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Analytical approach to quantum many body systems

PD 24/2020), financed by UEFISCDI.

 

Team: Dr. Virgil V. Baran (Director), Dr. Peter Schuck (Mentor)

 

Abstract

A large amount of effort has been devoted to the understanding of the proton-neutron correlations responsible for the appearance of the quartet degrees of freedom in nuclear systems. Despite significant advances in the field, several computational shortcomings still prevent the quartet models for achieving their full potential. However, with the recent introduction of new analytical techniques by the project leader, these may finally be addressed.

As such, this project aims to provide a highly efficient approach for the description of the nuclear properties within an analytically upgraded quartet model and to study its new physical implications. In order to achieve this, multiple issues need to be addressed, in particular regarding the generalization of the quartet models to the description of excited states of nuclei.

The first objective of the project is related to fixing the last remaining broken symmetry of the quartet models, the rotational symmetry. This enables the following two objectives, that of developing a description of nuclear electromagnetic transitions and beta decay based on quartets and that of relating quartet condensation and alpha decay in heavy nuclei. The final objective is an attempt at cross-fertilization between various fields, i.e. to apply a quartet-BCS theory recently proposed by the project leader for nuclear systems to the study of quartet correlation in neutron stars and condensed matter systems like cold atomic gases.

Beside providing the nuclear physics community with a physically transparent alternative to the weighty shell model approach operating at the same level of precision, the work done within this project brings unique theoretical contributions to the understanding of physical phenomena of interest at top facilities, like ELI-NP. Also, new physical insight may be obtained regarding long standing open problems, for example why clustering occurs in the ground states of some nuclei but only in the excited states of others.

 

Conclusions

The most significant result obtained within the project has been the unification of two theoretical approaches for the description of the proton-neutron pairing correlations in nuclear systems, the Quartet Condensation Model (QCM) and the symmetry-restored BCS theory (PNTBCS), initially considered to be distinct in the literature [Phys. Rev. C 85, 061303(R), 2012]. The equivalence QCM=PNTBCS is significant both from the physical point of view (it links the structure of the states of the proton-neutron system to its fundamental symmetry properties), and from the computational point of view (the numerical calculations within the PNTBCS approach are more efficient than within QCM). This result, not initially foreseen in the original project proposal, has allowed the development of theoretical tools for the description of quantum many-body systems with applicability beyond nuclear physics, e.g. to quantum chemistry and condensed matter physics.

 

Scientific Report

 

Main Results

 

Publications

[1]  Bridging the quartet and pair pictures of isovector proton-neutron pairing,  V. V. Baran, D. R. Nichita, D. Negrea, D. S. Delion, N. Sandulescu, P. Schuck, Physical Review C 102, 061301(R) (2020).

[2] Structure of the quartetting ground state of N=Z nuclei, A. G. Serban, D. R. Nichita, D. Negrea, V. V. Baran, The European Physical Journal A 57 (1), 1-7 (2021).

[3] Variational theory combining number-projected BCS and coupled-cluster doubles, V.V. Baran, J. Dukelsky, Physical Review C 103, 054317 (2021).