As an example for nuclear recoils that also illustrates nicely the modular structure of obscura, we compute the nuclear recoil spectrum
For the definition and details of the nuclear recoil spectrum, see e.g. chapter 3.5 of [Emken2019].
- First we define the DM particle objects that describe SI and SD interactions
The Print_Summary() function is a member of many of the classes and provides a terminal output that summarizes the object.
- For the DM distribution we use the standard halo model with default parameters.
- As target nuclei, we choose xenon and import the nuclear data.
- With these three objects, we can compute the differential nuclear recoil spectrum for a given recoil energy ER.
- The results are given in natural units in powers of GeV. To convert it to another unit, we can use the unit functionality of the libphysica library.
The full main.cpp
#include <iostream>
#include "libphysica/Natural_Units.hpp"
#include "obscura/DM_Halo_Models.hpp"
#include "obscura/DM_Particle_Standard.hpp"
#include "obscura/Direct_Detection_Nucleus.hpp"
#include "obscura/Target_Nucleus.hpp"
using namespace libphysica::natural_units;
int main()
{
// 1. DM particle (SI and Sd)
obscura::DM_Particle_SI dm_SI(10.0 * GeV);
dm_SI.Set_Sigma_Proton(1.0e-40 * cm * cm);
dm_SI.Print_Summary();
obscura::DM_Particle_SD dm_SD(10.0 * GeV);
dm_SD.Set_Sigma_Proton(1.0e-40 * cm * cm);
dm_SD.Print_Summary();
// 2. DM distribution
obscura::Standard_Halo_Model shm;
shm.Print_Summary();
// 3. Direct detection targets
obscura::Nucleus xenon = obscura::Get_Nucleus("Xe");
xenon.Print_Summary();
// 4. Evalute the nuclear recoil spectrum
double E_R = 1.0 * keV;
double dRdER_SI = obscura::dRdER_Nucleus(E_R, dm_SI, shm, xenon);
double dRdER_SD = obscura::dRdER_Nucleus(E_R, dm_SD, shm, xenon);
std::cout << "SI-interactions: \tdR/dER (1 keV) = " << In_Units(dRdER_SI, 1.0 / kg / year / keV) << " events / kg / year / keV" << std::endl;
std::cout << "SD-interactions: \tdR/dER (1 keV) = " << In_Units(dRdER_SD, 1.0 / kg / year / keV) << " events / kg / year / keV" << std::endl;
return 0;
}The terminal output
----------------------------------------
DM particle summary:
Mass: 10 GeV
Spin: 0.5
Low mass: [ ]
Interaction: Spin-Independent (SI)
Coupling ratio fixed: [x]
Isospin conservation: [x]
Coupling ratio: fn/fp = 1
Sigma_P[cm^2]: 1e-40
Sigma_N[cm^2]: 1e-40
Sigma_E[cm^2]: 1e-40
Interaction type: Contact
----------------------------------------
----------------------------------------
DM particle summary:
Mass: 10 GeV
Spin: 0.5
Low mass: [ ]
Interaction: Spin-Dependent (SD)
Coupling ratio fixed: [x]
Isospin conservation: [x]
Coupling ratio: fn/fp = 1
Sigma_P[cm^2]: 1e-40
Sigma_N[cm^2]: 1e-40
Sigma_E[cm^2]: 1e-40
----------------------------------------
Dark matter distribution - Summary
Standard halo model (SHM)
Local DM density[GeV/cm^3]: 0.4
Speed domain [km/sec]: [0,777]
Average DM velocity [km/sec]: (-11.1 , -232 , -7.3)
Average DM speed [km/sec]: 330
Speed dispersion v_0[km/sec]: 220
Gal. escape velocity [km/sec]: 544
Observer's velocity [km/sec]: (11.1 , 232 , 7.3)
Observer's speed [km/sec]: 233
Xe
Isotope Z A Abund.[%] Spin <sp> <sn>
------------------------------------------------------------
Xe-124 54 124 0.095 0 0 0
Xe-126 54 126 0.089 0 0 0
Xe-128 54 128 1.91 0 0 0
Xe-129 54 129 26.4 0.5 0.01 0.329
Xe-130 54 130 4.07 0 0 0
Xe-131 54 131 21.2 1.5 -0.009 -0.272
Xe-132 54 132 26.9 0 0 0
Xe-134 54 134 10.4 0 0 0
Xe-136 54 136 8.86 0 0 0
Total: 131 99.999
SI-interactions: dR/dER (1 keV) = 13621.8 events / kg / year / keV
SD-interactions: dR/dER (1 keV) = 0.132525 events / kg / year / keVAs a second example for an application of obscura, we will compute the 95% confidence level exclusion limit on the DM-electron cross section for a sub-GeV DM particle.
