unified 10-slice fix fitted spectra

A.6 Erlang distribution

5.46 unified 10-slice fix fitted spectra

Chapter 6

Conclusions and prospects

One of the consequences of this study is that it can be used to provide predictions of the yields of these cosmogenic isotopes for future experiments. Previous studies ([28, 23, 20]) have shown that the yields of cosmogenic isotopes can be effectively modeled using the power law, that is

Y = Y₀

Eµ,avg

1GeV

(6.1)

where Y is the yield of a certain kind of cosmogenic isotope, E_µ is the muon energy, Y₀ and α are free parameters. Here we perform a global fit of the yields of⁹Li using data from this study and other experiments, namely Borexino, KamLAND and Double Chooz (DC). First we need to convert our results into yields which can be done by (for simplicity, we will be using the nGd results for this analysis)

Y = R9Li

R_µP_µL_avgρϵ_branchϵ_Gd (6.2)

where R⁹_Li is the⁹Li rate, R_µ is the muon rate, P_µ is the probability of muons passing through the GdLS region, Lavg is the average track length of the muon inside the GdLS region, ρ is the density of the materials inside the GdLS region, ϵ_branch is the branching ratio for β-n decays of⁹Li and ϵGd is the fraction of neutron captures on Gd inside the GdLS region. The values of these parameters are summarized in table 6.1.

Finally, we summarize the yields and average muon energies from various experiments in table 6.2, and a global fit using equation 6.1 is shown in figure 6.1.

Parameter EH1 EH2 EH3 R⁹_Li[d⁻¹] 5.87± 1.04 5.09 ± 0.85 0.60 ± 0.05

R_µ[Hz] 20.5 15.4 1.1

Pµ 62.36% 62.40% 62.42%

L_avg[cm] 204.1 204.5 204.9

δ(P_µL_avg) 5.53% 5.58% 3.80%

ρ[g/cm³] 0.86

ϵ_branch 50%

ϵ_Gd 85.4%

E_µ,avg[GeV] 63.9± 3.8 64.7± 3.9 143.0 ± 8.6

Table 6.1: Yield conversion parameters. Most of the parameters were estimated in a previous study of cosmogenic neutron productions [29].

Mean Muon Energy [GeV]

50 100 150 200 250 300

]2cm-1g-1µ-8 Yield [10

4 5 6 7 8 9 10 20 30

Lithium-9 Yield

DYB EH1 DYB EH2 DYB EH3 DC Near DC Far KamLAND Borexino Best Fit

Lithium-9 Yield

Figure 6.1: ⁹Li yield power-law fit. The fit gives Y₀ = (0.40± 0.10) × 10⁻⁸µ⁻¹g⁻¹cm² and α = 0.73± 0.05 with χ²/ndf = 3.4/5.

Mean Muon Energy [GeV]

50 100 150 200 250 300

]2cm-1g-1µ-7Yield [10

20 30 40 50 60

Boron-12 Yield

DYB EH1 DYB EH2 DYB EH3 KamLAND Borexino Boron-12 Yield

Figure 6.2: ¹²B yield power-law fit. The fit gives Y₀ = (1.27± 0.45) × 10⁻⁷µ⁻¹g⁻¹cm² and α = 0.65± 0.07 with χ²/ndf = 5.23/3.

Experiment E_µ,avg[GeV] Yield [10⁻⁷µ⁻¹g⁻¹cm²]

9Li ¹²B

Borexino 283± 19 2.9± 0.3 56± 3

KamLAND 260± 8 2.2± 0.2 42.9± 3.3

Double Chooz (Near) 32.1± 2.0 0.55± 0.05 -Double Chooz (Far) 63.7± 5.5 0.79± 0.05 -Daya Bay (EH1) 63.9± 3.8 0.71± 0.13 18.2 ± 2.0 Daya Bay (EH2) 64.7± 3.9 0.82± 0.14 21.4 ± 2.6 Daya Bay (EH3) 143.0± 8.6 1.40 ± 0.13 34.9 ± 4.4

Table 6.2: Summary of⁹Li and¹²B yields, and average muon energies for each experiment.

The data from other experiments were taken from [28, 23, 20].

Similarly, we can perform the yield analysis to isotope ¹²B using the results from section 5.2 and the data from KamLAND and Borexino. Note that the average muon track length for this analysis (L_avg = 258± 26 cm) is slightly longer than the previous one because we are now considering both LS and GdLS regions for the analysis. The yield is simply

Y¹²_B = R12B

R_µρL_avg (6.3)

where R¹²_Bcan be estimated using equation 5.2. The yields are also summarized in table 6.2. The result of the power-law fit is shown in figure 6.2

generation experiments such as the Jiangmen Underground Neutrino Observatory (JUNO) which is also a liquid scintillator based neutrino experiment that aims to measure the oscillation parameters with high precision. With an average muon energy∼215GeV [30], the power-law predicts the⁹Li yield to be∼ 19.7 × 10⁻⁸µ⁻¹g⁻¹cm² and¹²B yield to be

∼ 41.7 × 10⁻⁷µ⁻¹g⁻¹cm².

In this thesis, we have reviewed previous works on measuring cosmogenic isotopes⁹Li and⁸He, and built upon it to include spectral information to further enhance the method.

With the enormous amount of data acquired from the Daya Bay experiment, we have empirically showed that our method achieved consistent results with previous studies with similar or lower uncertainties on the rate estimations compared to previous methods that relied on the neutron tagging strategy which imposes strong assumptions on the relationship between spallation neutrons and cosmogenic isotopes. Our method, on the other hand, requires only a very loose assumption on the relationship between deposited energies of the decays of the isotopes and the originating muon energies. Aside from the rate measurements, we also used our method to measure the spectra of these isotopes directly through maximum likelihood estimation to check for consistencies between our predictions. Furthermore, by this method, we discovered some previously overlooked cosmogenic components in the analysis (i.e. ¹²B/¹²N induced accidentals) and compared with our predictions to support our claims. Finally, we have adopted this method to three different analysis schemes which, hopefully, can be used in future unified analysis of oscillations.

