spine.utils.energy_loss

Module of functions that approximate the energy loss of particles through matter. It includes function to compute the CSDA KE of particles given their range and vice-versa.

Functions

W_max(beta, gamma, M)	Maximum energy transfer in a single colision.
bethe_bloch_lar(T, M[, z])	Bethe-Bloch energy loss function for liquid argon.
bethe_bloch_mpv_lar(T, M, x[, z])	Most-probable value of energy loss through a thin layer of liquid argon.
csda_ke_lar(R, M[, z, T_max, epsrel, epsabs])	Numerically optimizes the kinetic energy necessary to observe the range of a particle that has been measured, under the CSDA.
csda_range_lar(T0, M[, z, epsrel, epsabs])	Numerically integrates the inverse Bethe-Bloch formula to find the CSDA range of a particle for a given initial kinetic energy.
csda_table_spline(particle_type[, value, ...])	Interpolates a CSDA table to form a spline which maps a range to a kinematic energy estimate.
delta_lar(bg)	Density correction
inv_bethe_bloch_lar(T, M[, z])	Inverse Bethe-Bloch energy loss function for liquid argon.
le_corr_lar(beta[, z])	Low energy corrections to the Bethe-Bloch formula.
step_energy_loss_lar(T0, M, dx[, z, num_steps])	Steps the initial energy of a particle down by pushing it through steps of dx of liquid argon.

spine.utils.energy_loss.csda_table_spline(particle_type, value='T', table_dir='csda_tables')

Interpolates a CSDA table to form a spline which maps a range to a kinematic energy estimate.

Parameters:

• particle_type (int) – Particle type ID to construct splines. Maps are avaible for muons, pions, kaons and protons.

• value (str, default 'T') – Value to provide for each range value (one of ‘T’ or ‘dE/dx’)

• table_dir (str, default 'csda_tables') – Relative path to the CSDA range tables

Returns:

Function mapping range (cm) to Kinetic E (MeV) or dE/dx (MeV/cm)

Return type:

callable

spine.utils.energy_loss.csda_ke_lar(R, M, z=1, T_max=1000000.0, epsrel=0.001, epsabs=0.001)

Numerically optimizes the kinetic energy necessary to observe the range of a particle that has been measured, under the CSDA.

Parameters:

• R (float) – Range that the particle travelled through liquid argon in cm

• M (float) – Particle mass in MeV/c^2

• z (int, default 1) – Impinging partile charge in multiples of electron charge

• T_max (float, default 1e6) – Maximum allowed kinetic energy

• epsrel (float, default 1e-3) – Relative error tolerance

• epsabs (float, default 1e-3) – Asbolute error tolerance

Returns:

CSDA kinetic energy in MeV

Return type:

float

spine.utils.energy_loss.csda_range_lar(T0, M, z=1, epsrel=0.001, epsabs=0.001)

Numerically integrates the inverse Bethe-Bloch formula to find the CSDA range of a particle for a given initial kinetic energy.

Parameters:

• T0 (float) – Initial kinetic energy in MeV

• M (float) – Particle mass in MeV/c^2

• z (int, default 1) – Impinging partile charge in multiples of electron charge

• epsrel (float, default 1e-3) – Relative error tolerance

• epsabs (float, default 1e-3) – Asbolute error tolerance

Returns:

CSDA range in cm

Return type:

float

spine.utils.energy_loss.step_energy_loss_lar(T0, M, dx, z=1, num_steps=None)

Steps the initial energy of a particle down by pushing it through steps of dx of liquid argon. If num_steps is not specified, it will iterate until the particle kinetic energy reaches 0.

Parameters:

• T0 (float) – Initial kinetic energy in MeV

• M (float) – Particle mass in MeV/c^2

• dx (float) – Step size in cm

• z (int, default 1) – Impinging partile charge in multiples of electron charge

• num_steps (int, optional) – If specified, only step a maximum of num_steps times

Returns:

Array of kinetic energies at each step

Return type:

np.array

spine.utils.energy_loss.inv_bethe_bloch_lar(T, M, z=1)

Inverse Bethe-Bloch energy loss function for liquid argon.

Parameters:

• T (float) – Kinetic energy in MeV

• M (float) – Impinging particle mass in MeV/c^2

• z (int, default 1) – Impinging partile charge in multiples of electron charge

Returns:

Value of the inverse energy loss rate in liquid argon in MeV/cm

Return type:

float

spine.utils.energy_loss.bethe_bloch_lar(T, M, z=1)

Bethe-Bloch energy loss function for liquid argon.

Reference:

https://pdg.lbl.gov/2019/reviews/rpp2018-rev-passage-particles-matter.pdf

Corrections taken from:

https://pdg.lbl.gov/2023/AtomicNuclearProperties/adndt.pdf

Parameters:

• T (float) – Kinetic energy in MeV

• M (float) – Impinging particle mass in MeV/c^2

• z (int, default 1) – Impinging partile charge in multiples of electron charge

Returns:

Value of the energy loss rate in liquid argon in MeV/cm

Return type:

float

spine.utils.energy_loss.bethe_bloch_mpv_lar(T, M, x, z=1)

Most-probable value of energy loss through a thin layer of liquid argon.

https://pdg.lbl.gov/2019/reviews/rpp2018-rev-passage-particles-matter.pdf

Parameters:

• T (float) – Kinetic energy in MeV

• M (float) – Impinging particle mass in MeV/c^2

• x (float) – Material thickness in cm

• z (int, default 1) – Impinging partile charge in multiples of electron charge

Returns:

Value of the energy loss in liquid argon in MeV

Return type:

float

spine.utils.energy_loss.W_max(beta, gamma, M)

Maximum energy transfer in a single colision.

Parameters:

• beta (float) – Lorentz beta (v/c)

• gamma (float) – Lorentz gamma (1/sqrt(1-beta**2))

• M (float) – Mass of the impinging particle in MeV/c^2

Returns:

Maximum energy transferred in a single colision

Return type:

float

spine.utils.energy_loss.delta_lar(bg)

Density correction

Parameters:

bg (float) – Product of Lorentz beta and gamma (beta/sqrt(1-beta**2))

Returns:

Density correction to the Bethe-Bloch function

Return type:

float

spine.utils.energy_loss.le_corr_lar(beta, z=1)

Low energy corrections to the Bethe-Bloch formula.

Parameters:

• beta (float) – Lorentz beta (v/c)

• z (int, default 1) – Impinging partile charge in multiples of electron charge

Returns:

Low energy correction to the energy loss function

Return type:

float