Detailed Description

Reaction parameters for heavy-ion collisions from systematics of Wilcke et al.

Examples: ClassTraj.cpp.

Definition at line 21 of file KVWilckeReactionParameters.h.

#include <KVWilckeReactionParameters.h>

Public Member Functions
	KVWilckeReactionParameters ()
	Default constructor.

	KVWilckeReactionParameters (const KVNucleus &proj, const KVNucleus &targ)

virtual	~KVWilckeReactionParameters ()
	Destructor.

Double_t	CentrifugalPotential (Double_t x, Double_t l)

void	DrawAllPotentials (Double_t l=0) const

Double_t	ECM (Double_t e_sur_a) const

Double_t	Eta (Double_t e_sur_a) const

Int_t	GetAC () const

Double_t	GetAngularMomentumFromImpactParameter (Double_t e_sur_a, Double_t b) const

Int_t	GetAP () const

Int_t	GetAT () const

Double_t	GetBassReactionCrossSection (Double_t e_sur_a)
	Bass reaction cross-section [mb] for incident energy [MeV/nucleon].

TF1 *	GetBSSCoulombPotential () const

TF1 *	GetCentrifugalPotential (Double_t e_sur_a, Double_t b) const

TF1 *	GetCentrifugalPotential (Double_t l) const

TF1 *	GetCMQuarterPointAngle () const

Double_t	GetCP () const

Double_t	GetCrossSectionFromMaxAngularMomentum (Double_t e_sur_a, Double_t lmax) const

Double_t	GetCrossSectionFromMaxImpactParameter (Double_t bmax) const

Double_t	GetCT () const

Double_t	GetFullDampingTKE () const

TF1 *	GetFusionCrossSection () const

Double_t	GetImpactParameterFromAngularMomentum (Double_t e_sur_a, Double_t l) const

TF1 *	GetLmax () const

Double_t	GetMaxAngularMomentumFromCrossSection (Double_t e_sur_a, Double_t sigma) const

Double_t	GetMaxImpactParameterFromCrossSection (Double_t sigma) const

Double_t	GetMaximumAngularMomentumWithPocket ()

Double_t	GetMu () const

TF1 *	GetNuclearProximityPotential () const

TF1 *	GetReactionCrossSection () const

Double_t	GetRint () const

TF1 *	GetTotalPotential () const

Double_t	k (Double_t e_sur_a) const

Double_t	Lmax (Double_t x, Double_t ) const

Double_t	Potential (Double_t r, Double_t )

Double_t	PotentialMaximumRadius (Double_t l)

Double_t	PotentialPocketRadius (Double_t l)

void	Print () const

Double_t	ProjectileLabEQP (Double_t e) const

Double_t	ProjectileLabQP (Double_t e) const

Double_t	ProxPot (Double_t r, Double_t )

Double_t	QuarterPointAngle (Double_t x, Double_t ) const

void	SetEntranceChannel (const KVNucleus &proj, const KVNucleus &targ)
	(Re)set entrance channel to calculate

Double_t	SigmaFus (Double_t e_sur_a, Double_t ) const

Double_t	SigmaR (Double_t x, Double_t ) const

Double_t	VC (Double_t r, Double_t )

Static Public Member Functions
static Double_t	BSS_V0 (Int_t zp, Int_t ap, Int_t zt, Int_t at)

static Double_t	ChargeRadius_Myers (Int_t Z, Int_t A)

static Double_t	delta_bar_Myers (Int_t Z, Int_t A)
	delta_bar, Eq.(8) in W.D. Myers, Phys. Lett. B 30, 451 (1969)

static Double_t	epsilon_bar_Myers (Int_t Z, Int_t A)
	epsilon_bar, Eq.(7) in W.D. Myers, Phys. Lett. B 30, 451 (1969)

static Double_t	InteractionRadius (Int_t aproj, Int_t atarg)

static Double_t	MatterHalfDensityRadius (Int_t A)

static Double_t	NLDSurfaceTensionCoefficient (Int_t Z, Int_t A)

static Double_t	r0_Wilcke (Int_t aproj, Int_t atarg)

static Double_t	RLDCriticalAngularMomentum (Int_t z, Int_t a)

static Double_t	SharpRadius (Int_t A)

static Double_t	SWaveFusionBarrierRadius (Int_t zp, Int_t ap, Int_t zt, Int_t at)

static Double_t	TKESymFiss (Int_t Z, Int_t A)

Private Member Functions
void	init ()

Private Attributes
Int_t	AC

Int_t	AP

Double_t	ASYMMFISSIONTKE
	TKE of completely relaxed events in strongly damped collisions.

