CYGNUS

A CODE FOR COULOMB-EXCITATION ANALYSIS IN C++

CYGNUS is still in a testing phase and should not be used for analysis in isolation, but should be used alongside a traditional code such as GOSIA.

Requirements

• Cygnus requires C++11 and ROOT v6 with the MathMore and MINUIT2 libraries
• In order to run compiled scripts, the Cygnus/bin directory must be added to LD_LIBRARY_PATH

Running Cygnus

In a ROOT terminal:

• Run rootstart.C on root startup (loads libraries)

A compiled code:

• Examples and makefiles are included in the Examples directory

Data format

Cygnus ignores any line containing an exclamation mark (!)

Nucleus file (an example is included):

1st line: A, Z, NStates, MaxLambda

• A and Z are mass number and proton number of the nucleus
• NStates is the number of states in the nucleus
• MaxLambda is the maximum lambda (1-6 = E1-E6, 7 = M1) recommended to leave MaxLambda = 7

Lines 2 -> 2 + NStates: Index, E, J, P

• Index is the state index, ordered by energy (0 = ground state)
• E is the energy, in units of MeV
• J and P are the spin and parity of the state

Lines 2 + NStates -> End: Index_I, Index_F, ME, Lambda

• Index_I is the initial state (by convention, lower energy)
• Index_F is the final state (higher energy)
• ME is the matrix element in eb units (note: Not efm)
• Lambda is the multipolarity of the transition (same convention as previously stated)

Data file (an example is included):

For every experiment:

Line 1: EXPT, Index, Energy, Theta_min, Theta_max

• EXPT (text: "EXPT")
• Index is the experiment number
• Energy is the beam energy - not presently used
• Theta_min is the minimum theta - not presently used
• Theta_max is the maximum theta - not presently used

Line 2 -> 2+nData: Index_I, Index_F, Yield, Uncertainty

• Index_I is initial state. Note that now, the initial state is the higher energy state.
• Index_F is the final state. Note that now, the final state is the lower energy state.
• Yield is the experimental counts
• Uncertainty is the uncertainty on the experimental data

Basic Usage

Class: NucleusReader

Loads data from a nucleus file (formatted as above) and puts it into a Nucleus format.

Class: Nucleus

Class holding the nucleus information, as loaded from the nucleus data file. Can be grabbed from NucleusReader:

Nucleus *nucl = NucleusReader->GetNucleus();

Class: Reaction

Deals with the reaction kinematics of the experiment:

Reaction *reac = new Reaction(aB,zB,aT,zT,eBeam)

• aB and zB are mass and proton number of the beam
• aT and zT are mass and proton number of the target
• eBeam is the beam energy in the lab (MeV)

Can set actual nuclear masses using:

reac->SetMasses(mB,mT)

• mB and mT are beam and target masses (amu)

Class: PointCoulEx

Performs a Coulomb excitation calculation for a single energy at a single theta value. Requires a Nucleus and Reaction:

PointCoulEx *poin = new PointCoulEx(nucl,reac)

To run the calculation:

poin->CalculatePointProbabilities(theta)

• theta in the center of mass frame, in units of degrees

To get the excitation probabilities:

TVectorD vec = point->GetProbabilitiesVector()

Class: StoppingPower

Holder class for stopping power information. Performs a cubic fit to stopping power data.

StoppingPower dEdX;
dEdX.AddStoppingPower(E,SP)

• E and SP are the energy (MeV) and stopping power (MeV/mg/cm2) meshpoint

dEdX.FitStoppingPowers()

• Fits stopping power data with cubic polynomial

Class: Experiments

Performs integrations of Coulomb excitation values and determines the correction for a point calculation to a full integral over theta and energy. Requires Nucleus and Reaction:

Experiments *expt = new Experiments(nucl,reac);

To define a new experimental range:

expts->NewExperimentRange(tmin,tmax,nt,emin,emax,ne,tarDet)

• tmin and tmax are the min and max theta in degrees, in the lab frame
• nt is the number of theta meshpoints to use
• emin and emax are th min and max energies, in MeV
• ne is the number of energy meshpoints to use
• tarDet is a bool which is TRUE for target detection and FALSE for projectile detection

expts->SetStopping(dEdX)

• THIS IS A NECESSARY STEP FOR THE INTEGRATION PROCESS TO WORK - without the stopping powers, the integration is invalid

expts->PointCorrections

• Determines the point correction factors

Fitting Data

Cygnus uses the ROOT::Minimizer package. This comes with a number of minimization options. The user can define a minimizer choice and select an algorithm for that minimizer. The options are:

MINIMIZER:	ALGORITHM:
Minuit2	Migrad
	Simplex
	Combined
	Scan
	Fumili2
Genetic	-
GSLMultiMin	ConjugateFR
	ConjugatePR
	BFGS
	BFGS2
	SteepestDescent
GSLMultiFit
GSLSimAn

By default, Cygnus uses the user defined experimental uncertainties in the minimization routine. In this case it is assumed that the data are efficiency corrected and a simple chisquare statistic. In general this is suitable, with large amounts of data, however when dealing with smaller data samples, the symmetric uncertainty assumption and the standard Neyman's chisquare ceases to be a good statistic. Cygnus therefore allows the user the option of a likelihood-derived chisquare statistic (see: https://www.sciencedirect.com/science/article/pii/0167508784900164). This statistic is suitable for low statistics data but requires the user to provide the observed counts, rather than the corrected.

This can be specified by calling the CoulExFitter function SetPoissonUncertainties(). Then, the fitter no-longer uses the user defined uncertainties. Because the minimizer uses the observed counts, the detection efficiency must be user specified and is then incorporated into the fit.

The minimizer by default creates and stores a (symmetric) covariance matrix. If the user wants access to asymmetric uncertainties (in general, CoulEx uncertainties are asymmetric), they can specify it using the SetDoFullUncertainty() function in CoulExFitter.

License

CYGNUS is distributed under the GPL v3 license.

LLNL-CODE-761182