def plot_ibd(nu_spec):
figure = plt.figure()
e_arr = np.linspace(0., 55e6, 1000)
# IBD Cross Section
xsec_ibd_0th = total_XSec_ibd_0th(e_arr)
plt.plot(e_arr*1e-6,xsec_ibd_0th*1.e42, color='red', linestyle="--", label=r'0$^{th}$ Order')
xsec_ibd = total_XSec_ibd(e_arr)
plt.plot(e_arr*1e-6,xsec_ibd*1.e42, color='blue', linestyle=":", label=r'1$^{st}$ Order')
plt.xlabel("Energy (MeV)")
plt.ylabel(r'Cross Section ($10^{-42}$ cm$^2$)')
plt.title("IBD Cross Section")
plt.legend()
plt.grid()
plt.xlim(0., 10.)
plt.ylim(0., 10.)
plt.savefig("plots/ibd_xsec.png")
def f(x, a, b):
if x<b:
return 0.
else:
return a*(x-b)**2
f = np.vectorize(f)
res = curve_fit(f, e_arr, xsec_ibd_0th, [1.e-42, 1.e6])
print("a*(x-b)^2 Fit Parameters: %s"%res[0])
def compare_ibd_cevns(nu_spec):
figure = plt.figure()
e_arr = np.linspace(0., 55e6, 1000)
# CEvNS Cross Sections
xsec_Cs = total_XSec_cns(0., e_arr, 55., 132.9-55.)
plt.semilogy(e_arr*1e-6,xsec_Cs*1.e38, color='blue', linestyle="--", label=r'CEvNS Cs')
xsec_I = total_XSec_cns(0., e_arr, 53., 126.9-53.)
plt.semilogy(e_arr*1e-6,xsec_I*1.e38, color='blue', linestyle=":", label=r'CEvNS I')
xsec_Ge = total_XSec_cns(0., e_arr, 32., 72.64-32.)
plt.semilogy(e_arr*1e-6,xsec_Ge*1.e38, color='green', linestyle="-.", label=r'CEvNS Ge')
# IBD Cross Section
xsec_ibd = total_XSec_ibd(e_arr)
plt.semilogy(e_arr*1e-6,xsec_ibd*1.e38, color='red', linestyle="-", label=r'IBD')
plt.xlabel("Energy (MeV)")
plt.ylabel(r'Cross Section ($10^{-38}$ cm$^2$)')
plt.legend()
plt.grid()
plt.xlim(0., 10.)
plt.ylim(1.e-6, 1.e0)
plt.savefig("plots/ibd_cevns_xsec.png")
plt.xlim(5., 55.)
plt.ylim(4.e-4, 3.e1)
plt.savefig("plots/ibd_coherent_plot.png")
def fit_daya_bay_data():
fig1, (a0, a1) = plt.subplots(2, 1,
gridspec_kw={'height_ratios': [2, 1],})
plt.subplots_adjust(bottom=0.075, top=0.95)
#sharex=True)
fig1.patch.set_facecolor('white')
fig1.set_figheight(8.5)
# Plot data from Daya Bay paper arXiv:1607.05378v2
db_data = np.loadtxt("data/daya_bay_unfolded_spectrum.csv", delimiter=",")
bin_low = db_data[:,0]
bin_high = db_data[:,1]
xvals = (bin_low+bin_high)/2.
