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We construct effective two-body Hamiltonians and E2 operators for the p-shell by performing $16\hbar\Omega$ ab initio no-core shell model (NCSM) calculations for A=5 and A=6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the $0\hbar\Omega$ space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei., Comment: 9 pages, 8 figures

The chiral low-energy constants c_D and c_E are constrained by means of accurate ab initio calculations of the A=3 binding energies and, for the first time, of the triton beta decay. We demonstrate that these low-energy observables allow a robust determination of the two undetermined constants. The consistency of the interactions and currents in chiral effective field theory is crucial to this remarkable result. The two- plus three-nucleon interactions from chiral effective field theory defined by properties of the A=2 system and the present determination of c_D and c_E are successful in predicting properties of the A=3, and 4 systems., Comment: 4 pages, 3 figures, published version

In their comment on our recent Letter [1] Dean et al. [2] criticize the calculations for the ground-state energy of {sup 40}Ca within the importance truncated no-core shell model (NCSM). In particular they address the role of configurations beyond the 3p3h level, which have not been included in the {sup 40}Ca calculations for large N{sub max} {h_bar}{Omega} model spaces. Before responding to this point, the following general statements are in order. For the atomic nucleus as a self-bound system, translational invariance is an important symmetry. The only possibility to preserve translational invariance when working with a Slater determinant basis is to use the harmonic oscillator (HO) basis in conjunction with a basis truncation according to the total HO excitation energy, i.e. N{sub max} {h_bar}{Omega}, as done in the ab initio NCSM. This is important not only for obtaining proper binding or excitation energies, but also for a correct extraction of physical wavefunctions. The spurious center-of-mass components can be exactly removed only if the HO basis and the N{sub max} {h_bar}{Omega} truncation are employed. The minimal violation of the translational invariance was one of the main motivations for developing the importance-truncation scheme introduced in the Letter. In this scheme, we startmore » with the complete N{sub max} {h_bar}{Omega} HO basis space and select important configurations via perturbation theory. All symmetries are under control and our importance-truncated NCSM calculations are completely variational and provide an upper bound of the ground-state energy of the system. The restriction to the 3p3h level, made for computational reasons in the N{sub max} > 8 calculations for {sup 40}Ca, is not inherent to the importance truncation scheme. The explicit inclusion of 4p4h configurations--though computationally more demanding--is straight-forward, even for the largest N{sub max} {h_bar}{Omega} model spaces discussed. To demonstrate this fact we have performed full 4p4h calculations for {sup 40}Ca in a 14{h_bar}{Omega} no-core model space at {h_bar}{Omega} = 24 MeV using the V{sub low k} interaction employed in the Letter. The resulting ground state energy of E{sub 4p4h} = -471.0 MeV can be compared with E{sub 3p3h} = -461.2 MeV for the 3p3h calculation reported in Fig. 5(b) with an uncertainty of typically 1 MeV due to the extrapolation {kappa}{sub min} {yields} 0. Thus the 4p4h configurations change the resulting ground-state energy of {sup 40}Ca by approximately 2%. In addition to the explicit inclusion of 4p4h or higher-order configurations in the importance truncated space, there are various other means to account for their effect on the energy. We are presently developing a perturbative method for the inclusion of up to 6p6h configurations using the ground state obtained from the NCSM diagonalization as unperturbed state. Furthermore, there are even simpler methods, such as multireference Davidson corrections, which are employed successfully in quantum chemistry [3], for estimating the contribution of excluded configurations to the energy. They even restore size extensivity in an approximate way. The coupled-cluster method (CCM) used by the authors of the Comment lacks the above discussed features important for the nuclear many-body problem, in particular it violates translational invariance from the very beginning and it does not fulfill the variational principle. The problem of a spurious center-of-mass contamination of the many-body states in CCM is not resolved and often not even mentioned (see e.g. Ref. [4]). Moreover, non-iterative triples corrections like CCSD(T), as referred to in the comment, tend to overestimate the correlation energy or even collapse. It is claimed that the CCM is very accurate. A closer inspection of recently published nuclear many-body results does not support this statement. In Ref. [5], the {sup 4}He binding energy with the chiral N{sup 3}LO NN potential was determined with an uncertainty of several MeV. The same is obtained in the ab initio NCSM with accuracy of 10 keV [6, 7]. The CCM binding energy results for {sup 16}O with the identical chiral N{sup 3}LO NN potential obtained in Refs. [8] and [9] differ by more than 5 MeV. According to Ref. [9], the CD-Bonn NN potential overbinds {sup 16}O. This is contrary to results obtained in Ref. [10] and also contrary to expectations as the CD-Bonn underbinds lighter nuclei. The CCSD(T) ground state energy for {sup 40}Ca with V{sub low k} reported in Ref. [4] is about 30 MeV lower than our 4p4h-result (CCSD is about 20MeV lower). Taking into account the small 2% difference of our 3p3h and 4p4h results and the violation of the variational principle and the translational invariance in the CCM method, we believe that the CCM result overestimates the exact ground-state energy in this case.« less