However, this method is not perfect as the slicing strategy is heavily reliant on the amount of data available which, fortunately, is the case for the Daya Bay experiment, also, the computation is quite intensive and volatile as it needs to simultaneously fit dozens of histograms with dozens of free parameters which would require careful tuning to work properly. Another thing of great importance is to test how our measurements of⁹Li and

8He might affect our measurements on the oscillation parameters. Unfortunately our local group is still at the early stages of the analysis and do not have the tools required to do such analysis at the time of this writing. Last but not least, remember that the enhancements of our model come from the spectral information of the cosmogenic isotopes, a natural question to ask is whether we can include the information from the muons to further enhance our model since we have imposed nearly no assumptions on the muons except for

their deposited energies and them following Poisson distributions. For example, in a recent work by the Double Chooz collaboration ([23]), they have included such information by considering the distances between the isotopes and the muons, and the number of neutrons after the muons.

Appendices

Appendix A

Review of probability theory

In this chapter we give a short review on probability theories. Readers interested in more rigorous discussions on the subject are referred to [31].

A.1 Random variables

In physical experiments, we often have to deal with outcomes that are stochastic in nature.

For example, the decay time of radioactive elements, the counts of of the muons passing through our detectors or the noise inside our instruments etc. Since they do not have a certain value and, in fact, can take on multiple values, they cannot be described using ordinary variables. To deal with these situations, a branch of mathematics, probability theory, was developed to tackle these problems.

In probability theory, we use random variables to describe outcomes that are stochastic in nature. Roughly speaking, a random variable is a function that maps the outcome to a value (usually a real number). For example, when we flip a coin, the possible outcome is either head or tail. We can then define a random variable X to map the outcome to 1 if it’s a head and 0 otherwise. The next thing we are interested in is to quantify how likely it is to be a head or a tail. This is usually denoted by P (X = 1) (probability of head) or P (X = 0) (probability of tail).

A.2 Distribution

Here is another example, in physical exaperiments, we often have to count the number of certain events that occur randomly¹ during a fixed period of time. We can then describe the counts by a random variable Y that maps the outcome (number of counts in a fixed period) to a natural number (0, 1, 2...), which we normally assume to follow the Poisson distribution which has the following form

P (Y = y) = n^ye⁻ⁿ

y! (A.1)

where n is the average count in the fixed period. The function P (Y = y) is usually called the probability mass function if the outcomes are finite or countably infinite, or the probability density function if the outcomes are uncountable, or simply probability distribution. Frankly speaking, the mass/density function encodes how likely each outcome will happen.

A.3 Joint distribution

Sometimes we may by interested in dealing with two random variables simultaneously.

For example, we would like to count two different processes at the same time. This can be modeled by two random variables X and Y which model the count of the first and the second process respectively. Since we have two variables, the probability mass function will now take in two variables to encode the probabilities of each outcome. That is P (X = x, Y = y), which is called the joint distribution of X and Y . Two random variables are called independent if P (X = x, Y = y) = P (X = x)P (Y = y). The above definition can be trivially extended beyond two random variables which we omit here.

A.4 Sum of two random variables

Continuing the above example, suppose we only care about the sum of the counts from both processes (denoted by Z = X + Y ) and not the individual process. The distribution

1In fact, “randomly” is a vague statement and can lead to vastly different properties when different kinds of randomness are concerned, but here let’s just assume they are Poisson process.

of Z can then be calculated by

P (Z = z) = P (X + Y = z) = Xz

k=0

P (X = z− k, Y = k). (A.2)

If we assume X and Y are independent, then Xz

k=0

P (X = z− k, Y = k) = Xz

k=0

P (X = z − k)P (Y = k) (A.3)

which is actually the convolution of the two distributions.

A.5 Poisson distribution

One of the most used distributions in experimental particle physics is the Poisson distribution. This distribution can be used to model the counts of independently arrived events which has the form in equation A.1. Another interesting property is that the inter-arrival time of consecutive event can be modelled by the exponential distribution, that is

P (Tinter-arrival = t) = λe^−λt (A.4)

where λ is the average of inter-arrival time.

A.6 Erlang distribution

In deriving the time-since-last-muon distribution, we are concerned about cases where the cosmogenic isotope and the originating muon are intervened by other uncorrelated muons. To describe the time between the isotope and its preceding muon, we need to consider the timing interval between the preceding muon and its originating muon. This can be achieved by summing n independent Poisson inter-arrival time random variables since we assumed they follow the Poisson distribution.

What we want is the distribution of U_n = P_n

i=1T_i where T_i’s are independent and identically distributed Poisson inter-arrival time random variables, which is also known

as the Erlang distribution. The Erlang distribution has the following form

P (U_n = t) = λⁿtⁿ⁻¹e^−λt

(n− 1)! (A.5)

where λ is the average of the inter-arrival time, which can be easily proved by induction.

For n = 1, the above formula holds trivially. For n = k, assume P (U_k = t) follows the above formula, then for n = k + 1 we have

P (U_k+1 = t) = P (U_k+ T_k+1 = t) (A.6)

= Z t

dxP (U_k = t− x)P (Tk+1 = x) (A.7)

= Z t

dxλ^k(t− x)^k⁻¹e^−λ(t−x)

(k− 1)! λe^−λx (A.8)

= λ^k+1e^−λt (k− 1)!

Z t 0

dx(t− x)^k⁻¹ (A.9)

= λ^k+1t^ke^−λt

k! (A.10)

which is just equation A.5, concluding our proof.

Appendix B

Reparameterization trick

In chapter 3, we discussed how to incorporate spectral information into our model which would require the minimization of the likelihood function under linear constraints

minL(θ, ϵ) (B.1)

subject to X

ϵ_i = 1 (B.2)

hereP

iϵ_i is a linear function of the ϵ’s hence linear constraint. Although many novel algorithms have been developed to solve such problems,MINUIT2, unfortunately, does not support any of them. However, it does support box constrained (a_i < ϵ_i < b_i) optimizations which can be exploited to solve our problem through a reparameterization.

In our parameterization, we set w₀ = 1 and let w_i ≥ 0 (i = 1, 2, ...) be free parameters.