Int_t	AT
	Mass number of the projectile, target.

Double_t	BSS_K

Double_t	BSS_N

Double_t	CBAR

Double_t	CP

Double_t	CT
	Matter half-density radii.

TF1 *	fBSS
	BSS Coulomb potential for heavy-ions.

TF1 *	fCentPot

TF1 *	fCMThetaQuart
	CM quarter point angle.

Double_t	FISSIONTKE
	TKE for symmetric fission of combined system.

TF1 *	fLmax
	Grazing angular momentum.

TF1 *	fPotential
	total (nuclear+coulomb) potential for heavy-ions

TF1 *	fProx
	Nuclear proximity potential for heavy-ions.

TF1 *	fSigmaFus
	Fusion cross section.

TF1 *	fSigmaR
	Reaction cross section.

Double_t	GAMMA
	Nuclear liquid drop surface-tension coefficient.

Double_t	LCRIT
	The maximum critical angular momentum for fusion.

Double_t	MU

Int_t	NC

Int_t	NP

Int_t	NT
	Neutron number of the projectile, target.

Double_t	PROXFACTOR
	Proximity potential factor.

Double_t	R0

Double_t	RBARRIER
	Fusion barrier radius RB for s-waves.

Double_t	RCP

Double_t	RCT

Double_t	RCTOTAL
	Coulomb radius.

Double_t	RINT

Double_t	RP

Double_t	RT
	Sharp radius.

Double_t	V0
	BSS potential at r=0.

Double_t	VC_RINT
	BSS Coulomb potential at Rint.

Double_t	VRB
	The total conservative potential at r=RB for s-waves.

Int_t	ZC

Int_t	ZP

Int_t	ZT
	Atomic number of the projectile, target.

Static Private Attributes
static Double_t	a1_Myers = 15.677
	volume energy coefficient

static Double_t	a2_Myers = 22.0
	surface energy coefficient

static Double_t	c1_Myers = 0.745
	Coulomb energy coefficient.

static Double_t	e2_Wilcke = 1.438
	e**2 = 1.438 is value used by Wilcke et al.

static Double_t	J_Myers = 35.0
	symmetry energy coefficient

static Double_t	K_Myers = 300.0
	compressibility coefficient

static Double_t	L_Myers = 99.0
	density-symmetry coefficient

static Double_t	M_Myers = 4.5
	symmetry anharmonicity coefficient

static Double_t	mu_Wilcke = 931.5
	mu = 931.5 is value used by Wilcke et al.

static Double_t	Q_Myers = 25.0
	effective surface stiffness

static Double_t	r0_Myers = 1.16
	nuclear radius constant

Constructor & Destructor Documentation

◆ KVWilckeReactionParameters() [1/2]

KVWilckeReactionParameters::KVWilckeReactionParameters ( )

Default constructor.

Definition at line 86 of file KVWilckeReactionParameters.cpp.

◆ KVWilckeReactionParameters() [2/2]

KVWilckeReactionParameters::KVWilckeReactionParameters	(	const KVNucleus &	proj,
		const KVNucleus &	targ
	)

Definition at line 96 of file KVWilckeReactionParameters.cpp.

◆ ~KVWilckeReactionParameters()

KVWilckeReactionParameters::~KVWilckeReactionParameters ( )

virtual

Destructor.

Definition at line 107 of file KVWilckeReactionParameters.cpp.

Member Function Documentation

◆ BSS_V0()

static Double_t KVWilckeReactionParameters::BSS_V0	(	Int_t	zp,
		Int_t	ap,
		Int_t	zt,
		Int_t	at
	)

inlinestatic

Corrected V0 formula (2.24) from Bondorf et al. Phys. Rep. C15, 83 (1974) In Wilcke et al. there is a mistake: (RCT**1/3 + RCP**1/3)**3 instead of (RCT**3+RCP**3)**1/3 The Wilcke formula gives negative V0 values and an incorrect form of potential. The actual values in Wilcke correspond to the correct Bondorf formula

Definition at line 108 of file KVWilckeReactionParameters.h.

◆ CentrifugalPotential()

Double_t KVWilckeReactionParameters::CentrifugalPotential	(	Double_t *	x,
		Double_t *	l
	)

inline

Total heavy-ion potential (nuclear proximity+coulomb+centrifugal) at distance r x[0] = r l[0] = angular momentum

Definition at line 154 of file KVWilckeReactionParameters.h.

