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The Effect of the E1 Strength Function on Neutron Capture Cross Sections
Berkley J.T. Starks
Brigham Young University-Idaho
2009 March 18
1. Introduction
The myriad of phenomena that are observed throughout the universe stem from the interactions of 4 main forces. These forces in order of weakest to strongest are gravity, the weak nuclear force, the electromagnetic force, and the strong nuclear force. The electromagnetic force and the strong nuclear force are the primary factors as to the physical makeup of matter throughout the universe. The interplay of these forces is made clearly manifest within the atomic nucleus.
Key to the study of nuclear physics is the nuclear cross section. Nuclear cross sections are a measure of the probability of certain reaction occurring. Dr. Krane defines the differential cross section, dσ/dΩ, as the probability that an incident particle, dσ, is scattered into the unit solid angle, dΩ. The probability of dσ being scattered into dΩ is the ration of the scattered current through dΩ to the incident current.
The total cross section, σ, is the total probability of scattering in any direction.
1A. Nucleosynthesis
Nucleosynthesis “attempts to interpret the measured abundances of the nuclear species in terms of their nuclear properties and a set of environments in which nuclei can be synthesized by nuclear reactions.”(Clayton, 69).
Nucleosynthesis depends on networks of nuclear reactions/processes in order to produce all “heavy” elements. Key to these reaction networks is the cross section.
It is theorized that most of the lighter elements (Z ≤ 6) were synthesized during the Big Bang. The rest of the elements “with nuclear charge Z ≥ 6 are in fact the ashes of nuclear burning during stellar evolution.”(Clayton, 71). The basic hypothesis of these studies as stated by Chandrasekhar is that:
Apart from secondary effects of minor importance, the transmutation of of elements is the entire cause of the presence of all elements in the stars; they are all being synthesized continually in the stars which are assumed to have started as pure masses of hydrogen; (Chandrasekhar, 469)
From this we can see the importance of nucleosynthesis studies in astrophysics. By using particle fluences and thermodynamic conditions in stars, we are able to understand the observed abundances of stable isotopes.
1B. Nuclear Cross Sections
Nuclear cross sections determine the probability of of a process occurring. A cross section is highly dependent on the energy of the incident particle(s). As was discussed above, the differential cross section, dσ/dΩ, is the probability that an incident particle, dσ, is scattered into the unit solid angle, dΩ. From nucleosynthesis we can see the importance of cross sections in the creation of elements through the reaction networks.
While we measure all cross sections that we are able to do, there are many unstable isotopes that it is impossible to test on. The problem lies in that these isotopes are produced in reaction networks, and will influence and interact with the other particles involved in the reaction. Because we are not able to test upon these isotopes, theory must provide cross sections for them if we are to fully understand the reaction networks.
In measuring these cross sections there are several different reaction networks depending on the type of incident energy. One of the most critical is neutron capture cross sections.
Neutron capture cross sections, n , , have several important ingredients. Most important at low energies is the photon transmission coefficient. Making up the photon transmission coefficient is the gamma ray strength function, f XL
, the energy dependent width of the giant dipole resonance, GDR , T f , and the E1 strength function.
In order to be able to increase the accuracy of theory, we must be able to reproduce measured cross sections on stable isotopes. The issue comes from that there are several ways to model the E1 strength function. Each of these models reproduces experimental cross sections in localized regions of the periodic table, but none are able to globally reproduce experimental cross sections.
What we will be doing is modeling the E1 strength function using several different schemes and attempting to see if one model as a better global fit to the others. When calculating these models there are two ways to normalize the photon transmission coefficient, specifically to the model used for the E1 strength function. This can be normalized either to the average radiation widths, , at the neutron binding energy, Bn , or the E1 strength can be normalized to the Maxwellian averaged cross section (MACS).
What we are trying to do is see what effect the E1 strength function has upon the cross section, and if by finding the appropriate f E1 we are endeavoring to be able to reproduce the experimental n ,cross sections and be able to replicate both Bn and 30 keV MACS.
1C. Some Basic Notation
The following section will give a brief overview of the notation throughout this document. The notation used is the same as found in reference 4.
Z - Proton number of the nucleus
N - Neutron number of the nucleus
A - mass of the nucleus in atomic mass units (generally A=Z+N)
J - angular momentum
π - parity
lower case letters - n, p, α, or γ particles
capital letters - nucleus (not n, p, α, or γ particles)
A further and more in-depth explanation of the notation will explained within chapter 2 of this thesis under the section entitled “The Hauser-Feshbach Statistical Model.”
2. Review of Theory
2A. Direct and Compound Reactions
In a nuclear reaction there are two main types of processes that occur. These reactions types are called direct processes and compound processes.
Direct reactions involve “only very few nucleons...with the remaining nucleons of the target serving as passive spectators” (Krane p. 379). These reactions only remove or insert a single nucleon from the target nucleus and are used to help explore and analyze the spectroscopic states in nuclei.
Compound reactions happen when the incoming and target nuclei briefly merge and completely share the incident energy before the outgoing nucleons are ejected. One of the most important assumptions of the compound-nucleus model is “that the relative probability for decay into any specific set of final products is independent of the means of formation of the compound nucleus” (Krane pp. 416-417).
An example of a compound process is the formation and then decay of 64Zn. 64Zn can be formed by either p + 63Cu or α + 60Ni. After 64Zn* is formed it can then decay into 63Zn + n, 62Cu + n + p, or 62Zn + 2n. The decay of 64Zn is completely independent of the way that it is formed. Whether it is through a proton capture, or and alpha capture, the formation does not affect the decay of the compound nucleus.
As can be seen from the graphs below, the shape of the cross sections are relatively the same with only slight perturbations.
The two experimentally observable differences between direct and compound reactions are “(1) Direct processes occur very rapidly, in a time of the order of 10-22 s, while compound-nuclear processes typically take much longer, perhaps 10-16 to 10-18 s...(2) The angular distributions of the outgoing particles in direct reactions tend to be more sharply peaked than in the case of compound-nuclear reactions” (Krane pp. 419-420). This last point is due to the fact the since the nucleus remembers how it was made, the momentum of the incident particle is going to transfer its momentum in the same incident direction upon the target nucleons.
One other difference between direct and compound reactions is summarized by Dr. Krane in that incident 1-MeV neutrons have a wavelength of ~ 4 fm. Because of this a 1-MeV neutron is most likely
to interact through compound nuclear reactions. Direct reactions involve higher energies (~20-MeV) have a de Broglie wavelength of 1 fm. Because of the higher wavelength the incident neutrons are more likely to interact with a single nucleon through direct nuclear processes.
In stellar nucleosynthesis the energies involved are generally at most in the 5 MeV range, but typically far less.
2B. The Hauser-Feshbach Statistical Model
With the formation of the compound nucleus at less energetic excitation levels the nuclear reactions proceed through narrow resonances. Resonances are a systematic excitation of the nucleus that go up in quantified steps instead of as a continuous spectrum. These resonances range in width from a few eV to several keV. These resonances correspond to nuclear states above the bound region.
As the excitation energy increases, the spacings between the resonances decreases, eventually leading to the point where resonances are too tightly packed together to so that the specification of individual resonance properties is not possible.
In order to analyze and predict what happens with the cross section, statistical models are used. These statistical models take the myriad of factors that influence the cross section and produce modeled cross sections. One of the statistical models used in statistical nuclear theory is the Hauser-Feshbach formula (see reference 8). This formula is given by:
j kE j
=ƛ j
2
g I g j
∑J ,
g J
T j J T k
J T tot J
W J
where j is the incident particle, k is the outgoing particle,
j kE j
− the average cross section for the reaction. The average is taken over an energyrange that contains several compound nuclear resonances of spin and parity.
ƛ j − wavelength related to the wave number by ƛ j=1k j
.
For n, p, particles, k j in the center of mass frame is k j=2
ℏ2 M UA j E j
g I − the statisical weight, 2J I1 of the target.g j − the statisical weight, 2J j1 of the incident light particle. For photons g j=1 .gJ − the statisical weight, 2J1 of the compound state.
T j J − the total transmission coefficient for forming the state J in the compound nucleus
at energy E j .
T k J − the total transmission coefficient for forming the state J in the compound nucleus
at Ek .
T tot J − the sum of all transmission functions related to decay of the state of interest.
W J − width fluctuation corrections (WFC). These define correlation factors with whichall partial channels of incoming energy j and outgoing particle k , passing throughexcited state (E, J, ), should be multiplied.
Looking at the Hauser-Feshbach formula in parts we see that:
ƛ j2
g I g j
∑J ,
g J T j J is for forming the compound nucleus in state J with incident paricle j. And
T k J
T tot J
is the probability that the compound nucleus in state J will decay by emitting particle k.