This way, we can rewrite ϵ_iby

ϵ_i = w_i P

jw_j (B.3)

which has the properties (0 ≤ ϵi ≤ 1 andP

iϵ_i = 1) we needed. Another thing to note is that while we can estimate the ϵ_i’s this way, their uncertainties have to be calculated from the covariance matrix of the w_i’s. In general, the variance of the ratio of two random variables cannot be calculated analytically hence we will be using an approximation here, that is

Var[A B]≈

E[A]

E[B]

Var[A]

E[A]² +Var[B]

E[B]² − 2Cov[A, B]

E[A]E[B]

(B.4)

here Var is the variance of the random variable, Cov is the covariance of the two random variables and E is the expected value of the random variable. In our case, it would be

Var[ϵ_i] = Var[ w_i P

jw_j] (B.5)

= ϵ²_i σ_w²_i

w²_i +Var[P

jwj] (P

jw_j)² − 2Cov[wi,P

jwj] w_iP

jw_j

(B.6)

which can be easily calculated considering that MINUIT2 can estimate the covariance matrix during the default minimization routine (MIGRAD).

Appendix C

List of fitted parameters

For future reproducibilities, we list the fitted parameters and their corresponding errors in this chapter. Naming conventions are summarized in table C.1. Again, due to spacing issues, we will only be able to show the 4 slices fit paramters here. The values listed below are organized by µ/σ where µ is the maximum likelihood estimate and σ is its corresponding error, if σ = 0 then the parameter is considered fixed during the estimation.

Name Description

rmu_i Muon rate in muon regioni n_iso_i ⁹Li/⁸He rate in muon regioni

eps_iso_dc_v_s Slice parameter ϵ in variablev and slice s for component iso n_dc Muon uncorrelated IBD candidate rate

Table C.1: Naming convention for the fitting paramters. i=0(low),1(mid),2(high) muon regions.iso=li(⁹Li/⁸He),bo(¹²B),ni(¹²N). v=0(E_p),1(E_d),2(dist),3(dt).

s=0,1,...,n depending on the number of slices.

site EH1 EH2 EH3

rmu_0 1.178e-02/ 6.507e-06 8.118e-03/ 4.558e-06 5.825e-04/ 8.690e-07 n_li_0 1.024e-08/ 1.368e+00 7.758e-08/ 3.447e-01 9.874e-11/ 1.394e-02 n_bo_0 1.446e+00/ 1.371e-01 1.128e+00/ 1.411e-01 8.615e-02/ 1.226e-02 n_ni_0 1.270e-01/ 1.412e-01 4.084e-03/ 4.170e-01 1.560e-03/ 6.309e-03 rmu_1 8.614e-03/ 6.268e-06 7.127e-03/ 5.354e-06 4.616e-04/ 8.818e-07 n_li_1 8.595e-01/ 1.127e+00 1.497e+00/ 9.902e-01 1.407e-01/ 3.484e-02 n_bo_1 1.469e+00/ 1.264e-01 1.185e+00/ 1.480e-01 1.296e-01/ 1.477e-02 n_ni_1 3.247e-01/ 1.371e-01 8.492e-02/ 8.970e-02 7.669e-10/ 1.114e-02 rmu_2 1.441e-04/ 1.745e-07 1.412e-04/ 1.777e-07 1.374e-05/ 6.135e-08 n_li_2 4.620e+00/ 1.409e-01 3.750e+00/ 1.414e-01 4.492e-01/ 1.259e-02 n_bo_2 1.322e+00/ 8.334e-02 1.225e+00/ 1.338e-01 1.770e-01/ 1.823e-02 n_ni_2 9.426e-01/ 7.477e-02 5.191e-01/ 1.025e-01 8.696e-02/ 1.541e-02 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 7.222e-01/ 1.239e-03 7.285e-01/ 1.435e-03 7.240e-01/ 2.346e-03 eps_s_dc_0_2 4.775e-02/ 7.922e-04 4.846e-02/ 6.381e-04 4.853e-02/ 5.400e-04 eps_s_dc_0_3 1.022e-03/ 1.363e-04 7.808e-04/ 1.219e-04 6.218e-04/ 1.245e-04 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 9.594e-01/ 1.475e-01 1.219e+00/ 2.165e-01 1.186e+00/ 1.699e-01 eps_s_li_0_2 6.806e-01/ 7.914e-02 6.983e-01/ 1.030e-01 7.593e-01/ 9.358e-02 eps_s_li_0_3 1.080e-01/ 1.387e-02 1.241e-01/ 1.915e-02 1.584e-01/ 2.658e-02 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 7.532e-11/ 9.328e-02 8.484e-09/ 1.377e-01 1.369e-02/ 1.022e-01 eps_s_bo_0_2 1.876e-02/ 4.913e-02 2.259e-02/ 4.486e-02 1.060e-10/ 3.823e-02 eps_s_bo_0_3 6.251e-12/ 6.026e-03 8.330e-11/ 6.309e-03 8.369e-03/ 1.014e-02 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 