The No Core Shell Model (NCSM) has been successful in describing the properties of light nuclei, A ≤ 16, starting from the fundamental interactions among the A nucleons, but it is currently difficult to extend the NCSM to heavier nuclei, because of the extremely large model spaces involved in the calculations. We present a new procedure, based on performing two unitary transformations on the Hamiltonian, so as to obtain the core, one-body, two-body and perhaps three-body input necessary for performing Standard Shell Model (SSM) calculations for nuclei. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. We demonstrate the accuracy of our approach by applying to it nuclei within the 0p-shell.

We outline two complementary approaches based on the no core shell model (NCSM) and present recent results. In the ab initio approach, nuclear properties are evaluated with two-nucleon (NN) and three-nucleon interactions (TNI) derived within effective field theory (EFT) based on chiral perturbation theory (ChPT). Fitting two available parameters of the TNI generates good descriptions of light nuclei. In a second effort, an ab exitu approach, results are obtained with a realistic NN interaction derived by inverse scattering theory with off-shell properties tuned to fit light nuclei. Both approaches produce good results for observables sensitive to spin-orbit properties.

A permanent electric dipole moment (EDM) of a physical system requires time-reversal (T) and parity (P) violation. Experimental programs are currently pushing the limits on EDMs in atoms, nuclei, and the neutron to regimes of fundamental theoretical interest. Here we calculate the magnitude of the PT-violating EDM of 3He and the expected sensitivity of such a measurement to the underlying PT-violating interactions. Assuming that the coupling constants are of comparable magnitude for pi-, rho-, and omega-exchanges, we find that the pion-exchange contribution dominates. Our results suggest that a measurement of the 3He EDM is complementary to the planned neutron and deuteron experiments, and could provide a powerful constraint for the theoretical models of the pion-nucleon PT-violating interaction., 6 pages, 1 figure

We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We present phase shifts for neutron scattering on 3H, 4He, and 10Be and proton scattering on 3,4He, using realistic nucleon-nucleon potentials. Our A=4 scattering results are compared to earlier ab initio calculations. We demonstrate that a proper treatment of the coupling to the n-10Be continuum is successful in explaining the parity-inverted ground state in 11Be.

We report on an ab initio calculation of the 4He total photo‐absorption cross section using two‐ and three‐nucleon interactions based upon chiral effective field theory. The microscopic treatment of the continuum problem is achieved using the Lorentz integral transform method, applied within the no‐core shell model approach.

We demonstrate the existence of multiple converging sequences in the ab initio no-core shell model. By examining the underlying theory of effective operators, we expose the physical foundations for the alternative pathways to convergence. This leads us to propose a revised strategy for evaluating effective interactions for $A$-body calculations in restricted model spaces. We suggest that this strategy is particularly useful for applications to nuclear processes in which states of both parities are used simultaneously, such as for transition rates. We demonstrate the utility of our strategy with large-scale calculations in light nuclei.

We propose an importance truncation scheme for the no-core shell model, which enables converged calculations for nuclei well beyond the p-shell. It is based on an a priori measure for the importance of individual basis states constructed by means of many-body perturbation theory. Only the physically relevant states of the no-core model space are considered, which leads to a dramatic reduction of the basis dimension. We analyze the validity and efficiency of this truncation scheme using different realistic nucleon-nucleon interactions and compare to conventional no-core shell model calculations for {sup 4}He and {sup 16}O. Then, we present the first converged calculations for the ground state of {sup 40}Ca within no-core model spaces including up to 16{h_bar}{Omega}-excitations using realistic low-momentum interactions. The scheme is universal and can be easily applied to other quantum many-body problems.

