Collective nuclear motion at finite temperature investigated with fission reactions induced by 238 U at 1 A GeV on deuterium Jorge Pereira Conca Universidad de Santiago de Compostela (USC)
Dec 20, 2015
Collective nuclear motion at finite temperature investigated with fission
reactions induced by 238U at 1 A GeV on deuterium
Jorge Pereira Conca Universidad de Santiago de Compostela (USC)
Collective phenomena in hot nuclei
VibrationsRotations Fission
Nucleus: N-body mesoscopic system
Presence and nature of collective nuclear phenomena
Deexcitation of hot compound nuclei (wide range of excitation energies)
Nuclear Physics: nature of the nuclei
•Individual excitations of nucleons
•Collective excitations of nucleons
Single-particle model
Collective model
Spectroscopic technique (Low Lying states)
Study of collective nuclear phenomena from the competition fission vs. evaporation
Experimental observable: fission and evaporation production cross section
Excited nuclei (pre-fragments):
•Well defined initial conditions (Small deformations and low angular momenta)
•Wide range of excitation energies
Spallation reaction 238U at 1AGeV on deuterium
Collective phenomena: competition between fission and evaporation
•High fissilities
•Experiment: measurement of fission and evaporation residue productions in 238U(1AGeV)+d
•Analysis of fission residues
•Investigation of collective phenomena from the competition fission vs. evaporation
Rotational and vibrational motion
Dynamics of fission
Study of the spallation reaction 238U(1AGeV)+d in inverse kinematics
at GSI, Germany
Separation and Identification of the reaction products with the FRS
•(A/Z) identification:βγBρ
ZA
1
4220 D
xMx1(BρBρ )
1/2
22
2
ToFcL
1ToFcL
βγ
•Z identification: ΔEZ
•Longitudinal velocities:
BρAZ
βγv
A/Z-resolution ~10-3
Separation of fission residues with the FRS
Measurement of fission residue productions in 238U(1AGeV)+d
Measurement of fission residue productions in 238U(1AGeV)+d
Production cross sections of 780 fission residues were measured (uncetainties ~ 10-20%)
Evaporation residue productions (E. Casarejos Ph.D. USC, 2001)
Velocity measurements of fission residues
Velocities of fission residues were determined with uncertainties 15%
Particularities of the reaction 238U (1AGeV)+d
•Competition between fission and evaporation extends over a wide excitation energy distribution
•High fissilities of decaying pre-fragments
•Strong correlation between the mass of evaporation residues with excitation energy
•Influence of shell effects and collective excitations at different deformations
(Calculation)
Spherical
Deformed
•Kinematical properties of fission residues provide valuable information of the fissioning nuclei
•Experiment: measurement of fission and evaporation residue productions in 238U(1AGeV)+d
•Analysis of fission residues
•Investigation of collective phenomena from the competition fission vs. evaporation
Rotational and vibrational motion
Dynamics of fission
Influence of rotational and vibrational motion on the competition fission vs. evaporation
•Influence of Shell Structure
•Level density enhancement due to the presence of rotational and vibrational bands: (E)=Kcoll.int(E)
Correction of the level density and binding energy due to structural effects
Fermi-gas model
At low excitation energies:
5/41/4FG *E12a
*aE2expπ(E)ρ
Level density
fissev ΓΓ
Collective enhancement (rotations and vibrations) at different deformations modifies
the competition fission VS. evaporation
•Large deformations: Rotations
•Small deformations: Vibrations
Description of spallation residue productions with model calculations
1. First step: pre-fragment formation (ISABEL intranuclear cascade)Y.Yariv and Z.Fraenkel, Phys. Rev. C20 (1979)
