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The integrated response functions for:

• the xenon_1t_2018.response_functions experiment;
• the WD.SI effective Hamiltonian;
• $$j_\chi=\frac{1}{2}$$

are contained in the tuple:
tuple=xenon_1t_2018.response_functions[WD.SI,0.5]

In particular the table for
$$\left [\bar{{\cal R}}^{a}_{T,[E_1^{\prime},E_2^{\prime}]}\right ]_{jk}^{\tau\tau^{\prime}}(E_R)$$
can be accessed by:
er=tuple[n_coeff_squared]][n_vel][tau][tau_prime][n_bin][n_element][0]
r=tuple[n_coeff_squared][n_vel][tau][tau_prime][n_bin][n_element][n_isotope+1]

where:
• n_coeff_squared$$\rightarrow$$ index pointing to one of the products $${\cal O}_j{\cal O}_k$$ of the operators of the effective Hamiltonian $${\cal H}=\sum_{\tau=0,1} \sum_{j} c_j^{\tau}(w_i,q) {\cal O}_{j}^{\tau}$$ that contribute to the squared amplitude. Such contributions are listed in:
>>>WD.SI.coeff_squared_list
[(1, 1)]
so n_coeff_squared is one of the values contained in the list:
>>>list(range(len(WD.SI.coeff_squared_list)))
[0]
(for the WD.SI Hamiltonian only the $${\cal O}_1{\cal O}_1$$ combination is present).

• n_vel=0,1,2,3$$\rightarrow a=0,1,1E,1E^{-1}$$
tau,tau_prime$$\rightarrow \tau=0,1$$

• n_bin$$\rightarrow$$ index of the tuple xenon_1t_2018.data corresponding to one of the energy bins $$[E_1^{\prime},E_2^{\prime}]$$, i.e. one of the values contained in the list:
>>>list(range(len(xenon_1t_2018.data)))
[0]
(in this case only one energy bin (i.e. one line) included in data.tab).

• n_element $$\rightarrow$$ index of the xenon_1t_2018.target.element array containing the elements of the target, i.e. one of the values contained in the list:
>>>list(range(len(xenon_1t_2018.target.element)))
[0]
(in this case only xenon contained in the xenon_1t_2018.target.element array).

• n_isotope $$\rightarrow$$ index of one of the isotopes of xenon_1t_2018.target.element[n_element], i.e. one of the values contained in the list:
>>>list(range(xenon_1t_2018.target.element[0].n_isotopes))
[0, 1, 2, 3, 4, 5, 6, 7, 8]
There are 9 xenon isotopes, they can be printed by:
>>>xenon_1t_2018.target.element[0].isotopes
['124Xe', '126Xe', '128Xe', '129Xe', '130Xe', '131Xe', '132Xe',
'134Xe', '136Xe']

#### Example 1

• Xenon1T experiment $$\rightarrow$$ WD.XENON_1T_2018
• Hamiltonian $${\cal H}=\sum_{\tau=0,1} c_1^{\tau}(w_i,q) {\cal O}_{1}^{\tau}$$ $$\rightarrow$$ WD.SI.coeff_squared_list=[(1, 1)] ;
• $$j_\chi$$=1/2;
• $$^{129}Xe$$ target $$\rightarrow$$ n_element=0, n_isotope=3
• $$[3PE,70PE]$$ energy bin $$\rightarrow$$ n_bin=0
• $${\cal O}_1{\cal O}_1$$ contribution $$\rightarrow$$ n_coeff_squared=0
• $$\tau$$=0, $$\tau^{\prime}$$=1 $$\rightarrow$$ tau=0, tau_prime=1
• $$a=1E$$ $$\rightarrow$$ n_vel=2
$$\left [\bar{{\cal R}}^{1E}_{^{129}Xe,[3PE,70PE]}\right ]_{11}^{01}(E_R)$$ $$\rightarrow$$ xenon_1t_2018.response_functions[WD.SI,0.5][0][2][0][1][0][0][4]

#### Example 2

• Xenon1T experiment $$\rightarrow$$ WD.XENON_1T_2018
• Hamiltonian $${\cal H}=\sum_{\tau=0,1}\left [ c_4^{\tau}(w_i,q) {\cal O}_{4}^{\tau}+ c_6^{\tau}(w_i,q) {\cal O}_{6}^{\tau}\right ]$$ $$\rightarrow$$ coeff_squared_list=[(4, 4), (4, 6), (6, 4), (6, 6)] ;
• $$j_\chi$$=1/2;
• $$^{131}Xe$$ target $$\rightarrow$$ n_element=0, n_isotope=5
• $$[3PE,70PE]$$ energy bin $$\rightarrow$$ n_bin=0
• $${\cal O}_6{\cal O}_4$$ contribution $$\rightarrow$$ n_coeff_squared=2
• $$\tau$$=1, $$\tau^{\prime}$$=1 $$\rightarrow$$ tau=0, tau_prime=1
• $$a=1E^{-1}$$ $$\rightarrow$$ n_vel=3
$$\left [\bar{{\cal R}}^{1E^{-1}}_{^{129}Xe,[3PE,70PE]}\right ]_{64}^{11}(E_R)$$ $$\rightarrow$$ xenon_1t_2018.response_functions[WD.SI,0.5][2][3][1][1][0][0][6]