Shell model Monte Carlo studies of N = Zpf-shell nuclei with pairing-plus-quadrupole Hamiltonian

We perform shell model Monte Carlo calculations of selected N = Z pf-shell nuclei with a schematic Hamiltonian containing isovector pairing and quadrupole-quadrupole interactions. Compared to realistic interactions, this Hamiltonian does not give rise to the SMMC “sign problem”, while at the same time resembles essential features of the realistic interactions. We study pairing correlations in the ground states of N = Z nuclei and investigate the thermal dependence of selected observables for the odd-odd nucleus ⁵⁴Co and the even-even nuclei ⁶⁰Zn and ⁶⁰Ni. Comparison of the present results to those with the realistic KB3 interaction indicates a transition with increasing temperature from a phase of isovector pairing dominance to one where isoscalar pairing correlations dominate. In addition, our results confirm the qualitative reliability of the procedure used to cure the sign problem in the SMMC calculations with realistic forces.     

Variational calculations of resonant states in 4He

We present a modified R-matrix method which allows microscopic calculations of nucleon-nucleus scattering at low energies. This method may be applied in conjunction with any of the commonly used methods for the ground states of few-body systems, i.e. the Green function Monte Carlo, Faddeev and variational techniques. We then report results of variational calculations of low-energy tp scattering in the region of 0⁺, 0^? and 2^? resonances in ⁴He. The energies and widths of these resonances are calculated using realistic two- and three-nucleon interactions; but, the Coulomb interaction is neglected. The three-nucleon interaction is found to have a much smaller effect on the energies of the resonances than on the ground-state energy.     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Accurate evaluation of the 1s wave functions of kaonic hydrogen

Kaonic hydrogen is studied with realistic potentials in an accurate numerical approach based on Sturmian functions. It is found that the ground-state wave function of the exotic atom with realistic strong interactions is considerably different from the hydrogen-like ones at small distances. The K ^???p scattering length extracted from the 1s energy shift of the kaonic hydrogen by applying the Deser-Trueman formula is severely inconsistent with the one derived directly by solving the Schödinger equation. We pay special attention to the recent measurement of the energy shift and decay width of the 1s kaonic hydrogen state by the DEAR Collaboration. Our work strongly supports the argument that the DEAR data of the K ^???p scattering length extracted with the Deser-Trueman formula from the measured 1s energy shift and decay width are not accurate, if not to say, unreliable.     

Stabilization of spatiotemporal solitons in second-harmonic-generating media

We report the results of a systematic analysis of the existence and stability of spatiotemporal (two-dimensional) solitons (STSs) in the model of a planar waveguide with the intrinsic χ⁽²⁾ nonlinearity. Fundamental obstacles to the creation of STSs under physically realistic conditions are the normal sign of the group-velocity dispersion (GVD) at the second harmonic (SH), and the significant group-velocity mismatch (GVM) between the SH and fundamental-frequency (FF) components. To construct STS solutions in a numerical form, we adjust the iterative method, which was recently used for finding temporal (one-dimensional) χ⁽²⁾ solitons in a similar setting. We identify effective existence borders for the STSs, within which the energy loss to the generation of extended “tails” in the SH component (due to the normal sign of the GVD) is negligible. It is demonstrated that the existence region can be made much broader by means of the GVD-management and GVM-management techniques. We also explore interactions between the STSs, and find robust two-soliton bound states, with a moderate separation in the longitudinal (temporal) direction. Head-on collisions between the STSs are always destructive.     

Stochastic approach to nuclear shell model

We propose a Quantum Monte Carlo diagonalization method for solving the quantum many-body interacting systems. Not only the ground state but also low-lying excited states are obtained with their wave functions. Consequently the level structure of low-lying states can be studied with realistic interactions. After testing this method with⁴⁸Cr, we report that the doubly closed shell probability of⁵⁶Ni is shown to be only 53% in a full pf shell calculation, in contrast to the corresponding probability of⁴⁸Ca which reaches 86%. The most recent results on³²Mg are presented. Presented by T. Otsuka at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work was supported in part by Grant-in-Aid for Scientific Research (B) (No. 08454058) from the Ministry of Education, Science and Culture.     