This formulation of Hauser-Feshbach is for the binary reaction (j,k). The Hauser Feshbach formula can be modified such that it can allow for multiple particle emission. This requires multiple compound steps.
Of prime importance to our studies at present is the T factor found within. At the lower energies when particle transmission is impossible/highly improbable the T tot is dominated by the photon transmission coefficient. Also, for capture reactions, T is in the numerator of Hauser-Feshbach, so ~T . (See references 4 and 6 for further information on Hauser-Feshbach.)
2C. Nuclear Level Density
There are several different models for nuclear structure. A few of these models are the shell model, the liquid-drop model, and the interacting boson model. (Nuclear Physics)
The shell model at its simplest level “predicts that nuclei having closed (completely occupied) shells of protons and neutrons should be unusually stable-as is, in fact, observed” (Nuclear Physics p. 37). This fact is observed in nature. This trait is analogous with the chemical analysis of the noble gases that have filled outer electron shells and are non reactive.
The nuclear level density, tot E x , J ,, is defined as the number of excited nuclear states with spin, J, and parity, , per MeV around the excitation energy E x . The total level density is the sum of ll nuclear states around a given energy, i.e.
tot E x =∑J∑
E x , J ,
When these level densities are analytically expressed they are generally factorized by:
E x , J ,=P E x , J ,RE x , J tot E x
with P E x , J , being the parity distribution, and generally is taken to be ½, and with RE x , J being representing the spin distribution.
The specific model that is incorporated into the TALYS code and that we will be using is the Fermi Gas Model.
The Backshifted Fermi Gas Model (FGM) is based on the assumption of evenly spaced single particle excitations. Collective excitations, or the excitations of multiple particles are not considered.
Assuming that the projections of total angular momentum are randomly coupled, the FGM level density is:
F E x , J ,=12
2J1
223 e−
J12
2
22 12
e2aU
a14U
54
with the ½ in the front being P E x , J ,, and 2 being the spin-cutoff parameter. a is the level density parameter, and U is the ___ and U=E− with being the backshift related to the pairingenergy. Using the FGM the Fermi gas distribution is given by:
RF E x , J =2J1
2 2 e−
J122
22
using this definition to sum over all F E x , J , we get the total Fermi gas level to be:
Ftot E x =
1
212
e2aU
a14U
54
showing that Ftot E x is dependent on the level density parameter a, and 2 , the spin-cutoff
parameter.
Energy-dependent shell effects are taken into account by making the level density parameter, a, energy dependent. This formulation is:
a=a E x = a 1W 1−e−U
U
where a is the asymptomatic level density value obtained in the absence of any shell effects (i.e.a=a E x∞, and W is the shell corrrection energy. The asymptotic value a is typically
parameterised by a= A A2/3 where A is the atomic mass number of the element in question, and and are parameters that that have been chosen to give the best average level density
description over a large range of nuclei.
2 can be related to the undeformed moment of inertia, I 0 , and the thermodynamic temperature, t. This is related by 2= ||
2= I 0 t . In this ||2 is the parallel spin cut-off parameter, or the projection
of the angular momentum onto the spin axis. Due to the fact that 2/ t suffers from shell effects and is not constant, 2 is rewritten as:
2= ||2=F
2 E x = I 0aat , or substituting in a : I 0=
25m0R
2 A
ℏ c 2
R=1.2A1/3 is the radius, and m0 is the neutron mass in AMU's. This can be rewritten as:
F2 E x =0.01389 A
5 /3
aaU
2D. Particle and Photon Transmission Coefficients
At sufficiently low incident neutron energies, the average radiative capture width, Γγ, is due entirely tothe s-wave interaction, and it is Γγ at the neutron separation energy Sn that is often used to normalize gamma-ray transmission coefficients. (Gardner, p. 62)
The gamma-ray strength function is related to the photon transmission coefficient by:
T XL =22L1 f XL
because T XL is directly dependent on f XL
the normalization of f XL is of prime importance
to the photon transmission coefficient.
When normalizing the gamma-ray strength function, there are several ways to model the strength function. The 5 models that we will be considering are the Blatt-Weisskopf method, using a Brink-Axel Lorentzian, a Kopecky-Uhl generalized Lorentzian, the Hartree-Fock BCS tables, or the Hartree-Fock Bogolyubov tables.
2D-1. Blatt-Weisskopf
Use of the Blatt-Weisskopf is f E1=constant. While at higher other levels, E2, M2, etc., the Blatt-Weisskopf may be a sufficient model for f E2 , f M2 and so on, but it is not a sufficient model atf E1 .
2D-2. Brink-Axel Lorentzian
The Brink-Axel model describes the standard Lorentzian form of the transmission coefficient at the giant dipole resonance and is calculated by:
f Xl E=K Xl
Xl E Xl2
E2−E Xl
2 2E2 Xl
2
where Xl is the strength of the dipole resonance, E Xl is the energy, and Xl is the width of thedipole resonance. And K Xl is
K Xl=1
2l12ℏ 2c 2
Use of the Brink-Axel Lorentzian is the commonly used model for all other transmissions besides for M1.
2D-3. Kopecky-Uhl generalized Lorentzian
The general way that many models depict the photon transmission for E1 radiation is through the use of a Kopecky-Uhl generalized Lorentzian. This is calculated by:
f E1E , T =K E1[E
E1E
E2−E E1
2 2E2 E1E
20.7 E142T 2
E E13 ]E1 E1
where E1 , E1 , and E E1 are the peak, width, and energy of the giant dipole resonance of the nucleusin question. E1 is the energy dependent damping and is given by:
E1 =E1
E242T 2
EE12
and T, the nuclear temperature:
T= EnS n−−E
a S n
E n is the incident neutron energy, S n is the neutron seperation energy, and is the pairingconnection.
2D-4. Hartree-Fock BCS & Hartree-Fock-Bogolyubov tables
The last two ways of modeling the E1 strength function is to allow for microscopic corrections (Goriely et al). Using the Hartree-Fock Method the E1 strength function is calculated by:
f L E , E i =2
GDR /2 E2
E2−Ei22GDR /2
2 E2
where GDR is the giant dipole resonance width and is taken from experimental data when experimental data is to be had, otherwise is taken for empirical statistics.
Using the BCS tables with the Hartree-Fock Method or combining Hartree-Fock with the Bogolyubuv method leads to sight perturbations in the calculations of the transmission coefficient, but as will be seen in the data, the perturbations are are only slight.
2D-5. Normalization of E1
When normalizing the gamma ray transmission coefficient it can be either normalized to the average radiation widths, or to the Maxwellian averaged cross section.
2D-5a. Radiation Widths
When normalizing to the radiation widths, on most isotopes the radiative widths, GDR , is measured. For unmeasured radiation widths on unstable isotopes, the average radiation widths are calculated by:
⟨ ⟩0= J1
2J1⟨ Bn , J
12⟩ J
2J1⟨ Bn , J−
12⟩
where J is the spin of the target nucleus and ⟨ Bn , J−12⟩=¿ .
2F. Maxwellian Averaged Cross Section
Another way of normalizing the E1 strength function is to normalize to the Maxwellian-averaged cross section. The Maxwellian-averaged cross section is “the reaction rate <> divided by the mean velocity vT=2kT / at a given temperature T.” (Hoffman p. 18). μ is the reduced mass and k is Boltzman's constant. What the Maxwellian-averaged cross sections endeavor to do is to analyze a thermally averaged cross section set for a group of atoms. This becomes of prime importance in astrophysical studies.
The Maxwellian-averaged cross section reduces to:
<>vT
=∫0
∞
nd
vT
=2
kT 2∫0
∞
n E W E , kT dE
where W E , kT =E e−E / kT and E is the center of mass energy.
3. Code
3A. TALYS
In order to calculate the cross sections relevant to the study found herein, the TALYS nuclear reaction code was used. TALYS gives us a wide range of control over the inputs into the Hauser-Feshbach statistical model.
The TALYS code can either be used with a variety of different options, or can be used in a “black-box” mode where standardized global inputs are used. In this latter mode, it is possible to generate a cross section very easily with minimal input by the user.
For the studies contained herein we used TALYS in a primarily black-box mode, altering only the E1 strength function.
A basic TALYS input file is as follows:
projectile n element Fe mass 56 energy 14
These four lines are all that is needed to run up a basic cross section. The line projectile tells TALYS what the incident light particle is (n, p, alpha, etc...). On the element line we define what element the target is by using the nomenclature found on the periodic table. Mass is the target's mass where we define which isotope of the element we are using. Finally the energy line lets us know what energies we are using for our reaction. These energies are given in MeV.