Properties of finite nuclei are evaluated with two-nucleon (NN) and three-nucleon (NNN) interactions derived within chiral effective field theory (EFT). The nuclear Hamiltonian is fixed by properties of the A = 2 system, except for two low-energy constants (LECs) that parameterize the short range NNN interaction. We constrain those two LECs by a fit to the A = 3 system binding energy and investigate sensitivity of {sup 4}He, {sup 6}Li, {sup 10,11}B and {sup 12,13}C properties to the variation of the constrained LECs. We identify a preferred choice that gives globally the best description. We demonstrate that the NNN interaction terms significantly improve the binding energies and spectra of mid-p-shell nuclei not just with the preferred choice of the LECs but even within a wide range of the constrained LECs. At the same time, we find that a very high quality description of these nuclei requires further improvements to the chiral Hamiltonian.

We report on recent microscopic calculations of reaction properties based upon the nuclear structure of the ab initio no-core shell model (NCSM)., Comment: 3 pages, 2 figures, proceedings of the 20th European Conference on Few-Body Problems in Physics (EFB20)

Recent developments in nuclear theory allow us to make a connection between quantum chromodynamics (QCD) and low-energy nuclear physics. First, chiral effective field theory (chiEFT) provides a natural hierarchy to define two-nucleon (NN), three-nucleon (NNN), and even four-nucleon interactions. Second, ab initio methods have been developed capable to test these interactions for light nuclei. In this contribution, we discuss ab initio no-core shell model (NCSM) calculations for s-shell and p-shell nuclei with NN and NNN interactions derived within chiEFT., Comment: 6 pages, 6 figures, proceedings of the 20th European Conference on Few-Body Problems in Physics (EFB20)

The three-nucleon (NNN) interaction derived within the chiral effective field theory at the next-to-next-to-leading order (N2LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction is then local in the coordinate space, which is advantages for some many-body techniques. Matrix elements of the local chiral NNN interaction are evaluated in a three-nucleon basis. Using the ab initio no-core shell model (NCSM) the NNN matrix elements are employed in 3H and 4He bound-state calculations., Comment: 17 pages, 9 figures

The total photo-absorption cross section of $^4$He is evaluated microscopically using two- (NN) and three-nucleon (NNN) interactions based upon chiral effective field theory ($\chi$EFT). The calculation is performed using the Lorentz integral transform method along with the {\em ab initio} no-core shell model approach. An important feature of the present study is the consistency of the NN and NNN interactions and also, through the Siegert theorem, of the two- and three-body current operators. This is due to the application of the $\chi$EFT framework. The inclusion of the NNN interaction produces a suppression of the low-energy peak and enhancement of the high-energy tail of the cross section. We compare to calculations obtained using other interactions and to representative experiments. The rather confused experimental situation in the giant resonance region prevents discrimination among different interaction models., Comment: 6 pages, 4 figures

Nuclear structure of 7Be, 8B and 7,8Li is studied within the ab initio no-core shell model (NCSM). Starting from the high-precision CD-Bonn 2000 nucleon-nucleon (NN) interaction, wave functions of 7Be and 8B bound states are obtained in basis spaces up to 10 hbar Omega and used to calculate channel cluster form factors (overlap integrals) of the 8B ground state with 7Be+p. Due to the use of the harmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic properties. We fix this problem in two alternative ways. First, by a Woods-Saxon (WS) potential solution fit to the interior of the NCSM overlap integrals. Second, by a direct matching with the Whittaker function. The corrected overlap integrals are then used for the 7Be(p,gamma)8B S-factor calculation. We study the convergence of the S-factor with respect to the NCSM HO frequency and the model space size. Our S-factor results are in agreement with recent direct measurement data., Comment: 4 pages, 3 figures

Using the no-core shell model approach, we report on the first results for 7Li based on the next-to-next-to-leading order chiral nuclear interaction. Both, two-nucleon and three-nucleon interactions are taken into account. We show that the p-shell nuclei are sensitive to the subleading parts of the chiral interactions including three-nucleon forces. Though chiral interactions are soft, we do not observe overbinding for this p-shell nucleus and find a realistic description for the binding energy, excitation spectrum and radius., 12 pages, 12 figures

