#include <deformednucleus.h>

DeformedNucleus: Child of nucleus for deformed nuclei.

All options from the nucleus will still apply. The deformed nucleus adds new or updated features which are outlined below.

Definition at line 38 of file deformednucleus.h.

Inheritance diagram for smash::DeformedNucleus:

Public Member Functions
	DeformedNucleus (const std::map< PdgCode, int > &particle_list, int nTest, SpinInteractionType spin_interaction_type=SpinInteractionType::Off)
	Constructor for DeformedNucles which takes a particle list and the number of testparticles. More...

	DeformedNucleus (Configuration &config, int nTest, bool auto_deformation)
	Constructor for DeformedNucleus, that needs the configuration parameters from the inputfile and the number of testparticles. More...

ThreeVector	distribute_nucleon () override
	Deformed Woods-Saxon sampling routine. More...

void	set_deformation_parameters_automatic ()
	Sets the deformation parameters of the radius according to the current mass number. More...

void	set_deformation_parameters_from_config (Configuration &config)
	Set parameters for spherical deformation of the nucleus from the values specified in the configuration file. More...

double	get_saturation_density () const

double	nucleon_density (double r, double cosx, double phi) const override
	Return the deformed Woods-Saxon probability density for the given position. More...

double	nucleon_density_unnormalized (double r, double cosx, double phi) const override
	Return the unnormalized deformed Woods-Saxon distribution for the given position. More...

double	integrant_nucleon_density_phi (double r, double cosx) const
	Return the integral over the azimuthal angle phi. More...

double	calculate_saturation_density () const override

void	set_beta_2 (double b2)
	Set deformation coefficient for Y_2_0. More...

void	set_gamma (double ga)
	Set the triaxiality coefficient gamma for Y_2_0 and Y_2_2. More...

void	set_beta_3 (double b3)
	Set deformation coefficient for Y_3_0. More...

void	set_beta_4 (double b4)
	Set deformation coefficient for Y_4_0. More...

double	get_beta2 ()
	return the beta2 value. More...

double	get_beta3 ()
	return the beta3 value. More...

double	get_beta4 ()
	return the beta4 value. More...

Public Member Functions inherited from smash::Nucleus
	Nucleus ()=default
	default constructor More...

	Nucleus (Configuration &config, int nTest)
	Constructor for Nucleus, that needs the configuration parameters from the inputfile and the number of testparticles. More...

	Nucleus (const std::map< PdgCode, int > &particle_list, int nTest, SpinInteractionType spin_interaction_type=SpinInteractionType::Off)
	Constructor which directly initializes the Nucleus with particles and respective counts. More...

virtual	~Nucleus ()=default

double	mass () const

double	woods_saxon (double x)
	Woods-Saxon distribution. More...

virtual void	arrange_nucleons ()
	Sets the positions of the nucleons inside a nucleus. More...

virtual void	set_parameters_automatic ()
	Sets the deformation parameters of the Woods-Saxon distribution according to the current mass number. More...

virtual void	generate_fermi_momenta ()
	Generates momenta according to Fermi motion for the nucleons. More...

void	boost (double beta_scalar)
	Boosts the nuclei into the computational frame, such that the nucleons have the appropriate momentum and the nuclei are lorentz-contracted. More...

void	fill_from_list (const std::map< PdgCode, int > &particle_list, int testparticles)
	Adds particles from a map PDG code => Number_of_particles_with_that_PDG_code to the nucleus. More...

void	shift (double z_offset, double x_offset, double simulation_time)
	Shifts the nucleus to correct impact parameter and z displacement. More...

virtual void	rotate ()
	Rotates the nucleus using the three euler angles phi, theta and psi. More...

void	copy_particles (Particles *particles)
	Copies the particles from this nucleus into the particle list. More...

size_t	size () const
	Number of numerical (=test-)particles in the nucleus: More...

size_t	number_of_particles () const
	Number of physical particles in the nucleus: More...

size_t	number_of_protons () const
	Number of physical protons in the nucleus: More...

FourVector	center () const
	Calculate geometrical center of the nucleus. More...

void	set_label (BelongsTo label)
	Sets target / projectile labels on nucleons. More...

void	align_center ()
	Shifts the nucleus so that its center is at (0,0,0) More...

virtual void	set_saturation_density (double density)
	Sets the saturation density of the nucleus. More...

std::vector< ParticleData >::iterator	begin ()
	For iterators over the particle list: More...

std::vector< ParticleData >::iterator	end ()
	For iterators over the particle list: More...

std::vector< ParticleData >::const_iterator	cbegin () const
	For const iterators over the particle list: More...

std::vector< ParticleData >::const_iterator	cend () const
	For const iterators over the particle list: More...

void	set_diffusiveness (double diffuse)
	Sets the diffusiveness of the nucleus. More...

double	get_diffusiveness () const

double	get_saturation_density () const

double	default_nuclear_radius ()
	Default nuclear radius calculated as: More...

void	set_nuclear_radius (double rad)
	Sets the nuclear radius. More...

double	get_nuclear_radius () const

void	set_orientation_from_config (Configuration &orientation_config)
	Set angles for rotation of the nucleus from config file. More...