2.035e-01/ 8.115e-02 1.492e-01/ 1.307e-01 4.877e-01/ 3.968e-01 eps_s_ni_0_2 2.467e-01/ 1.097e-01 2.693e-01/ 1.743e-01 4.725e-01/ 2.272e-01 eps_s_ni_0_3 1.328e-01/ 2.637e-02 1.907e-01/ 6.925e-02 2.979e-01/ 1.471e-01 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 5.992e+00/ 1.838e-02 6.270e+00/ 1.941e-02 5.947e+00/ 2.736e-02 eps_s_dc_1_2 7.325e-02/ 1.073e-03 7.851e-02/ 1.040e-03 7.494e-02/ 1.385e-03 eps_s_dc_1_3 3.003e-03/ 4.417e-04 2.557e-03/ 3.923e-04 2.027e-03/ 4.913e-04 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 4.591e+00/ 7.588e-01 5.219e+00/ 1.032e+00 4.657e+00/ 6.558e-01 eps_s_li_1_2 2.291e-01/ 5.681e-02 2.291e-01/ 6.982e-02 2.459e-01/ 6.000e-02 eps_s_li_1_3 7.571e-02/ 2.143e-02 7.142e-02/ 2.421e-02 1.045e-01/ 2.942e-02 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.178e+00/ 6.866e-01 6.512e-01/ 3.827e-01 9.495e-01/ 3.327e-01 eps_s_bo_1_2 8.951e-01/ 3.182e-01 5.801e-01/ 1.515e-01 5.580e-01/ 1.201e-01 eps_s_bo_1_3 5.931e-01/ 1.980e-01 3.390e-01/ 8.053e-02 2.517e-01/ 5.869e-02 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 7.333e-01/ 4.222e-01 2.128e+00/ 2.214e+00 5.894e-01/ 5.268e-01 eps_s_ni_1_2 5.684e-01/ 1.899e-01 1.295e+00/ 1.047e+00 8.123e-01/ 3.540e-01 eps_s_ni_1_3 2.072e-01/ 8.618e-02 5.980e-01/ 4.834e-01 5.371e-01/ 2.308e-01 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 8.255e-03/ 1.714e-04 7.642e-03/ 1.504e-04 9.562e-03/ 2.023e-04 eps_s_dc_2_2 2.745e-03/ 1.489e-04 2.341e-03/ 1.292e-04 4.205e-03/ 1.631e-04 eps_s_dc_2_3 7.516e-04/ 6.014e-05 6.599e-04/ 5.180e-05 1.220e-03/ 8.241e-05 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 7.104e-02/ 9.983e-03 6.135e-02/ 1.051e-02 7.973e-02/ 1.309e-02 eps_s_li_2_2 6.554e-02/ 8.157e-03 6.109e-02/ 8.455e-03 8.820e-02/ 1.282e-02 eps_s_li_2_3 6.217e-03/ 3.316e-03 9.743e-03/ 3.636e-03 1.242e-02/ 4.780e-03 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 1.296e+05/ 4.641e+04 4.236e+00/ 4.678e+00 1.226e+00/ 4.964e-01 eps_s_bo_2_2 1.739e+05/ 6.041e+04 4.916e+00/ 5.380e+00 1.584e+00/ 6.283e-01 eps_s_bo_2_3 5.345e+04/ 1.790e+04 1.242e+00/ 1.364e+00 4.422e-01/ 1.833e-01 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 9.426e-01/ 1.979e-01 1.368e+00/ 8.679e-01 1.537e+01/ 4.067e+01 eps_s_ni_2_2 4.791e-01/ 1.548e-01 5.634e-01/ 4.162e-01 7.688e+00/ 2.037e+01 eps_s_ni_2_3 2.070e-08/ 1.773e-01 1.229e-02/ 2.135e-01 7.724e-01/ 2.209e+00 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 2.150e-01/ 5.985e-04 2.146e-01/ 5.987e-04 2.188e-01/ 9.274e-04 eps_s_dc_3_2 4.254e-02/ 2.838e-04 4.264e-02/ 2.728e-04 4.476e-02/ 4.120e-04 eps_s_dc_3_3 1.238e-02/ 1.849e-04 1.188e-02/ 1.756e-04 1.347e-02/ 2.457e-04 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 2.262e-01/ 4.064e-02 2.350e-01/ 4.522e-02 2.271e-01/ 3.403e-02 eps_s_li_3_2 8.007e-02/ 1.865e-02 5.793e-02/ 1.943e-02 1.154e-01/ 1.949e-02 eps_s_li_3_3 5.105e-02/ 1.105e-02 4.533e-02/ 1.179e-02 5.248e-02/ 1.227e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.385e+00/ 1.164e+00 3.852e+00/ 4.521e+00 1.127e+00/ 4.983e-01 eps_s_bo_3_2 1.761e+00/ 1.136e+00 2.791e+00/ 3.263e+00 8.429e-01/ 3.302e-01 eps_s_bo_3_3 1.253e+00/ 7.787e-01 2.908e+00/ 3.355e+00 7.760e-01/ 2.842e-01 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_1 6.201e-01/ 4.041e-01 1.623e-01/ 3.080e-01 1.147e+00/ 1.205e+00 eps_s_ni_3_2 3.384e-01/ 2.262e-01 4.325e-01/ 2.848e-01 1.423e+00/ 1.260e+00 eps_s_ni_3_3 6.659e-01/ 2.675e-01 3.648e-01/ 2.226e-01 1.854e+00/ 1.551e+00 n_dc 7.215e+02/ 1.391e+00 6.395e+02/ 1.023e+00 7.584e+01/ 6.735e-02

