# Restoration of symmetry in time-dependent calculations. The Josephson effect studied with the Gogny TDHFB calculation.

G. Scamps (Department of Physics, Tohoku University)

### 11h GANIL seminar room (105)

### a coffee will be served 15mn before

Heavy ion transfer reactions are an ideal tool to study the pair correlations. New experimental data show that the probability to transfer a pair of neutrons is enhanced compared to the expected value in the uncorrelated limit or pure sequential transfer [1,2]. This enhancement is expected to be due partially to the Josephson effect. This effect is well understood in macroscopic systems where the transfer arises from systems with a define gauge angle. Nevertheless, in nuclear reactions, the initial particle number of both fragments is a good quantum number and so the symmetry of the relative gauge angle must be restored.

In order to study the transfer reaction, we use the Time-Dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The calculation is done with a Gogny interaction in a hybrid basis of two-dimensional harmonic oscillator eigenfunctions and a one-dimensional Lagrange mesh. With that model, the Josephson effect is quantitatively described in the reaction 20O+20O and 14O+20O as well as the dependency of the Nucleus-Nucleus potential with respect to the Gauge angle [3].

The restoration of the gauge angle symmetry is then studied with a projection method. This calculation consists in making several TDHFB calculations with different initial relative gauge angle. The final observable is then obtained by a triple projection method, that include the calculation of overlap between final state of the different TDHFB calculations. The Pfaffian method is used to compute the overlap between the quasiparticle vacuum states. The accuracy of this method is discussed in a simple model [4] and then applied to the realistic model [5].

[1] L. Corradi et al., “Single and pair neutron transfers at sub-barrier energies“, Phys. Rev. C 84, 034603 (2011).

[2] K. Hagino and G. Scamps, “Enhancement factor for two-neutron transfer reactions with a schematic coupled-channels model“, Phys. Rev. C92 (2015) 064602

[3] Y. Hashimoto and G. Scamps, “Gauge angle dependence in time-dependent Hartree-Fock-Bogoliubov calculations of 20O+20O head-on collisions with the Gogny interaction“, Phys. Rev. C 94, 014610 (2016).

[4] G. Scamps and Y. Hashimoto, “Superfluid effects in collision between systems with small particle number“, arXiv:1704.00930

[5] G. Scamps and Y. Hashimoto, “Transfer probabilities for the reactions 14,20O+20O in terms of multiple time-dependent Hartree-Fock-Bogoliubov trajectories“, arXiv:1708.01994.