The integrated response functions for:

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

tuple=xenon_1t_2018.response_functions[WD.SI,0.5]

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]

• 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

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