Table C.2: nGd 4 slice free fit parameters.

site EH1 EH2 EH3

rmu_0 1.178e-02/ 6.703e-06 8.117e-03/ 4.418e-06 5.824e-04/ 8.668e-07 n_li_0 1.837e-07/ 1.665e+00 1.366e-07/ 3.359e-01 1.932e-14/ 1.397e-02 n_bo_0 1.562e+00/ 2.058e-01 1.270e+00/ 1.060e-01 8.916e-02/ 1.096e-02 n_ni_0 1.140e-01/ 1.432e-01 1.982e-02/ 6.230e-02 8.235e-04/ 1.018e-02 rmu_1 8.614e-03/ 5.815e-06 7.126e-03/ 4.365e-06 4.617e-04/ 8.713e-07 n_li_1 6.750e-01/ 9.167e-01 1.288e+00/ 5.529e-01 1.270e-01/ 3.142e-02 n_bo_1 1.594e+00/ 1.888e-01 1.356e+00/ 1.185e-01 1.335e-01/ 1.133e-02 n_ni_1 3.065e-01/ 1.417e-01 7.348e-02/ 7.610e-02 1.188e-10/ 1.025e-02 rmu_2 1.443e-04/ 1.709e-07 1.414e-04/ 1.714e-07 1.376e-05/ 6.083e-08 n_li_2 4.241e+00/ 1.155e-01 3.372e+00/ 1.027e-01 4.345e-01/ 1.134e-02 n_bo_2 1.473e+00/ 1.256e-01 1.441e+00/ 7.229e-02 1.918e-01/ 1.463e-02 n_ni_2 8.747e-01/ 1.022e-01 4.012e-01/ 6.731e-02 7.723e-02/ 1.254e-02 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 7.212e-01/ 1.313e-03 7.286e-01/ 1.375e-03 7.233e-01/ 2.282e-03 eps_s_dc_0_2 4.762e-02/ 8.461e-04 4.813e-02/ 4.796e-04 4.802e-02/ 5.215e-04 eps_s_dc_0_3 9.847e-04/ 1.417e-04 7.465e-04/ 8.337e-05 6.688e-04/ 1.064e-04 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 1.625e+00/ 0.000e+00 1.625e+00/ 0.000e+00 1.625e+00/ 0.000e+00 eps_s_li_0_2 1.182e+00/ 0.000e+00 1.182e+00/ 0.000e+00 1.182e+00/ 0.000e+00 eps_s_li_0_3 1.948e-01/ 0.000e+00 1.948e-01/ 0.000e+00 1.948e-01/ 0.000e+00 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 1.569e-09/ 3.203e-02 1.193e-02/ 8.636e-02 6.371e-10/ 7.212e-02 eps_s_bo_0_2 5.922e-09/ 3.163e-02 3.762e-12/ 2.674e-02 2.167e-13/ 1.320e-02 eps_s_bo_0_3 1.417e-11/ 3.914e-03 1.863e-11/ 3.843e-03 9.732e-03/ 9.498e-03 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 1.946e-01/ 8.498e-02 2.627e-01/ 4.094e-01 6.490e-01/ 4.731e-01 eps_s_ni_0_2 2.767e-01/ 7.040e-02 4.417e-01/ 1.998e-01 4.991e-01/ 2.766e-01 eps_s_ni_0_3 1.364e-01/ 3.331e-02 2.935e-01/ 1.247e-01 3.741e-01/ 2.057e-01 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 5.991e+00/ 1.815e-02 6.269e+00/ 1.668e-02 5.946e+00/ 2.729e-02 eps_s_dc_1_2 7.338e-02/ 1.062e-03 7.857e-02/ 9.495e-04 7.498e-02/ 1.382e-03 eps_s_dc_1_3 3.048e-03/ 4.378e-04 2.592e-03/ 3.563e-04 2.045e-03/ 4.902e-04 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 4.516e+00/ 8.063e-01 5.176e+00/ 1.008e+00 4.667e+00/ 6.752e-01 eps_s_li_1_2 2.370e-01/ 6.179e-02 2.417e-01/ 7.328e-02 2.481e-01/ 6.175e-02 eps_s_li_1_3 7.906e-02/ 2.325e-02 7.706e-02/ 2.560e-02 1.067e-01/ 3.039e-02 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.402e+00/ 7.357e-01 9.329e-01/ 2.353e-01 1.019e+00/ 3.190e-01 eps_s_bo_1_2 8.584e-01/ 2.956e-01 5.516e-01/ 9.397e-02 5.536e-01/ 1.164e-01 eps_s_bo_1_3 5.718e-01/ 1.857e-01 3.204e-01/ 4.429e-02 2.514e-01/ 5.732e-02 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 6.253e-01/ 4.360e-01 1.603e+00/ 1.433e+00 4.701e-01/ 5.139e-01 eps_s_ni_1_2 5.726e-01/ 2.001e-01 1.576e+00/ 9.483e-01 8.394e-01/ 4.015e-01 eps_s_ni_1_3 2.007e-01/ 8.985e-02 7.273e-01/ 4.298e-01 5.582e-01/ 2.616e-01 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 8.245e-03/ 1.668e-04 7.662e-03/ 1.316e-04 9.574e-03/ 2.015e-04 eps_s_dc_2_2 2.745e-03/ 1.450e-04 2.361e-03/ 1.106e-04 4.216e-03/ 1.624e-04 eps_s_dc_2_3 7.600e-04/ 6.033e-05 6.659e-04/ 5.000e-05 1.222e-03/ 8.225e-05 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 7.437e-02/ 1.102e-02 6.705e-02/ 1.135e-02 8.034e-02/ 1.337e-02 eps_s_li_2_2 6.935e-02/ 9.058e-03 6.693e-02/ 9.119e-03 8.950e-02/ 1.309e-02 eps_s_li_2_3 6.408e-03/ 3.604e-03 1.054e-02/ 3.929e-03 1.250e-02/ 4.889e-03 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 5.662e+00/ 6.450e+00 1.535e+00/ 2.752e-01 1.104e+00/ 2.260e-01 eps_s_bo_2_2 7.483e+00/ 8.329e+00 1.804e+00/ 2.959e-01 1.421e+00/ 2.663e-01 eps_s_bo_2_3 2.229e+00/ 2.701e+00 4.554e-01/ 1.270e-01 3.940e-01/ 8.648e-02 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 9.343e-01/ 3.295e-01 3.173e+00/ 3.476e+00 1.314e+04/ 3.197e+04 eps_s_ni_2_2 4.434e-01/ 2.191e-01 1.185e+00/ 1.339e+00 6.110e+03/ 1.505e+04 eps_s_ni_2_3 4.307e-09/ 7.111e-02 7.584e-06/ 1.144e+00 5.105e+02/ 1.489e+03 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 2.150e-01/ 5.918e-04 2.146e-01/ 5.309e-04 2.188e-01/ 9.254e-04 eps_s_dc_3_2 4.257e-02/ 2.800e-04 4.267e-02/ 2.491e-04 4.478e-02/ 4.111e-04 eps_s_dc_3_3 1.240e-02/ 1.822e-04 1.190e-02/ 1.595e-04 1.348e-02/ 2.452e-04 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 2.267e-01/ 4.442e-02 2.354e-01/ 4.548e-02 2.258e-01/ 3.484e-02 eps_s_li_3_2 8.185e-02/ 2.043e-02 5.870e-02/ 2.059e-02 1.157e-01/ 1.995e-02 eps_s_li_3_3 5.361e-02/ 1.210e-02 4.817e-02/ 1.263e-02 5.259e-02/ 1.254e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.031e+00/ 7.167e-01 1.800e+00/ 5.399e-01 1.037e+00/ 4.019e-01 eps_s_bo_3_2 1.267e+00/ 6.777e-01 1.233e+00/ 3.276e-01 7.689e-01/ 2.566e-01 eps_s_bo_3_3 8.958e-01/ 4.571e-01 1.268e+00/ 2.879e-01 7.070e-01/ 2.152e-01 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_1 6.774e-01/ 4.881e-01 1.040e-01/ 2.857e-01 1.366e+00/ 1.687e+00 eps_s_ni_3_2 3.594e-01/ 2.750e-01 5.910e-01/ 3.195e-01 1.806e+00/ 1.907e+00 eps_s_ni_3_3 7.430e-01/ 3.579e-01 5.037e-01/ 2.559e-01 2.394e+00/ 2.406e+00 n_dc 7.217e+02/ 1.234e+00 6.396e+02/ 6.001e-01 7.585e+01/ 6.637e-02