Private Attributes
double	beta2_ = 0.0
	Deformation parameter for angular momentum l=2. More...

double	gamma_ = 0.0
	Triaxiality parameter for angular momentum l=2. More...

double	beta3_ = 0.0
	Deformation parameter for angular momentum l=3. More...

double	beta4_ = 0.0
	Deformation parameter for angular momentum l=4. More...

Additional Inherited Members
Protected Member Functions inherited from smash::Nucleus
void	random_euler_angles ()
	Randomly generate Euler angles. More...

Protected Attributes inherited from smash::Nucleus
std::vector< ParticleData >	particles_
	Particles associated with this nucleus. More...

double	saturation_density_ = nuclear_density
	Saturation density of this nucleus. More...

double	euler_phi_ = 0.0
	The Euler angle phi of the three Euler angles used to apply rotations to the nucleus. More...

double	euler_theta_ = 0.0
	Euler angle theta. More...

double	euler_psi_ = 0.0
	Euler angle psi. More...

bool	random_rotation_ = false
	Whether the nucleus should be rotated randomly. More...

Constructor & Destructor Documentation

◆ DeformedNucleus() [1/2]

smash::DeformedNucleus::DeformedNucleus	(	const std::map< PdgCode, int > &	particle_list,
		int	nTest,
		SpinInteractionType	spin_interaction_type = `SpinInteractionType::Off`
	)

Constructor for DeformedNucles which takes a particle list and the number of testparticles.

This constructor is only used for testing purposes.

Parameters

[in]	particle_list	Map with PDGCode and number of particles which make up the nucleus
[in]	nTest	number of testparticles
[in]	spin_interaction_type	which type of spin interaction to use

Definition at line 22 of file deformednucleus.cc.

25 : Nucleus(particle_list, nTest, spin_interaction_type) {}

smash::Nucleus::Nucleus

Nucleus()=default

default constructor

◆ DeformedNucleus() [2/2]

smash::DeformedNucleus::DeformedNucleus	(	Configuration &	config,
		int	nTest,
		bool	auto_deformation
	)

Constructor for DeformedNucleus, that needs the configuration parameters from the inputfile and the number of testparticles.

Parameters

[in]	config	contains the parameters from the inputfile on the numbers of particles with a certain PDG code
[in]	nTest	number of testparticles
[in]	auto_deformation	whether or not deformation parameters should be set automatically

Definition at line 27 of file deformednucleus.cc.

     : Nucleus(config, nTest) {
   if (auto_deformation) {
     set_deformation_parameters_automatic();
     set_saturation_density(calculate_saturation_density());
   } else {
     set_deformation_parameters_from_config(config);
   }
   /* If the config does not contain (anymore) a target or a projectile
   sub-section, this code should not be executed, because e.g. the
   is_about_projectile function would fail. */
   if (has_projectile_or_target(config)) {
     const auto &orientation_section = [&config]() {
       return is_about_projectile(config) ? InputSections::m_c_p_orientation
                                          : InputSections::m_c_t_orientation;
     }();
     if (config.has_section(orientation_section)) {
       Configuration sub_conf =
           config.extract_complete_sub_configuration(orientation_section);
       set_orientation_from_config(sub_conf);
     }
   }
 }

Member Function Documentation

◆ distribute_nucleon()

ThreeVector smash::DeformedNucleus::distribute_nucleon ( )

overridevirtual

Deformed Woods-Saxon sampling routine.

Returns: Spatial position from uniformly sampling the deformed woods-saxon distribution

Reimplemented from smash::Nucleus.

Definition at line 52 of file deformednucleus.cc.

                                                 {
   double a_radius;
   Angles a_direction;
   // Set a sensible maximum bound for radial sampling.
   double radius_max =
       Nucleus::get_nuclear_radius() / Nucleus::get_diffusiveness() +
       Nucleus::get_nuclear_radius() * Nucleus::get_diffusiveness();
  
   // Sample the distribution.
   do {
     a_direction.distribute_isotropically();
     // sample r**2 dr
     a_radius = radius_max * std::cbrt(random::canonical());
   } while (random::canonical() > nucleon_density(a_radius,
                                                  a_direction.costheta(),
                                                  a_direction.phi()) /
                                      Nucleus::get_saturation_density());
  
   // Update (x, y, z) positions.
   return a_direction.threevec() * a_radius;
 }

◆ set_deformation_parameters_automatic()

void smash::DeformedNucleus::set_deformation_parameters_automatic ( )

Sets the deformation parameters of the radius according to the current mass number.

