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)

Collective phenomena in hot nuclei VibrationsRotationsFission 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 238 U at 1AGeV on deuterium Collective phenomena: competition between fission and evaporation High fissilities

Experiment: measurement of fission and evaporation residue productions in 238 U(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 238 U(1AGeV)+d in inverse kinematics at GSI, Germany

Separation and Identification of the reaction products with the FRS (A/Z) identification: Z identification: Longitudinal velocities:

A/Z-resolution ~10 -3 Separation of fission residues with the FRS

Measurement of fission residue productions in 238 U(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 d 15%

Particularities of the reaction 238 U (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 238 U(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)=K coll.  int (E) Correction of the level density and binding energy due to structural effects Fermi-gas model At low excitation energies: Level density 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 enhancement A.Junghans et al., Nucl. Phys. A629 (1998)  Decay probability from statistical model with dynamical correction for fission according to Kramers and Grangé, Jun-Quing and Weidenmüller  (E)=K coll.  int (E)

Influence of rotational and vibrational motion on the evaporation residue productions Fermi-gas model Shell effects Coll. Enh. S=25 (A.Junghans) K vib 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 K vib 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 238 U(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: Drift forceFriction force Diffussion (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 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 Step function Exponential in-growth function Approximated solution of FPE for a parabolic potential (B.Jurado et al., Phys.Lett. B (2003))

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  =2x10 21 s -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 At large deformations, dissipation damps the fission motion due to the friction force  ssc can be determined from saddle-to-scission neutron multiplicities ssc 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 238 U (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 238 U (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: Z fiss, A’ fiss = “Reconstructed” Fissioning nucleus Z fiss, A fiss = Real fissioning nucleus Hypothesis: Real fissioning nuclei are located along the evaporation corridor No neutrons are evaporated “post scission” v fiss (Z,A)  fiss (Z,A) A fiss = A’ fiss + sc

Evaluation of dissipation at large deformation from saddle-to-scission neutron multiplicities Hilsher’s systematics sc (Z fiss,E*) D.Hilsher and H.Rossner, Ann. Phys. Fr. 17 (1992) 471 All ssc (Z fiss ) are compatible with  >3; (  t6 ) Agreement of sc with Hilsher’s systematics validates the hypothesis  =24  =10  =6  =3  =1 These values are larger than  =2x10 21 s -1 at small deformations

Saddle-to-scission neutron multiplicites  >6x10 21 s -1 (large deformations) Evaporation residues  =2x10 21 s -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 K vib to the survival probability against fission Measured evaporation residue productions provided valuable information to investigate the dynamics of fission at small deformations  =2x10 21 s -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  >6x10 21 s -1 Possible indications of deformation-dependent dissipations

Determination of production cross sections s(Z,A) =Y(Z,A).f sc2.f eff.f chs.f Ti.f mr.f T f sc2 : Interactions of nuclei in the plastic SC2 f eff : Detection efficiencies f chs : Charge-state contamination f Ti : Nuclear reactions in the Ti target container f mr : Multiple-reactions in the target f T :Angular transmission

Influence of dissipation on total fission cross section Spallation reactions induced by 238 U 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 238 U(1AGeV)+d is not sensitive to dissipation Total fission cross sections at different E* are well described with  FPE (t) and  =2x10 21 s -1

Collective enhancement of the level density Phenomenological description of K coll (E) (A.R.Junghans et al. Nucl. Phys. A629 (1998) 635): Transition from vibrational to rotational enhancement: Damping of K coll with excitation energy:   : 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 Limited  -acceptance Limited 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

Ingredients of the Monte Carlo code Level density (Fermi-gas state density) 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 Washing out of the pairing correlations Fission 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 Time-dependent probability flux of trajectories across the saddle-point Probability that the system is at x<x b

Approximated solution of the FPE for a parabolic potential

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:  =2x10 21 s -1 Monte Carlo calculation (ISABEL+ABLA): post-saddle neutron multiplicity Hilscher’s systematics: post-scission neutron multiplicity Saddle-to-scission neutron multiplicity:  >10x10 21 s -1