For our studies we wished to calculate our cross sections over a range of energies ranging from 10 eV to 20 MeV. Also, we wanted to test the effects of the different models for the photon transmission coefficient. In order to do this our input file looked like:
projectile n element ca mass 40energy erange strength 1
Here all the inputs are the same as above, except that the file erange contained our range of energies and the line strength. Even though on the line energy we do not contain on specific energy, but rather a file that contains a range of energies, these values are still considered blackbox making the only change being that of the E1 strength function.
What the strength key does is it allows us to define which strength function for the E1 transmission coefficient we will use. A value of 1 specifies a Kopecky-Uhl generalized Lorentzian. Value 2 specifies a Brink-Axel Lorentzian. Value 3 uses the Hartree-Fock BCS tables, and value 4 uses the Hartree-Fock-Bogolyubov tables. (See reference 6 for a complete listing of all TALYS input commands).
In order to quickly and efficiently run our code a wrapper was used to generate the individual input files from Z=1 to Z=84. The different strength functions were used on all the isotopes tested in order to see the affect that they had upon the calculations. These cross sections were later turned into Maxwellian-averaged cross sections and compared to experimental data.
The other use for the wrapper is that most calculations using TALYS are done for one incident energy and take very little time. Because we are calculating cross sections over a range of energies, the code takes a lot longer to run. What the wrapper does is it distributes the jobs over a series of Beowulf cluster nodes and allows for multiple cross sections to be calculated at the same time.
3B. MACS+
After TALYS has calculated the cross sections, it is necessary to convert these cross sections into the thermally averaged Maxwellian averaged cross sections. To do this a code written by Dr. Kevin Kelley is used. This code is called macs+.
This code was developed during Dr. Kelley's time at Lawrence Livermore National Laboratory (LLNL). This code as originally made to be used with the STAPRE nuclear reaction code, but in conjunction with the wrapper, can be used to convert cross sections produced with TALYS into Maxwellian averaged cross sections.
In order to produce a MACS, an input file looks like:
macs+ n-084210-000.tot.int 210
where macs+ calls the code, n-084210-000.tot.int is the interpolated cross section produced by the TALYS wrapper, and 210 is the atomic mass of the initial heavy particle.
When the code runs it produces a *.ps graph of the file with experimental data points graphed along with the systematic calculation.
4. Effect of the Photon Transmission Coefficient
Provided below will be an analysis of the effect of the photon transmission coefficient on the Maxwellian averaged cross section. We will be looking at the overall systematic and how well each model globally fits to experimental data.
In the plots that follow the data for Nitrogen 14 has been left out because on a global basis, using all 4 models for the E1 strength function the MACS for Nitrogen 14 was off by over a factor of 80 when compared to experimental data.
For a full listing of all data and graphs the reader is referred to the appendixes.
4A. Brink-Axel Lorentzian
Figure 1: Global Comparison of calculated MACS vs. experimental MACS – Brink-Axel Lorentzian
As can be seen from the plot above of the ratio of calculated MACS over the experimental MACS for the use of a Brink-Axel Lorentzian, the data is reasonably good, with a few outliers. But even the data points that are close to a ratio of 1, there are still many that are off by a factor of 2 or 3.
Looking at a specific cross section, in this case (and the case for al strength functions that we will be
comparing at this time) we will use Nickel 61. The MACS for Nickel 61 using the Brink-Axel Lorentzian is:
The plot here is a logarithmic plot of the cross section (in millibarns) versus the energy (in MeV). By observing the graph we can see that the systematic is close to the measured data, but is still high, at some points by a factor of 2 or 3.
4B. Kopecky-Uhl Generalized Lorentzian
The Kopecky-Uhl generalized lorentzian is similar in calculation to the Brink-Axel Lorentzian, except that it allows for energy and width fluctuations and corrections, but it still has a general Lorentzian shape.
Looking at the data for Nickel 61 using the Kopecky-Uhl Lorentzian (see figure 3 on next page) it can be seen that the data is roughly the same as when the Brink-Axel Lorentzian was used.
Looking at an overall systematic (figure 4) it can be seen that like is brother, the Brink-Axel Lorentzian, it is still off by several orders of magnitude.
Figure 3: MACS for Nickel 61 using a Kopecky-Uhl Generalized Lorentzian
Figure 4: Global Comparison of calculated MACS vs. experimental MACS – Kopecky-Uhl Generalized Lorentzian
By looking at these two global systematics it can be seen that while in some cases a Lorentzian is an adequate model for the E1 strength function, globally it does not fit very well. In order to better model the E1 strength function, other models must be looked at. One of these models is the Hartree-Fock model.
4C. Hartree-Fock BCS Tables
When calculating the E1 strength function using the Hartree-Fock method, it is customary to have preciously calculated the E1 strength functions and to have tabulated them. This is because of the myriad of different inputs that go into the Hartree-Fock method, it would considerably lengthen calculation time to calculate the E1 strength function every time.
What can be seen from us of the Hartree-Fock method is a better global fit for the overall Maxwellian averaged cross section.
Figure 5: Global Comparison of calculated MACS vs. experimental MACS – Hartree-Fock BCS Tables First off, it can be seen that the Hartree-Fock BCS tables are more closely centered around a ratio of 1. Also, the outliers in data tend to have a lower calculated over experimental ratio than that of using a Lorentzian.
Looking at the MACS for Nickel 61 we see:
Figure 6: MACS for Nickel 61 using the Hartree-Fock BCS Tables
As can be immediately seen, the Hartree-Fock BCS tables are a lot more accurate on Nickel 61. Also, it can be seen that unlike the Lorentzian's, the BCS tables actually fall within the error of the measured cross sections. This is a vast improvement.
4D. Hartree-Fock-Bogolyubov Tables
Lastly for our considerations is the use of the Hartree-Fock-Bogolyubuv Tables. This table is another set of calculated E1 strength functions using the Hartree-Fock method, but with slight alterations made by Bogolyubuv.
Looking at Figure 7 we can see the global fit is approximately the same as the BCS tables with some minor differences between them.
In the BCS tables we can see that the ratio of calculated over experimental never grow larger than a factor of about 13 or 14 while the Bogolyubuv tables have a data point at a factor of 20 times larger. But even with that, it can be seen that the rest of the outliers are tightly packed close to a ratio of 1.
Figure 7: Global Comparison of calculated MACS vs. experimental MACS – Hartree-Fock Bogolyubuv Tables
Looking at the data for Nickel 61 using the Bogolyubuv tables:
Figure 8: MACS for Nickel 61 using the Hartree-Fock-Bogolyubuv Tables
It can be seen from figure 8, that in this case the Bogolybuv tables provided a closer fit to experimental data than the BCS tables did. While this may be the case for Nickel 61, other targets are not the same.
4E. Conclusions and Future Research
From the data provided above, and from the data seen in the appendixes it can be seen that the Hartree-Fock Tables provide a better fit for the normalization of the photon transmission coefficient. While in many cases a generalized or even an enhanced Lorentzian may be adequate, globally speaking the Hartree-Fock method provides a better model for the E1 strength function.
The differences between these four models presented show us that the E1 strength function strongly impacts the cross section for neutron capture cross section.
But even with the better global fit of the E1 strength function using the Hartree-Fock method it is important to note that other models can be used for the E1 strength function, and that there are a myriad of other inputs to the Hauser-Feshbach statistical model that could possible effect the calculation of the nuclear cross section.
While the research presented herein has been extremely comprehensive for an analysis of these 4 models on neutron capture cross sections, future research should be done on the influence of the other factors that go into the HF model. Also, the actual calculation of BCS and Bogolybuv tables would warrant merit in that it could be used to better calculate these tables for an improved cross section.
While a lot as been learned about neutron capture cross sections, more work is still needed to better understand the calculation of nuclear cross sections.