bin_widths = bin_high-bin_low
yvals = db_data[:,2]
yerrs = np.sqrt(db_data[:,3])
a0.errorbar(xvals, yvals, yerr=yerrs, xerr=bin_widths/2.,
color='k', linestyle='None',
label="Daya Bay Data")
# Huber/Mueller Prediction for Daya Bay
# Mueller spectra
nu_spec_mueller = NeutrinoSpectrum(nu_spec.distance, nu_spec.power, True,
0.561, 0.076, 0.307, 0.056) # Daya Bay Numbers (arXiv:1607.05378v2)
nu_spec_mueller.initialize_d_r_d_enu("u235", "txt",
"../../data/huber/U235-anti-neutrino-flux-250keV.dat")
nu_spec_mueller.initialize_d_r_d_enu("u238", "mueller")
nu_spec_mueller.initialize_d_r_d_enu("pu239", "txt",
"../../data/huber/Pu239-anti-neutrino-flux-250keV.dat")
nu_spec_mueller.initialize_d_r_d_enu("pu241", "txt",
"../../data/huber/Pu241-anti-neutrino-flux-250keV.dat")
nu_spec_mueller.initialize_d_r_d_enu("other", "mueller")
pred_spectrum = []
for i in range(len(bin_low)):
res = spint.quad(lambda e_eV:
nu_spec_mueller.d_phi_d_enu_ev(e_eV)*\
total_XSec_ibd(e_eV),
bin_low[i]*1.e6, bin_high[i]*1.e6)[0]
res /= (bin_high[i]-bin_low[i])
res *= 1.e46/nu_spec.nuFlux() # Convert to cm^2/fission/MeV x 10^-46
pred_spectrum.append(res)
a0.errorbar(xvals, pred_spectrum, xerr=bin_widths/2.,
color='r', linestyle='None',
label="Huber/Mueller Prediction")
# Plot Settings
a0.legend()
a0.set_xlim(1.8, 8.4)
a0.set(ylabel=r'$\phi_{\bar{\nu}_e}*\sigma_{IBD}$ (cm^2/fission/MeV $\times$ 10^-46)')
a1.errorbar(xvals, yvals/pred_spectrum,
xerr=bin_widths/2., yerr=yerrs/yvals,
color='k', linestyle='None')
a1.plot(xvals, xvals*0.+1., color='k')
a1.set_xlim(1.8, 8.4)
a1.set_ylim(0.6, 1.25)
a1.set(xlabel="Antineutrino Energy (MeV)",
ylabel="Ratio")
plt.savefig("plots/fit_daya_bay_plot_reproduction.png")
# Fit the spectrum
fig1, (a0, a1) = plt.subplots(2, 1,
gridspec_kw={'height_ratios': [2, 1],})
plt.subplots_adjust(bottom=0.075, top=0.95)
#sharex=True)
fig1.patch.set_facecolor('white')
fig1.set_figheight(8.5)
def get_bin(x):
if(x<bin_low[0]):
return -1
for i in range(0, len(bin_low)):
if(bin_low[i]<=x and
x<bin_high[i]):
return i
return len(bin_low)
def f(x, k0, b0, mu, sig):
i = get_bin(x)
if(i<0 or i>=len(bin_low)):
return 0.
else:
return k0*pred_spectrum[get_bin(x)]+b0*np.exp(-(x-mu)**2/ (2*sig**2))*total_XSec_ibd(x*1.e6)
f = np.vectorize(f)
x_fit = xvals[np.logical_and(3.<xvals, xvals<7.5)]
y_fit = yvals[np.logical_and(3.<xvals, xvals<7.5)]
res = curve_fit(f, x_fit, y_fit, [1., 1.e44, 5.7, 0.5])
print("Unfolded Spectrum Fit Parameters: %s"%res[0])
a0.errorbar(xvals, yvals, yerr=yerrs, xerr=bin_widths/2.,
color='k', linestyle='None',
label="Daya Bay Data")
a0.errorbar(xvals, res[0][0]*np.array(pred_spectrum),
xerr=bin_widths/2.,
color='red', linestyle='None',
label="Huber/Mueller Rescaled")
a0.errorbar(xvals, f(xvals, *res[0]),
xerr=bin_widths/2.,
color='blue', linestyle='None',
label=r'Huber/Mueller+Gaussian*$\sigma_{IBD}$ Fit')
a0.legend()
a0.set_xlim(3., 7.5)
a0.set(ylabel=r'$\phi_{\bar{\nu}_e}*\sigma_{IBD}$ (cm^2/fission/MeV $\times$ 10^-46)',
title=r'Reactor Spectrum Gaussian Fit: $\mu$=%.2f, $\sigma=$%.3f'%(res[0][2], res[0][3]))
def g(x, a0, b0, mu, sig):
i = get_bin(x)
if(i<0 or i>=len(bin_low)):
return 1.
else:
return a0 + b0*np.exp(-(x-mu)**2/ (2*sig**2))
g = np.vectorize(g)
x_fit_ratio = xvals[np.logical_and(3.<xvals, xvals<7.5)]
y_fit_ratio = np.array(yvals)[np.logical_and(3.<xvals, xvals<7.5)]/np.array(pred_spectrum)[np.logical_and(3.<xvals, xvals<7.5)]
res = curve_fit(g, x_fit_ratio, y_fit_ratio, [0.9, 0.1, 5.7, 0.5])
print("Ratio Fit Parameters: %s"%res[0])
a1.errorbar(xvals, yvals/pred_spectrum,
xerr=bin_widths/2., yerr=yerrs/yvals,
color='k', linestyle='None')
a1.plot(xvals, xvals*0.+1., color='k')
a1.plot(xvals, xvals*0.+res[0][0], 'r--')
a1.errorbar(xvals, g(xvals, *res[0]),
xerr=bin_widths/2.,
color='blue', linestyle='None')
a1.set_xlim(3., 7.5)
a1.set_ylim(0.6, 1.25)
a1.set(xlabel="Antineutrino Energy (MeV)",
ylabel="Ratio",
title=r'Ratio Gaussian Fit: $\mu$=%.2f, $\sigma=$%.3f'%(res[0][2], res[0][3]))
plt.savefig("plots/fit_daya_bay_gaussian_fits.png")
def plot_nu_bump_ibd(nu_spec,
bump_fracs=[0.01, 0.05]):
old_frac = nu_spec.bump_frac
# Plot unzoomed neutrino flux and ratio
fig1, (a0, a1) = plt.subplots(2, 1,
gridspec_kw={'height_ratios': [2, 1],})
plt.subplots_adjust(bottom=0.075, top=0.95)
#sharex=True)
fig1.patch.set_facecolor('white')
fig1.set_figheight(8.5)
lines_arr = ['b--', 'r-.', 'y:',
'c-', 'g--', 'm-.']
