Measuring fusion excitation functions with RIBs using the stacked target technique: problems and possible solutions Maria Fisichella Nucleus Nucleus June 2015

Activation technique and determination of the fusion excitation function

STEP 2 Off-line measurement of the produced activity (X or α or γ ) STEP 1 Single or multiple target activation Activation Technique Disadvantage: the beam energy distribution degrades as the beam traverses the different stack elements Advantages: It is possible to measure fusion cross-section for reaction induced by a low-energy light projectile onto a medium-mass target, where the produced RADIOACTIVE ER have low kinetic and their direct detection is not always possible ; By activating a stack of targets it is possible to extract the cross section at different energies without changing the beam energy.

σ(E) σ mean ErEr D(E,t) E out E in Which is the energy to associate to the measured  mean ? Easy solution : Apparently better solution : We define E r such that  mean =  (E r ) Are E or E eff good approximations of E r ? -  (E)=  0 exp(-  (E 0 -E)) - E=E 0 -  t Only for the ideal case of a mono-energetic beam and for thin targets will E r, E mean, E eff coincide. δ incoming distribution Gaussian incoming distribution FWHM=2 MeV 9 Li 17 MeV 120 Sn D(E,t 0 ) = energy distribution inside the target

A possible deconvolution procedure to extract  (E) After charaterising the target it is possible to determine D(E,t) by using simulation codes It can be determined by using a deconvolution procedure We looked for a g(E,μ) and calculated: We determine the best set parameters by minimising :

Energy distribution inside the target and target characterisation

ENERGY DISTRIBUTION INSIDE THE TARGET - D(E,t) If the incoming distribution FWHM << E loss => D(E,t) has not a gaussian shape EiEi EfEf The energy distribution inside the target depends on: 1. incoming beam energy distribution 2. energy loss 3. energy straggling 4. target non-uniformity Very different shapes and energy ranges in the two cases 0.5mg/cm 2

Foil non-uniformity No structures on the Nb substrate 120 Sn target  0.45 mg/cm 2 (0.6  m), evaporated onto 93 Nb 2mg/cm 2 Size of grains up to 2  m on Sn side 93 Nb rolled foil  1.5 mg/cm 2 SEM view α residual energy spectra The shape of the α residual energy spectra mirrors the Sn surface morphology Very good looking targets can be not really uniform….

6 Li 21 MeV Au Sn Nb Detector 6 Li 21 MeV Au For checking the procedure… Target thickness distribution By assuming this behaviour for the 120 Sn thickness distribution it is possible to reproduce the experimental spectra !! Polynomial target thickness distribution

Simulation study for 9 Li+ 120 Sn

1)Uniform 120 Sn and 93 Nb foils 2) ‘Polynomial’ w(t)for 120 Sn and Gaussian for 93 Nb (FWHM=15%) Simulation study for 9 Li+ 120 Sn FIRST target FIFTH target D(E,t) incoming outgoing a)

Deconvolution procedure : the best method for determining the fusion excitation function Simulation results FIFTH target D(E,t) Deconvolution

Considerations on some published fusion studies with RIBs - 6 He+ 206 Pb Pb targets alternated with Al degraders. 6 MeV FWHM energy dispersion after the stack. Authors estimate 2 orders of magnitude effect on data due to large energy dispersion but do not unfold data Pb targets alternated with Ti degraders. 1.3 MeV FWHM energy dispersion after the stack. Measured sigma factor 10 lower than Peniozhkevich one Effective energy approach applied, authors state: ‘if energy averaging procedure is disregarded  overestimated by factor 3’. They used an E eff approach. E c.m. FF Peniozhkevich et al. PRL 96,162701,(2006) Wolski et al. EPJ A47, 111, (2011)

Summary and conclusions In the papers information concerning the beam, target and degrader characteristic should be reported together with the statement of how these characteristic have influenced the data analysis and error propagation. For this technique to be successful: beam energy distribution and target non-uniformity have to be taken properly into account. A possible procedure to determine the target thickness distribution has been proposed. Simulations are needed to determine the energy distribution inside the target. The best procedure to determine the fusion excitation function is the deconvolution one. Thank you ! M. Fisichella, A. C. Shotter, A. Di Pietro, P. Figuera, M. Lattuada, C. Marchetta, V. Privitera, L. Romano, C. Ruiz and M. Zadro

Characterization of the Sn targets α (5.49 MeV) Sn Nb D1D1 D2D2 D3D3 D4D4 D5D5 D T = ∑ D i w i D i w i /D T =

SEM 165 Ho rolled foil  1.5 mg/cm Sn target  0.5 mg/cm 2 (0.65  m), evaporated onto 165 Ho 2mg/cm 2 64 Zn target 250 μg/cm2 (0.35 μm), evaporated onto 165 Ho 2mg/cm 2

What happens if thin targets are used? We considered incoming energy distributions with the same centroid but different FWHM impinging in the same thin target:

Stacked target experiment with a stable beam : 6 Li+ 120 LNS Small effects observed due to the use of a good quality stable beam and a stack of few relatively thin targets. Stack 1 (25 MeV) Stack 2 (21 MeV)