Appendix A – Calculated Cross Sections Z=1 to Z=84
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
03 007 n-003007 0.042000 0.004000 2.925550E-03 3.721079E-03 2.925550E-03 2.925550E-03
07 014 n-007014 0.041000 0.060000 2.154701E+00 3.140149E+00 2.154701E+00 2.154701E+00
07 015 n-007015 0.005800 0.000500 8.559628E-03 1.427683E-02 8.559628E-03 8.559628E-03
08 016 n-008016 0.038000 0.004000 1.080230E-01 1.837643E-01 1.253546E-01 1.197564E-01
08 018 n-008018 0.008900 0.000800 1.570923E-01 2.756397E-01 1.953793E-01 1.779470E-01
09 019 n-009019 5.800000 1.200000 1.919127E+00 3.086111E+00 2.303823E+00 2.042061E+00
10 020 n-010020 0.119000 0.011000 1.136425E+00 2.231801E+00 1.648498E+00 1.409397E+00
10 021 n-010021 1.500000 0.900000 4.901853E+00 7.984066E+00 7.236576E+00 6.061551E+00
10 022 n-010022 0.059000 0.006000 3.194999E-01 6.938807E-01 4.400843E-01 3.959206E-01
11 023 n-011023 2.100000 0.200000 2.022618E+00 3.853830E+00 2.495820E+00 2.176321E+00
12 024 n-012024 3.300000 0.400000 2.185904E+00 5.099266E+00 3.238783E+00 2.798434E+00
12 025 n-012025 6.400000 0.400000 7.536136E+00 1.404865E+01 1.064633E+01 9.575419E+00
12 026 n-012026 0.126000 0.009000 9.846475E-01 2.721936E+00 1.442512E+00 1.404571E+00
13 026 n-013026 3.700000 0.000000 6.873161E+00 7.682245E+00 9.919382E+00 8.582369E+00
13 027 n-013027 3.740000 0.300000 4.845379E+00 9.100670E+00 5.596961E+00 5.311856E+00
14 028 n-014028 2.900000 0.300000 4.012543E+00 9.310085E+00 5.865685E+00 5.237112E+00
14 029 n-014029 7.900000 0.900000 9.905760E+00 1.711426E+01 1.314633E+01 1.346387E+01
14 030 n-014030 6.500000 0.600000 1.324662E+00 3.683474E+00 1.874111E+00 1.878212E+00
15 031 n-015031 1.740000 0.090000 7.180507E+00 1.460498E+01 8.775233E+00 8.048680E+00
16 032 n-016032 4.100000 0.200000 7.528139E+00 1.594542E+01 1.108990E+01 9.427842E+00
16 033 n-016033 7.400000 1.500000 1.599088E+01 2.667901E+01 1.919843E+01 1.836650E+01
16 034 n-016034 0.226000 0.010000 2.193083E+00 5.368666E+00 2.756585E+00 2.648232E+00
16 036 n-016036 0.171000 0.014000 1.471708E-01 4.594705E-01 2.012398E-01 2.026599E-01
17 035 n-017035 10.000000 0.300000 1.243010E+01 2.165878E+01 1.315247E+01 1.227988E+01
17 036 n-017036 12.000000 1.000000 1.848531E+01 2.929238E+01 1.908615E+01 1.832117E+01
17 037 n-017037 2.150000 0.080000 2.254961E+00 4.436195E+00 2.217727E+00 2.171562E+00
18 036 n-018036 9.000000 1.500000 9.709868E+00 1.925415E+01 1.215866E+01 1.104343E+01
18 038 n-018038 3.000000 0.300000 2.062786E+00 5.021069E+00 2.417315E+00 2.370714E+00
18 039 n-018039 8.000000 2.000000 9.362359E+00 1.985050E+01 1.099776E+01 1.030437E+01
18 040 n-018040 2.600000 0.200000 1.503983E+01 9.748759E+00 2.368398E+00 2.289455E+00
19 039 n-019039 11.800000 0.400000 1.023461E+01 1.805489E+01 9.966572E+00 9.533952E+00
19 040 n-019040 31.000000 7.000000 8.652582E+01 8.548793E+01 3.877005E+01 3.745433E+01
19 041 n-019041 22.000000 0.700000 2.782961E+01 2.499592E+01 2.391871E+01 2.280182E+01
20 040 n-020040 6.700000 0.700000 2.785843E+01 2.874696E+01 8.022990E+00 7.902287E+00
20 041 n-020041 30.000000 7.000000 6.516032E+01 5.700425E+01 3.636622E+01 3.450969E+01
20 042 n-020042 15.600000 2.000000 3.670263E+01 3.471651E+01 1.432902E+01 1.406629E+01
20 043 n-020043 51.000000 6.000000 7.122530E+01 6.234604E+01 4.850064E+01 4.532923E+01
20 044 n-020044 9.400000 1.300000 4.273586E+01 3.185991E+01 8.242145E+00 8.151855E+00
20 045 n-020045 17.500000 3.500000 6.641892E+01 5.702471E+01 1.649280E+01 1.627801E+01
20 046 n-020046 5.300000 0.500000 1.880598E+01 1.613899E+01 2.423849E+00 2.483811E+00
20 048 n-020048 0.870000 0.090000 7.858999E+00 2.196957E+00 6.095502E-01 6.710274E-01
21 045 n-021045 69.000000 5.000000 8.838400E+01 8.510768E+01 6.096320E+01 5.852341E+01
22 046 n-022046 26.799999 3.200000 4.342441E+01 3.214693E+01 2.804309E+01 2.772045E+01
22 047 n-022047 64.400002 7.700000 1.095829E+02 9.796895E+01 8.563709E+01 8.515210E+01
22 048 n-022048 31.799999 5.500000 4.878250E+01 3.824233E+01 1.201941E+01 1.230301E+01
22 049 n-022049 22.100000 2.100000 3.768596E+01 3.304253E+01 2.385444E+01 2.484724E+01
22 050 n-022050 3.600000 0.400000 1.263330E+01 5.168278E+00 2.679234E+00 2.855339E+00
23 050 n-023050 50.000000 9.000000 5.237787E+01 4.552015E+01 2.979338E+01 3.281595E+01
23 051 n-023051 38.000000 4.000000 6.255881E+01 4.994662E+01 1.252973E+01 1.330563E+01
24 050 n-024050 49.000000 13.000000 7.153080E+01 5.481053E+01 2.737211E+01 2.818492E+01
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
24 051 n-024051 87.000000 16.000000 1.688954E+02 1.533096E+02 7.164184E+01 7.402203E+01
24 052 n-024052 8.800000 2.300000 3.744530E+01 2.376862E+01 1.268235E+01 1.348297E+01
24 053 n-024053 58.000000 10.000000 5.432665E+01 4.317466E+01 2.469698E+01 2.544091E+01
24 054 n-024054 6.700000 1.600000 4.040600E+01 2.175976E+01 6.172091E+00 6.353194E+00
25 055 n-025055 39.599998 3.000000 5.485488E+01 5.002533E+01 3.303167E+01 3.414599E+01
26 054 n-026054 27.600000 1.800000 6.529237E+01 4.994753E+01 4.297879E+01 4.552139E+01
26 055 n-026055 75.000000 12.000000 1.637302E+02 1.504868E+02 8.402212E+01 8.635303E+01
26 056 n-026056 11.700000 0.500000 3.120243E+01 2.138931E+01 2.238555E+01 2.330776E+01
26 057 n-026057 40.000000 4.000000 5.834891E+01 4.672072E+01 3.443636E+01 3.510017E+01
26 058 n-026058 12.100000 1.300000 6.782011E+01 5.531710E+01 1.350419E+01 1.501097E+01
27 059 n-027059 38.000000 4.000000 7.374050E+01 6.567153E+01 3.022791E+01 3.394058E+01
28 058 n-028058 41.000000 2.000000 1.064382E+02 8.511571E+01 5.303654E+01 5.543875E+01
28 059 n-028059 87.000000 14.000000 1.521012E+02 1.396904E+02 1.105955E+02 1.270219E+02
28 060 n-028060 30.000000 3.000000 8.046020E+01 5.897483E+01 2.757181E+01 2.939778E+01
28 061 n-028061 82.000000 8.000000 1.387152E+02 1.282218E+02 8.936667E+01 8.942702E+01
28 062 n-028062 12.500000 4.000000 4.655475E+01 2.966956E+01 1.473717E+01 1.526792E+01
28 063 n-028063 31.000000 6.000000 9.233369E+01 8.323387E+01 4.508896E+01 4.152620E+01
28 064 n-028064 8.700000 0.900000 8.171327E+01 4.902215E+01 7.407284E+00 7.909033E+00
29 063 n-029063 94.000000 10.000000 8.728926E+01 7.945662E+01 7.035903E+01 7.309550E+01
29 065 n-029065 41.000000 4.000000 5.707926E+01 5.182380E+01 3.348197E+01 3.331024E+01