Deep-inelastic scattering in κ factorization and the anatomy of the differential gluon structure function of the proton

The differential gluon structure function of the proton, ?(x, Q ²), introduced by Fadin, Kuraev, and Lipatov in 1975 is extensively used in small-x QCD. We report here the first determination of ?(x, Q ²) from experimental data on the small-x proton structure function F _2p (x, Q ²). We give convenient parametrizations for ?(x, Q ²) based partly on the available DGLAP evolution fits (GRV, CTEQ, and MRS) to parton distribution functions and on realistic extrapolations into the soft region. We discuss the impact of soft gluons on various observables. The x dependence of the so-determined ?(x, Q ²) varies strongly with Q ² and does not exhibit simple Regge properties. Nonetheless, the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F _2p (x, Q ²) by the soft and hard Regge components with intercepts Δ_soft=0 and Δ_hard ～ 0.4.     

The structure,transition probabilities and the π− capture rates of the A = 6 nuclei

The energy spectrum, electromagnetic properties, β-decay and π^? absorption rates of the A = 6 system are calculated using realistic interactions. The results are in good agreement with experiment and other theories of semileptonic weak processes. Strong π^? absorption rates are predicted for the 2^? and 3^? collective states around 25 MeV.     

A unified description of the perturbative photon structure function inx space

We give here in detail the derivation of the various contributions to the photon structure function in the perturbative region. The lowx region problem is pointed out and the QCD corrections to the hadronic part are discussed, including the quasi perturbative region of higher twist effects. The transition from highQ ² to lowQ ² is examined and the basis for a realistic and consistent simulation of higher order QCD processes is given.     

No-Core Shell Model for Nuclear Systems with Strangeness

We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique (Navrátil et al. in J Phys G 36:083101, 2009) which we successfully applied in first calculations of the lightest Λ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon–nucleon and nucleon–hyperon interactions [such as those derived from EFT (Polinder et al. in Nucl Phys A 779:244, 2006)]. We discuss formal aspects of the methodology, show first demonstrative results for _Λ ³ H, _Λ ⁴ H and ⁴ _Λ He, and give outlook.     

Variational calculations of realistic models of nuclear matter

We report variational calculations of nuclear matter with a semi-realistic Reid v₁₂ model, and a realistic v₁₄ model of the two-nucleon interaction operator. The v₁₄ model fits the available nucleon-nucleon scattering data up to 425 MeV lab energy, and has relatively weak L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions in addition to the standard central, tensor and ($\text{L}\text{·}\text{S}$). The L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions are treated semiperturbatively; their contribution reduces the overbinding of nuclear matter. However, the equilibrium k_F = 1.7 fm^?1 and E₀ = ?17.5 MeV obtained with the v₁₄ model are both higher than their empirical values k_F = 1.33 fm^? and E₀ = ?16 MeV. We assume that the difference between the calculated and empirical E(ρ) is entirely due to three-nucleon interactions (TNI). The TNI contributions are phenomenologically added to the nuclear matter energy, and their parameters are adjusted to obtain the correct equilibrium energy, density and compressibility. The required TNI contributions appear to be of reasonable magnitude.     

Electronic density of states of group-IV semiconductors: A cluster-Bethe lattice approach for realistic Hamiltonians

We have extended the cluster-Bethe lattice method to study realistic tight-binding Hamiltonians. The numerical solution of the transfer matrix in the Bethe lattice is very stable and requires about 50 steps of our iterative procedure to reach convergency. We apply this method to study the density of states of group-IV semiconductors (C, Si, Ge) using a five-parameter sp³ Hamiltonian, which takes into account all possible interactions between sp³ hybrids in nearest-neighbor atoms. Our results show clearly that the main features of the density of states are due to short-range order. Clusters of about 30 atoms reproduce very well the crystalline density of states. Based on our results we propose a model for the density of states in the gap region of an amorphous semiconductor.     

Pairing effects at finite temperature and finite rotational frequencies: An exactly soluble model

We propose a new type of experiment to look for parity violation due to neutral current interactions in deuterium. This involves measuring a certain angular momentum transfer from an atomic beam of polarized 2S _1/2 deuterium to a capacitor producing a constant electric field. The torque exerted on the capacitor which is to be measured turns out to be of order 10⁷ ?/s in a realistic situation.     