Nuclear structure of {sup 7}Be, {sup 8}B, and {sup 7,8}Li is studied within the ab initio no-core shell model (NCSM). Starting from high-precision nucleon-nucleon (NN) interactions, wave functions of {sup 7}Be and {sup 8}B bound states are obtained in basis spaces up to 10({Dirac_h}/2{pi}){omega} and used to calculate channel cluster form factors (overlap integrals) of the {sup 8}B ground state with {sup 7}Be+p. Due to the use of the harmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic properties. We fix this problem in two alternative ways. First, by a Woods-Saxon potential solution fit to the interior of the NCSM overlap integrals. Second, by a direct matching with the Whittaker function. The corrected overlap integrals are then used for the {sup 7}Be(p,{gamma}){sup 8}B S-factor calculation. We study the convergence of the S factor with respect to the NCSM HO frequency and the model space size. Our S factor results agree with recent direct measurement data. We also test the spectroscopic factors and the corrected overlap integrals from the NCSM in describing the momentum distributions in knockout reactions with {sup 8}B projectiles. A good agreement with the available experimental data is also found, attesting to the overall consistency of themore » calculations.« less

A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the {beta} decay of the A = 14 multiplet is presented. The GT strength distributions to excited states in {sup 14}C and {sup 14}O was studied in high-resolution (d,{sup 2}He) and ({sup 3}He,t) charge-exchange reactions on {sup 14}N. No-core shell-model (NCSM) calculations capable of reproducing the suppression of the {beta} decays predict a selective excitation of J{sup {pi}} = 2{sup +} states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the {sup 14}N ground state wave function. However, the fragmentation of the GT strength over three 2{sup +} final states remains a fundamental issue not explained by the present NCSM using a 6 {h_bar}{omega} model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way.

No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing experimental nuclear spectra. The main theoretical approach is the use of effective operators, which include correlations left out by the truncation of the model space to a numerically tractable size. We review recent applications of the effective operator approach, within a NCSM framework, to the renormalization of the nucleon-nucleon interaction, as well as scalar and tensor operators., To be submited to J. Phys. A, special issue on "The Physics of Non-Hermitian Operators"

Recently, precision laser spectroscopy on {sup 6}He atoms determined accurately the isotope shift between {sup 4}He and {sup 6}He and, consequently, the charge radius of {sup 6}He. A similar experiment for {sup 8}He is under way. We have performed large-scale ab initio calculations for {sup 4,6,8}He isotopes using high-precision nucleon-nucleon (NN) interactions within the no-core shell model (NCSM) approach. With the CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of {sup 4}He and {sup 6}He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment and predict the {sup 8}He point proton rms radius to be 1.88(6) fm. At the same time, our calculations show that the recently developed nonlocal INOY NN potential gives binding energies closer to experiment, but underestimates the charge radii.

In the framework of the ab-initio no-core shell model (NCSM), we describe the longitudinal-longitudinal distribution function, part of the inclusive (e,e') longitudinal response. In the two-body cluster approximation, we compute the effective operators consistent with the unitary transformation used to obtain the effective Hamiltonian. When short-range correlations are probed, the results display independence from the model space size and length scale. Long-range correlations are more difficult to model in the NCSM and they can be described only by increasing the model space or increasing the cluster size. In order to illustrate the model space independence for short-range observables, we present results for a large set of model spaces for 4He, and in 0-4hw model spaces for 12C., Comment: 4 pages, 4 figures

We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short‐range operators, such as the nucleon‐nucleon potential, the unitary‐transformation method works extremely well at the two‐body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A ⩽ 16). However, for long‐range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two‐body cluster level does not include the higher‐order correlations needed to renormalize these long‐range operators adequately. Usually, such correlations can be obtained either by increasing the order of the cluster approximation or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher‐order correlations in small model spaces.

Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method. The test is performed on the four-body nuclear system, within a simple potential model. The quality of the agreement in the various cases is discussed, together with the perspectives for rigorous ab initio calculations of cross sections of heavier nuclei., Comment: 9 pages, to be submitted for publication

We implement an effective operator formalism for general one- and two-body operators, obtaining results consistent with the no-core shell model (NCSM) wave functions. The Argonne V8' nucleon-nucleon potential was used in order to obtain realistic wave functions for 4He, 6Li and 12C. In the NCSM formalism, we compute electromagnetic properties using the two-body cluster approximation for the effective operators and obtain results which are sensitive to the range of the bare operator. To illuminate the dependence on the range, we employ a Gaussian two-body operator of variable range, finding weak renormalization of long range operators (e.g., quadrupole) in a fixed model space. This is understood in terms of the two-body cluster approximation which accounts mainly for short-range correlations. Consequently, short range operators, such as the relative kinetic energy, will be well renormalized in the two-body cluster approximation., Comment: 9 pages, figure added, clarified discussion, to be published in Phys. Rev. C

