Fission Hindrance A K Sinha UGC DAE CSR, Kolkata Centre May 17 &19, 2014 Summer School on Nuclear Fission and Related Phenomena May 2014, Variable Energy Cyclotron Centre, Kolkata, INDIA

Admittedly, nuclear fission is a rather cumbersome process. As nucleus initially of span length of ~ 14 fm elongates to span length of the order of ~28 fm (5 fm + 18 fm + 5 fm) mediating a large scale re-arrangement of couple of hundred of nucleons. A dynamical description must be the necessity to understand it. This dynamical elongation should be essentially driven through the intrinsic motion of nucleons.

Kramer’s paper in 1940 considered probability of stochastically driving a trapped particle (in a potential hole) to bring it out of the hole, akin to the Brownian motion of a relatively larger particle (compared to molecule) by collisions with surrounding molecules. This concept of culmination of movement in fission degree due to the dominant thermal motion in other degrees of freedom (other than the fission degree) has come to use (Weidenmueller) in understanding the fission hindrance perceived in the decay of hot, heavy rotating nuclei.

Having said all of the above, it is a great surprise in the evolution of nuclear physics that such dynamical description was not used/required in the first forty years. Statistical decay of excited nuclei deemed fit enough if one adds the transition state fission model (introduced by Bohr & Wheeler) in this statistical description.

The statistical model’s success in surprising however can be appreciated (in perspective) if one considers time – scales (characteristic times) of various processes involved. The statistical description of any process concerns with the no. of “micro-states” that conforms to the end-product (of the process). Each micro-state is equi-probable and a given final “macro-(bulk) state” has a probability simply proportional to the total no. of micro-states that conform to the given final “macro-state”.

The statistical description is thus like our elections where each one has equal vote-power and it ends as a pure Number-game. The model completely ignores any dynamics and concerns solely with “micro-state counting”. Finally failing of such model description in understanding heavy ion induced reactions involving large scale nuclear re-arrangement like fusion-fission has given rise to probe beyond this a-priori-blind but very effective statistical approach for system with large no. of degrees of freedom.

thus run through the effects of Fission Hindrance whereby fission seems to occur less profusely as compared to what the Statistical Model suggests. This hindrance is seen in perspective of decay rates of other rapid competing processes which are not large- scale-re-arrangement. (the neutron clock; gdr clock ….)

To understand Compound Nucleus and its decay modes, we need to do the counting of micro-states. We will discuss the level- densities of nuclear system briefly looking into the various level density models of nuclei.

Under the basic thought behind this model, formation and decay of a certain nuclear state (compound Nucleus state) are not coupled beyond the conversation laws relating to energy, momentum and angular momentum, we use decay width T of this CN state which relates to mean decay life time, τ and decay rate λ = 1/τ

fission EMISSIONS (before, after fission) of n, gamma, FF EMISSIONS before CN ? EMISSIONS FROM THE PROCESS OF HEAVY ION FUSION AND DECAY NOT WHEN FISSION OCCURS BUT FF THEMSELVES EMIT LIGHT PARTICLES AND GAMMA RAYS (BOTH STATISITICAL & DISCRETE GAMMAS)

One normally identifies certain milestones in the evolution dynamics of such heavy nuclear systems, viz., complete equilibration stage or the Compound Nucleus formation, saddle state and nuclear scission.

Same final state; different initial state Varying energies for p and  GHOSHAL CN EXPERIMENT

From Krane’s book

Sum through all final channels (also elastic scattering) → total cross section of compound nucleus creation: It is valid: Thus independency of creation and decay of compound nucleus. For E = E res it is valid (we assume elastic σ aa and one inelastic σ ab channel → Γ = Γ a + Γ b ): Maximum for elastic part (Γ b = 0, Γ a = Γ): Maximum for inelastic part (Γ b = Γ a = Γ/2): Resonance fast changes are given by reactions through compound nucleus, slow changes are given by direct reactions Energy [eV] Cross section [barn]

σ(α,β) = σ C (α) G C (β) σ C (α) = K λ 2 Γ α G C (β) = Γ β / Γ σ(α,β) = K λ 2 Γ α Γ β / Γ Blatt & Weiskopf

Time of Flight Experiment t = L/v Measure t  you know v Maxwell velocity neutron beam shutter Target/detector L tt gate Cd  Example

 Resonances m In-116 c 2 m n c 2 + m In c 2 m In-116 c 2 E*E* 0 Ti*Ti* Tf*Tf* TOF Exp’t

FUSION Channel coupling approach near barrier; CASE OF Two degenerate states for the approximate Hamiltonian; Include coupling term to better approximate; the degeneracy is lifted; two Barriers split out of the original one barrier 0ε ε0 a1 a2 a1 a2 = λ λ 2 = ε 2 ; λ = +/- ε

Expected excitation-energy dependence of the level-density parameter loss of collective enhancement excitation-energy dependence from many-body effects decreasing effective mass A/10 =intrinsic a (Ignatyuk) A/7-A/8 (neutron resonance counting) A/13 50 MeV loss of collective enhancement 250 MeV a eff A=160

How do we measure the level density at high excitation energies.

Temperature can be obtained from the exponential slope of kinetic-energy spectra of evaporated particles First-chance emission Account for multichance emission with statistical-model calculations with GEMINI

Comparison to expectation

Isospin dependence of level density parameter If there is a significantly larger dependence it will be important for r-process. In the Fermi-gas model there is a very small isospin dependence

Al-Quaraishi et al. PRC (2001) fitted low- energy level-density data for 20<A<70 (Ohio Univ.) We have taken the liberty of extrapolating Al-Quraishi fitted forms to A~160 and high excitation energies to use as examples of isospin dependent level-density parameters.

Evaporation attractor line With no isospin dependent level density. The action of evaporation on the location in the chart of nuclides of a hot system is move it towards a line called the Evaporation attractor line (on average) One cannot cross the attractor line. PRC (1998) Experimentally determine mean location of residues from multiplicities of evaporated n,p,d,t, 3 He, a

At the SADDLE : Collective enhancements FF angular dist.