30 064 n-030064 59.000000 5.000000 1.052674E+02 9.266618E+01 6.305903E+01 6.238576E+01
30 065 n-030065 162.000000 27.000000 2.459910E+02 2.417264E+02 1.759927E+02 1.600132E+02
30 066 n-030066 35.000000 3.000000 5.968033E+01 4.897438E+01 3.040866E+01 2.966940E+01
30 067 n-030067 153.000000 15.000000 1.553175E+02 1.491037E+02 1.118883E+02 1.021629E+02
30 068 n-030068 19.200001 2.400000 4.385069E+01 3.746901E+01 1.587070E+01 1.636678E+01
30 070 n-030070 21.500000 2.000000 3.947175E+01 2.798817E+01 8.243075E+00 8.422108E+00
31 069 n-031069 139.000000 6.000000 1.179988E+02 1.146443E+02 1.112663E+02 1.095163E+02
31 071 n-031071 123.000000 8.000000 1.044145E+02 1.044546E+02 6.926772E+01 7.010715E+01
32 070 n-032070 88.000000 5.000000 1.080113E+02 9.798924E+01 7.616943E+01 7.329702E+01
32 072 n-032072 73.000000 7.000000 7.418167E+01 7.041314E+01 5.777410E+01 5.695501E+01
32 073 n-032073 243.000000 47.000000 3.044852E+02 3.052458E+02 1.398185E+02 1.662937E+02
32 074 n-032074 53.000000 7.000000 5.307602E+01 4.751698E+01 3.938872E+01 4.111917E+01
32 076 n-032076 33.000000 15.000000 2.227634E+01 2.402402E+01 1.912262E+01 2.088188E+01
33 075 n-033075 568.000000 35.000000 3.874680E+02 3.841937E+02 2.516309E+02 2.586882E+02
34 074 n-034074 267.000000 25.000000 2.782157E+02 2.733805E+02 1.847805E+02 1.811391E+02
34 076 n-034076 164.000000 8.000000 1.607104E+02 1.524258E+02 8.360230E+01 8.757554E+01
34 077 n-034077 418.000000 71.000000 4.608962E+02 4.540357E+02 2.518895E+02 2.608081E+02
34 078 n-034078 109.000000 41.000000 7.005849E+01 6.558743E+01 6.558716E+01 6.829856E+01
34 079 n-034079 263.000000 46.000000 4.206985E+02 4.260793E+02 1.778426E+02 1.714859E+02
34 080 n-034080 42.000000 3.000000 7.009468E+01 6.565251E+01 2.688449E+01 2.765755E+01
34 082 n-034082 9.000000 8.000000 2.801018E+01 3.838009E+01 1.037565E+01 1.249078E+01
35 079 n-035079 627.000000 42.000000 5.645390E+02 5.602300E+02 4.344806E+02 4.374234E+02
35 081 n-035081 313.000000 16.000000 3.422865E+02 3.368954E+02 1.528374E+02 1.644633E+02
36 078 n-036078 321.000000 26.000000 3.505042E+02 3.440105E+02 2.381065E+02 2.425514E+02
36 079 n-036079 959.000000 162.000000 8.904902E+02 8.878626E+02 5.436783E+02 5.444833E+02
36 080 n-036080 267.000000 14.000000 3.055253E+02 2.982502E+02 1.338318E+02 1.357771E+02
36 081 n-036081 607.000000 105.000000 8.640297E+02 8.663258E+02 5.253975E+02 5.050307E+02
36 082 n-036082 90.000000 6.000000 1.470170E+02 1.333928E+02 6.526701E+01 6.565080E+01
36 083 n-036083 243.000000 15.000000 1.269379E+02 1.267759E+02 1.060202E+02 1.157735E+02
36 084 n-036084 38.000000 4.000000 1.111176E+02 1.108748E+02 2.712871E+01 3.080640E+01
36 085 n-036085 55.000000 45.000000 1.503139E+02 1.548823E+02 5.065403E+01 5.945589E+01
36 086 n-036086 3.400000 0.300000 9.051975E+00 1.528026E+01 3.917190E+00 4.758818E+00
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
37 085 n-037085 240.000000 9.000000 1.840842E+02 1.870202E+02 1.980202E+02 2.159947E+02
37 086 n-037086 202.000000 163.000000 3.423529E+02 3.543742E+02 2.531371E+02 2.825047E+02
37 087 n-037087 15.500000 0.500000 2.272959E+01 2.950970E+01 1.503415E+01 1.824444E+01
38 084 n-038084 368.000000 126.000000 3.516711E+02 3.389369E+02 1.740506E+02 1.829715E+02
38 086 n-038086 64.000000 3.000000 6.927120E+01 6.001610E+01 4.584237E+01 5.027383E+01
38 087 n-038087 92.000000 4.000000 1.567945E+02 1.508619E+02 8.824210E+01 1.030806E+02
38 088 n-038088 6.200000 0.300000 8.609921E+00 1.325119E+01 4.928689E+00 5.721329E+00
38 089 n-038089 19.000000 14.000000 3.591252E+01 4.228145E+01 1.515122E+01 1.591780E+01
39 089 n-039089 19.000000 0.600000 1.532860E+01 1.706384E+01 1.606710E+01 1.893509E+01
40 090 n-040090 21.000000 2.000000 1.996427E+01 2.502095E+01 1.304110E+01 1.630277E+01
40 091 n-040091 60.000000 8.000000 4.790004E+01 5.496385E+01 4.261222E+01 4.837974E+01
40 092 n-040092 33.000000 4.000000 2.979778E+01 3.839787E+01 2.474197E+01 2.411820E+01
40 093 n-040093 95.000000 10.000000 1.531388E+02 1.652507E+02 5.126321E+01 5.476767E+01
40 094 n-040094 26.000000 1.000000 2.324252E+01 3.237372E+01 2.245261E+01 1.915371E+01
40 095 n-040095 79.000000 12.000000 1.205649E+02 1.257551E+02 3.145813E+01 3.106335E+01
40 096 n-040096 10.700000 0.500000 3.398477E+01 4.745811E+01 9.279010E+00 9.239777E+00
41 093 n-041093 266.000000 5.000000 2.626758E+02 2.692278E+02 1.295504E+02 1.371554E+02
41 094 n-041094 482.000000 92.000000 5.351777E+02 5.348939E+02 2.171103E+02 2.147269E+02
41 095 n-041095 310.000000 65.000000 4.948683E+02 4.985308E+02 1.809135E+02 1.801969E+02
42 092 n-042092 70.000000 10.000000 5.039633E+01 6.109239E+01 3.669867E+01 4.345372E+01
42 094 n-042094 102.000000 20.000000 7.256184E+01 8.643731E+01 6.418711E+01 7.192889E+01
42 095 n-042095 292.000000 12.000000 2.355989E+02 2.476548E+02 1.710720E+02 1.566365E+02
42 096 n-042096 112.000000 8.000000 7.450532E+01 8.598748E+01 7.643011E+01 7.591769E+01
42 097 n-042097 339.000000 14.000000 2.752187E+02 2.787508E+02 1.930559E+02 1.707879E+02
42 098 n-042098 99.000000 7.000000 6.243437E+01 7.195748E+01 4.854471E+01 4.997304E+01
42 099 n-042099 240.000000 40.000000 3.448521E+02 3.512400E+02 2.285220E+02 1.594615E+02
42 100 n-042100 108.000000 14.000000 8.148736E+01 8.652262E+01 5.340111E+01 5.718398E+01
43 099 n-043099 781.000000 50.000000 1.189483E+03 1.190918E+03 4.146587E+02 4.194319E+02
44 096 n-044096 238.000000 60.000000 9.097681E+01 1.088402E+02 9.430406E+01 1.081347E+02
44 098 n-044098 173.000000 36.000000 1.288702E+02 1.409552E+02 1.086097E+02 1.162901E+02
44 099 n-044099 631.000000 99.000000 8.501904E+02 8.534821E+02 5.374302E+02 5.508294E+02
44 100 n-044100 206.000000 13.000000 1.509334E+02 1.587550E+02 1.258380E+02 1.368451E+02
44 101 n-044101 996.000000 40.000000 1.026223E+03 1.037416E+03 4.560906E+02 4.433466E+02
44 102 n-044102 186.000000 11.000000 1.144241E+02 1.217646E+02 1.005145E+02 1.056940E+02
44 103 n-044103 343.000000 52.000000 5.698919E+02 5.740394E+02 2.362313E+02 2.356207E+02
44 104 n-044104 161.000000 10.000000 1.753536E+02 1.812185E+02 1.037711E+02 1.123802E+02
45 103 n-045103 811.000000 14.000000 8.192718E+02 8.091658E+02 3.775034E+02 4.024099E+02
46 102 n-046102 375.000000 118.000000 1.742379E+02 1.859706E+02 2.003868E+02 2.008484E+02
