def dsigmadERdEb_bs(Eb, ER, v, mDM, sigma_nucleon):
halo_model = hm.HaloModels()
v_max = hm.v_max(halo_model.v_esc)
if Eb > DMNR.mu_T(mDM) * v_max**2 / 2.:
ret = 0.
else:
# X-ray form factor
F_atomic = np.abs(f1_Ar(Eb / nu.keV) + 1j * f2_Ar(Eb / nu.keV))
ret = (4 * nu.alphaFS / (3 * np.pi * Eb) * ER / (DMNR.mT() * nu.c0**2)
* F_atomic**2 * DMNR.dsigmadER(ER, v, mDM, sigma_nucleon))
return ret
def rate_NR(ER, mDM, sigma_nucleon):
halo_model = hm.HaloModels()
v_min = vmin_el(ER, mDM)
v_max = hm.v_max(halo_model.v_esc)
if v_min >= v_max:
return 0
def integrand(v):
return (dsigmadER(ER, v, mDM, sigma_nucleon) * v *
halo_model.velocity_dist_SHM(v))
ret = halo_model.rho_DM / mDM / mT() * quad(integrand, v_min, v_max)[0]
return ret
def rate_migdalN(Ne, mDM, sigma_nucleon, nstate):
E = LAr.Eer(Ne)
halo_model = hm.HaloModels()
ME_rate = 0
for state, E_binding in Enl_migdal.items():
E_binding *= nu.eV
if nstate == 1:
if state[0] not in ['1']:
continue
elif nstate == 2:
if state[0] not in ['2']:
continue
elif nstate == 3:
if state[0] not in ['3']:
continue
elif nstate == 12:
if state[0] not in ['1','2']:
continue
prob = interp1d(df_migdal['E'].values * nu.eV,
df_migdal[state].values / nu.eV,
bounds_error=False,fill_value=0)
def diff_rate(v, ER):
Ee = E - E_binding
if Ee < 0:
return 0
dsdER = DMNR.dsigmadER(ER, v, mDM, sigma_nucleon)
SMHalo = halo_model.velocity_dist_SHM(v)
#rescale the probability, see note added in 1707.07258
qe2 = (nu.me * (2 * ER / DMNR.mT())**0.5 / (nu.eV / nu.c0))**2
return (dsdER * v * SMHalo * qe2 / (2 * pi) * prob(Ee))
r = dblquad(diff_rate, 0, DMNR.Emax(mDM, hm.v_max(halo_model.v_esc), DMNR.mT()),
lambda ER: vmin_ME(E, ER, mDM), lambda _: hm.v_max(halo_model.v_esc))[0]
ME_rate += r
rateE = halo_model.rho_DM / mDM / DMNR.mT() * ME_rate
rateN = LAr.dEerdN(Ne)*rateE
return rateN
def rate_bremsstrahlung(Eb, mDM, sigma_nucleon):
halo_model = hm.HaloModels()
rhoDM = halo_model.rho_DM
v_min = vmin_bs(Eb, mDM)
v_max = hm.v_max(halo_model.v_esc)
if v_min >= v_max:
return 0
def sigma(v):
return (dsigmadEb(Eb, v, mDM, sigma_nucleon) * v * halo_model.velocity_dist_SHM(v))
ret = rhoDM / mDM / DMNR.mT() * quad(sigma,v_min,v_max)[0]
return ret