Table C.3: nGd 4 slice fix fit parameters.

site EH1 EH2 EH3

rmu_0 1.179e-02/ 1.007e-05 8.110e-03/ 6.576e-06 5.822e-04/ 7.928e-07 n_li_0 1.040e+00/ 1.132e+00 7.789e-01/ 6.838e-01 3.338e-02/ 2.560e-02 n_bo_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_1 8.608e-03/ 7.090e-06 7.134e-03/ 5.775e-06 4.624e-04/ 7.415e-07 n_li_1 2.316e+00/ 8.928e-01 5.050e-01/ 6.015e-01 1.120e-01/ 2.505e-02 n_bo_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_2 1.430e-04/ 2.043e-07 1.414e-04/ 2.084e-07 1.342e-05/ 5.255e-08 n_li_2 2.408e+00/ 9.790e-02 1.935e+00/ 9.010e-02 2.300e-01/ 9.187e-03 n_bo_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 3.572e-01/ 1.689e-03 3.587e-01/ 1.069e-03 1.731e-01/ 6.874e-04 eps_s_dc_0_2 1.762e-02/ 9.136e-04 1.841e-02/ 6.433e-04 8.764e-03/ 1.974e-04 eps_s_dc_0_3 1.186e-03/ 1.778e-04 9.759e-04/ 1.544e-04 3.109e-04/ 4.770e-05 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 1.398e+00/ 2.850e-01 9.343e-01/ 2.054e-01 1.531e+00/ 3.256e-01 eps_s_li_0_2 7.331e-01/ 1.224e-01 5.917e-01/ 9.543e-02 9.681e-01/ 1.916e-01 eps_s_li_0_3 1.322e-01/ 2.539e-02 1.340e-01/ 2.402e-02 1.835e-01/ 4.436e-02 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 3.096e+00/ 1.241e-02 3.186e+00/ 1.108e-02 1.652e+00/ 6.559e-03 eps_s_dc_1_2 2.945e+00/ 1.198e-02 3.161e+00/ 1.102e-02 1.676e+00/ 6.642e-03 eps_s_dc_1_3 7.435e-01/ 3.927e-03 8.001e-01/ 3.660e-03 1.071e+00/ 4.645e-03 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 3.976e+00/ 1.186e+00 3.090e+00/ 8.360e-01 3.739e+00/ 1.182e+00 eps_s_li_1_2 3.863e+00/ 1.157e+00 2.862e+00/ 7.878e-01 4.113e+00/ 1.287e+00 eps_s_li_1_3 9.233e-01/ 3.415e-01 6.114e-01/ 2.498e-01 8.397e-01/ 3.884e-01 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 2.492e+00/ 1.005e-02 2.492e+00/ 8.796e-03 2.886e+00/ 1.545e-02 eps_s_dc_2_2 2.262e+00/ 9.290e-03 2.256e+00/ 7.996e-03 3.531e+00/ 1.846e-02 eps_s_dc_2_3 1.785e+00/ 7.576e-03 1.792e+00/ 6.504e-03 4.165e+00/ 2.143e-02 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 2.136e+00/ 5.271e-01 3.440e+00/ 1.071e+00 2.381e+00/ 4.857e-01 eps_s_li_2_2 2.264e+00/ 5.482e-01 2.837e+00/ 9.089e-01 2.022e+00/ 4.440e-01 eps_s_li_2_3 1.597e+00/ 4.132e-01 1.605e+00/ 5.899e-01 1.433e+00/ 3.724e-01 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 4.592e-01/ 1.398e-03 4.621e-01/ 1.226e-03 6.177e-01/ 2.157e-03 eps_s_dc_3_2 2.953e-01/ 1.056e-03 2.999e-01/ 9.300e-04 5.012e-01/ 1.872e-03 eps_s_dc_3_3 1.991e-01/ 8.363e-04 2.032e-01/ 7.470e-04 4.305e-01/ 1.691e-03 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 4.528e-01/ 8.648e-02 4.162e-01/ 9.308e-02 4.160e-01/ 7.869e-02 eps_s_li_3_2 2.821e-01/ 6.483e-02 3.102e-01/ 7.373e-02 2.985e-01/ 6.692e-02 eps_s_li_3_3 1.999e-01/ 5.205e-02 1.371e-01/ 5.413e-02 1.327e-01/ 5.288e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 n_dc 5.092e+02/ 1.543e+00 4.596e+02/ 9.931e-01 9.840e+01/ 7.627e-02

Table C.4: nH 4 slice free fit parameters.