46 104 n-046104 289.000000 29.000000 2.718789E+02 2.815796E+02 1.760884E+02 1.900726E+02
46 105 n-046105 1200.000000 60.000000 1.251158E+03 1.253508E+03 6.915013E+02 7.017331E+02
46 106 n-046106 252.000000 25.000000 2.329938E+02 2.423726E+02 1.104629E+02 1.175956E+02
46 107 n-046107 1340.000000 60.000000 1.079515E+03 1.078911E+03 5.487463E+02 5.624642E+02
46 108 n-046108 203.000000 20.000000 3.243237E+02 3.301611E+02 1.645439E+02 1.814470E+02
46 110 n-046110 146.000000 20.000000 2.397243E+02 2.410852E+02 7.665943E+01 9.366099E+01
47 107 n-047107 792.000000 30.000000 8.518655E+02 8.438953E+02 4.667302E+02 5.026719E+02
47 109 n-047109 788.000000 30.000000 1.123849E+03 1.118306E+03 4.824501E+02 5.246441E+02
47 110 n-047110 1172.000000 188.000000 1.488679E+03 1.484690E+03 1.029415E+03 1.060548E+03
48 106 n-048106 302.000000 24.000000 4.901854E+02 5.023380E+02 2.678343E+02 3.049586E+02
48 108 n-048108 202.000000 9.000000 4.081385E+02 4.130889E+02 1.896426E+02 1.901212E+02
48 110 n-048110 246.000000 10.000000 2.464537E+02 2.508780E+02 1.638601E+02 1.790785E+02
48 111 n-048111 1063.000000 125.000000 7.634822E+02 7.660639E+02 5.464073E+02 5.116317E+02
48 112 n-048112 235.000000 30.000000 2.229854E+02 2.309516E+02 1.038486E+02 1.131841E+02
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
48 113 n-048113 728.000000 80.000000 9.014435E+02 9.050363E+02 4.315938E+02 4.094047E+02
48 114 n-048114 127.000000 5.000000 1.365522E+02 1.444470E+02 7.235886E+01 7.794953E+01
48 115 n-048115 290.000000 62.000000 5.922363E+02 5.988341E+02 3.346607E+02 3.135363E+02
48 116 n-048116 59.000000 2.000000 8.238394E+01 8.949576E+01 6.479967E+01 6.831049E+01
49 113 n-049113 787.000000 70.000000 6.153801E+02 6.144808E+02 4.515579E+02 4.775574E+02
49 114 n-049114 2595.000000 1300.000000 1.510678E+03 1.507794E+03 9.881434E+02 1.078804E+03
49 115 n-049115 706.000000 70.000000 7.932709E+02 7.923272E+02 4.064601E+02 4.423977E+02
50 112 n-050112 210.000000 12.000000 3.179276E+02 3.266430E+02 1.667597E+02 1.855568E+02
50 114 n-050114 134.399994 1.800000 1.762876E+02 1.883349E+02 9.647840E+01 1.074683E+02
50 115 n-050115 342.399994 8.700000 6.149691E+02 6.167798E+02 3.279480E+02 3.718396E+02
50 116 n-050116 91.400002 0.900000 9.048044E+01 9.763746E+01 7.716253E+01 9.011374E+01
50 117 n-050117 319.000000 5.000000 3.161358E+02 3.197480E+02 2.470691E+02 2.761629E+02
50 118 n-050118 62.099998 0.600000 1.289270E+02 1.431959E+02 4.566538E+01 5.523978E+01
50 119 n-050119 180.000000 10.000000 2.195289E+02 2.221691E+02 1.605806E+02 1.754925E+02
50 120 n-050120 36.000000 0.500000 4.815716E+01 5.728691E+01 2.966043E+01 3.461226E+01
50 121 n-050121 167.000000 30.000000 3.375763E+02 3.405187E+02 1.708319E+02 1.960096E+02
50 122 n-050122 21.900000 1.500000 4.572508E+01 5.188257E+01 2.498783E+01 3.068638E+01
50 124 n-050124 12.000000 1.800000 1.909561E+01 2.875271E+01 9.338586E+00 1.141340E+01
50 125 n-050125 59.000000 9.000000 7.475712E+01 7.504127E+01 5.250196E+01 6.869406E+01
50 126 n-050126 10.000000 4.000000 9.155574E+00 1.288285E+01 9.480113E+00 1.264401E+01
51 121 n-051121 532.000000 16.000000 6.059400E+02 6.038875E+02 3.901085E+02 4.202266E+02
51 122 n-051122 894.000000 162.000000 1.248415E+03 1.244183E+03 8.647256E+02 9.322438E+02
51 123 n-051123 303.000000 9.000000 4.369279E+02 4.338577E+02 2.755149E+02 3.165815E+02
51 125 n-051125 260.000000 70.000000 2.404220E+02 2.386838E+02 1.222584E+02 1.559249E+02
52 120 n-052120 420.000000 103.000000 4.274826E+02 4.286746E+02 2.628419E+02 2.871390E+02
52 122 n-052122 295.000000 3.000000 3.780151E+02 3.863610E+02 1.698887E+02 1.757572E+02
52 123 n-052123 832.000000 8.000000 8.128760E+02 8.099985E+02 5.107527E+02 5.217917E+02
52 124 n-052124 155.000000 2.000000 2.635873E+02 2.706537E+02 1.095129E+02 1.267941E+02
52 125 n-052125 431.000000 4.000000 5.090803E+02 5.083938E+02 2.341884E+02 2.606088E+02
52 126 n-052126 81.300003 1.400000 1.430035E+02 1.526098E+02 6.064378E+01 7.207574E+01
52 128 n-052128 44.400002 1.300000 7.655808E+01 8.224633E+01 5.234262E+01 6.694398E+01
52 130 n-052130 14.700000 2.800000 4.313559E+01 4.708765E+01 2.372313E+01 3.127603E+01
53 127 n-053127 635.000000 30.000000 5.189426E+02 5.173630E+02 3.947624E+02 4.739752E+02
53 129 n-053129 441.000000 22.000000 3.231792E+02 3.218393E+02 2.787776E+02 3.502321E+02
54 124 n-054124 644.000000 83.000000 6.014657E+02 6.008845E+02 3.743872E+02 4.086941E+02
54 126 n-054126 359.000000 51.000000 3.817388E+02 3.861352E+02 2.277562E+02 2.555226E+02
54 128 n-054128 248.000000 66.000000 1.779187E+02 1.829666E+02 1.383899E+02 1.624903E+02
54 129 n-054129 472.000000 71.000000 4.137006E+02 4.122180E+02 2.810340E+02 3.242145E+02
54 130 n-054130 141.000000 51.000000 1.783944E+02 1.860307E+02 8.912510E+01 1.117097E+02
54 131 n-054131 340.000000 65.000000 3.086385E+02 3.103597E+02 2.204650E+02 2.599247E+02
54 132 n-054132 64.599998 5.300000 7.312544E+01 8.204666E+01 4.281370E+01 5.334557E+01
54 133 n-054133 127.000000 34.000000 8.713935E+01 8.845424E+01 1.338477E+02 1.647699E+02
54 134 n-054134 20.200001 1.700000 3.808390E+01 4.724640E+01 2.170638E+01 2.834911E+01
54 136 n-054136 0.910000 0.080000 6.781281E+00 4.905751E+00 1.050990E+00 1.629103E+00
55 133 n-055133 509.000000 21.000000 5.135665E+02 5.119769E+02 3.881684E+02 4.946060E+02
55 134 n-055134 664.000000 174.000000 7.963199E+02 7.944494E+02 4.190428E+02 5.290538E+02
55 135 n-055135 198.000000 17.000000 1.526825E+02 1.519255E+02 1.595879E+02 2.079998E+02
56 130 n-056130 760.000000 110.000000 4.716471E+02 4.753376E+02 2.634507E+02 3.035036E+02
56 132 n-056132 379.000000 137.000000 2.766689E+02 2.829526E+02 1.580194E+02 1.929329E+02
56 134 n-056134 176.000000 5.600000 1.156369E+02 1.223767E+02 8.493716E+01 1.063468E+02
56 135 n-056135 455.000000 15.000000 3.938521E+02 3.949739E+02 2.759311E+02 3.320054E+02
56 136 n-056136 61.200001 2.000000 5.247912E+01 6.199535E+01 3.751630E+01 4.568145E+01
56 137 n-056137 76.300003 2.400000 6.416602E+01 6.570678E+01 7.920880E+01 9.647799E+01
56 138 n-056138 4.000000 0.200000 3.998870E+00 3.063980E+00 2.324353E+00 3.303218E+00
57 139 n-057139 38.400002 2.700000 4.609125E+01 4.355745E+01 2.389887E+01 3.470769E+01