The deformation parameters are taken from Moller:1993ed [43]. Corrections to the deformation parameter beta2 in Uranium come from Kuhlman:2005ts [35]. For finite nucleon size corrections to the nuclear density and radius for copper and gold, see Hirano:2009ah [27], and Hirano:2010jg [29] for uranium.

Definition at line 74 of file deformednucleus.cc.

                                                            {
   // Set the deformation parameters
   // reference for U, Pb, Au, Cu: \iref{Moller:1993ed}
   // reference for Zr and Ru: \iref{Schenke:2019ruo}
   // reference for Xe: \iref{Moller:2015fba}
   bool listed = 0;
   const std::map<int, std::string> A_map = {{238, "Uranium"},
                                             {208, "Lead"},
                                             {197, "Gold"},
                                             {63, "Copper"},
                                             {129, "Xenon"}};
   const std::map<std::string, std::string> Z_map = {{"Uranium", "92"},
                                                     {"Lead", "82"},
                                                     {"Gold", "79"},
                                                     {"Copper", "29"},
                                                     {"Xenon", "54"}};
   int A = Nucleus::number_of_particles();
   int Z = Nucleus::number_of_protons();
   switch (A) {
     case 238:  // Uranium
       if (Z == 92) {
         set_beta_2(0.28);
         set_beta_4(0.093);
       } else {
         listed = true;
       }
       break;
     case 208:  // Lead
       if (Z == 82) {
         set_beta_2(0.0);
         set_beta_4(0.0);
       } else {
         listed = true;
       }
       break;
     case 197:  // Gold
       if (Z == 79) {
         set_beta_2(-0.131);
         set_beta_4(-0.031);
       } else {
         listed = true;
       }
       break;
     case 129:  // Xenon
       if (Z == 54) {
         set_beta_2(0.162);
         set_beta_4(-0.003);
       } else {
         listed = true;
       }
       break;
     case 63:  // Copper
       if (Z == 29) {
         set_beta_2(0.162);
         set_beta_4(-0.006);
       } else {
         listed = true;
       }
       break;
     case 96:
       if (Z == 40) {  // Zirconium
         set_beta_2(0.0);
         set_beta_4(0.0);
       } else if (Z == 44) {  // Ruthenium
         set_beta_2(0.158);
         set_beta_4(0.0);
       } else {
         throw std::domain_error(
             "Number of protons for nuclei with mass number A = 96 does not "
             "match that of Zirconium or Ruthenium. The deformation parameters "
             "for additional isobars are currently not implemented."
             " Please specify at least \"Beta_2\" and \"Beta_4\" "
             "manually and set \"Automatic: False.\" ");
       }
       break;
     default:
       throw std::domain_error(
           "Mass number not listed for automatically setting deformation "
           "parameters. Please specify at least \"Beta_2\" and \"Beta_4\" "
           "manually and set \"Automatic: False.\" ");
   }
   if (listed) {
     throw std::domain_error("Mass number is listed under " + A_map.at(A) +
                             " but the proton "
                             "number of " +
                             std::to_string(Z) +
                             " does not match "
                             "its " +
                             Z_map.at(A_map.at(A)) +
                             " protons."
                             "Please specify at least \"Beta_2\" and \"Beta_4\" "
                             "manually and set \"Automatic: False.\" ");
   }
 }

◆ set_deformation_parameters_from_config()

void smash::DeformedNucleus::set_deformation_parameters_from_config ( Configuration & config )

Set parameters for spherical deformation of the nucleus from the values specified in the configuration file.

Parameters

config The configuration for the deformation of this nucleus (projectile or target).

Definition at line 169 of file deformednucleus.cc.

