Stage 1 (02/05/2022 - 31/12/2022) An executive summary of the activities carried out during the implementation period (max. 1 page). This may be published by the Contracting Authority on the competition website. Act 1.1 - Implementation of a hardware infrastructure for high performance computing. "Upgrade the computing hardware available in CIFRA. Commissioning of a hardware infrastructure for high performance computing." To implement the project and obtain the numerical results it was necessary to prepare a high performance cluster corresponding to the size of the problems studied. In this respect, following benchmarks to evaluate performance and power consumption, it was decided to use three computation servers and one storage server from CIFRA, together with 12 other computation servers from INCDFM, reorganized in a cluster with 3 partitions. Act 1.2 - Theoretical derivation and verification of new analytical formulas for new NME and PSF contrubutions to be introduced in the new calculation codes. "Obtain new equations to consider new contributions to nuclear matrix elements and phase space factors for beta-double decays." Considering new beyond standard model physics theories, new analytical equations for the contribution of 20 nuclear matrix elements and 9 phase space factors in neutrinoless beta-double decays were derived.  They are part of an effective field theory and their constants for leptonic number violation have a wider significance than in the model-based interpretation. Act 1.3 - Implementation of new equations in new calculation routines for NME. Realization and testing of new numerical routines for the calculation of nuclear matrix elements. The new equations from Act 1.2 were programmed into codes and routines for the calculation of nuclear matrix elements with which the calculations for the dedicated 48Ca study published by us in Phys.Rev.C. were done. Act 1.4 - Implementation of new equations in new routines for PSF calculations. Development and testing of new numerical routines for the calculation of phase space factors. For the calculation of the phase space factors new equations were programmed in a very easy to read and modify Mathematica code with which the calculations for the dedicated 48Ca study published by us in Phys.Rev.C. were done. Dissemination of the results: The results obtained in this phase were presented in the following circumstances: R1) 1 ISI indexed article published in Phys. Rev. C. "Statistical analysis for the neutrinoless double-β-decay matrix element of 48Ca", M. Horoi, A. Neacsu, and S. Stoica, Phys. Rev. C 106, 054302 - Published 2 November 2022. https://journals.aps.org/prc/abstract/10.1103/PhysRevC.106.054302

R2) 1 paper in progress dedicated to matrix elements in the 136Xe isotope, with authors M. Horoi, A. Neacsu, and S. Stoica, to be submitted to Phys. Rev. C.

R3) 3 presentations in the MEDEX'22 workshop (https://indico.utef.cvut.cz/event/32/): -Andrei Neacsu - "A Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix element of 48Ca". -Vasile Sevestrean - "Finding the Dominant Mechanism Contributing to Neutrinoless Double-Beta Decay". -Ovidiu Nitescu - "Angular Distributions of Emitted Electrons in the Two-Neutrino Double-Beta Decay".

R4) 2 proceeding papers following MEDEX'22 (contributions 2a and 2b published in extenso) to appear in AIP Conference Proceedings.

R5) Seminars in the department of Andrei Neacsu, Ovidiu Nitescu and Vasile Sevestrean.   Stage 2 (01/01/2023 - 31/12/2023) An executive summary of the activities carried out during the implementation period (max. 1 page).This can be published by the Contracting Authority on the competition website. Act 2.1 and Act 2.2 During Stage 2 "Calculation of NME and PSF for 2νββ and 0νββ transitions, together with the determination of new limits for BSM parameter values." (01/01/2023 - 31/12/2023) in the framework of the project PN-III-P1-1.1-TE-2021-0343 "Physics investigations beyond the standard model by double beta decay studies" new nuclear matrix elements (NME) for 2νββ and 0νββ transitions were calculated on ground and excited states.   Act 2.3 and Act 2.4 Also, new values for the leptonic phase space factors (PSF) for the decay of 2νββ on ground and excited states and 0νββ on ground states were calculated.   Act 2.5 Using the new NME and PSF values, new parameter values were obtained for leptonic number violation (LNV) in mechanisms beyond the standard model (BMS) that have upper limits on the electron neutrino mass . R1)The results of these studies have been published by the project team in papers: 1) Phys. Rev. A108, 012810 (2023) https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.012810, 2) Phys. Rev. C 107, 045501 (2023) https://journals.aps.org/prc/abstract/10.1103/PhysRevC.107.045501, 3) is accepted for publication in Phys. Rev. C https://journals.aps.org/prc/accepted/0707cP6dWb11490ab8945e454271ec01c25649070.   R2) Dissemination of the results was done in presentations at the international conferences MEDEX '23 in Prague (2023), CSSP23 in Sinaia (2023), at the national PFF conference in Iasi 2023, as well as in seminars of the nuclear physics group at the University of Jyvaskyla. During this stage, Mr. Ovidiu Nitescu publicly defended his PhD thesis entitled "Contributions in the study of nuclear β, 2νββ and 0νββ decays", thesis elaborated within this project (https://doctorat.unibuc.ro/events/nitescu-ovidiu-vasile). Other dissemination activities consisted of seminars at CIFRA and IFIN-HH, as well as online meetings with our collaborators from Central Michigan University, Comenius University and University of Jyväskylä. These meetings between those working in the field of beta and double beta decays are of great importance for the exchange of ideas and preparation of future activities.