Pre-fragment (Z,N,A; J; E)
2. Second step: pre-fragment deexcitation (ABLA)
Level density: Fermi-gas model
Shell and pairing effects
Collective enhancementA.Junghans et al., Nucl. Phys. A629 (1998)
f(E))(βσ)β(E,K0.15)β(E,K 22
2rot2coll
f(E))(βσN)(Z,βS)β(E,K0.15)β(E,K 22
eff2
2vib2coll
Decay probability from statistical model with dynamical correction for fission according to Kramers
and Grangé, Jun-Quing and Weidenmüller
25S
(E)=Kcoll.int(E)
Influence of rotational and vibrational motion on the evaporation residue productions
Fermi-gas model
Shell effects
Coll. Enh. S=25
(A.Junghans)
Kvib underestimates survival probability against fission for small-deformed nuclei
Influence of rotational and vibrational motion on the evaporation residue productions
•Highly precise measurements enable to investigate the sensitivity of the evaporation residue productions to the presence of collective motion (rotations and vibrations)
•Vibrational enhancement factor Kvib must be increased (S=75) with respect to the formulation of A.Junghans et al. in order to properly describe the survival probability against fission
•Evaporation residue productions offer a complementary approach to the spectroscopic techniques for analyzing the presence of collective excitations
•Experiment: measurement of fission and evaporation residue productions in 238U(1AGeV)+d
•Analysis of fission residues
•Investigation of collective phenomena from the competition fission vs. evaporation
Rotational and vibrational motion
Dynamics of fission
Dynamics of fission
Statistical model: Available phase-space at the saddle point
Dynamical model: Time evolution of the probability flow across the saddle point
Coupling of collective deformation degree of freedom Q with internal degrees of freedom through dissipation
Fission probability
Langevin equation:
F(t)βMT
dtdQ
βdQ
(Q)VdM1
dtQd2
2
~
Drift force Friction forceDiffussion (stochastic) force
Fission: diffusion process governed by the Reduced Dissipation Coefficient
•Fission probability needs time to go up to the stationary value (transient effects)
Transient effects increase evaporation residue productions with respect to fission
(specially at high energies)
•During this time the compound nucleus can evaporate nucleons
•Dynamics of fission from the ground-state to the saddle-point: evaporation residue productions
•Dynamics of fission beyond the saddle point: kinematical properties and production cross sections of fission residues
Dynamical calculation of the fission probability
Solution of FPE:
•Stationary solution of FPE (Kramers): K Fission width is reduced compared to BW
BWK ΓΓ K
0
2
0 221
ωβ
ωβ
K
•Time-dependent solution of FPE (Grangé, Jun-Qing, Weidenmüller): f(t) Time evolution of fiss(t) before the stationary regime (K )(transient effects)
Fokker-Planck equation (FPE) ~ Langevin equation
)τΘ(tΓ(t)Γ fKstep
)exp(-t/τ-1Γ(t)Γ fKexp
(t)WΓ(t)Γ FPEKFPE
•Step function
•Exponential in-growth function
•Approximated solution of FPE for a parabolic potential (B.Jurado et al., Phys.Lett. B (2003))
)()( tft Kfiss
Influence of dissipation on the evaporation residue productions
•Transient effects due to dissipation are expected at high energies E*
•At lower energies, dissipation hinders the fission decay according to Kramers factor
Strong sensitivity to
Strong sensitivity to (t)
•Experimental data enable to investigate (t): validation of fpe(t)
•Measured residue productions are compatible with =2x1021s-1 (small deformations)
•Strong correlation between mass and excitation energy of evaporation residues enables to
separate dissipation effects due to Kramers factor and transient times
