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S. Isaev, R. Prieels, Th. Keutgen, Y. El Masri, J. Van Mol, M. Delval

Study of proton-induced fission of actinides based on the measurements of fission fragment's characteristics by Multi-Wire Proportional gas Counters (MWPC). S. Isaev, R. Prieels, Th. Keutgen, Y. El Masri, J. Van Mol, M. Delval Institut de Physique Nuclaire, UCL, Louvain-la-Neuve, Belgium.

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S. Isaev, R. Prieels, Th. Keutgen, Y. El Masri, J. Van Mol, M. Delval

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  1. Study of proton-induced fission of actinides based on the measurements of fission fragment's characteristics by Multi-Wire Proportional gas Counters (MWPC) S. Isaev, R. Prieels, Th. Keutgen, Y. El Masri, J. Van Mol, M. Delval Institut de Physique Nuclaire, UCL, Louvain-la-Neuve, Belgium

  2. General scheme of the experimental set-up Counters for radioactivity control MWPC 1,2 large active area X,Y Multi Wire Proportional Counters GJ 1 MWPC 1 Actinide’s target Proton beam FARADAY GJ 2 MWPC 2 GJ 1,2 Microchannel-Si diode assembly DEMON liquid-scintillator cells

  3. MWPC experimental set-up(top view) 60cm Xanode Yanode MASK 30cm MWPC-1 position actinide’s target 45º Proton beam Cathode MASK Cathode -135º Yi1 MWPC-2 position 30cm Yi2 Yanode T0i Xanode 60cm Xi1 Xi2

  4. Y X Y12 MASK X12 X11 Y11 Calibration of anode's signal X11-X12 [ch.] Y11-Y12 [ch.] Y1[mm]=C*(Y11-Y12)[ch]+D X1[mm]=A*(X11-X12)[ch]+B Y1[mm] X1[mm] X11-X12[ch] Y11-Y12[ch]

  5. 30cm 60cm Calibration of cathode's signal for the same solid angle limitation: Toffset=2·T01 – T01~ T01=Toffset+D/v T01~=Toffset+D~/v D~=2·D 0º<Θ<1º T01 T01~ 1º<Θ<2º T01 T01~ 4º<Θ<5º 2º<Θ<3º 3º<Θ<4º T01~ T01 T01~ T01 T01 T01~

  6. Monitoring of cyclotron time-characteristics ΔTγ= ΔToffset 1ch(MWPC)=0.5ns 1ch(DEMON)=1.0ns Observation of gamma-peak by DEMON’s detector (liquid scintillator) Tγ(DEMON)

  7. Coincidence of cathode’s signals MWPC-1 Min<T01<Max MWPC-2 Min<T02<Max T02 T01

  8. T01 X12 X11 Anode’s signals association: delay-line conditions T01 – cathode fast signal X11, X12 – anode signals from both edges of delay-line Const-1<{X11+X12-2·T01+Anorm} {X11+X12-2·T01+Anorm}<Const-2 T01

  9. Fission event reconstruction: MWPCs->LAB(Dekart) Ymwpc1 XLAB YLAB X(Y)1=(X(Y)11-X(Y)12)·A+B ; T1=T01·0.5+Toffset-1 X(Y)2=(X(Y)22-X(Y)21)·A+B ; T2=T02·0.5+Toffset-2 Ymwpc2 D1 Z1LAB {X2,Y2,T2} Xmwpc1 L2 θ1=45º Y2LAB X1LAB Y1LAB L1 X2LAB ZLAB Z2LAB θ2=-135º {X1,Y1,T1} D2 Fission fragment #1 X1LAB=D1·Sinθ1-X1·Cosθ1 Z1LAB=D1·Cosθ1+X1·Sinθ1 Y1LAB=Y1 Xmwpc2 Fission fragment #2 X2LAB=D2·Sinθ2+X2·Cosθ2 Z2LAB=D2·Cosθ2-X2·Sinθ2 Y2LAB=Y2

  10. Fission event reconstruction (LAB): Dekart->Polar XLAB YLAB θ2s=arcCos(Z2LAB/L2) φ2s=arcTan(Y2LAB/X2LAB) θ1s=arcCos(Z1LAB/L1) φ1s=arcTan(Y1LAB/X1LAB) φ2s Z1LAB θ2s L2 Y1LAB Y2LAB X1LAB θ1s X2LAB φ1s ZLAB L1 Z2LAB -180º<φs<180º 0º<θs<180º φ1s θ1s

  11. m1 v1LAB v1CM mp, vp ψ1 θ1s vcm M, v=0 Mc, vc.m. θ2s ψ2 v2LAB v2CM m2 Center-mass coordinates Known values: θ1s, θ2s, v1LAB, v2LAB Velocity of center of mass: Velocities of fragments in CM:

  12. m1 v1LAB (v1LAB)┴ v1CM θ1s vcm θ2s (v2LAB)┴ v2CM v2LAB m2 Determination of FF’s masses: first approximation Momentum conservation perpendicular to the beam axis: (m10·v10)┴= (m20·v20)┴ Masses of FF, target nucleus and projectile: m10+m20=Mtarget+Mprojectile-Mpre R = (v20)┴ / (v10)┴ m10= Mtarget+Mprojectile-Mpre/ ( 1 + 1 / R ) m20= Mtarget+Mprojectile-Mpre/ ( 1 + R ) Conservation of charge’s density: MC’ / ZC’ = m10 / z10 = m20 / z20 z10= m10·ZC’/ MC’ z20= m20·ZC’/ MC’ Non-relativistic formula for kinetic energy: E10= (1/2)·m10·(v10)2 E20= (1/2)·m20·(v20)2

  13. Target θtarget θ1S d1 d d2 θ2S Calculation of energy losses Correction for thickness d1=|d/Cos(θ1S - θtarget)| d2=|d/Cos(θ2S + θtarget)| Correction of energy: E11= E10+E1loss E21= E20+E2loss Velocities “in target”: Velocity of center of mass “in target”: Velocities of fragments in CM “in target”

  14. Algorithm for FF mass determination Known: v10, v20 – velocities “in MWPC” 1. First approximation “in MWPC”: m10, m20, z10, z20, E10, E20 2. Calculation of energy loss: E11=E10+ΔE1 & E22=E20+ ΔE2 Recalculation of velocities “in target” (using m10, m20): v11 and v21 3. Check the momentum conservation “in target”: (v11·m11)┴= (v21·m21)┴ Recalculate new masses m11, m21 4. Come back to the point of registration “in MWPC”: v10, v20 Set: m10 = m11, m20 = m21 Recalculation of E10, E20, z10, z20

  15. Calculations of energy loss in reaction: 23892U(p,f)→10541Nb+13452Te 1. SRIM – The Stopping and Range of Ions in Matter (J. Ziegler et. all) www.srim.org 2. Bethe-Bloch formula (by W. Leo) 3. Bethe-Bloch formula (by K. Krane) re – classical electron radius Z – atomic number of absorbing material me – electron mass A – atomic weight of absorbing material Na – Avogadro’s number I – mean excitation potential I = 9.76·Z + 58.8·Z-0.19 ρ – density of absorbing material z – charge of incident particle in units of e β=v/c of the incident particle γ = 1/(1-β2)1/2 Wmax – maximum energy transfer in a single collision Wmax = 2·me·c2·(β· γ)2

  16. Calculations of energy loss in reaction: 23892U(p,f)→10541Nb+13452Te ρtarget = 19.043 g/cm3 Dx = 180 μg/cm2 10541Nb 13452Te

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