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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:

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:

  • 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:
    [(1, 1)]
    so n_coeff_squared is one of the values contained in the list:
    (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:
    (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:
    (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:
    [0, 1, 2, 3, 4, 5, 6, 7, 8] 
    There are 9 xenon isotopes, they can be printed by:
    ['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]