deformation.C

Explore nuclear deformation

This example macro produces the correlation between normalized transition strength B(E2)/A expressed in Weisskopf unit and the ratio between the energy of the first 4 \(^+\) and 2 \(^+\) states for all even-even nuclei. The color scale and the shape of the points reflect the quadrupole deformation \(\beta_2\) of the ground state while the size of each point in proportional to A \(^{2/3}\).

Start tkn-root, compile and execute this macro :

tkn-root
 _____    _   _   |  Documentation: https://tkn.in2p3.fr/
(_   _)  | \ | |  |  Source: https://gitlab.in2p3.fr/tkn/tkn-lib
  | |_  _|  \| |  |
  | | |/ /     |  |  Version 1.0
  | |   <| |\  |  |
  |_|_|\_\_| \_|  |  Database: TkN_ensdf_221101_xundl_210701_v1.0.db
 
 
tkn [0] .L deformation.C+
tkn [1] draw_deformation()

It produces the following plot:

Source code :

#include "TH2F.h"
#include "TStyle.h"
#include "TGraph2D.h"
#include "TGraph.h"
#include "TLatex.h"
#include "TLegend.h"
#include "TView.h"
#include "TEllipse.h"
#include "TMath.h"
#include "TArrow.h"
#include "TROOT.h"
 
#include "tkmanager.h"
#include "tknuclear_chart.h"
 
#define COLORS 20
 
using namespace  tkn;
 
TH2F* setup_histo(double ts = .05);
void draw_legend(int palette[COLORS], double betamax, double ts = .05);
 
void draw_deformation()
{
    gROOT->SetStyle("tkn-histo");
    gStyle->SetOptStat(0);
    gStyle->SetOptTitle(0);
 
    glog.set_warnings(false);
 
    int cs = 1300;
    TCanvas *c = new TCanvas("c","c",cs,cs*.7);
    c->SetLeftMargin(0.15);
    c->SetBottomMargin(0.15);
    c->SetRightMargin(0.05);
    c->SetTopMargin(0.05);
    c->SetTickx();
    c->SetTicky();
    c->SetBorderMode(0);
    c->SetBorderSize(0);
 
    TH2F *h = setup_histo();
    h->Draw();
 
    Double_t r[]    = {0.0, 0.0, 1.0, 1.0};
    Double_t g[]    = {0.0, 1.0, 1.0, 0.0};
    Double_t b[]    = {1.0, 1.0, 0.0, 0.0};
    Double_t stop[] = {0.0, 0.3, 0.7, 1.0};
 
    int colu=TColor::CreateGradientColorTable(4, stop, r, g, b, COLORS);
    int palette[COLORS];
    for(int k=0;k<COLORS;k++) palette[k]=colu+k;
 
    double betamax = .6;
    int col=0;
 
    tkn::tkmanager dtm;
    for(const auto &nuc : dtm.get_nuclei([](auto nuc) {return (nuc->get_z()%2==0 && nuc->get_n()%2==0);})) {
 
        auto lev_scheme = nuc->get_level_scheme();
 
        auto lvl2 = lev_scheme->get_level("2+1",true);
        auto lvl4 = lev_scheme->get_level("4+1",true);
        if(!lvl2||!lvl4) continue;
 
        if(!lvl2->has_property("energy")||!lvl4->has_property("energy")) continue;
        double e2 = lvl2->get_energy();
        double e4 = lvl4->get_energy();
        double r42 = e4/e2;
 
        auto gamma = lev_scheme->get_decay<tkgammadecay>("2+1->0+1",false);
        if(!gamma) continue;
        auto BE2W = gamma->get_trans_prob(true,2,true);
        if(BE2W<=0||std::isnan(BE2W)) continue;
 
        auto quad_def = nuc->get("quadrupoleDeformation");
        if(!quad_def) continue;
 
        double beta = quad_def->get_value();
        if(beta>betamax) continue;
        col = palette[TMath::Nint((COLORS-1)*beta/betamax)];
 