site EH1 EH2 EH3

rmu_0 1.179e-02/ 9.486e-06 8.110e-03/ 6.523e-06 5.821e-04/ 7.972e-07 n_li_0 8.652e-01/ 9.799e-01 8.099e-01/ 6.726e-01 3.783e-02/ 2.729e-02 n_bo_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_1 8.608e-03/ 6.747e-06 7.135e-03/ 5.733e-06 4.623e-04/ 7.424e-07 n_li_1 2.141e+00/ 7.892e-01 3.742e-01/ 5.624e-01 1.215e-01/ 2.547e-02 n_bo_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_2 1.431e-04/ 1.997e-07 1.415e-04/ 2.035e-07 1.341e-05/ 5.176e-08 n_li_2 2.323e+00/ 7.666e-02 1.872e+00/ 6.916e-02 2.344e-01/ 8.190e-03 n_bo_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 3.582e-01/ 1.192e-03 3.581e-01/ 1.038e-03 1.731e-01/ 6.589e-04 eps_s_dc_0_2 1.741e-02/ 9.064e-04 1.818e-02/ 7.260e-04 8.734e-03/ 1.840e-04 eps_s_dc_0_3 1.252e-03/ 1.430e-04 1.099e-03/ 1.157e-04 3.495e-04/ 3.638e-05 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 1.259e+00/ 0.000e+00 1.259e+00/ 0.000e+00 1.259e+00/ 0.000e+00 eps_s_li_0_2 8.272e-01/ 0.000e+00 8.272e-01/ 0.000e+00 8.272e-01/ 0.000e+00 eps_s_li_0_3 1.256e-01/ 0.000e+00 1.256e-01/ 0.000e+00 1.256e-01/ 0.000e+00 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 3.096e+00/ 1.154e-02 3.186e+00/ 1.099e-02 1.652e+00/ 6.568e-03 eps_s_dc_1_2 2.945e+00/ 1.108e-02 3.161e+00/ 1.092e-02 1.675e+00/ 6.652e-03 eps_s_dc_1_3 7.436e-01/ 3.730e-03 8.001e-01/ 3.629e-03 1.071e+00/ 4.652e-03 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 4.012e+00/ 1.152e+00 3.083e+00/ 8.576e-01 3.678e+00/ 1.128e+00 eps_s_li_1_2 3.897e+00/ 1.113e+00 2.851e+00/ 8.071e-01 4.044e+00/ 1.226e+00 eps_s_li_1_3 9.312e-01/ 3.414e-01 6.043e-01/ 2.554e-01 8.439e-01/ 3.777e-01 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 2.492e+00/ 9.674e-03 2.492e+00/ 8.726e-03 2.886e+00/ 1.549e-02 eps_s_dc_2_2 2.262e+00/ 8.883e-03 2.256e+00/ 7.927e-03 3.531e+00/ 1.851e-02 eps_s_dc_2_3 1.785e+00/ 7.295e-03 1.792e+00/ 6.447e-03 4.165e+00/ 2.149e-02 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 2.124e+00/ 5.312e-01 3.469e+00/ 1.111e+00 2.386e+00/ 4.819e-01 eps_s_li_2_2 2.264e+00/ 5.465e-01 2.851e+00/ 9.406e-01 2.036e+00/ 4.417e-01 eps_s_li_2_3 1.589e+00/ 4.172e-01 1.591e+00/ 6.052e-01 1.455e+00/ 3.712e-01 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 4.592e-01/ 1.366e-03 4.621e-01/ 1.217e-03 6.178e-01/ 2.161e-03 eps_s_dc_3_2 2.953e-01/ 1.032e-03 2.999e-01/ 9.236e-04 5.013e-01/ 1.876e-03 eps_s_dc_3_3 1.991e-01/ 8.231e-04 2.031e-01/ 7.422e-04 4.306e-01/ 1.694e-03 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 4.528e-01/ 8.959e-02 4.146e-01/ 9.594e-02 4.184e-01/ 7.798e-02 eps_s_li_3_2 2.815e-01/ 6.716e-02 3.108e-01/ 7.606e-02 3.007e-01/ 6.628e-02 eps_s_li_3_3 1.999e-01/ 5.463e-02 1.355e-01/ 5.572e-02 1.358e-01/ 5.238e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 n_dc 5.096e+02/ 1.339e+00 4.598e+02/ 9.690e-01 9.839e+01/ 7.615e-02

Table C.5: nH 4 slice fix fit parameters.

site EH1 EH2 EH3

rmu_0 1.178e-02/ 5.181e-06 8.114e-03/ 3.605e-06 5.820e-04/ 3.437e-07 n_li_0 2.896e+00/ 1.703e+00 1.177e+00/ 1.101e+00 3.755e-02/ 3.829e-02 n_bo_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_1 8.615e-03/ 3.742e-06 7.126e-03/ 3.155e-06 4.619e-04/ 3.212e-07 n_li_1 3.780e+00/ 1.321e+00 3.080e+00/ 1.046e+00 2.431e-01/ 3.958e-02 n_bo_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_2 1.436e-04/ 1.162e-07 1.411e-04/ 1.176e-07 1.347e-05/ 2.331e-08 n_li_2 6.671e+00/ 1.729e-01 5.485e+00/ 1.585e-01 6.257e-01/ 1.936e-02 n_bo_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 4.350e-01/ 8.235e-04 4.309e-01/ 7.171e-04 1.139e-01/ 2.316e-04 eps_s_dc_0_2 2.823e-02/ 5.418e-04 2.866e-02/ 3.973e-04 7.629e-03/ 7.071e-05 eps_s_dc_0_3 7.625e-04/ 1.045e-04 5.892e-04/ 8.794e-05 1.300e-04/ 1.537e-05 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 1.448e+00/ 2.089e-01 1.315e+00/ 1.991e-01 2.102e+00/ 4.042e-01 eps_s_li_0_2 9.925e-01/ 1.142e-01 8.163e-01/ 9.755e-02 1.378e+00/ 2.501e-01 eps_s_li_0_3 1.851e-01/ 2.250e-02 1.761e-01/ 2.174e-02 3.116e-01/ 6.058e-02 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 6.500e-02/ 2.421e-04 6.356e-02/ 2.147e-04 1.577e-02/ 8.178e-05 eps_s_dc_1_2 5.931e-01/ 9.936e-04 5.828e-01/ 8.794e-04 1.385e-01/ 2.626e-04 eps_s_dc_1_3 2.315e-04/ 2.044e-05 2.261e-04/ 1.597e-05 5.679e-05/ 6.298e-06 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 1.836e-01/ 2.909e-02 1.453e-01/ 2.861e-02 1.531e-01/ 2.664e-02 eps_s_li_1_2 1.261e+00/ 1.322e-01 1.169e+00/ 1.332e-01 1.309e+00/ 1.495e-01 eps_s_li_1_3 1.324e-02/ 2.651e-03 9.605e-03/ 2.397e-03 1.536e-02/ 4.558e-03 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 3.121e+00/ 7.348e-03 3.124e+00/ 7.124e-03 3.879e+00/ 1.141e-02 eps_s_dc_2_2 3.298e+00/ 7.791e-03 3.302e+00/ 7.484e-03 6.082e+00/ 1.723e-02 eps_s_dc_2_3 2.957e+00/ 7.406e-03 2.983e+00/ 6.933e-03 8.478e+00/ 2.358e-02 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 2.740e+00/ 3.914e-01 2.971e+00/ 5.231e-01 2.762e+00/ 3.949e-01 eps_s_li_2_2 2.542e+00/ 3.737e-01 2.963e+00/ 5.254e-01 2.646e+00/ 4.044e-01 eps_s_li_2_3 1.531e+00/ 2.700e-01 1.958e+00/ 3.910e-01 1.464e+00/ 3.174e-01 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 2.584e-01/ 4.739e-04 2.614e-01/ 4.695e-04 5.839e-01/ 9.306e-04 eps_s_dc_3_2 1.829e-01/ 3.892e-04 1.871e-01/ 3.778e-04 5.411e-01/ 8.837e-04 eps_s_dc_3_3 1.492e-01/ 3.535e-04 1.536e-01/ 3.430e-04 5.218e-01/ 8.631e-04 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 1.742e-01/ 2.767e-02 1.461e-01/ 2.987e-02 1.723e-01/ 3.609e-02 eps_s_li_3_2 1.044e-01/ 2.253e-02 1.125e-01/ 2.523e-02 1.374e-01/ 3.412e-02 eps_s_li_3_3 6.407e-02/ 1.986e-02 6.852e-02/ 2.222e-02 4.270e-02/ 3.084e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_rni_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 n_dc 1.595e+03/ 2.230e+00 1.438e+03/ 1.619e+00 5.007e+02/ 1.636e-01

