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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
General scheme of the experimental set-up
FARADAY
GJ 1
GJ 2
MWPC 1
MWPC 2
Actinide’starget
DEMONliquid-scintillator cells
Proton beam
MWPC 1,2large active area X,YMulti Wire Proportional Counters
GJ 1,2Microchannel-Sidiode assembly
Counters forradioactivity control
MWPC experimental set-up(top view)
actinide’starget
Proton beam
MWPC-1 position
MWPC-2 position
MASK
MASK
Yanode
Yanode
Xanode
Xanode
Cathode
Cathode
45º
-135º
30cm
30cm
60cm
60cm
Yi1
Yi2
Xi1 Xi2
T0i
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
Calibration of cathode's signal
T01=Toffset+D/vT01~=Toffset+D~/vD~=2·D
for the same solid angle limitation:Toffset=2·T01 – T01~
30cm 60cm
0º<Θ<1º
1º<Θ<2º
2º<Θ<3º3º<Θ<4º4º<Θ<5º
T01~
T01
T01
T01 T01
T01
T01~
T01~T01~T01~
Monitoring of cyclotron time-characteristics
Observation of gamma-peakby DEMON’s detector(liquid scintillator)
ΔTγ= ΔToffset1ch(MWPC)=0.5ns1ch(DEMON)=1.0ns
Tγ(DEMON)
Coincidence of cathode’s signals
MWPC-1Min<T01<Max
MWPC-2Min<T02<Max
T01 T02
Anode’s signals association: delay-line conditions
Const-1<{X11+X12-2·T01+Anorm}
T01 – cathode fast signalX11, X12 – anode signals from both edges of delay-line
X11 X12T01
T01
{X11+X12-2·T01+Anorm}<Const-2
Fission event reconstruction: MWPCs->LAB(Dekart)
Xmwpc2
Xmwpc1
Ymwpc2
Ymwpc1YLAB
XLAB
ZLAB
θ1=45º
θ2=-135º
{X2,Y2,T2}
{X1,Y1,T1}
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
D2
D1
L2
L1
2)2(1
2)2(1
2)2(1)2(1 DYXL )2(1)2(1)2(1 TLv LAB
X 2LAB
Z2LAB
Y2
LA
B
X 1LAB
Z1LAB
Y1
LA
B
Fission fragment #1X1
LAB=D1·Sinθ1-X1·Cosθ1
Z1LAB=D1·Cosθ1+X1·Sinθ1
Y1LAB=Y1
Fission fragment #2X2
LAB=D2·Sinθ2+X2·Cosθ2
Z2LAB=D2·Cosθ2-X2·Sinθ2
Y2LAB=Y2
Fission event reconstruction (LAB): Dekart->Polar
YLAB
XLAB
ZLAB
L2
L1
X 2LAB
Z2LAB
Y2
LA
B
X 1LAB
Z1LAB
Y1
LA
B
θ1s
θ2s
φ1s
φ2s
-180º<φs<180º0º<θs<180º
θ1s
φ1s
θ1s=arcCos(Z1
LAB/L1)φ1
s=arcTan(Y1LAB/X1
LAB)
θ2s=arcCos(Z2
LAB/L2)φ2
s=arcTan(Y2LAB/X2
LAB)
)2(1)2(1)2(1 TLv LAB
Center-mass coordinates
mp, vp
M, v=0 Mc, vc.m.
v2LAB
m2
m1
v1LAB v1
CM
v2CM
vcm
θ1s
θ2s
ψ1
ψ2
Known values:θ1
s, θ2s, v1
LAB, v2LAB
Velocity of center of mass:
SLABSLAB
SSLABLAB
mc SinvSinv
Sinvvv
2211
2121..
)(
Velocities of fragments in CM:
SLABmc
LABmc
CM
SLABmc
LABmc
CM
Cosvvvvv
Cosvvvvv
22..2
22
..2
11..2
12
..1
2)()(
2)()(
Determination of FF’s masses: first approximation
(v1LAB)┴
v2LAB
m2
m1
v1LAB
v1CM
v2CM
vcmθ1
s
θ2s
(v2LAB)┴
Momentum conservation perpendicular to the beam axis: (m10·v1
0)┴= (m20·v2
0)┴
m10
+m20=Mtarget+Mprojectile-Mpre
m10= Mtarget+Mprojectile-Mpre/ ( 1 + 1 / R )
m20= Mtarget+Mprojectile-Mpre / ( 1 + R )
R = (v20)┴ / (v1
0)┴
Conservation of charge’s density:MC’ / ZC’ = m1
0 / z10 = m2
0 / z20
Non-relativistic formula for kinetic energy:
E10= (1/2)·m1
0·(v10)2 E2
0= (1/2)·m20·(v2
0)2
Masses of FF, target nucleus and projectile:
z10= m1
0·ZC’/ MC’
z20= m2
0·ZC’/ MC’
Calculation of energy losses
Correction for thicknessd1=|d/Cos(θ1
S - θtarget)|d2=|d/Cos(θ2
S + θtarget)|
θ1S
θ2S
θtarget
Target
d
d1
d2
Correction of energy:E1
1= E10+E1
loss
E21= E2
0+E2loss
Velocities “in target”:02
12
12
01
11
11
2
2
mEv
mEv
Velocity of center of mass “in target”:
SS
SS
CM SinvSinv
Sinvvv
2121
11
2112
111 )(
Velocities of fragments in CM “in target”
SCMCM
CM
SCMCM
CM
Cosvvvvv
Cosvvvvv
212
1212
2112
111
1211
2111
2)()()(
2)()()(
Algorithm for FF mass determination
Known: v10, v2
0 – velocities “in MWPC”
1. First approximation “in MWPC”: m10, m2
0, z10, z2
0, E10, E2
0
2. Calculation of energy loss: E11=E1
0+ΔE1 & E22=E2
0+ ΔE2
Recalculation of velocities “in target” (using m10, m2
0): v11 and v2
1
3. Check the momentum conservation “in target”: (v11·m1
1)┴= (v21·m2
1)┴
Recalculate new masses m11, m2
1
4. Come back to the point of registration “in MWPC”: v10, v2
0
Set: m10 = m1
1, m20 = m2
1
Recalculation of E10, E2
0, z10, z2
0
Calculations of energy loss in reaction: 23892U(p,f)→105
41Nb+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)
2
2max
22
2
222 2
2ln2
I
Wvmz
A
ZcmrN
dx
dE eeea
3. Bethe-Bloch formula (by K. Krane)
2222
22
2
0
2
1ln2
ln4
4
I
cm
Acm
ZNze
dx
dE e
e
a
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 eβ=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
Bohreff v
vzz 3/11
3/22 exp1
zv
vzz
Bohreff
Calculations of energy loss in reaction: 23892U(p,f)→105
41Nb+13452Te
ρtarget = 19.043 g/cm3 Dx = 180 μg/cm2
E
MeV
Leo Krane
SRIM presentzeff1 zeff
2 zeff1 zeff
2
80 2.80 4.83 2.82 4.86 2.34 2.37
136.5 5.32 6.58 5.34 6.62 2.84 2.85
E
MeV
Leo Krane
SRIM presentzeff1 zeff
2 zeff1 zeff
2
80 1.93 4.65 1.95 4.70 2.41 2.65
136.5 4.88 8.56 4.91 8.61 3.09 3.31
13452Te
10541Nb