coulomb excitation data analysis codes; gosia 2007 - Physics and ...

5.12.5 TOTAL COINCIDENT γ-RAY YIELDSNote that OP.INTG evaluates the integrated coincident γ-ray yield in the laboratory frame for transitionI → I f that is defined by equation 4.22. That is:Y i (I → I f )=Z EmaxE mindE 1( dEdx ) Z θp,maxθ p,minY Point (I → I f )dθ p (4.22)where the integrand is given byZY Point d 2 σ(I → I f )(I → I f )=sin(θ p )dφφ pdΩ γ dΩ p (4.16)pwhere this integrand is given byd 2 σ(I → I f )dΩ p dΩ γ= σ R (θ p ) X R kχ (I,I f ; θ p )P kχ (θ γ )(2 cos χ(φ p − φ γ ) − δ χ0 ) (4.13)kχ≥0Note that Y (I → I f ) includes the Rutherford cross section, the sin(θ p ) term, the target thickness,integration over the θ p ,φ p for the detected coincident particles, the deorientation effect and γ-detector Q Kattenuation coefficients. Note that OP,INT does not include the detection efficiencies per unit solid anglefor charged particle and γ-rays, ε p and ε γ .The total number of coincident γ-raysdetectedthenisgivenbyDetected events N i =10 −30 ·∙ Qˆqe¸·∙NAA¸· Y (I → I f ) · ε p · ε γ · ∆Ω γwhere:Q is the integrated beam charge [C]ˆq the average charges state of the beame the proton charge [1.602 × 10 −19 C]N A Avogadro number (6.022 × 10 23 Atoms/mol)A target mass number (gm/mol)dEMeVdxenergy loss in target in [mg/cm] 2Y (I → I f ) OP.INT output in [mb · mg/cm 2 /sr]ε p particle detection efficiency which normally is perfect, that is, ε p =1regardless of solid anglecovered by the integration in OP,INTG.ε γ γ-ray detection efficiency per unit solid angle ∆Ω γ . That is, for a perfect blackbody γ-ray detectorof solid angle ∆Ω γ the ε γ =1. Note that for a 4π array like Gammasphere the product ε γ · ∆Ω γ ≈ 0.09 at1.33 MeV.EXAMPLE:During a complete experiment 1.71 × 10 15 136 Xe ions bombarded a 178 Hf target of areal density ρ · dx =0.50mg/cm 2 and A = 178g/mol. A GOSIA integration over the CHICO charged particle detector plustarget thickness produces Y 14 +(14 + → 12 + )=9.65mb · mg/cm 2 /sr for the 626keV 14 + → 12 + ground-bandtransition. The particle detection efficiency ε p =1and γ-ray detection efficiency of Gammasphere for this626keV transition is ε γ · ∆Ω γ =0.14. Thus the total number of detected events is∙ ¸6.02 × 10N 14 + = 10 −30 · 1.71 × 10 15 23·· 9.65 · 1 · 0.14178= 7.8 × 10 6 detected events84