Effects of dissipation at deformations beyond the saddle point
H.Hofmann and J.R.Nix, Phys. Lett. B122 (1983): Dissipation enlarges the saddle-to-scission time ssc
γγ1ττ 20sscssc ΔV/TR
ω2
τ0
0ssc
02ωβ
γ
At large deformations, dissipation damps the fission motion due to the friction force
ssc can be determined from saddle-to-scission neutron multiplicities ssc
sscν
1i nssc E*)J,A,(Z,Γ
τ
•Dynamics of fission from the ground-state to the saddle-point (Fission probability)
•Dynamics of fission beyond the saddle-point
Analysis of saddle-to-scission neutron multiplicities in 238U (1AGeV)+d
•Post-saddle neutron multiplicities were calculated with a deexcitation code: sad is very sensitive to E*sad
Saddle-to-scission ssc = Post-saddle sad – Post-scission sc
Comparison of isotopic distributions for fission and evaporation residues
Evaporation
Fission
Analysis of saddle-to-scission neutron multiplicities in 238U (1AGeV)+d
•Post-saddle neutron multiplicities were calculated with a deexcitation code: sad is very sensitive to E*sad
Saddle-to-scission ssc = Post-saddle sad – Post-scission sc
•Post-scission neutron multiplicities:
Zfiss, A’fiss = “Reconstructed” Fissioning nucleus
Zfiss, Afiss = Real fissioning nucleus
Hypothesis: Real fissioning nuclei are located along the evaporation corridor
No neutrons are evaporated “post scission”
vfiss(Z,A)
fiss(Z,A)
Afiss = A’fiss + sc
Evaluation of dissipation at large deformation from saddle-to-scission neutron multiplicities
Hilsher’s systematics sc(Zfiss,E*) D.Hilsher
and H.Rossner, Ann. Phys. Fr. 17 (1992) 471
)(Zν)(Zν)(Zν fissscfisssadfissssc
γγ1ττ 20sscssc
sscν
1i nssc E*)J,A,(Z,Γ
τ
All ssc(Zfiss) are compatible with >3; ( 6 )
Agreement of sc with Hilsher’s systematics validates the hypothesis
=24
=10
=6
=3
=1
These values are larger than =2x1021s-1 at small
deformations
•Saddle-to-scission neutron multiplicites >6x1021s-1
(large deformations)
•Evaporation residues =2x1021s-1 (small deformations)
Values of at small and large deformations are compatible with the results obtained from GDR -ray spectra (Shaw et al.; Diószegi et al.) and from pre-
scission neutron multiplicities (Fröbrich et al.)
Indications of deformation-dependent dissipation
Summary and conclusions
•Production cross sections and kinematical properties of 780 fission residues have been measured with high accuracy at the FRS
•U+d system constitutes an optimum scenario to investigate collective phenomena
•The measured productions of evaporation residues in regions of small deformation revealed a greater contribution of Kvib to the survival probability against fission
•Measured evaporation residue productions provided valuable information to investigate the dynamics of fission at small deformations
• =2x1021s-1
• Validation of the formulation of B.Jurado fpe(t)
•Kinematical properties and production cross sections of fission residues enabled to investigate the dynamics of fission at large deformations
•Post-scission neutron multiplicities agreed with Hilscher’s systematics
•Saddle-to-scission multiplicities are compatible with >6x1021s-1
•Possible indications of deformation-dependent dissipations
Determination of production cross sections
(Z,A) =Y(Z,A).fsc2.feff.fchs.fTi.fmr.fT
•fsc2: Interactions of nuclei in the plastic SC2
•feff: Detection efficiencies
•fchs: Charge-state contamination
•fTi: Nuclear reactions in the Ti target container
•fmr: Multiple-reactions in the target
•fT:Angular transmission
Influence of dissipation on total fission cross section
Spallation reactions induced by 238U at 1GeV/u on different targets
Excitation energy of pre-fragments E* Target mass
Transient effects are important for heavier targets