We present the first ab initio structure investigation of the loosely bound $^{11}\mathrm{Be}$ nucleus, together with a study of the lighter isotope $^{9}\mathrm{Be}$. The nuclear structure of these isotopes is particularly interesting because of the appearance of a parity-inverted ground state in $^{11}\mathrm{Be}$. Our study is performed in the framework of the ab initio no-core shell model. Results obtained using four different, high-precision two-nucleon interactions, in model spaces up to $9\ensuremath{\hbar}\ensuremath{\Omega}$, are shown. For both nuclei, and all potentials, we reach convergence in the level ordering of positive- and negative-parity spectra separately. Concerning their relative position, the positive-parity states are always too high in excitation energy, but a fast drop with respect to the negative-parity spectrum is observed when the model space is increased. This behavior is most dramatic for $^{11}\mathrm{Be}$. In the largest model space we were able to reach, the $1/{2}^{+}$ level has dropped down to become either the first or the second excited state, depending on which interaction we use. We also observe a contrasting behavior in the convergence patterns for different two-nucleon potentials and argue that a three-nucleon interaction is needed to explain the parity inversion. Furthermore, large-basis calculations of $^{13}\mathrm{C}$ and $^{11}\mathrm{B}$ are performed. This allows us to study the systematics of the position of the first unnatural-parity state in the $N=7$ isotone and the $A=11$ isobar. The $^{11}\mathrm{B}$ run in the $9\ensuremath{\hbar}\ensuremath{\Omega}$ model space involves a matrix with dimension exceeding $1.1\ifmmode\times\else\texttimes\fi{}{10}^{9}$, and is our largest calculation so far. We present results on binding energies, excitation spectra, level configurations, radii, electromagnetic observables, and $^{10}\mathrm{Be}+n$ overlap functions.

We discuss the motivation, theory, and formulation of the ab initio No‐Core Shell Model (NCSM). In this method the effective Hamiltonians are derived microscopically from realistic nucleon‐nucleon (NN) and theoretical three‐nucleon (NNN)potentials, as a function of the finite harmonic‐oscillator (HO) basis space. We present converged results for the A = 3 and 4 nucleon systems, which are in agreement with results obtained by other exact methods, followed by results for p‐shell nuclei. Binding energies, rms radii, excitation spectra, and electromagnetic properties are discussed. The favorable comparison with available data is a consequence of the underlying NN and NNN interactions rather than a phenomenological fit.

Translationally invariant nuclear density is derived from the shell model one-body densities by removing their spurious $0\ensuremath{\hbar}\ensuremath{\Omega}$ center-of-mass (c.m.) motion component. This paves the way to utilizing the ab initio no-core shell-model (NCSM) nuclear structure in folding approaches to optical potentials. As an illustration, the $^{6}\mathrm{He}$ diagonal and transitional densities are calculated from the NCSM wave functions obtained using the CD-Bonn nucleon-nucleon potential in the $10\ensuremath{\hbar}\ensuremath{\Omega}$ basis space. A particularly significant impact of the exact removal of the spurious c.m. motion is found for the spin-orbit part of the optical potential proportional to the derivative of the nuclear density.

The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy., Comment: 19 pages, 9 figures, submitted to PRC

We calculate properties of A=6 system using the accurate charge-dependent nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory. By application of the ab initio no-core shell model (NCSM) and a variational calculation in the harmonic oscillator basis with basis size up to 16 hbarOmega we obtain the 6Li binding energy of 28.5(5) MeV and a converged excitation spectrum. Also, we calculate properties of 10B using the same NN potential in a basis space of up to 8 hbarOmega. Our results are consistent with results obtained by standard accurate NN potentials and demonstrate a deficiency of Hamiltonians consisting of only two-body terms. At this order of chiral perturbation theory three-body terms appear. It is expected that inclusion of such terms in the Hamiltonian will improve agreement with experiment., 9 pages, 14 figures