                            {
   if (has_projectile_or_target(config)) {
     const bool is_projectile = is_about_projectile(config);
     const auto &[beta2_key, beta3_key, beta4_key,
                  gamma_key] = [&is_projectile]() {
       return is_projectile
                  ? std::make_tuple(
                        InputKeys::modi_collider_projectile_deformed_beta2,
                        InputKeys::modi_collider_projectile_deformed_beta3,
                        InputKeys::modi_collider_projectile_deformed_beta4,
                        InputKeys::modi_collider_projectile_deformed_gamma)
                  : std::make_tuple(
                        InputKeys::modi_collider_target_deformed_beta2,
                        InputKeys::modi_collider_target_deformed_beta3,
                        InputKeys::modi_collider_target_deformed_beta4,
                        InputKeys::modi_collider_target_deformed_gamma);
     }();
     // Deformation parameters
     if (config.has_value(beta2_key)) {
       beta2_ = config.take(beta2_key);
     }
     if (config.has_value(gamma_key)) {
       gamma_ = config.take(gamma_key);
     }
     if (config.has_value(beta3_key)) {
       beta3_ = config.take(beta3_key);
     }
     if (config.has_value(beta4_key)) {
       beta4_ = config.take(beta4_key);
     }
   }
 }

◆ get_saturation_density()

double smash::DeformedNucleus::get_saturation_density ( ) const

inline

Returns: the saturation density of the deformed_nucleus

See also: saturation_density_

Definition at line 94 of file deformednucleus.h.

94 { return saturation_density_; }

smash::Nucleus::saturation_density_

double saturation_density_

Saturation density of this nucleus.

Definition: nucleus.h:293

◆ nucleon_density()

double smash::DeformedNucleus::nucleon_density	(	double	r,
		double	cosx,
		double	phi
	)		const

overridevirtual

Return the deformed Woods-Saxon probability density for the given position.

This corresponds to the nuclear density at the very same position.

Parameters

[in]	r	The radius at which to sample
[in]	cosx	The cosine of the polar angle at which to sample
[in]	phi	The azimuthal angle at which to sample

Returns: The Woods-Saxon density

Reimplemented from smash::Nucleus.

Definition at line 221 of file deformednucleus.cc.

                                                           {
   return Nucleus::get_saturation_density() /
          (1 + std::exp((r - Nucleus::get_nuclear_radius() *
                                 (1 +
                                  beta2_ * (std::cos(gamma_) *
                                                y_l_m(2, 0, cosx, phi) +
                                            std::sqrt(2) * std::sin(gamma_) *
                                                y_l_m(2, 2, cosx, phi)) +
                                  beta3_ * y_l_m(3, 0, cosx, phi) +
                                  beta4_ * y_l_m(4, 0, cosx, phi))) /
                        Nucleus::get_diffusiveness()));
 }

◆ nucleon_density_unnormalized()

double smash::DeformedNucleus::nucleon_density_unnormalized	(	double	r,
		double	cosx,
		double	phi
	)		const

overridevirtual

Return the unnormalized deformed Woods-Saxon distribution for the given position.

Parameters

[in]	r	The radius
[in]	cosx	The cosine of the polar angle
[in]	phi	The azimuthal angle

Returns: The unnormalized Woods-Saxon distribution

Reimplemented from smash::Nucleus.

Definition at line 235 of file deformednucleus.cc.

                                                                        {
   return 1.0 /
          (1 + std::exp((r - Nucleus::get_nuclear_radius() *
                                 (1 +
                                  beta2_ * (std::cos(gamma_) *
                                                y_l_m(2, 0, cosx, phi) +
                                            std::sqrt(2) * std::sin(gamma_) *
                                                y_l_m(2, 2, cosx, phi)) +
                                  beta3_ * y_l_m(3, 0, cosx, phi) +
                                  beta4_ * y_l_m(4, 0, cosx, phi))) /
                        Nucleus::get_diffusiveness()));
 }

◆ integrant_nucleon_density_phi()

double smash::DeformedNucleus::integrant_nucleon_density_phi	(	double	r,
		double	cosx
	)		const

Return the integral over the azimuthal angle phi.

Parameters

[in]	r	The radius
[in]	cosx	The cosine of the polar angle

Returns: The unnormalized Woods-Saxon distribution integrated over dphi

Definition at line 249 of file deformednucleus.cc.

                                                                          {
   Integrator integrate;
   // Perform the phi integration. This is needed if the triaxiality coefficient
   // gamma is included, which includes a dependency around the phi axis.
   // Unfortunately the Integrator class does not support 3d integration which is
   // why this intermediate integral is needed. It has been checked that the
   // integral factorizes.
   const auto result = integrate(0.0, 2.0 * M_PI, [&](double phi) {
     return nucleon_density_unnormalized(r, cosx, phi);
   });
   return result.value();
 }

◆ calculate_saturation_density()

double smash::DeformedNucleus::calculate_saturation_density ( ) const

overridevirtual

Returns: the normalized ground state density for the corresponding Woods-Saxon parameter. This is done by integrating the Woods-Saxon distribution and setting the normalization such that the integral of the Woods-Saxon distribution yields the number of particles in the nucleus \(\int\rho(r)d^3r = N_{particles}\).

