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Light elements were produced in the first few minutes of the Universe through a sequence of nuclear reactions known as Big Bang nucleosynthesis (BBN) 1 , 2 . Among the light elements produced during BBN 1 , 2 , deuterium is an excellent indicator of cosmological parameters because its abundance is highly sensitive to the primordial baryon density and also depends on the number of neutrino species permeating the early Universe. Although astronomical observations of primordial deuterium abundance have reached percent accuracy 3 , theoretical predictions 4 – 6 based on BBN are hampered by large uncertainties on the cross-section of the deuterium burning D( p , γ ) 3 He reaction. Here we show that our improved cross-sections of this reaction lead to BBN estimates of the baryon density at the 1.6 percent level, in excellent agreement with a recent analysis of the cosmic microwave background 7 . Improved cross-section data were obtained by exploiting the negligible cosmic-ray background deep underground at the Laboratory for Underground Nuclear Astrophysics (LUNA) of the Laboratori Nazionali del Gran Sasso (Italy) 8 , 9 . We bombarded a high-purity deuterium gas target 10 with an intense proton beam from the LUNA 400-kilovolt accelerator 11 and detected the γ-rays from the nuclear reaction under study with a high-purity germanium detector. Our experimental results settle the most uncertain nuclear physics input to BBN calculations and substantially improve the reliability of using primordial abundances to probe the physics of the early Universe. High-precision cross-sections of the nuclear reaction that burns deuterium to create helium-3 are used to produce theoretical estimates of the primordial baryon density that are in agreement with recent astronomical observations.

We investigate the properties of the excited state of 4He, 4He∗, within the framework of Efimov physics and its connection to the unitary point of the nuclear interaction. We explore two different approaches to track the trajectory of 4He∗ as it crosses the 3H+p threshold and potentially becomes a resonant state. The first approach involves an analytical continuation of the energy with respect to the Coulomb coupling, while the second approach introduces an artificial four-body force that it is gradually released. By utilizing Padé approximants and extrapolation techniques, we estimate the energy and width of the resonance. Our results suggest a central energy value of ER=0.060(3) MeV and a width of Γ/2=0.036(6) MeV using the Coulomb analysis, and ER=0.068(1) MeV and Γ/2=0.007(5) MeV with the four-body force analysis. Interestingly, these results are consistent with calculations based on ab-initio nuclear interactions but differ from the accepted values of the 0+ resonance energy and width. This highlights the challenges in accurately determining the properties of resonant states in light nuclei and calls for further investigations and refinements in theoretical approaches.

The correlation function is a useful tool to study the interaction between hadrons. The theoretical description of this observable requires the knowledge of the scattering wave function, whose asymptotic part is distorted when two or more particles are charged. For a system of three (or more) particles, with more than two particles asymptotically free and at least two of them charged, the asymptotic part of the wave function is not known in a closed form. In the present study we introduce a screened Coulomb potential and analyze the impact of the screening radius on the correlation function. As we will show, when a sufficiently large screening radius is used, the correlation function results almost unchanged if compared to the case in which the unscreened Coulomb potential is used. This fact allows the use of free asymptotic matching conditions in the solution of the scattering equation simplifying noticeably the calculation of the correlation function. As an illustration we discuss the pp and ppp correlation functions.

The 4He monopole form factor is studied by computing the transition matrix element of the electromagnetic charge operator between the 4He ground-state and the p+3H and n+3He scattering states. The nuclear wave functions are calculated using the hyperspherical harmonic method, by starting from Hamiltonians including two- and three-body forces derived in chiral effective field theory. The electromagnetic charge operator retains, beyond the leading order (impulse approximation) term, also higher order contributions, as relativistic corrections and meson-exchange currents. The results for the monopole form factor are in fair agreement with recent MAMI data. Comparison with other theoretical calculations are also provided.

The processes d(d, p)3H and d(d, n)3 He at energies of interest for energy production and for big-bang nucleosynthesis are studied using the hyperspherical harmonic method. The interactions include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S-factor and the quintet suppression factor.

Starting from a complete set of relativistic nucleon–nucleon contact operators up to order O(p4) of the expansion in the soft (relative or nucleon) momentum p, we show that non-relativistic expansions of relativistic operators involve twenty-six independent combinations, two starting at O(p0), seven at order O(p2) and seventeen at order O(p4). This demonstrates the existence of two low-energy free constants that parameterize interactions dependent on the total momentum of the pair of nucleons P. The latter, through the use of a unitary transformation, can be removed in the two-nucleon fourth-order contact interaction of the Chiral Effective Field Theory, generating a three-nucleon interaction at the same order. Within a hybrid approach in which this interaction is considered together with the phenomenological potential AV18, we show that the LECs involved can be used to fit very accurate data on the polarization observables of the low-energy p-d scattering, in particular the Ay asymmetry.

The equal mass three-fermion system having 1/2 spin-isospin symmetry is study around the unitary limit. The two body system has two different scattering lengths, a0 and a1, corresponding to the spin singlet state S = 0 and the spin triplet state S = 1, respectively. The unitary limit is defined when the two quantities a0, a1 → ∞. The three-nucleon system is located very close to this limit, the singlet and triplet n − p scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about a0/a1 ≈ −4.31. This value defines a plane in which a 0 and a 1 can be varied. Using a nucleon-nucleon spin dependent potential with variable strength it is possible to study the behavior of the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three 1/2-spin-isospin fermions.

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme.

Two integral relations, that have been recently derived from the Kohn variational principle (KVP), are used to describe scattering states. In usual applications the variational scattering wave function requires the explicit form of its asymptotic behavior. This is not the case when the integral relations are applied since, due to their short range nature, the only condition is that the scattering wave function Ψ be the solution of (H – E)Ψ 0 in the internal region. In order to show the applicability of the method, two examples are analyzed as the computation of phase-shifts from bound state type wave functions in the A 2 using a model potential. As a last example we discuss the use of the integral relations in the A 3 system using a realistic nucleon-nucleon potential.