◆ ChargeRadius_Myers()

static Double_t KVWilckeReactionParameters::ChargeRadius_Myers	(	Int_t	Z,
		Int_t	A
	)

inlinestatic

Charge (Coulomb) radius for nucleus charge Z mass A

Definition at line 103 of file KVWilckeReactionParameters.h.

◆ delta_bar_Myers()

Double_t KVWilckeReactionParameters::delta_bar_Myers	(	Int_t	Z,
		Int_t	A
	)

static

delta_bar, Eq.(8) in W.D. Myers, Phys. Lett. B 30, 451 (1969)

Definition at line 147 of file KVWilckeReactionParameters.cpp.

◆ DrawAllPotentials()

void KVWilckeReactionParameters::DrawAllPotentials ( Double_t l = 0 ) const

inline

Definition at line 330 of file KVWilckeReactionParameters.h.

◆ ECM()

Double_t KVWilckeReactionParameters::ECM ( Double_t e_sur_a ) const

inline

Centre of mass energy from projectile E/A in laboratory

Definition at line 307 of file KVWilckeReactionParameters.h.

◆ epsilon_bar_Myers()

Double_t KVWilckeReactionParameters::epsilon_bar_Myers	(	Int_t	Z,
		Int_t	A
	)

static

epsilon_bar, Eq.(7) in W.D. Myers, Phys. Lett. B 30, 451 (1969)

Definition at line 133 of file KVWilckeReactionParameters.cpp.

◆ Eta()

Double_t KVWilckeReactionParameters::Eta ( Double_t e_sur_a ) const

inline

Coulomb parameter

Definition at line 260 of file KVWilckeReactionParameters.h.

◆ GetAC()

Int_t KVWilckeReactionParameters::GetAC ( ) const

inline

Definition at line 371 of file KVWilckeReactionParameters.h.

◆ GetAngularMomentumFromImpactParameter()

Double_t KVWilckeReactionParameters::GetAngularMomentumFromImpactParameter	(	Double_t	e_sur_a,
		Double_t	b
	)		const

inline

For beam energy e_sur_a [MeV/nucleon] and impact parameter b [fm], calculate the equivalent angular momentum [hbar]

Definition at line 164 of file KVWilckeReactionParameters.h.

◆ GetAP()

Int_t KVWilckeReactionParameters::GetAP ( ) const

inline

Examples: ClassTraj.cpp.

Definition at line 363 of file KVWilckeReactionParameters.h.

◆ GetAT()

Int_t KVWilckeReactionParameters::GetAT ( ) const

inline

Definition at line 367 of file KVWilckeReactionParameters.h.

◆ GetBassReactionCrossSection()

Double_t KVWilckeReactionParameters::GetBassReactionCrossSection ( Double_t e_sur_a )

Bass reaction cross-section [mb] for incident energy [MeV/nucleon].

Definition at line 352 of file KVWilckeReactionParameters.cpp.

◆ GetBSSCoulombPotential()

TF1 * KVWilckeReactionParameters::GetBSSCoulombPotential ( ) const

inline

Definition at line 216 of file KVWilckeReactionParameters.h.

◆ GetCentrifugalPotential() [1/2]

TF1 * KVWilckeReactionParameters::GetCentrifugalPotential	(	Double_t	e_sur_a,
		Double_t	b
	)		const

inline

Total (nuclear+coulomb+centrifugal) potential for given beam energy (E/A) and impact parameter (fm)

Definition at line 201 of file KVWilckeReactionParameters.h.

◆ GetCentrifugalPotential() [2/2]

TF1 * KVWilckeReactionParameters::GetCentrifugalPotential ( Double_t l ) const

inline

Total (nuclear+coulomb+centrifugal) potential for given angular momentum (hbar)

Definition at line 210 of file KVWilckeReactionParameters.h.

◆ GetCMQuarterPointAngle()

TF1 * KVWilckeReactionParameters::GetCMQuarterPointAngle ( ) const

inline

Definition at line 294 of file KVWilckeReactionParameters.h.

◆ GetCP()

Double_t KVWilckeReactionParameters::GetCP ( ) const

inline

Examples: ClassTraj.cpp.

Definition at line 375 of file KVWilckeReactionParameters.h.

◆ GetCrossSectionFromMaxAngularMomentum()

Double_t KVWilckeReactionParameters::GetCrossSectionFromMaxAngularMomentum	(	Double_t	e_sur_a,
		Double_t	lmax
	)		const

inline

Calculate cross-section [mb] for a given beam energy [MeV/nucleon] and maximum entrance channel angular momentum [hbar]

Definition at line 176 of file KVWilckeReactionParameters.h.

