Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

Abstract

Phenomenological effective interactions like Skyrme forces are currently used in mean-field calculations in nuclear physics. Mean-field models have strong analogies with the first order of the perturbative many-body problem and the currently used effective interactions are adjusted at the mean-field level.In this work, we analyze the renormalizability of the nuclear many-body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.

Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory

“…The expressions of second-order EoSs listed in Refs. [61,63,64,78] are the asymptotic form after expanding the results in power series of Λ. Whereas an analytic result of the triple integral can be obtained for the EoS of matter, Eq.…”

“…Studies performed for nuclear matter in Refs. [63,64,78] suggest that a t 0 − t 3 model of Skyrmetype interactions is most likely to be a suitable candidate for V LO . MF calculations of Eq.…”

“…However, the truncation applied to the excited states in the single-particle basis cannot be directly matched with the truncation performed for the EoS of matter in Refs. [63,64,78]-where a relative momentum cutoff Λ is applied. Moreover, Moshinsky transformations require all excited states X α,β to be represented in terms of the HO basis 2 , which complicates the matching between different nuclei, as they correspond to different ω and upper limit of X α(β) .…”

Constraining input parameters of AMPT model with ϕ meson production

“…The first phase of the beam energy scan program has been completed and the results are being available to understand the properties of produced matter created in heavy-ion collisions [6,7,8,9,10,11,12,13,14,15,16]. Various observables are compared to theoretical calculations to understand the physical mechanism behind the measurements [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. One of the frequently used models in heavy-ion collisions is AMPT [36].…”

Counteracting systems of diabaticities using DRAG controls: The status after 10 years (a)

“…Other techniques to deal with harmful transitions were developed [31,32] but do not feature the flexibility of DRAG pulses, particularly with regards to spectral selectivity. We review here some of the main developments, including: connections drawn to other STA methods [15], a better understanding of the convergence properties of the expansion [3]; the application to spins, optical lattices and Rydberg atoms [3,[33][34][35], and the development of the closely related technique of WAHWAH [36,37].…”