Nuclear many-body calculations are computationally demanding. An estimate of their accuracy is often hampered by the limited amount of computational resources even on present-day supercomputers. We provide an extrapolation method based on perturbation theory, so that the binding energy of a large basis-space calculation can be estimated without diagonalizing the Hamiltonian in this space. The extrapolation method is tested for 3H and 6Li nuclei. It will extend our computational abilities significantly and allow for reliable error estimates., Comment: 8 pages, 7 figures, PRC accepted

We derive expressions for cluster overlap integrals or channel cluster form factors for ab initio no-core shell model (NCSM) wave functions. These are used to obtain the spectroscopic factors and can serve as a starting point for the description of low-energy nuclear reactions. We consider the composite system and the target nucleus to be described in the Slater determinant (SD) harmonic oscillator (HO) basis while the projectile eigenstate to be expanded in the Jacobi coordinate HO basis. This is the most practical case. The spurious center of mass components present in the SD bases are removed exactly. The calculated cluster overlap integrals are translationally invariant. As an illustration, we present results of cluster form factor calculations for , , , , , , , , and , with all the nuclei described by multi-hbar Omega NCSM wave functions., 28 pages, 16 figures

The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. They present results of first applications using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increase of binding energy, they observe a trend toward level-ordering and level-spacing improvement in comparison to experiment. With the TNI they obtain a correct ground-state spin for {sup 10}B contrary to calculations with NN potentials only. They also investigate neutrino-{sup 12}C exclusive cross sections and muon capture on {sup 12}C. They show that realistic nucleon-nucleon interactions underpredict the experimental cross sections by a factor of two or more. By including the TNI a much better agreement with experiment is achieved along with an encouraging trend.

We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 variant Planck's over 2pi Omega we show that realistic nucleon-nucleon interactions, like, e.g., the CD-Bonn, underpredict the experimental cross sections by more than a factor of 2. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time, the TM'(99) interaction improves the calculated level ordering in 12C. The comparison between the CD-Bonn and the three-body calculations provides strong confirmation for the need to include a realistic three-body interaction to account for the spin-orbit strength in p-shell nuclei.

The spherical Hartree-Fock approximation is applied to the ab initio no-core shell model, with a realistic effective nucleon-nucleon interaction in order to investigate the range of its utility. Hartree-Fock results for binding energies, one-body density distributions, and occupation probabilities are compared with results from exact diagonalization in similar model spaces. We show that this mean-field approximation, especially with second-order corrections, is able to provide some useful approximations for $^{4}\mathrm{He}$ and $^{16}\mathrm{O}$. We also explore the physical insights provided by the Hartree-Fock results for single-particle properties such as spin-orbit splittings. We find single-particle state ordering consistent with the phenomenological shell model.

The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are discussed in detail. We present results of first applications to 6,7Li, 6He, 7,8,10Be, 10,11,12B, 12N and 10,11,12,13C using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence of the realistic three-body force and an overall improvement in the level-ordering and level-spacing in comparison to experiment. The greatest sensitivity occurs for states where the spin-orbit interaction strength is known to play a role. In particular, with the TNI we obtain the correct ground-state spin for 10,11,12B and 12N, contrary to calculations with NN potentials only., Comment: 25 pages, 8 figures

We investigate properties of $A=10$ nuclei in the ab initio, no-core shell model using realistic Argonne and CD-Bonn nucleon-nucleon $(\mathrm{NN})$ potentials and basis spaces through $9\ensuremath{\Elzxh}\ensuremath{\Omega}$ (with basis dimensions reaching $5.5\ifmmode\times\else\texttimes\fi{}{10}^{8}).$ Results for binding energies, excitation spectra (including negative parity and $2\ensuremath{\Elzxh}\ensuremath{\Omega}$-dominated intruder states), electromagnetic properties, and the isospin-mixing correction of the ${}^{10}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{C}}}^{10}\mathrm{B}$ Fermi transition are presented. For ${}^{10}\mathrm{B},$ these $\mathrm{NN}$ potentials produce a ${J}^{\ensuremath{\pi}}{T=1}^{+}0$ ground state, contrary to the experimental ${3}^{+}0,$ a clear indication of the need for true three-body forces.

