We report quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A ≤ 7 using a realistic Hamiltonian containing the Argonne v 18 two-nucleon and Urbana IX three-nucleon potentials. A detailed description of the Green's function Monte Carlo algorithm for systems with state-dependent potentials is given and a number of tests of its convergence and accuracy are performed. We find that the Hamiltonian being used results in ground states of both 6 Li and 7 Li that are stable against breakup into subclusters, but somewhat underbound compared to experiment. We also have results for 6 He, 7 He, and their isobaric analogs. The known excitation spectra of all these nuclei are reproduced reasonably well and we predict a number of excited states in 6 He and 7 He. We also present spin-polarized onebody and several different two-body density distributions. These are the first microscopic calculations that directly produce nuclear shell structure from realistic interactions that fit NN scattering data.

▪ Abstract  Accurate quantum Monte Carlo calculations of ground states and low-lying excited states of light p-shell nuclei are now possible for realistic nuclear Hamiltonians that fit nucleon-nucleon scattering data. Results for more than 30 different (Jπ;T) states, plus isobaric analogs, in A ≤ 8 nuclei have been obtained with an excellent reproduction of the experimental energy spectrum. These microscopic calculations show that nuclear structure, including both single-particle and clustering aspects, can be explained starting from elementary two- and three-nucleon interactions. Various density and momentum distributions, electromagnetic form factors, and spectroscopic factors have also been computed, as well as electroweak capture reactions of astrophysical interest.

Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

We present realistic models of pion-exchange three-nucleon interactions obtained by fitting the energies of all the 17 bound or narrow states of 3 ≤ A ≤ 8 nucleons, calculated with less than 2% error using the Green's function Monte Carlo method. The models contain two-pion-exchange terms due to πN scattering in S-and P-waves, three-pion-exchange terms due to ring diagrams with one ∆ in the intermediate states, and a phenomenological repulsive term to take into account relativistic effects, the suppression of the two-pion-exchange two-nucleon interaction by the third nucleon, and other effects. The models have five parameters, consisting of the strength of the four interactions and the short-range cutoff. The 17 fitted energies are insufficient to determine all of them uniquely. We consider five models, each having three adjustable parameters and assumed values for the other two. They reproduce the observed energies with an rms error < 1% when used together with the Argonne v 18 two-nucleon interaction. In one of the models the πN S-wave scattering interaction is set to zero; in all others it is assumed to have the strength suggested by chiral effective field theory. One of the models also assumes that the πN P-wave scattering interaction has the strength suggested by effective field theories, and the cutoff is adjusted to fit the data. In all other models the cutoff is taken to be the same as in the v 18 interaction. The effect of relativistic boost correction to the two-nucleon interaction on the strength of the repulsive three-nucleon interaction is estimated. Many calculated properties of A ≤ 8 nuclei, including radii, magnetic dipole and electric quadrupole moments, isobaric analog energy differences, etc., are tabulated. Results obtained with only Argonne v ′ 8 and v 18 interactions are also reported. In addition, we present results for 7-and 8-body neutron drops in external potential wells.