e_arr = np.linspace(0., 1e7, 100000)
nu_spec.bump_frac = 0.
spec_tot = nu_spec.d_phi_d_enu_ev(e_arr)*total_XSec_ibd(e_arr)/nu_spec.nuFlux()
a0.plot(e_arr*1e-6,spec_tot*1e6,'k-',label="No Distortion",linewidth=2)
ibd_yield_0 = ibd_yield(nu_spec)
bump_specs = []
ibd_yields = []
for i in range(len(bump_fracs)):
nu_spec.bump_frac = bump_fracs[i]
spec = nu_spec.d_phi_d_enu_ev(e_arr)*total_XSec_ibd(e_arr)/nu_spec.nuFlux()
bump_specs.append(spec)
a0.plot(e_arr*1e-6,spec*1e6,lines_arr[i],
label="Bump=%.2f%%"%(100.*bump_fracs[i]),linewidth=2)
ibd_yields.append(ibd_yield(nu_spec))
#a0.set_ylim(0., 2e17)
a0.set_xlim(0., 10.)
a0.set(ylabel='Reactor Spectrum * IBD xsec, cm^2/fission/MeV')
a0.set_title('Reactor Spectrum * IBD xsec at Commercial Reactor')
a1.plot(e_arr*1e-6,spec_tot/spec_tot,'k-',label="No Distortion",linewidth=2)
for i in range(len(bump_fracs)):
spec = bump_specs[i]
plt.plot(e_arr*1e-6,spec/spec_tot,lines_arr[i],
label="Bump=%.2f%%"%(100.*bump_fracs[i]),linewidth=2)
print("Bump=%.2e, Ratio=%s"%(bump_fracs[i], spec/spec_tot))
print("tot int: %s"%spint.simps(spec_tot*1.e6, e_arr*1e-6))
print("bump int: %s"%spint.simps(spec*1.e6, e_arr*1e-6))
print("ibd yield no bump: %.3e cm^2/fission"%ibd_yield_0)
print("ibd yield bump: %.3e cm^2/fission"%ibd_yields[i])
a1.legend(loc=2, prop={'size':11})
a1.set_xlim(0., 10.)
a1.set_ylim(0.75, 1.25)
a1.set(xlabel='Neutrino Energy (MeV)', ylabel='Ratio')
'''axins = inset_axes(a0, width=3.5, height=2.5, loc=3,
bbox_to_anchor=(0.24, 0.3),
bbox_transform=a0.transAxes)
axins.plot(e_arr*1e-6,spec_tot*1e6,'k-',label="No Distortion",linewidth=2)
for i in range(len(bump_fracs)):
spec = bump_specs[i]
axins.plot(e_arr*1e-6,spec*1e6,lines_arr[i],
label="Bump=%.2f%%"%(100.*bump_fracs[i]),linewidth=2)
axins.set_xlim(4.5, 7.5)
#axins.set_ylim(0., 4.e15)'''
plt.savefig('plots/reactor_bump_ibd_product.png')
nu_spec.bump_frac = old_frac
def ratio(e):
nu_spec.bump_frac = 0.0
rate0 = nu_spec.d_phi_d_enu_ev(e)*total_XSec_ibd(e)
nu_spec.bump_frac = bump_frac
rate1 = nu_spec.d_phi_d_enu_ev(e)*total_XSec_ibd(e)
return rate1/rate0
def f(x, k0, b0, mu, sig):
i = get_bin(x)
if(i<0 or i>=len(bin_low)):
return 0.
else:
return k0*pred_spectrum[get_bin(x)]+b0*np.exp(-(x-mu)**2/ (2*sig**2))*total_XSec_ibd(x*1.e6)