          (1969) [22]
[Zr.sub.49]             Pavli et al.
                         (1982) [23]
                  ZhaoWenrong et al.
                         (1984) [24]
                        Molla et al.
                         (1991) [25]

                      Semkova et al.
                         (2010) [26]

[sup.96.sub.40]  Ikeda et al.
[Zr.sub.56]        (1988) [27]
[Zr.sub.56]
[sup.95.sub.40]  IbnMajah and Qaim
[Zr.sub.55]        (1990) [28]
                 LuHanlin et al.
                   (1990) [29]
                 Raics et al.
                   (1990) [30]
                 Molla et al.
                   (1991) [25]
                 Filatenkov et al.
                   (1999) [31]

Table 3 : Optical potential parameters used for zirconium (A= 90, 96)
from Riple-3 Library. Where [W.sub.g] = [W.sub.so] = 0.00MeV and
[r.sub.wso] = [r.sub.c] =[a.sub.wso]=000fm.

90Zr (Koning et al., 1997) [32]

Energy  [V.sub.v]   [r.sub.v]   [r.sub.v]   [a.sub.v]   [W.sub.v]
(MeV)
          (MeV)       (fm)        (fm)        (MeV)       (fm)

12.13     45.70       1.23        0.67        0.30        1.23
12.33     45.60       1.23        0.67        0.30        1.23
12.37     45.60       1.23        0.67        0.30        1.23
13.20     45.30       1.23        0.67        0.40        1.23
13.57     45.20       1.23        0.67        0.40        1.23
13.64     45.20       1.23        0.67        0.40        1.23

96Zr (Yamamuro, 1988) [33]

10.23     46.8        1.22        0.69        0.60        1.42
10.61     46.7        1.22        0.69        0.70        1.42
14.43     45.5        1.22        0.69        1.20        1.42
14.80     45.4        1.22        0.69        1.30        1.42

Energy  [r.sub.wv]   [a.sub.wv]   [r.sub.ws]   [a.sub.ws]
(MeV)
           (fm)        (MeV)         (fm)         (fm)

12.13      0.67         5.80         1.24         0.58
12.33      0.67         5.80         1.24         0.58
12.37      0.67         5.80         1.24         0.58
13.20      0.67         5.80         1.24         0.58
13.57      0.67         5.70         1.24         0.58
13.64      0.67         5.70         1.24         0.58

96Zr (Yamamuro, 1988) [33]

10.23      0.51         5.20         1.28         0.51
10.61      0.51         5.20         1.28         0.51
14.43      0.51         5.20         1.28         0.51
14.80      0.51         5.20         1.28         0.51

Energy  [V.sub.so]   [r.sub.vso]   [a.sub.vso]
(MeV)
          (MeV)         (fm)          (fm)

12.13      6.40         1.14          0.50
12.33      6.40         1.14          0.50
12.37      6.40         1.14          0.50
13.20      6.40         1.14          0.50
13.57      6.40         1.14          0.50
13.64      6.40         1.14          0.50

96Zr (Yamamuro, 1988) [33]

10.23      5.90         1.10          0.56
10.61      5.90         1.10          0.56
14.43      5.90         1.10          0.56
14.80      5.90         1.10          0.56

Table 4: Experimental (IAEA) (Erdtmann, 1976) [34] and calculated
recommended cross sections at 14.5MeV for (n,2n) reaction with the
activation product yields of Zirconium target elements at (1 x
[10.sup.9]n/[cm.sup.2].s) fast neutron flux, and the properties of
their products.

Target              Cross    Activation products (decays/sec
                  section    per 1 [micro]g element)
                     (mb)
                              1 sec     1 min    1 hour

[sup.90.sub.40]       120    1.12e-3   6.22e-2     Sat
[Zr.sub.50]       339(pw)    3.2e-3    1.78E-1     Sat

[sup.96.sub.40]      1456    3.3E-8    1.98E-4   1.19E-4

[Zr.sub.56]       1545(pw)   3.33E-8   1.67E-5   1.16E-4

Target            Activation products (decays/
                  sec per 1 [micro]g element)

                   1day    20 days    sat

[sup.90.sub.40]    Sat       Sat     0.407
[Zr.sub.50]        Sat       Sat     0.500

[sup.96.sub.40]   2.83E-   5.13E-2   0.269
                  [beta]
[Zr.sub.56]       2.85E-   5.18E-2   0.135

Target
                  Properties of Product

                  [T.sub.   [E.sub.    [I.sub.
                   1/2]     [gamma]]   [gamma]]
                             (MeV)       (%)

[sup.90.sub.40]               511        2.8
[Zr.sub.50]        3.27d     587.8        93
                              1508       6.7

[sup.96.sub.40]    65.5d     724.2     43 54.8

[Zr.sub.56]                  751.7

Table 5 Decay mode of the product nuclei and the properties of the
nuclides after decay.

          First route
Product   Beta decay mode
nuclide
          [T.sub.  Q Value   Abundance
          1/2]     (MeV)     (%)

89Zr      3.27d    2.834     [beta]-0.2,
                               EC 0.03

95Zr      65.5d    1.121     [beta]-1 49%

                             [beta]-2 49%

                             [beta]-3 2%

          Second route                           Nuclide
Product   Gamma decay mode                       after
nuclide                                          Decay
          [T.sub.  [E.sub.           Abundance
          1/2]     [gamma]]          (%)
                   (MeV)

89Zr      16 s     [(9/2).sup.+] -     -----     89Y
                    [(1/2).sup.-],
                   0.91(M4)

95Zr               [(5/2).sup.+] -   -----
                   [(1/2).sup.-],
                   (M1+E2)

          35d      [(5/2).sup.+] -
                   [(7/2).sup.+],                95Nb
                   (M1+E2)

                   [(5/2).sup.+] -
                   [(1/2).sup.-],
                   (M4)

Product   Ref.
nuclide

89Zr      Erdtmann
          (1976)[34];
          Browne and
          Firestone
95Zr      (1986)[35]
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