Reimplemented from smash::Nucleus.

Definition at line 263 of file deformednucleus.cc.

                                                            {
   Integrator2d integrate;
   // Transform integral from (0, oo) to (0, 1) via r = (1 - t) / t.
   // To prevent overflow, the integration is only performed to t = 0.01 which
   // corresponds to r = 99fm. Additionally the precision settings in the
   // Integrator2d scheme are equally important. However both these point affect
   // the result only after the seventh digit which should not be relevant here.
   if (gamma_ == 0.0) {
     const auto result = integrate(0.01, 1, -1, 1, [&](double t, double cosx) {
       const double r = (1 - t) / t;
       return twopi * std::pow(r, 2.0) *
              nucleon_density_unnormalized(r, cosx, 0.0) / std::pow(t, 2.0);
     });
     const auto rho0 = number_of_particles() / result.value();
     return rho0;
   } else {
     const auto result = integrate(0.01, 1, -1, 1, [&](double t, double cosx) {
       const double r = (1 - t) / t;
       return std::pow(r, 2.0) * integrant_nucleon_density_phi(r, cosx) /
              std::pow(t, 2.0);
     });
     const auto rho0 = number_of_particles() / result.value();
     return rho0;
   }
 }

◆ set_beta_2()

void smash::DeformedNucleus::set_beta_2 ( double b2 )

inline

Set deformation coefficient for Y_2_0.

Parameters

[in] b2 deformation coefficient for l=2

Definition at line 137 of file deformednucleus.h.

137 { beta2_ = b2; }

◆ set_gamma()

void smash::DeformedNucleus::set_gamma ( double ga )

inline

Set the triaxiality coefficient gamma for Y_2_0 and Y_2_2.

Parameters

[in] ga triaxiality coefficient for l=2

Definition at line 142 of file deformednucleus.h.

142 { gamma_ = ga; }

◆ set_beta_3()

void smash::DeformedNucleus::set_beta_3 ( double b3 )

inline

Set deformation coefficient for Y_3_0.

Parameters

[in] b3 deformation coefficient for l=3

Definition at line 147 of file deformednucleus.h.

147 { beta3_ = b3; }

◆ set_beta_4()

void smash::DeformedNucleus::set_beta_4 ( double b4 )

inline

Set deformation coefficient for Y_4_0.

Parameters

[in] b4 deformation coefficient for l=4

Definition at line 152 of file deformednucleus.h.

152 { beta4_ = b4; }

◆ get_beta2()

double smash::DeformedNucleus::get_beta2 ( )

inline

return the beta2 value.

Definition at line 156 of file deformednucleus.h.

156 { return beta2_; }

◆ get_beta3()

double smash::DeformedNucleus::get_beta3 ( )

inline

return the beta3 value.

Definition at line 160 of file deformednucleus.h.

160 { return beta3_; }

◆ get_beta4()

double smash::DeformedNucleus::get_beta4 ( )

inline

return the beta4 value.

Definition at line 164 of file deformednucleus.h.

164 { return beta4_; }

Member Data Documentation

◆ beta2_

double smash::DeformedNucleus::beta2_ = 0.0

private

Deformation parameter for angular momentum l=2.

Definition at line 168 of file deformednucleus.h.

◆ gamma_

double smash::DeformedNucleus::gamma_ = 0.0

private

Triaxiality parameter for angular momentum l=2.

Definition at line 170 of file deformednucleus.h.

◆ beta3_

double smash::DeformedNucleus::beta3_ = 0.0

private

Deformation parameter for angular momentum l=3.

Definition at line 172 of file deformednucleus.h.

◆ beta4_

double smash::DeformedNucleus::beta4_ = 0.0

private

Deformation parameter for angular momentum l=4.

Definition at line 174 of file deformednucleus.h.

The documentation for this class was generated from the following files:

src/include/smash/deformednucleus.h
src/deformednucleus.cc

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ DeformedNucleus() [1/2]

◆ DeformedNucleus() [2/2]

Member Function Documentation

◆ distribute_nucleon()

◆ set_deformation_parameters_automatic()

◆ set_deformation_parameters_from_config()

◆ get_saturation_density()

◆ nucleon_density()

◆ nucleon_density_unnormalized()

◆ integrant_nucleon_density_phi()

◆ calculate_saturation_density()

◆ set_beta_2()

◆ set_gamma()

◆ set_beta_3()

◆ set_beta_4()

◆ get_beta2()

◆ get_beta3()

◆ get_beta4()

Member Data Documentation

◆ beta2_

◆ gamma_

◆ beta3_

◆ beta4_