We present a qualitative improvement of the ab initio no-core shell model (NCSM) approach by implementing three-body interaction capability for $p$-shell nuclei. We report the first calculations using three-body effective interactions derived from realistic nucleon-nucleon potentials for ${}^{6}\mathrm{Li}$, ${}^{8}\mathrm{Be}$, and ${}^{10}\mathrm{B}$ and demonstrate that the use of three-body effective interactions speeds up the convergence of the NCSM approach. For ${}^{10}\mathrm{B}$, we predict ${J}^{\ensuremath{\pi}}{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{+}0$ ground state, contrary to the experimental observation of ${3}^{+}0$, when the $\mathrm{AV}{8}^{\ensuremath{'}}$ potential is used, indicating the need for true three-body forces.

Recently, new cross section measurements by the GEANIE collaboration have been published for {sup 239}Pu(n, 2n{gamma}) [Ber00] and {sup 235}U(n, 2n{gamma}) [You00] from threshold to 20 MeV. When combined with nuclear reaction calculations [Che00, Cha99, Cha01], these measurements provide the most accurate information available on the shape and magnitude of the {sup 239}Pu(n, 2n) cross section for incident neutron energies, E{sub n} {approx}< 14 MeV. This new data has prompted a re-evaluation of the {sup 239}Pu(n, 2n) {sup 238}Pu reaction cross section considering all available experimental data. The data prior to the measurement of Bernstein et al. [Ber00] is illustrated in Figure 1a. These data sets were considered by previous evaluations [ENDL] of the {sup 239}Pu(n, 2n) cross section. The most precise experiment was an activation measurement done by Lougheed et al. [Lou00] for incident neutron energies, E{sub n}, between 13-15 MeV. In addition, there were two neutron-counting experiments, one by Mather et al. [Mat72] and one by Frehaut et al. [Fre85]. These two measurements cover a wide incident neutron range, with data points from threshold to E{sub n} {approx} 14 MeV. The available data sets are in poor agreement with each other and in some cases do not meetmore » basic expectations. These experiments will be reviewed in detail. The new contributions to this evaluation are (1) the GEANIE data coupled with reaction modeling, illustrated in Figure 1b, and (2) the systematic use of other nuclear data in order to put constraints on the shape and magnitude of the {sup 239}Pu(n, 2n) cross section. The approach of this evaluation has been to use consistency arguments supported by nuclear data to resolve the measurement differences, with the goal of providing: (1) A comprehensive picture of our knowledge on the {sup 239}Pu(n, 2n) cross section; and (2) A new evaluation including the best possible estimate of the cross section and a one-sigma estimate the uncertainties. This paper is organized in the following fashion: Section 2: Evaluation of {sup 239}Pu(n, 2n) measurements--Measurements of the {sup 239}Pu(n, 2n) cross section are evaluated for reliability (systematic uncertainties) and for renormalization possibilities. Section 3: Consistency with other experimental data--Experimental data and nuclear data evaluations for non-elastic, inelastic, fission, (n, 2n), and neutron production cross sections are reviewed in the context of unitarity and other constraints. Conclusions with regard to the shape and magnitude of the {sup 239}Pu(n, 2n) cross section are drawn. Section 4: Recommended {sup 239}Pu(n, 2n) cross section and uncertainties--The results of Section 2 and 3 are combined to provide an overall ''best'' data set with evaluated uncertainties. The recommended {sup 239}Pu(n, 2n) cross sections and relative uncertainties are given in tabular format and compared with other evaluations.« less

In the past, several efficient methods have been developed to solve the Schroedinger equation for four-nucleon bound states accurately. These are the Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis variational, the stochastic variational, the hyperspherical variational, the Green's function Monte Carlo, the no-core shell model and the effective interaction hyperspherical harmonic methods. In this article we compare the energy eigenvalue results and some wave function properties using the realistic AV8' NN interaction. The results of all schemes agree very well showing the high accuracy of our present ability to calculate the four-nucleon bound state., Comment: 17 pages, 1 figures

Recent experimental results by Metz, Jolie and collaborators have led to renewed interest in the notion of dynamical supersymmetry in fermion many-body systems. By considering the general problem of constructing a boson-fermion realization for Lie algebras with generators expressed in terms of fermion and bifermion operators, also when favored pairs dictate the structure of collective bosons, we demonstrate that dynamical “supersymmetry without bosons” can indeed emerge in a fermion system without any Pauli Violations. Our construction of the general realization utilizes the identification of a physical subspace and allows one to identify the images of single particle transfer operators uniquely, unlike the situation in phenomenological applications of dynamical supersymmetry.