◆ GetCrossSectionFromMaxImpactParameter()

Double_t KVWilckeReactionParameters::GetCrossSectionFromMaxImpactParameter ( Double_t bmax ) const

inline

Calculate cross-section [mb] for a given maximum entrance channel impact parameter [fm]

Definition at line 189 of file KVWilckeReactionParameters.h.

◆ GetCT()

Double_t KVWilckeReactionParameters::GetCT ( ) const

inline

Examples: ClassTraj.cpp.

Definition at line 379 of file KVWilckeReactionParameters.h.

◆ GetFullDampingTKE()

Double_t KVWilckeReactionParameters::GetFullDampingTKE ( ) const

inline

Returns total kinetic energy of completely relaxed events in strongly damped collisions

Definition at line 234 of file KVWilckeReactionParameters.h.

◆ GetFusionCrossSection()

TF1 * KVWilckeReactionParameters::GetFusionCrossSection ( ) const

inline

Definition at line 326 of file KVWilckeReactionParameters.h.

◆ GetImpactParameterFromAngularMomentum()

Double_t KVWilckeReactionParameters::GetImpactParameterFromAngularMomentum	(	Double_t	e_sur_a,
		Double_t	l
	)		const

inline

For beam energy e_sur_a [MeV/nucleon] and angular momentum l [hbar], calculate the equivalent impact parameter [fm]

Definition at line 170 of file KVWilckeReactionParameters.h.

◆ GetLmax()

TF1 * KVWilckeReactionParameters::GetLmax ( ) const

inline

Definition at line 298 of file KVWilckeReactionParameters.h.

◆ GetMaxAngularMomentumFromCrossSection()

Double_t KVWilckeReactionParameters::GetMaxAngularMomentumFromCrossSection	(	Double_t	e_sur_a,
		Double_t	sigma
	)		const

inline

Calculate maximum entrance channel angular momentum [hbar] for a given cross-section [mb] and beam energy [MeV/nucleon] (sharp cut-off approximatin)

Definition at line 182 of file KVWilckeReactionParameters.h.

◆ GetMaxImpactParameterFromCrossSection()

Double_t KVWilckeReactionParameters::GetMaxImpactParameterFromCrossSection ( Double_t sigma ) const

inline

Calculate maximum entrance channel impact parameter [fm] for a given cross-section [mb] (sharp cut-off approximation)

Definition at line 195 of file KVWilckeReactionParameters.h.

◆ GetMaximumAngularMomentumWithPocket()

Double_t KVWilckeReactionParameters::GetMaximumAngularMomentumWithPocket ( )

Retuns maximum angular momentum for which a pocket exists in the interaction potential which corresponds to a lower potential energy than the maximum Double_t lmin, lmax; lmin = 0; lmax = 200; Double_t l = lmin; while (lmax > lmin) { if (PotentialPocketRadius(l) > 0.) { if (lmax - lmin == 2.0) return l; lmin = l; } else { if (l < 1) return 0; lmax = l; } if (lmax - lmin == 1.0) return lmin; l = TMath::Nint((lmin + lmax) / 2.); } return 0;

Definition at line 284 of file KVWilckeReactionParameters.cpp.

◆ GetMu()

Double_t KVWilckeReactionParameters::GetMu ( ) const

inline

reduced mass number

Examples: ClassTraj.cpp.

Definition at line 358 of file KVWilckeReactionParameters.h.

◆ GetNuclearProximityPotential()

TF1 * KVWilckeReactionParameters::GetNuclearProximityPotential ( ) const

inline

Definition at line 220 of file KVWilckeReactionParameters.h.

◆ GetReactionCrossSection()

TF1 * KVWilckeReactionParameters::GetReactionCrossSection ( ) const

inline

Definition at line 312 of file KVWilckeReactionParameters.h.

◆ GetRint()

Double_t KVWilckeReactionParameters::GetRint ( ) const

inline

Examples: ClassTraj.cpp.

Definition at line 383 of file KVWilckeReactionParameters.h.

◆ GetTotalPotential()

TF1 * KVWilckeReactionParameters::GetTotalPotential ( ) const

inline

Definition at line 224 of file KVWilckeReactionParameters.h.

◆ init()

void KVWilckeReactionParameters::init ( )

private

Definition at line 26 of file KVWilckeReactionParameters.cpp.