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We first define a series of NN interaction models ranging from very simple to fully realistic. We then present Green's function Monte Carlo calculations of light nuclei to show how nuclear spectra evolve as the nuclear forces are made increasingly sophisticated. We find that the absence of stable five-and eight-body nuclei depends crucially on the spin, isospin, and tensor components of the nuclear force.PACS numbers: PACS numbers: 21.45.+v, 21.60.Ka A key feature of nuclear structure, of great importance to the universe as we know it, is the absence of stable five-or eight-body nuclei. This simple fact is crucial to both primordial and stellar nucleosynthesis. It leads to a universe whose baryonic content is dominated by hydrogen and 4 He, with trace amounts of deuterium, 3 He, and 7 Li. It also enables stars like our sun to burn steadily for billions of years, allowing time for the evolution of life intelligent enough to wonder about such issues.In this Letter we demonstrate that the binding energies, excitation structure, and relative stability of light nuclei, including the opening of the A = 5 and 8 mass gaps, are crucially dependent on the complicated structure of the nuclear force. We do this by calculating the energy spectra of light nuclei using a variety of nuclear force models ranging from very simple to fully realistic, and observing how features of the experimental spectrum evolve with the sophistication of the force. We find that the spin-isospin and tensor forces present in long-range one-pion-exchange (OPE) are vital, which in turn may allow us to make a closer connection between nuclear structure and the underlying features of QCD [1,2].Modern nucleon-nucleon (NN ) potentials, such as the Argonne v 18 [3], CD Bonn [4], Reid93, Nijm I, and Nijm II [5], fit over 4300 elastic NN scattering data with a χ 2 ≈ 1. These potentials are very complicated, including spin, isospin, tensor, spin-orbit, quadratic momentumdependent, and charge-dependent terms, with ∼40 parameters adjusted to fit the data. Despite this sophistication, these potentials cannot reproduce the binding energy of few-body nuclei like 3 H and 4 He without the assistance of a three-nucleon potential [6]. Three-nucleon (NNN ) potentials, such as the Tucson-Melbourne [7], Urbana [8], and Illinois [9] models, are also fairly complicated, depending on the positions, spins, and isospins of all three nucleons simultaneously. A combination of NN and NNN potentials, such as the Argonne v 18 and Illinois 2 (AV18/IL2), evaluated with exact Green's function Monte Carlo (GFMC) many-body calculations, can describe the spectra of light nuclei very well [9,10].The AV18 potential contains a complete electromagnetic (EM) interaction and a strong interaction part which is a combination of OPE and remaining shorterrange phenomenology. The strong interaction part is written as a sum of 18 operator terms:(1)The first eight operators,are the most important for fitting S-and P-wave NN data. The additional terms include six operators that are quadratic in ...

Two-nucleon momentum distributions are calculated for the ground states of nuclei with mass number A ≤ 8, using variational Monte Carlo wave functions derived from a realistic Hamiltonian with two-and three-nucleon potentials. The momentum distribution of np pairs is found to be much larger than that of pp pairs for values of the relative momentum in the range (300-600) MeV/c and vanishing total momentum. This order of magnitude difference is seen in all nuclei considered and has a universal character originating from the tensor components present in any realistic nucleonnucleon potential. The correlations induced by the tensor force strongly influence the structure of np pairs, which are predominantly in deuteron-like states, while they are ineffective for pp pairs, which are mostly in 1 S0 states. These features should be easily observable in two-nucleon knock-out processes, such as A(e, e ′ np) and A(e, e ′ pp). The two preeminent features of the nucleon-nucleon (NN ) interaction are its short-range repulsion and intermediate-to long-range tensor character. These induce strong spatial-spin-isospin NN correlations, which leave their imprint on the structure of ground-and excited-state wave functions. Several nuclear properties reflect the presence of these features. For example, the two-nucleon density distributions ρ MS T S (r) in states with pair spin S=1 and isospin T =0 are very small at small inter-nucleon separation r and exhibit strong anisotropies depending on the spin projection M S [1]. Nucleon momentum distributions N (k) [2,3] and spectral functions S(k, E) [4] have large high-momentum and, in the case of S(k, E), high-energy components, which are produced by short-range and tensor correlations. The latter also influence the distribution of strength in response functions R(k, ω), which characterize the response of the nucleus to a spin-isospin disturbance injecting momentum k and energy ω into the system [5,6]. Lastly, calculations of low-energy spectra in light nuclei (up to mass number A=10) have demonstrated that tensor forces play a crucial role in reproducing the observed ordering of the levels and, in particular, the observed absence of stable A = 8 nuclei [7].In the present study we show that tensor correlations also impact strongly the momentum distributions of NN pairs in the ground state of a nucleus and, in particular, that they lead to large differences in the np versus pp distributions at moderate values of the relative momentum in the pair. These differences should be observable in two-nucleon knock-out processes, such as A(e, e ′ np) and A(e, e ′ pp) reactions.The probability of finding two nucleons with relative momentum q and total momentum Q in isospin state T M T in the ground state of a nucleus is proportional to the densitywhere r 12 ≡ r 1 − r 2 , R 12 ≡ (r 1 + r 2 )/2, and similarly for r ′ 12 and R ′ 12 . P T MT (12) is the isospin projection operator, and ψ JMJ denotes the nuclear wave function in spin and spin-projection state JM J . The normalization iswhere N T MT is the ...

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