(high E*)
•Total fission cross section for 238U(1AGeV)+d is not sensitive to dissipation
•Total fission cross sections at different E* are well described with FPE(t) and =2x1021s-1
Collective enhancement of the level density
1
cr
cr
dEE
exp1f(E)
f(E)3
β1TARm
5
2f(E)
T(E)σ 22
022rot2
(E)σβS(E)σ rot
22effvib
2
•Phenomenological description of Kcoll(E) (A.R.Junghans et al. Nucl. Phys. A629 (1998) 635):
•Transition from vibrational to rotational enhancement:
Damping of Kcoll with excitation
energy:
Z 0.005ΔN 0.003Δ0.022βeff
0.15βtrans
1)f(E)(σ1K 2coll (E)ρ(E)Kρ(E) intcoll
: spin cut-off parameter
Rotational VS. Vibrational excitations
•Rotational modes: large deformation
•Vibrational modes: small deformations
•Shell effects enhance survival probability against fission
•Vibrational modes enhance survival probability against fission
•Rotational modes enhance fission probability
Reconstruction of kinematics
Kinematics of fission and fragmentation
ABρZ
βγv
Limited -acceptanceLimited angular-acceptance
Separation of fission and fragmentation from their kinematics measured with the FRS
Limited angular acceptance of the FRS enables the separation of fission and fragmentation from their kinematics
•Longitudinal velocity spectra of each nucleus was measured
• Fission and fragmentation components were separated by fitting the spectra to specific functions
•Fit parameters: mean velocities and yields of fission and fragmentation residues
New approach to determine the Angular Transmission
Determination of the angular acceptance a with Monte Carlo calculations
New analytical approach to determine the Angular Transmission
•Calculation of angular transmission for fission and fragmentation according to their kinematics
Fragmentation Fission
)σ(θ)α
(T fr 2
2
2exp1
2
cos1 ffT
2
cos1 bbT
Ingredients of the Monte Carlo code
Level density (Fermi-gas state density)4/54/1~12)exp(π
ρEa
S
))()((~2 EhPEkδUEaS 13/21 MeV A095.0MeVA 073.0~ sBa
U
)exp(1)( EEk a~/A4.0/1 3/4
241 2gP /6~ag
;,
,1
11)(
2
.
crit
crit
critEE
EEEE
Eh
MeV10critE
Entropy
Asymptotic level-density parameter (Ignatyuk)
Shell correction calculated in the finite-range liquid-drop model
Damping of shell effects with E
Effective pairing energy shift MeVA/12
Washing out of the pairing correlations
fBFission barriers (Sierk)
ISABEL VS. INCL CASCADES
ISABEL and INCL
Fission cross sections
overestimated with INCL
INCL overestimates angular momentum
Large angular momenta J reduce the fission barriers
Approximated solution of the FPE for a parabolic potential
W(x,v,t)vm
βkTU(x)
xmβv
vtv
tW(x,v,t)
2
21
Time-dependent probability flux of trajectories across the saddle-point
,v,t)dvW(xvΦ bxb
Probability that the system is at x<xb
bx
b W(x,v,t)dvdx,t)Π(x,t)Π(x
Φ(t)λ(t)Γ
b
xfissfiss
b
,t)W(x,t)(xv,v,t)dvW(x,t)(xv(t)Φ bbbbxb
),(
),(),()(
txtxWtxv
tb
bbfiss
Kb
bbfiss tx
txWtxvt
),(
),(),()( K
bb
bbfiss txWtxv
txWtxvt
),(),(),(),(
)(
Approximated solution of the FPE for a parabolic potential
Kbb
bbfiss txWtxv
txWtxvt
),(),(),(),(
)( ),(),( txvtxv bb
),(),( txWtxW bparb
Kbpar
bparfiss txW
txWt
),(
),()(
2
2
2exp
2
1),,(
x
par
xtvxW
1)(
22
1 11
122
1
2
22 tSinh
tSinhe
M
T t
g
x
221 4 g
Dissipation from saddle point to scission point
Pre-saddle particle multiplicity: Excitation energy at saddle point
Damping of the fission motion from the ground-state configuration to the saddle point:
=2x1021s-1
•Monte Carlo calculation (ISABEL+ABLA): post-saddle neutron multiplicity
14(Z)ν sadpost
•Hilscher’s systematics: post-scission neutron multiplicity
5E*)(Z,ν sciss-post
Saddle-to-scission neutron multiplicity: 9E*)(Z,ν(Z)νν sciss-postsadpostssc
sscν
1i nssc E*)J,A,(Z,Γ
τ γγ1ττ 20
sscssc ΔV/TRω
2τ
0
0ssc
>10x1021s-1