58 132 n-058132 1570.000000 420.000000 8.705195E+02 8.691139E+02 5.257539E+02 5.922666E+02
58 133 n-058133 2600.000000 400.000000 1.915179E+03 1.911660E+03 1.558165E+03 1.736733E+03
58 134 n-058134 967.000000 351.000000 5.922288E+02 5.921669E+02 2.773964E+02 3.476671E+02
58 135 n-058135 1320.000000 260.000000 1.088561E+03 1.086021E+03 7.467759E+02 8.973634E+02
58 136 n-058136 300.000000 21.000000 4.126163E+02 4.174981E+02 2.087302E+02 2.578750E+02
58 137 n-058137 973.000000 256.000000 8.587399E+02 8.559975E+02 6.948094E+02 8.235276E+02
58 138 n-058138 179.000000 5.000000 1.719111E+02 1.775182E+02 1.047597E+02 1.302343E+02
58 139 n-058139 214.000000 120.000000 2.862434E+02 2.865595E+02 2.081797E+02 2.668863E+02
58 140 n-058140 11.000000 0.400000 1.174642E+01 1.061947E+01 6.990414E+00 9.692866E+00
58 141 n-058141 76.000000 33.000000 1.500967E+02 1.472024E+02 5.810698E+01 7.545567E+01
58 142 n-058142 28.000000 1.000000 4.381609E+01 3.806682E+01 1.607477E+01 2.006065E+01
59 141 n-059141 111.400002 1.400000 1.247088E+02 1.207935E+02 5.246442E+01 7.345867E+01
59 142 n-059142 415.000000 178.000000 3.821084E+02 3.772680E+02 2.003761E+02 2.658062E+02
59 143 n-059143 350.000000 86.000000 3.777276E+02 3.747751E+02 1.764226E+02 2.243549E+02
60 142 n-060142 35.000000 0.700000 4.536246E+01 4.377671E+01 2.400936E+01 3.197416E+01
60 143 n-060143 245.000000 3.000000 3.004374E+02 2.966784E+02 1.399059E+02 1.735425E+02
60 144 n-060144 81.300003 1.500000 6.702935E+01 6.396872E+01 4.694993E+01 4.972111E+01
60 145 n-060145 425.000000 5.000000 5.102585E+02 5.064816E+02 2.407340E+02 2.501368E+02
60 146 n-060146 91.199997 1.000000 1.082912E+02 1.013022E+02 4.105628E+01 5.044404E+01
60 147 n-060147 544.000000 90.000000 1.205583E+03 1.199483E+03 3.804508E+02 4.421151E+02
60 148 n-060148 147.000000 2.000000 1.478503E+02 1.445884E+02 7.818202E+01 9.919374E+01
60 150 n-060150 159.000000 10.000000 1.783438E+02 1.758196E+02 6.359759E+01 6.537818E+01
61 147 n-061147 1290.000000 470.000000 1.032146E+03 1.027554E+03 3.566787E+02 4.650758E+02
61 148 n-061148 2970.000000 500.000000 1.634145E+03 1.627355E+03 8.700182E+02 1.018759E+03
61 149 n-061149 2510.000000 750.000000 1.644287E+03 1.637386E+03 4.555431E+02 6.010540E+02
62 144 n-062144 92.000000 6.000000 7.546566E+01 7.474403E+01 4.916358E+01 6.246971E+01
62 147 n-062147 973.000000 10.000000 1.068470E+03 1.063732E+03 5.002557E+02 5.551428E+02
62 148 n-062148 241.000000 2.000000 2.519940E+02 2.483496E+02 1.094160E+02 1.320635E+02
62 149 n-062149 1820.000000 17.000000 1.736638E+03 1.729368E+03 8.804231E+02 8.414320E+02
62 150 n-062150 422.000000 4.000000 5.040005E+02 4.998088E+02 1.829819E+02 2.251204E+02
62 151 n-062151 2710.000000 420.000000 3.199302E+03 3.188972E+03 1.249378E+03 1.451897E+03
62 152 n-062152 473.000000 4.000000 4.054797E+02 4.026417E+02 2.295348E+02 2.902326E+02
62 153 n-062153 1095.000000 175.000000 1.391163E+03 1.385358E+03 5.915649E+02 6.783631E+02
62 154 n-062154 206.000000 12.000000 2.562957E+02 2.532615E+02 9.753329E+01 1.009514E+02
63 151 n-063151 3775.000000 150.000000 4.364034E+03 4.350195E+03 1.578994E+03 1.995161E+03
63 152 n-063152 7600.000000 1200.000000 6.802910E+03 6.790957E+03 3.720353E+03 4.236389E+03
63 153 n-063153 2780.000000 100.000000 3.824238E+03 3.811898E+03 1.505439E+03 1.939590E+03
63 154 n-063154 4420.000000 670.000000 5.127749E+03 5.116585E+03 2.507031E+03 2.924688E+03
63 155 n-063155 1320.000000 84.000000 1.603818E+03 1.597023E+03 7.319838E+02 7.972000E+02
64 152 n-064152 1049.000000 17.000000 8.259820E+02 8.216380E+02 4.100182E+02 4.996821E+02
64 153 n-064153 4550.000000 700.000000 4.850316E+03 4.838569E+03 2.565700E+03 2.979595E+03
64 154 n-064154 1028.000000 12.000000 1.115281E+03 1.109994E+03 4.583061E+02 5.656584E+02
64 155 n-064155 2648.000000 30.000000 3.181913E+03 3.172009E+03 1.498685E+03 1.692679E+03
64 156 n-064156 615.000000 5.000000 6.882455E+02 6.842566E+02 2.576680E+02 2.816184E+02
64 157 n-064157 1369.000000 15.000000 1.356161E+03 1.351277E+03 5.325209E+02 5.260419E+02
64 158 n-064158 324.000000 3.000000 3.986337E+02 3.950700E+02 1.351159E+02 1.435007E+02
64 160 n-064160 154.000000 20.000000 2.312107E+02 2.254786E+02 7.247937E+01 7.405486E+01
65 159 n-065159 1580.000000 150.000000 1.627589E+03 1.620316E+03 7.973857E+02 8.578283E+02
65 160 n-065160 3240.000000 510.000000 5.653688E+03 5.638440E+03 2.476038E+03 2.602694E+03
66 156 n-066156 1567.000000 145.000000 2.532360E+03 2.522803E+03 7.779315E+02 1.006245E+03
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
66 158 n-066158 1060.000000 400.000000 9.349852E+02 9.304786E+02 4.127697E+02 5.110743E+02
66 160 n-066160 890.000000 12.000000 8.785675E+02 8.738282E+02 3.032186E+02 3.940497E+02
66 161 n-066161 1964.000000 19.000000 2.546613E+03 2.537777E+03 8.842169E+02 1.143818E+03
66 162 n-066162 446.000000 4.000000 5.186220E+02 5.147472E+02 2.587298E+02 2.808276E+02
66 163 n-066163 1112.000000 11.000000 1.372429E+03 1.365858E+03 5.561885E+02 5.575477E+02
66 164 n-066164 212.000000 3.000000 2.972700E+02 2.932501E+02 1.223568E+02 1.294590E+02
67 163 n-067163 2125.000000 95.000000 5.708049E+03 5.696076E+03 1.884387E+03 2.227298E+03
67 165 n-067165 1280.000000 100.000000 1.374094E+03 1.368448E+03 6.587605E+02 7.479827E+02
68 162 n-068162 1624.000000 124.000000 2.028878E+03 2.020773E+03 6.205012E+02 8.040919E+02
68 164 n-068164 1084.000000 51.000000 1.034691E+03 1.029482E+03 4.296853E+02 5.459654E+02
68 166 n-068166 563.000000 56.000000 6.527709E+02 6.483627E+02 2.863261E+02 3.275735E+02
68 167 n-068167 1425.000000 143.000000 1.628886E+03 1.622068E+03 6.678164E+02 7.598477E+02
68 168 n-068168 338.000000 44.000000 3.365373E+02 3.324060E+02 1.469104E+02 1.662812E+02
68 169 n-068169 653.000000 114.000000 6.118154E+02 6.076631E+02 3.045166E+02 3.145871E+02
68 170 n-068170 170.000000 7.000000 2.566962E+02 2.525927E+02 1.100429E+02 1.234832E+02
69 169 n-069169 1129.000000 56.000000 8.641300E+02 8.583866E+02 4.435075E+02 5.197137E+02
69 170 n-069170 1870.000000 330.000000 1.930075E+03 1.923371E+03 8.167578E+02 9.056044E+02
69 171 n-069171 486.000000 144.000000 9.635312E+02 9.590786E+02 3.808617E+02 4.554451E+02
70 168 n-070168 1160.000000 440.000000 1.469331E+03 1.463475E+03 5.908447E+02 7.848039E+02
