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