Table C.6: Unified 4 slice free fit parameters.

site EH1 EH2 EH3

rmu_0 1.178e-02/ 5.171e-06 8.114e-03/ 3.553e-06 5.820e-04/ 3.454e-07 n_li_0 2.769e+00/ 1.693e+00 1.164e+00/ 1.057e+00 4.644e-02/ 4.280e-02 n_bo_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_0 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_1 8.615e-03/ 3.700e-06 7.127e-03/ 3.104e-06 4.619e-04/ 3.217e-07 n_li_1 3.737e+00/ 1.278e+00 2.804e+00/ 9.937e-01 2.669e-01/ 4.098e-02 n_bo_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_1 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 rmu_2 1.437e-04/ 1.132e-07 1.412e-04/ 1.145e-07 1.346e-05/ 2.278e-08 n_li_2 6.528e+00/ 1.304e-01 5.220e+00/ 1.179e-01 6.403e-01/ 1.538e-02 n_bo_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 n_ni_2 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 0.000e+00/ 0.000e+00 eps_s_dc_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_0_1 4.349e-01/ 7.231e-04 4.308e-01/ 6.276e-04 1.139e-01/ 2.245e-04 eps_s_dc_0_2 2.803e-02/ 5.738e-04 2.832e-02/ 4.464e-04 7.581e-03/ 6.909e-05 eps_s_dc_0_3 8.033e-04/ 9.679e-05 6.573e-04/ 7.528e-05 1.572e-04/ 1.169e-05 eps_s_li_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_0_1 1.625e+00/ 0.000e+00 1.625e+00/ 0.000e+00 1.625e+00/ 0.000e+00 eps_s_li_0_2 1.182e+00/ 0.000e+00 1.182e+00/ 0.000e+00 1.182e+00/ 0.000e+00 eps_s_li_0_3 1.948e-01/ 0.000e+00 1.948e-01/ 0.000e+00 1.948e-01/ 0.000e+00 eps_s_bo_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_0_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_1_1 6.500e-02/ 2.427e-04 6.357e-02/ 2.138e-04 1.576e-02/ 8.197e-05 eps_s_dc_1_2 5.931e-01/ 9.950e-04 5.828e-01/ 8.767e-04 1.384e-01/ 2.638e-04 eps_s_dc_1_3 2.317e-04/ 2.048e-05 2.265e-04/ 1.591e-05 5.648e-05/ 6.336e-06 eps_s_li_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_1_1 1.872e-01/ 2.998e-02 1.510e-01/ 3.073e-02 1.473e-01/ 2.485e-02 eps_s_li_1_2 1.281e+00/ 1.366e-01 1.210e+00/ 1.443e-01 1.261e+00/ 1.345e-01 eps_s_li_1_3 1.364e-02/ 2.721e-03 1.027e-02/ 2.569e-03 1.464e-02/ 4.280e-03 eps_s_bo_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_1_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_2_1 3.121e+00/ 7.276e-03 3.124e+00/ 7.093e-03 3.879e+00/ 1.143e-02 eps_s_dc_2_2 3.298e+00/ 7.733e-03 3.302e+00/ 7.452e-03 6.083e+00/ 1.727e-02 eps_s_dc_2_3 2.957e+00/ 7.342e-03 2.982e+00/ 6.904e-03 8.479e+00/ 2.364e-02 eps_s_li_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_2_1 2.734e+00/ 3.935e-01 2.963e+00/ 5.437e-01 2.773e+00/ 3.927e-01 eps_s_li_2_2 2.531e+00/ 3.766e-01 2.948e+00/ 5.449e-01 2.674e+00/ 4.039e-01 eps_s_li_2_3 1.509e+00/ 2.704e-01 1.915e+00/ 4.013e-01 1.518e+00/ 3.158e-01 eps_s_bo_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_2_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_dc_3_1 2.584e-01/ 4.734e-04 2.614e-01/ 4.675e-04 5.840e-01/ 9.325e-04 eps_s_dc_3_2 1.829e-01/ 3.884e-04 1.870e-01/ 3.762e-04 5.412e-01/ 8.855e-04 eps_s_dc_3_3 1.492e-01/ 3.528e-04 1.536e-01/ 3.415e-04 5.219e-01/ 8.650e-04 eps_s_li_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_li_3_1 1.728e-01/ 2.813e-02 1.415e-01/ 3.090e-02 1.762e-01/ 3.566e-02 eps_s_li_3_2 1.031e-01/ 2.285e-02 1.096e-01/ 2.615e-02 1.414e-01/ 3.370e-02 eps_s_li_3_3 6.259e-02/ 2.015e-02 6.512e-02/ 2.298e-02 4.753e-02/ 3.038e-02 eps_s_bo_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_bo_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_0 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_1 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_2 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 eps_s_ni_3_3 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 1.000e+00/ 0.000e+00 n_dc 1.595e+03/ 2.178e+00 1.438e+03/ 1.534e+00 5.007e+02/ 1.636e-01

Table C.7: Unified 4 slice fix fit parameters.

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