70 170 n-070170 768.000000 7.000000 6.311844E+02 6.270656E+02 3.146013E+02 4.131186E+02
70 171 n-070171 1210.000000 12.000000 1.200068E+03 1.195265E+03 6.480189E+02 8.166266E+02
70 172 n-070172 341.000000 3.000000 4.076519E+02 4.037987E+02 2.106356E+02 2.462428E+02
70 173 n-070173 754.000000 7.000000 8.685092E+02 8.635811E+02 4.055580E+02 4.484199E+02
70 174 n-070174 151.000000 2.000000 2.419321E+02 2.381874E+02 1.033375E+02 1.199673E+02
70 175 n-070175 558.000000 83.000000 7.728369E+02 7.669024E+02 2.581078E+02 2.985073E+02
70 176 n-070176 116.000000 2.000000 1.846179E+02 1.812886E+02 9.825673E+01 1.106926E+02
71 175 n-071175 1146.000000 44.000000 1.619388E+03 1.613579E+03 6.944744E+02 8.563629E+02
71 176 n-071176 1532.000000 69.000000 1.862075E+03 1.854811E+03 7.044658E+02 8.371378E+02
72 174 n-072174 956.000000 283.000000 8.599363E+02 8.553246E+02 4.199321E+02 5.788499E+02
72 176 n-072176 455.000000 20.000000 5.675017E+02 5.644931E+02 3.017925E+02 4.054981E+02
72 177 n-072177 1500.000000 100.000000 1.612939E+03 1.605631E+03 8.145226E+02 9.196995E+02
72 178 n-072178 314.000000 10.000000 3.590087E+02 3.555571E+02 1.889528E+02 2.290492E+02
72 179 n-072179 956.000000 50.000000 1.055950E+03 1.050457E+03 5.768922E+02 6.672240E+02
72 180 n-072180 179.000000 5.000000 2.493698E+02 2.444014E+02 1.034233E+02 1.187488E+02
72 181 n-072181 194.000000 31.000000 3.678776E+02 3.645149E+02 1.050146E+02 1.166585E+02
72 182 n-072182 117.000000 41.000000 2.422193E+02 2.389883E+02 6.353631E+01 7.292201E+01
73 179 n-073179 1334.000000 422.000000 3.004482E+03 2.998256E+03 1.506821E+03 1.843845E+03
73 180 n-073180 1640.000000 260.000000 1.896064E+03 1.892068E+03 9.368301E+02 1.229675E+03
73 181 n-073181 766.000000 15.000000 9.987947E+02 9.934209E+02 4.807404E+02 6.003485E+02
73 182 n-073182 1120.000000 180.000000 1.166842E+03 1.162362E+03 5.181388E+02 6.024902E+02
74 180 n-074180 536.000000 60.000000 9.397216E+02 9.318273E+02 4.545551E+02 6.342833E+02
74 182 n-074182 274.000000 8.000000 3.895656E+02 3.836250E+02 2.040834E+02 2.793579E+02
74 183 n-074183 515.000000 15.000000 7.563709E+02 7.517904E+02 3.868400E+02 4.930202E+02
74 184 n-074184 224.000000 10.000000 3.330526E+02 3.270991E+02 1.246388E+02 1.485116E+02
74 185 n-074185 703.000000 113.000000 7.992129E+02 7.949202E+02 3.274810E+02 4.723282E+02
74 186 n-074186 176.000000 5.000000 2.993088E+02 2.919654E+02 9.623901E+01 1.146630E+02
75 185 n-075185 1535.000000 62.000000 1.111813E+03 1.107180E+03 6.177715E+02 8.427721E+02
75 186 n-075186 1550.000000 250.000000 1.812379E+03 1.806953E+03 9.451812E+02 1.208854E+03
75 187 n-075187 1160.000000 57.000000 9.657551E+02 9.608724E+02 4.949352E+02 5.992890E+02
76 184 n-076184 657.000000 202.000000 8.296354E+02 8.253446E+02 4.333971E+02 5.540367E+02
76 186 n-076186 422.000000 16.000000 5.991306E+02 5.949226E+02 3.052951E+02 3.804084E+02
76 187 n-076187 896.000000 30.000000 1.101880E+03 1.097844E+03 4.602107E+02 6.231081E+02
#Z A Element Recommended MACS dMACS Strength1 Strength2 Strength3 Strength4
76 188 n-076188 399.000000 15.000000 5.244943E+02 5.201742E+02 2.154988E+02 3.011233E+02
76 189 n-076189 1168.000000 47.000000 1.272156E+03 1.267479E+03 5.608731E+02 7.513142E+02
76 190 n-076190 295.000000 45.000000 3.733043E+02 3.691222E+02 1.798079E+02 2.453937E+02
76 191 n-076191 1290.000000 280.000000 1.192934E+03 1.187504E+03 5.203119E+02 7.024522E+02
76 192 n-076192 311.000000 45.000000 2.786164E+02 2.678660E+02 8.495893E+01 1.007836E+02
77 191 n-077191 1350.000000 43.000000 1.365925E+03 1.361006E+03 7.057573E+02 9.450421E+02
77 192 n-077192 2080.000000 450.000000 2.352064E+03 2.346711E+03 1.514276E+03 1.782018E+03
77 193 n-077193 994.000000 70.000000 8.397014E+02 8.343089E+02 4.760247E+02 5.949050E+02
78 190 n-078190 677.000000 183.000000 6.713510E+02 6.669934E+02 3.236449E+02 4.247898E+02
78 192 n-078192 590.000000 120.000000 6.623499E+02 6.575150E+02 2.917508E+02 3.908764E+02
78 193 n-078193 1123.000000 240.000000 7.962590E+02 7.930845E+02 4.893062E+02 5.615653E+02
78 194 n-078194 365.000000 85.000000 1.696137E+02 1.663957E+02 2.168403E+02 2.531207E+02
78 195 n-078195 860.000000 200.000000 6.326700E+02 6.292143E+02 3.396414E+02 4.203966E+02
78 196 n-078196 197.000000 23.000000 1.856390E+02 1.800200E+02 1.304033E+02 1.677149E+02
78 198 n-078198 82.000000 12.000000 2.273103E+02 2.154794E+02 7.317499E+01 9.706773E+01
79 197 n-079197 582.000000 9.000000 6.233910E+02 6.186913E+02 4.659083E+02 5.931998E+02
79 198 n-079198 840.000000 147.000000 8.705067E+02 8.655270E+02 4.188709E+02 5.186534E+02
80 196 n-080196 650.000000 82.000000 4.263688E+02 4.213478E+02 2.432930E+02 3.069559E+02
80 198 n-080198 173.000000 15.000000 3.743837E+02 3.691311E+02 1.954248E+02 2.447404E+02
80 199 n-080199 374.000000 23.000000 4.375384E+02 4.330742E+02 3.274788E+02 3.789767E+02
80 200 n-080200 115.000000 12.000000 2.488855E+02 2.383226E+02 9.729710E+01 1.189410E+02
80 201 n-080201 264.000000 14.000000 4.436143E+02 4.399589E+02 1.655447E+02 1.985520E+02
80 202 n-080202 74.000000 6.000000 1.356828E+02 1.171028E+02 4.774802E+01 5.605697E+01
80 203 n-080203 98.000000 17.000000 3.497037E+02 3.401677E+02 1.037485E+02 1.291886E+02
80 204 n-080204 42.000000 4.000000 5.632437E+01 4.499442E+01 1.565836E+01 1.944090E+01
81 203 n-081203 124.000000 8.000000 3.321219E+02 3.211944E+02 1.659021E+02 1.952169E+02
81 204 n-081204 215.000000 38.000000 4.989138E+02 4.897309E+02 1.930487E+02 2.239641E+02
81 205 n-081205 54.000000 4.000000 6.316836E+01 5.151866E+01 4.764542E+01 5.144757E+01
82 204 n-082204 89.500000 5.500000 1.500019E+02 1.364874E+02 8.069491E+01 9.232957E+01
82 205 n-082205 125.000000 22.000000 2.117684E+02 2.025131E+02 1.328585E+02 1.435016E+02
82 206 n-082206 15.800000 0.800000 7.134229E+00 5.525282E+00 2.694696E+01 2.434270E+01
82 207 n-082207 9.700000 1.300000 8.798019E-01 7.434698E-01 1.744930E+01 1.289054E+01
82 208 n-082208 0.360000 0.040000 3.311270E-01 3.886011E-01 2.301645E-01 3.235691E-01
83 209 n-083209 2.700000 0.480000 4.962499E+00 5.909774E+00 6.465640E+00 1.013332E+01
83 210 n-083210 6.000000 5.000000 8.601775E+00 9.000972E+00 1.376987E+01 2.095357E+01
84 210 n-084210 3.300000 3.000000 4.741924E+00 4.680534E+00 6.778359E+00 7.496910E+00
Appendix B – Charts and Figures