◆ InteractionRadius()

static Double_t KVWilckeReactionParameters::InteractionRadius	(	Int_t	aproj,
		Int_t	atarg
	)

inlinestatic

Interaction radius [fm]

Definition at line 79 of file KVWilckeReactionParameters.h.

◆ k()

Double_t KVWilckeReactionParameters::k ( Double_t e_sur_a ) const

inline

Asymptotic wave number in the centre-of-mass system

Definition at line 265 of file KVWilckeReactionParameters.h.

◆ Lmax()

Double_t KVWilckeReactionParameters::Lmax	(	Double_t *	x,
		Double_t *
	)		const

inline

Definition at line 290 of file KVWilckeReactionParameters.h.

◆ MatterHalfDensityRadius()

static Double_t KVWilckeReactionParameters::MatterHalfDensityRadius ( Int_t A )

inlinestatic

Matter half-density radius for nucleus mass A with width parameter b=1fm

Definition at line 95 of file KVWilckeReactionParameters.h.

◆ NLDSurfaceTensionCoefficient()

static Double_t KVWilckeReactionParameters::NLDSurfaceTensionCoefficient	(	Int_t	Z,
		Int_t	A
	)

inlinestatic

Nuclear liquid-drop surface-tension coefficient J. Blocki, J. Randrup, W.J. Swiatecki, and C.F. Tsang, Ann. Phys. (N. Y.) 105, 427 (1977)

Definition at line 239 of file KVWilckeReactionParameters.h.

◆ Potential()

Double_t KVWilckeReactionParameters::Potential	(	Double_t *	r,
		Double_t *
	)

inline

Total heavy-ion potential (nuclear proximity+coulomb) at distance r

Definition at line 149 of file KVWilckeReactionParameters.h.

◆ PotentialMaximumRadius()

Double_t KVWilckeReactionParameters::PotentialMaximumRadius ( Double_t l )

Find position (radial distance between centres) at which total potential has a maximum for the given angular momentum. Returns -1.0 if no maximum.

Definition at line 325 of file KVWilckeReactionParameters.cpp.

◆ PotentialPocketRadius()

Double_t KVWilckeReactionParameters::PotentialPocketRadius ( Double_t l )

Find position (radial distance between centres) at which total potential has a minimum for the given angular momentum. Returns -1.0 if no pocket.

Definition at line 240 of file KVWilckeReactionParameters.cpp.

◆ Print()

void KVWilckeReactionParameters::Print ( ) const

Definition at line 184 of file KVWilckeReactionParameters.cpp.

◆ ProjectileLabEQP()

Double_t KVWilckeReactionParameters::ProjectileLabEQP ( Double_t e ) const

inline

Laboratory energy of projectile elastically scattered at quarter-point angle

Definition at line 284 of file KVWilckeReactionParameters.h.

◆ ProjectileLabQP()

Double_t KVWilckeReactionParameters::ProjectileLabQP ( Double_t e ) const

inline

Quarter-point angle in the laboratory of projectile

Definition at line 278 of file KVWilckeReactionParameters.h.

◆ ProxPot()

Double_t KVWilckeReactionParameters::ProxPot	(	Double_t *	r,
		Double_t *
	)

inline

Nuclear proximity potential for nuclei separated by r J. Blocki, J. Randrup, W.J. Swiatecki, and C.F. Tsang Ann. Phys. (N. Y.) 105, 427-462 (1977)

< Matter half-density radii

Definition at line 129 of file KVWilckeReactionParameters.h.

◆ QuarterPointAngle()

Double_t KVWilckeReactionParameters::QuarterPointAngle	(	Double_t *	x,
		Double_t *
	)		const

inline

C.M. quarter point angle as a function of laboratory E/A of projectile

Definition at line 270 of file KVWilckeReactionParameters.h.

◆ r0_Wilcke()

static Double_t KVWilckeReactionParameters::r0_Wilcke	(	Int_t	aproj,
		Int_t	atarg
	)

inlinestatic

R0 [fm]

Definition at line 85 of file KVWilckeReactionParameters.h.

◆ RLDCriticalAngularMomentum()

Double_t KVWilckeReactionParameters::RLDCriticalAngularMomentum	(	Int_t	z,
		Int_t	a
	)

static

S. Cohen, F. Plasil and W.J. Swiatecki, Ann. Phys. (N. Y.) 82, 557 (1974) Rotating Liquid Drop model critical angular momentum Only y_I is returned (normally valid for fissility parameter > 0.81) as no parameterisation for y_II is given in the paper ???

Definition at line 164 of file KVWilckeReactionParameters.cpp.