### Dr Carlo Barbieri

### Biography

### Research interests

Carlo Barbieri Personal Research Page

### Teaching

Module leader for PHYM038 Non-Linear Physics

### Departmental duties

Programme Leader Maths & Physics

### University roles and responsibilities

- Chair of HPC Stakeholders Group

### Previous roles

### Courses I teach on

# Undergraduate

### My publications

### Publications

For all those processes, current research in nuclear astrophysics addresses the need for more precise reaction data involving radioactive isotopes. Depending on the particular reaction, direct or inverse kinematics, forward or time-reversed direction are investigated to determine or at least to constrain the desired reaction cross sections.

The Facility for Antiproton and Ion Research (FAIR) will offer unique, unprecedented opportunities to investigate many of the important reactions. The high yield of radioactive isotopes, even far away from the valley of stability, allows the investigation of isotopes involved in processes as exotic as the r or rp processes.

2, Physical Review C 97 (2) 021303(R) American Physical Society

40Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at

the pseudo-scalar meson mass of 469 MeV/c

2

. The nucleon-nucleon interaction is obtained using the HAL QCD

method and its short-distance repulsion is treated by means of ladder resummations outside the model space.

Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground

state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD.

Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved

by the full account of many-body correlations. The results suggest an interesting possible behaviour in which

nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doublymagic

numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral

distributions are qualitatively close to those of real nuclei even for the pseudo-scalar meson mass considered

here.

**Background:**

Self-consistent Green?s function theory has recently been extended to the basic formalism needed

to account for three-body interactions [A. Carbone, A. Cipollone, C. Barbieri, A. Rios, and A. Polls, Phys. Rev.

C 88, 054326 (2013)]. The contribution of three-nucleon forces has then been included in ab initio calculations

on nuclear matter and isotopic chains of finite nuclei.

**Purpose:**

ractical applications across post Hartree-Fock methods have mostly considered the contribution of

three-nucleon interactions in an effective way, as averaged two-nucleon forces. We derive the working equations

for all possible two- and three-nucleon terms that enter the expansion of the self-energy, including interactionirreducible

(i.e. not averaged) three-nucleon diagrams.

**Methods:**

We employ the algebraic diagrammatic construction up to third order as the organization scheme for

generating a non perturbative self-energy, in which ring (particle-hole) and ladder (particle-particle) diagrams are

resummed to all orders.

**Results:**

We derive expressions of the static and dynamic self-energy up to third order, by taking into account

also the set of diagrams required when the skeleton expansion of the single-particle propagator is not assumed. A

hierarchy of importance among different diagrams is revealed, and a particular emphasis is given to a third-order

diagram (see Fig. 2c) which is expected to play a significant role among those featuring an interaction-irreducible

three-nucleon force.

**Conclusion:**

A consistent formalism to resum at infinite order correlations induced by three-nucleon forces in the

self-consistent Green?s function theory is now available, and ready to be implemented in the many-body solvers.

Work is in progress to include the first interaction-irreducible three-nucleon diagram in calculations of closed-shell

medium-mass nuclei.

51

?

55

Ti

was performed at TRIUMF?s Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the

N

=

32

shell closure, and the overall uncertainties of the

52

?

55

Ti

mass values were significantly reduced. Our results conclusively establish the existence of the weak shell effect at

N

=

32

, narrowing down the abrupt onset of this shell closure. Our data were compared with state-of-the-art ab initio shell model calculations which, despite very successfully describing where the

N

=

32

shell gap is strong, overpredict its strength and extent in titanium and heavier isotones. These measurements also represent the first scientific results of TITAN using the newly commissioned multiple-reflection time-of-flight mass spectrometer, substantiated by independent measurements from TITAN?s Penning trap mass spectrometer.

study of the structure of stable and exotic oxygen isotopes at the R3B=LAND setup with incident beam

energies in the range of 300?450 MeV=u. The oxygen isotopic chain offers a large variation of separation

energies that allows for a quantitative understanding of single-particle strength with changing isospin

asymmetry. Quasifree knockout reactions provide a complementary approach to intermediate-energy onenucleon

removal reactions. Inclusive cross sections for quasifree knockout reactions of the type

AOðp; 2pÞA?1N have been determined and compared to calculations based on the eikonal reaction theory.

