Programme

I.9 -- Invited, VCTP-51

Date: Thursday, 6 August 2026

Time: 10:30 - 11:10

Finite Element Method for Collective Nuclear Models

Oleg O. Kovalev (1, 2), Alexander A. Gusev (1, 2, 3), Luong Le Hai (4), Ochbadrakh Chuluunbaatar (1, 2, 5), Evgenii V. Mardyban (1, 2, 6), Sergue I. Vinitsky (1, 2, 7)

(1) Joint Institute for Nuclear Research, Dubna, Russian Federation (2) Dubna State University, Dubna, Russian Federation (3) School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia (4) Ho Chi Minh city University of Education, Ho Chi Minh City, Viet Nam (5) Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia (6) Korkyt Ata Kyzylorda University, Kyzylorda, Kazakhstan (7) RUDN University, Moscow, Russian Federation

Finite element method schemes for solving elliptic boundary value problems with mixed partial derivatives describing collective nuclear models are presented. The coefficients of the elliptic equation and the potential energy surface are calculated in tabular form from the relativistic mean-field model. The finite element method scheme is implemented using Hermite interpolation polynomials with given multiplicity of nodes, which preserve the smooth of the desired solution at the finite element boundaries, unlike traditional schemes with Lagrange interpolation polynomials. To save the computer memory, especially in dimensions 4 and higher, we solve the problem in a restricted domain where the solution is localized, for example in classically allowed region and exclude local basis functions with large total multiplicity of the derivatives. The effectiveness of the schemes is demonstrated by calculating the reference degenerate spectrum of the Moshinsky atomic model and the rotational-vibrational spectra and electric quadrupole transitions for the isotopes 154Gd and 238U, with single-well and double-well potential energy surfaces.

Presenter: Gusev Alexander