Quark model and π+p-pp multiplicity difference

Hadron interactions at high energy are sensitive to the space-time structure of the parton model. Based on this structure we propose a model of particle production in which collective collisions among the constituents can take place. We show that the π⁺p-pp multiplicity difference and the asymmetry in π⁺p collisions should decrease with rising energy.     

Rho meson propagation and dilepton enhancement in hot hadronic matter

A realistic model for the free rho meson with coupling to two-pion states is employed to calculate the rho propagator in a hot and dense hadron gas. The medium modifications are based on hadronic rescattering processes: intermediate two-pion states are renormalized through interactions with surrounding nucleons and deltas, and rho meson scattering is considered off nucleons, deltas, pions and kaons. Constraints from gauge invariance as well as the full off-shell dynamics of the interactions are accounted for. Within the vector dominance model we apply the resulting in-medium rho spectral function to compute e⁺e⁻ production rates from π⁺π⁻ annihilation. The calculation of corresponding e⁺e⁻ spectra as recently measured in central collisions of heavy-ions at CERN/SpS energies gives reasonable agreement with the experimental data.     

Three-nucleon interaction in 3-, 4- and ∞-body systems

We report results of variational calculations of ³H, ³He, ⁴He and nuclear matter with the Urbana v₁₄ two-nucleon interaction and realistic models of the three-nucleon interaction (TNI). These include the Tucson and isobar intermediate-state models of the two-pion exchange TNI. The latter is also studied with an intermediate-range three-nucleon repulsion. In general, realistic TNI helps to bring the theory closer to experiment by giving extra binding energy to the A = 3 and 4 nuclei and providing extra saturation to the nuclear matter binding energy. The Coulomb energy of ³He and the rms radii of A = 3, 4 nuclei are also well described. However, some problems remain unresolved. There is a slight overbinding of ⁴He, an underbinding of nuclear matter, and the charge form factors of ³He and ⁴He, calculated with impulse approximation, deviate from the experimental at q²>5 fm^?2.     

Magnetic hyperfine interactions and compositional short range order in the Heusler alloys Cu2MnIn1-xSnx

A comprehensive study of the magnetic hyperfine interactions and the processes of crystallographic ordering in the Heusler alloy system Cu₂MnIn_1-xSn_x has been made. We report the results of Mössbauer effect experiments, X-ray diffraction studies, electrical transport, and Curie temperature measurements. By a rapid quenching, low temperature annealing technique we have been able to extend the ordered L2₁ structure to high Sn concentration. Observations of inequivalent Sn sites and nonunique ¹¹⁹Sn hyperfine field values in these alloys are shown to be due to difficulties in ordering the L2₁ structure and a basic instability of this phase for high Sn concentrations. The compositional variation of ¹¹⁹Sn hyperfine fields in the ordered L2₁ phase of the Cu₂MnIn_1-xSn_x system reveals a systematic increase with Sn composition. Calculations of these fields based on a homogeneously spin polarized electron gas model reproduce the observed field systematics quite well. The implications of these results on the nature of magnetic interactions in Heusler alloys are discussed.     

Relativistic Description of 3He (e, e�� p)2H

The relativistic distorted-wave impulse approximation is used to describe the ³He(e, e?? p)²H process. We describe the ³He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the ³He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S?CV) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S?CV optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.     

Systematic study of the single-state dominance in 2νββ decay transitions

The single-state-dominance hypothesis (SSDH) states that the decay rates of the two-neutrino double-beta decay are governed by a virtual two-step transition connecting the initial and final ground states through the first 1⁺ state, 1_l⁺, of the intermediate odd-odd nucleus, for those odd-odd nuclei where the 1_l⁺ state is the ground state. To investigate the validity of the SSDH we have performed a systematical theoretical analysis of all known double-beta-decay transitions where the SSDH conditions are fulfilled. the calculations are based on the quasiparticle random-phase approximation (QRPA) and the results have been obtained by using realistic single-particle bases and realistic interactions. We have studied the double β⁻ decays of ¹⁰⁰Mo, ¹¹⁰Pd, ¹¹⁴Cd, ¹¹⁶Cd and ¹²⁸Te and the double electron-capture transitions in ¹⁰⁶Cd and ¹³⁶Ce. The analysis shows that the SSDH is realized either through a true dominance of the first intermediate 1⁺ state or by cancellations among the contributions of higher lying 1⁺ states of the intermediate nucleus.