        double radius = .008*sqrt((1+beta)*pow(nuc->get_a(),2./3.));
        TEllipse* el = new TEllipse(r42,BE2W/nuc->get_a(),radius,radius*1.2*(1+beta));
        el->SetLineWidth(0);
        el->SetFillColorAlpha(col,.7);
        el->SetLineColorAlpha(col,0);
        el->Draw("same");
    }
 
    draw_legend(palette, betamax);
}
 
TH2F *setup_histo(double ts)
{
    TH2F *h = new TH2F("h","h",100,1,3.5,100,-0.1,2);
    h->GetXaxis()->SetNdivisions(209);
    h->GetYaxis()->SetNdivisions(209);
    h->GetXaxis()->SetLabelSize(ts);
    h->GetYaxis()->SetLabelSize(ts);
    h->GetXaxis()->SetTitleSize(ts+.01);
    h->GetYaxis()->SetTitleSize(ts+.01);
    h->GetXaxis()->SetTickLength(.02);
    h->GetYaxis()->SetTickLength(.02*.7);
    h->GetXaxis()->SetTitleOffset(1.1);
    h->GetYaxis()->SetTitle("B(E2)/A (in Weisskopf unit)");
    h->GetXaxis()->SetTitle("E(4^{+})/E(2^{+})");
    return h;
}
 
void draw_legend(int palette[], double betamax, double ts)
{
    TEllipse* el = 0;
    TLatex* txt = 0;
 
    double yy  = 1.7;
    double dyy = .02;
    int    col = 0;
 
    double val =betamax;
    el = new TEllipse(1.2,yy,.05,.05*1.2*(1+val));
    col = palette[TMath::Nint((COLORS-1)*val/betamax)];
    el->SetFillColorAlpha(col,.7);
    el->SetLineColorAlpha(kBlack,0);
    el->Draw("same");
 
    txt = new TLatex(1.3,yy, "0.6");
    txt->SetTextAlign(12);
    txt->SetTextFont(132);
    txt->SetTextSize(ts);
    txt->Draw("same");
 
    yy-= .05*1.2*(1+val)+dyy;
    val = 0.4;
    yy-= .05*1.2*(1+val);
 
    el = new TEllipse(1.2,yy,.05,.05*1.2*(1+val));
    col = palette[TMath::Nint((COLORS-1)*val/betamax)];
    el->SetFillColorAlpha(col,.7);
    el->SetLineColorAlpha(kBlack,0);
    el->Draw("same");
 
    txt = new TLatex(1.3,yy, "0.4");
    txt->SetTextAlign(12);
    txt->SetTextFont(132);
    txt->SetTextSize(ts);
    txt->Draw("same");
 
    yy-= .05*1.2*(1+val)+dyy;
    val = 0.2;
    yy-= .05*1.2*(1+val);
 
    el = new TEllipse(1.2,yy,.05,.05*1.2*(1+val));
    col = palette[TMath::Nint((COLORS-1)*val/betamax)];
    el->SetFillColorAlpha(col,.7);
    el->SetLineColorAlpha(kBlack,0);
    el->Draw("same");
 
    txt = new TLatex(1.3,yy, "0.2");
    txt->SetTextAlign(12);
    txt->SetTextFont(132);
    txt->SetTextSize(ts);
    txt->Draw("same");
 
    yy-= .05*1.2*(1+val)+dyy;
    val = 0.0;
    yy-= .05*1.2*(1+val);
 
    el = new TEllipse(1.2,yy,.05,.05*1.2*(1+val));
    col = palette[TMath::Nint((COLORS-1)*val/betamax)];
    el->SetFillColorAlpha(col,.7);
    el->SetLineColorAlpha(kBlack,0);
    el->Draw("same");
 
    txt = new TLatex(1.3,yy, "0.0");
    txt->SetTextAlign(12);
    txt->SetTextFont(132);
    txt->SetTextSize(ts);
    txt->Draw("same");
}