The reduction factors for the single-particle strength with respect to the independent-particle model were

obtained and compared to state-of-the-art ab initio predictions. The results do not show any significant

dependence on proton-neutron asymmetry.

4

He

and

16

O

obtained within the self-consistent Green's function approach. The removal of the center-of-mass contribution for both nuclei has been performed by using a metropolis Monte Carlo algorithm in which the center-of-mass coordinate can be exactly subtracted from the optimal reference state wave function generated during the self-consistent Green's function calculations. The spectral functions of the same two nuclei have been used to compute inclusive electron-nucleus cross sections. The formalism adopted is based on the factorization of the spectral function and the nuclear transition matrix elements. This allows us to provide an accurate description of nuclear dynamics and to account for relativistic effects in the interaction vertex. When final-state interactions for the struck particle are accounted for, we find nice agreement between the data and the theory for the inclusive electron-

16

O

cross section. The results lay the foundations for future applications of the self-consistent Green's function method, in both closed and open shell nuclei, to neutrino data analysis.

**Background:** Microscopic calculations of the electromagnetic response of light and medium-mass nuclei are now feasible thanks to the availability of realistic nuclear interactions with accurate saturation and spectroscopic properties, and the development of large-scale computing methods for many-body physics.

**Purpose:** To compute isovector dipole electromagnetic (E1) response and related quantities, i.e., integrated dipole cross section and polarizability, and compare with data from photoabsorption and Coulomb excitation experiments. To investigate the evolution pattern of the E1 response towards the neutron drip line with calculations of neutron-rich nuclei within a given isotopic chain.

**Methods:** The single-particle propagator is obtained by solving the Dyson equation, where the self-energy includes correlations nonperturbatively through the algebraic diagrammatic construction (ADC) method. The particle-hole (* ph*) polarization propagator is treated in the dressed random phase approximation (DRPA), based on an effective correlated propagator that includes some

*effects but keeps the same computation scaling as the standard Hartree-Fock propagator.*

**2p2h****Results:** The E1 responses for ^{14,16,22,24}O, ^{36,40,48,52,54,70}Ca, and ^{68}Ni have been computed: The presence of a soft dipole mode of excitation for neutron-rich nuclei is found, and there is a fair reproduction of the low-energy part of the experimental excitation spectrum. This is reflected in a good agreement with the empirical dipole polarizability values. The impact of different approximations to the correlated propagator used as input in the E1 response calculation is assessed.

**Conclusion:** For a realistic interaction that accurately reproduces masses and radii, an effective propagator of the mean-field type computed by the self-consistent Green's function provides a good description of the empirical E1 response, especially in the low-energy part of the excitation spectrum and around the giant dipole resonance. The high-energy part of the spectrum improves and displays an enhancement of the strength when quasiparticle fragmentation is added to the reference propagator. However, this fragmentation (without a proper restoration of dynamical self-consistency) spoils the predictions of the energy centroid of the giant dipole resonance.

_{sat}interaction against a previous SCGF calculation based on the T-matrix approach. The benchmark showed good convergence with respect to the model space but it yielded an apparent lack in the binding energy of ~30% at the saturation density of symmetric nuclear matter when compared to the SCGF T-matrix results and the available literature. After the benchmark a preliminary investigation in to modern N²{tLO nucleon-nucleon interactions extended to include the N²LO three-nucleon interaction was conducted. These results were reviewed with in the current perceived limitations of the SCGF formalism developed here. In this study, increasing the regulator cut off or the order of the chiral expansion for the nucleon-nucleon interaction decreased the observed binding energy whilst also lowering the saturation density. The calculation of finite nuclei used a potential derived from LQCD by the HAL QCD collaboration at an unphysical pion mass,

*M*=469 MeV/c². The short-range repulsion of this interaction requires one to include a resummation of ladder diagrams from the excluded model space. The effectiveness of the ladder resummation from outside the computational model space is considered by the infrared convergence of the total binding energies. The introduction of these missing ladder diagrams leads to a complete diagonalisation of short-range degrees of freedom independently of the choice of model space. The binding energy of Helium-4 was calculated to be -4.80 MeV. The heavier doubly magic nuclei, Oxygen-16 and Calcium-40, had binding energies of -17.9 MeV and -74.4 MeV respectively. This means whilst Calcium-40 is observed to be bound with respect to Alpha break up, Oxygen-16 is expected to be unstable.

_{PS}