We study low-lying states of even carbon isotopes in the range A = 10-20 within the large-scale no-core shell model. Using several accurate nucleon-nucleon (NN) as well as NN plus three-nucleon (NNN) interactions, we calculate excitation energies of the lowest 2(+) state, the electromagnetic B(E2; 2(1)(+) -> 0(1)(+)) transition rates, and the 2(1)(+) quadrupole moments as well as selected electromagnetic transitions among other states. Recent experimental campaigns to measure 2(+)-state lifetimes indicate an interesting evolution of nuclear structure that pose a challenge to reproduce theoretically from first principles. Our calculations do not include any effective charges or other fitting parameters. However, calculated results extrapolated to infinite model spaces are also presented. The model-dependence of those results is discussed. Overall, we find good agreement with the experimentally observed trends, although our extrapolated B(E2; 2(1)(+) -> 0(1)(+)) value for C-16 is lower compared to the most recent measurements. Relative transition strengths from higher excited states are investigated and the influence of NNN forces is discussed. In particular for 16C we find a remarkable sensitivity of the transition rates from higher excited states to the details of the nuclear interactions.

We are developing a formalism to generate effective neutrinoless double-beta decay (0νββ) operators within the shell model. We use lighter nuclei (A = 8,10) as a laboratory. We start with the A=6 system where the wavefunctions are generated using the No-Core Shell Model (NCSM) with the CD-Bonn potential in a relatively large space. Thereafter, both the 0νββ operator and the two-nucleon interaction are renormalized to the p-shell using the Lee-Suzuki transformation scheme. These renormalized p-shell operator and interaction are then used in the A = 8 system and compared with the 'full' result (in the large space). Here we present preliminary results for the 8He–8Be transition. Also worth mentioning is the fact that we are simultaneously evaluating other renormalization schemes.

The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of atomic nuclei, starting with the fundamental interactions among the nucleons and treating all A nucleons as being active. This approach has been successfully applied to nuclei with A ≤ 20, but it is difficult to treat heavier mass nuclei with existing computer technology, because of the extemely large basis spaces required to obtain converged results. In this presentation we outline a new formalism for extending the NCSM to heavier mass nuclei. It involves using the NCSM approach to determine the core, one-body and two-body (and perhaps also three-body) terms, which are the usual input for standard shell model (SSM) calculations. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. As a test of this new formalism, we apply it to nuclei in the 0p-shell, for which exact NCSM calculations can also be performed for making comparisons. Results are given both for energy spectra and electromagnetic properties.

The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the many-body quantum-mechanical problem in the continuum, represent a theoretical and computational challenge for ab initio approaches. After a brief overview of the field, we present a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei. By combining the resonating-group method with the ab initio no-core shell model, we complement a microscopic cluster technique with the use of realistic interactions and a microscopic and consistent description of the clusters. We show results for neutron and proton scattering on light nuclei, including p-7Be and n-8He. We also highlight the first results of the d-3He and d-3H fusion calculations obtained within this approach., Comment: To appear in the proceedings of the International Nuclear Physics Conference INPC 2010, Vancouver, Canada, July 4 - 9, 2010, 10 pages, 5 figures

We present an overview of recent results and developments of the no-core shell model (NCSM), an ab initio approach to the nuclear many-body problem for light nuclei. In this approach, we start from realistic two-nucleon or two- plus three-nucleon interactions. Many-body calculations are performed using a finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic inter-nucleon interactions that generate strong short-range correlations, we derive effective interactions by unitary transformations that are tailored to the HO basis truncation. For soft realistic interactions this might not be necessary. If that is the case, the NCSM calculations are variational. In either case, the ab initio NCSM preserves translational invariance of the nuclear many-body problem. In this review, we, in particular, highlight results obtained with the chiral two- plus three-nucleon interactions. We discuss efforts to extend the applicability of the NCSM to heavier nuclei and larger model spaces using importance-truncation schemes and/or use of effective interactions with a core. We outline an extension of the ab initio NCSM to the description of nuclear reactions by the resonating group method technique. A future direction of the approach, the ab initio NCSM with continuum, which will provide a complete description of nuclei as open systems with coupling of bound and continuum states, is given in the concluding part of the review., Comment: 64 pages, 24 figures