We assume a DM mass of 100 MeV, and two different direct detection experiments.
- An argon based experiment with an exposure of 100 kg years and an observational threshold of at least 4 ionized electrons.
- A semiconductor experiment with Si crystal targets, an exposure of 10 gram years, and an observational threshold of minimum 2 electron-hole pairs.
Let us set up the different objects to obtain the limits.
- First we define the DM particle object with 100 MeV mass.
- For the DM distribution we again use the standard halo model with default parameters.
- For the first experiment, we create an instance of the
DM_Detector_Ionization_ERclass and specify the desired detector properties of the toy experiment.
- The same for the semiconductor experiment:
- With these three objects, we can compute the limit on the DM-electron cross section.
- As in the previous example, the results are given in natural units in powers of GeV. We convert it to cm2, and print the result on the terminal.
The full main.cpp
#include <iostream>
#include "libphysica/Natural_Units.hpp"
#include "obscura/DM_Halo_Models.hpp"
#include "obscura/DM_Particle_Standard.hpp"
#include "obscura/Direct_Detection_Crystal.hpp"
#include "obscura/Direct_Detection_ER.hpp"
#include "obscura/Target_Atom.hpp"
#include "obscura/Target_Crystal.hpp"
using namespace libphysica::natural_units;
int main()
{
// 1. DM particle
obscura::DM_Particle_SI dm(100.0 * MeV);
dm.Print_Summary();
// 2. DM distribution
obscura::Standard_Halo_Model shm;
shm.Print_Summary();
// 3. Argon target experiment
obscura::DM_Detector_Ionization_ER argon_experiment("Argon toy experiment", 100.0 * kg * year, "Ar");
argon_experiment.Use_Electron_Threshold(4);
argon_experiment.Print_Summary();
// 4. Si target experiment
obscura::DM_Detector_Crystal silicon_experiment("Silicon toy experiment", 10.0 * gram * year, "Si");
silicon_experiment.Use_Q_Threshold(2);
silicon_experiment.Print_Summary();
// 5. Compute the 95% CL exclusion limits for m = 100.0 MeV
double limit_Ar = argon_experiment.Upper_Limit(dm, shm, 0.95);
double limit_Si = silicon_experiment.Upper_Limit(dm, shm, 0.95);
std::cout << "Argon experiment: \tsigma_e < " << In_Units(limit_Ar, cm * cm) << " cm^2 (95%CL)" << std::endl;
std::cout << "Silicon experiment: \tsigma_e < " << In_Units(limit_Si, cm * cm) << " cm^2 (95%CL)" << std::endl;
return 0;
}The terminal output
----------------------------------------
DM particle summary:
Mass: 100 MeV
Spin: 0.5
Low mass: [ ]
Interaction: Spin-Independent (SI)
Coupling ratio fixed: [x]
Isospin conservation: [x]
Coupling ratio: fn/fp = 1
Sigma_P[cm^2]: 1e-40
Sigma_N[cm^2]: 1e-40
Sigma_E[cm^2]: 1e-40
Interaction type: Contact
----------------------------------------
Dark matter distribution - Summary
Standard halo model (SHM)
Local DM density[GeV/cm^3]: 0.4
Speed domain [km/sec]: [0,777]
Average DM velocity [km/sec]: (-11.1 , -232 , -7.3)
Average DM speed [km/sec]: 330
Speed dispersion v_0[km/sec]: 220
Gal. escape velocity [km/sec]: 544
Observer's velocity [km/sec]: (11.1 , 232 , 7.3)
Observer's speed [km/sec]: 233
----------------------------------------
Experiment summary: Argon toy experiment
Target particles: Electrons
Exposure [kg year]: 100
Flat efficiency [%]: 100
Observed events: 0
Expected background: 0
Statistical analysis: Poisson
Electron recoil experiment (ionization).
Target(s):
Ar (100%)
Electron bins: [ ]
PE (S2) bins: [ ]
Ne threshold: 4
Ne max: 15
----------------------------------------
----------------------------------------
Experiment summary: Silicon toy experiment
Target particles: Electrons
Exposure [kg year]: 0.01
Flat efficiency [%]: 100
Observed events: 0
Expected background: 0
Statistical analysis: Poisson
Electron recoil experiment (semiconductor).
Target: Si semiconductor
eh pair threshold: 2
----------------------------------------
Argon experiment: sigma_e < 1.67038e-41 cm^2 (95%CL)
Silicon experiment: sigma_e < 1.1756e-39 cm^2 (95%CL)