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

3. MWPC experimental set-up (top view) actinide’s target Proton beam MWPC-1 position MWPC-2 position MASK Y anode X anode Cathode 45º -135º 30cm 60cm Yi1Yi1 Yi2Yi2 Xi1Xi1Xi2Xi2 T0 i

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

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

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

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

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

9. Fission event reconstruction: MWPCs->LAB(Dekart) X mwpc2 X mwpc1 Y mwpc2 Y mwpc1 Y LAB X LAB Z LAB θ 1 =45º θ 2 =-135º {X 2,Y 2,T 2 } {X 1,Y 1,T 1 } X(Y) 1 =(X(Y)11-X(Y)12)·A+B ; T 1 =T01·0.5+T offset-1 X(Y) 2 =(X(Y)22-X(Y)21)·A+B ; T 2 =T02·0.5+T offset-2 D2D2 D1D1 L2L2 L1L1 X 2 LAB Z 2 LAB Y 2 LAB X 1 LAB Z 1 LAB Y 1 LAB Fission fragment #1 X 1 LAB =D 1 ·Sinθ 1 -X 1 ·Cosθ 1 Z 1 LAB =D 1 ·Cosθ 1 +X 1 ·Sinθ 1 Y 1 LAB =Y 1 Fission fragment #2 X 2 LAB =D 2 ·Sinθ 2 +X 2 ·Cosθ 2 Z 2 LAB =D 2 ·Cosθ 2 -X 2 ·Sinθ 2 Y 2 LAB =Y 2

10. Fission event reconstruction (LAB): Dekart->Polar Y LAB X LAB Z LAB L2L2 L1L1 X 2 LAB Z 2 LAB Y 2 LAB X 1 LAB Z 1 LAB Y 1 LAB θ1sθ1s θ2sθ2s φ1sφ1s φ2sφ2s -180º<φ s <180º 0º<θ s <180º θ1sθ1s φ1sφ1s θ 1 s =arcCos(Z 1 LAB /L 1 ) φ 1 s =arcTan(Y 1 LAB /X 1 LAB ) θ 2 s =arcCos(Z 2 LAB /L 2 ) φ 2 s =arcTan(Y 2 LAB /X 2 LAB )

11. Center-mass coordinates m p, v p M, v=0 M c, v c.m. v 2 LAB m2m2 m1m1 v 1 LAB v 1 CM v 2 CM v cm θ1sθ1s θ2sθ2s ψ1ψ1 ψ2ψ2 Known values: θ 1 s, θ 2 s, v 1 LAB, v 2 LAB Velocity of center of mass: Velocities of fragments in CM:

12. Determination of FF’s masses: first approximation (v 1 LAB ) ┴ v 2 LAB m2m2 m1m1 v 1 LAB v 1 CM v 2 CM v cm θ1sθ1s θ2sθ2s (v 2 LAB ) ┴ Momentum conservation perpendicular to the beam axis: (m 1 0 ·v 1 0 ) ┴ = (m 2 0 ·v 2 0 ) ┴ m 1 0 +m 2 0 =M target +M projectile -M pre m 1 0 = M target +M projectile -M pre / ( 1 + 1 / R ) m 2 0 = M target +M projectile -M pre / ( 1 + R ) R = (v 2 0 ) ┴ / (v 1 0 ) ┴ Conservation of charge’s density: M C ’ / Z C ’ = m 1 0 / z 1 0 = m 2 0 / z 2 0 Non-relativistic formula for kinetic energy: E 1 0 = (1/2)·m 1 0 ·(v 1 0 ) 2 E 2 0 = (1/2)·m 2 0 ·(v 2 0 ) 2 Masses of FF, target nucleus and projectile: z 1 0 = m 1 0 · Z C ’/ M C ’ z 2 0 = m 2 0 ·Z C ’/ M C ’

13. Calculation of energy losses Correction for thickness d 1 =|d/Cos(θ 1 S - θ target )| d 2 =|d/Cos(θ 2 S + θ target )| θ1Sθ1S θ2Sθ2S θ target Target d d1d1 d2d2 Correction of energy: E 1 1 = E 1 0 +E 1 loss E 2 1 = E 2 0 +E 2 loss Velocities “in target”: Velocity of center of mass “in target”: Velocities of fragments in CM “in target”

14. Algorithm for FF mass determination Known: v 1 0, v 2 0 – velocities “in MWPC” 1. First approximation “in MWPC”: m 1 0, m 2 0, z 1 0, z 2 0, E 1 0, E 2 0 2. Calculation of energy loss: E 1 1 =E 1 0 +ΔE 1 & E 2 2 =E 2 0 + Δ E 2 Recalculation of velocities “in target” (using m 1 0, m 2 0 ): v 1 1 and v 2 1 3. Check the momentum conservation “in target”: (v 1 1 ·m 1 1 ) ┴ = (v 2 1 ·m 2 1 ) ┴ Recalculate new masses m 1 1, m 2 1 4. Come back to the point of registration “in MWPC”: v 1 0, v 2 0 Set: m 1 0 = m 1 1, m 2 0 = m 2 1 Recalculation of E 1 0, E 2 0, z 1 0, z 2 0

15. Calculations of energy loss in reaction: 238 92 U(p,f)→ 105 41 Nb+ 134 52 Te 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) r e – classical electron radius Z – atomic number of absorbing material m e – electron mass A – atomic weight of absorbing material N a – 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-β 2 ) 1/2 W max – maximum energy transfer in a single collision W max = 2·m e ·c 2 ·(β · γ) 2

16. Calculations of energy loss in reaction: 238 92 U(p,f)→ 105 41 Nb+ 134 52 Te ρ target = 19.043 g/cm 3 D x = 180 μg/cm 2 E MeV LeoKrane SRIMpresent z eff 1 z eff 2 z eff 1 z eff 2 802.804.832.824.862.342.37 136.55.326.585.346.622.842.85 E MeV LeoKrane SRIMpresent z eff 1 z eff 2 z eff 1 z eff 2 801.934.651.954.702.412.65 136.54.888.564.918.613.093.31 134 52 Te 105 41 Nb